Number Sense 2 Part 1 − Introduction

1

In this unit, students will explore numbers up to 100: they will count (match numbers with their corresponding quantities and numerals), order numbers using different materials (hundreds charts, number lines, place value), represent numbers in different ways (pictures, numerals, tens and ones blocks, number words, and lengths) and compare quantities (more, less, fewer, as many as). They will also learn to add and subtract using different strategies (pictures, number lines, hundreds charts, counting on, counting back, using addition to subtract, and using 10). Students will also begin solving and creating word problems.

MaterialsNumber Cards (0–20) and Number Word Cards (zero–twenty). Write each numeral from 0 through 20 and each number word from zero through twenty on an index card or piece of construction paper. Each student will also need a set of these cards, and you can use BLM Number Cards Template (p XXX) to make them. You will use these cards throughout the unit for demonstrations; students will use them as manipulatives (e.g., for sorting and ordering activities, to play Memory). The same numbers, in both forms, should be posted or displayed in the classroom for student reference.

Hundreds Charts and Base Ten Materials. Make a copy of BLM Hundreds Chart (p XXX) for each student, and laminate it if possible. Use additional photocopies of this BLM as required. Students will often use this hundreds chart with 1 cm connecting cubes and tens and ones blocks. If you do not have such cubes or blocks, or if your students need larger manipulatives, they can use BLM Hundreds Chart—Five Rows (p XXX) with paper ones and tens blocks from BLM Base Ten Materials (p XXX). Copy and laminate as many tens and ones blocks as required. Also available: a slightly larger hundreds chart on BLM A Larger Hundreds Chart (p XXX).

A Hundreds Chart for Whole-Class Teaching. For whole-class discussions and demonstrations, use a pocket hundreds chart, a hundreds chart poster, or an overhead projector. You could also create a large hundreds chart on the board or on chart paper.

Paper Sticks. Glue 1 cm grid paper (you can use BLM 1 Cm Grid Paper) to Bristol board or thin cardboard (e.g., a cereal box). Make paper sticks 1 cm wide of lengths 2 cm, 3 cm,…, 10 cm. As an alternative, if you have Cuisenaire rods, simply add grid markings at each 1 cm mark on one side of the rods. You could do this using a sharp tool, such as scissors. If using Cuisenaire rods, however, be careful not to create false associations between numbers and colours. Students will use these sticks/rods in several lessons, both in Part 1 and Part 2. You will need many copies of these sticks: for some activities, you will need only two of each length per student; for others, you will need six or seven of each length per student (in which case, you might choose to have students work at stations instead).

Dice. Have students make their own “dice.” There are two ways to do this, both of which will be useful in different situations.

Number Sense 2 Part 1 − Introduction

Number Sense 2− Introduction

2 TEACHER’S GUIDE

1. Use the nets on BLM Cubes (p XXX). You will need to show students how to cut out the flaps correctly if students use glue (if they use tape, this is not as important). Have students write the numbers on the net before folding and making the dice, and ensure that students put the numbers on the outside of the cube.

2. Use plastic or paper egg cartons to mimic rolling dice. Have students bring in 6-pack egg cartons (bring in extras in case students forget). Start collecting the cartons several weeks before you need them in NS2-30. A 12-pack cut in half will also work. Have students write different numbers in each hole in the carton, or write the numbers on paper and tape or glue them to the carton. To mimic rolling two dice, students put two counters into the carton and shake, then open the carton and see which numbers the counters landed on. Make sure that when students shake the carton, they cover up any holes where counters can fall out. Variations:• Write the numbers 4 through 9 instead of 1 through 6 in the carton. • Use a 12-egg carton to imitate 12-sided dice. • Put three counters in the egg carton to imitate rolling three dice.

Tens and ones blocks. You will often need tens and ones blocks. Two different colours of blocks is ideal for demonstrating addition (e.g., 3 red blocks + 4 blue blocks is 7 blocks altogether). As an alternative, you can use 1 cm connecting cubes, and have students link ten together to create a tens block. If you don’t have 1 cm connecting cubes or tens and ones blocks, you can use BLM Base Ten Materials (p XXX) to make some. Photocopy the BLM onto red and blue paper, glue it to Bristol board or thin cardboard (e.g., a cereal box), and cut out the materials for your students. Be aware, however, that many students will find these thin blocks hard to manipulate.

Coins or two-colour counters. Two-colour counters will be used repeatedly in this unit. If you don’t have any, play coins (using heads and tails as the two “colours”) can be used instead.

How to make a number line from a hundreds chart. Cut out a hundreds chart (you can use BLM Hundreds Chart or BLM A Larger Hundreds Chart) such that there is extra space to the left of the chart. Fold the chart to make a cylinder and tape it together so that when the first row ends, the second row starts. Cut out the rows in one long spiral starting underneath the 1; this will form one long strip with the numbers in order from 1 to 100. You can make the number line yourself, or make the cylinders and have students cut them.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

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Incorporate Math into Your Daily Classroom Routines You can easily link any of the following activities to the relevant lessons when they are taught.

Line up by number. Have students pick a number card and line up in order according to their numbers. At first, have numbers only go as high as the number of students; later, numbers can go higher than the number of students so that there are gaps in the numbers held by consecutive students.

Refer to students using ordinal numbers. EXAMPLE: Ask the 5th student in line for assistance. Using ordinal numbers throughout the year to call on students will help them learn ordinal numbers (in NS2-19) more easily.

Count back to indicate time remaining. You might count back from 3 to 0 when you need students to quiet down, or count back from 20 to 0 when you want them to line up for lunch. Eventually, end at numbers other than 0. Students who need to finish a task when you say 4 will learn quickly that 5 comes right before 4 when counting back.

If different groups line up at different times (everyone is not getting up together), count back and have one group get ready at 20, another at 15, then 10, and so on to 0. Once students become very familiar with this routine, vary which groups go at a certain number. Later, use different evenly spaced numbers, such as 18, 14, 10, 6, and 2.

Recurring Games The following games and activities recur throughout this unit and others. Rules and materials vary per lesson as students learn more about numbers and counting.

Go to page —. Make sure students can find the page numbers in their JUMP Math workbooks, in the bottom left and right corners. Have students turn to different pages, one at a time, in random order. Always ensure that the entire class has found one page before asking students to turn to another. Have students point to where they see each page number. This helps students grasp the order of numbers, as they learn which way to turn the pages.

Picking pairs. Use, for example, Number Cards and Number Word Cards (see above); the deck that students use will depend on the lesson. Students can play in teams or individually. Place a 3 × 4 array of cards face up on the table. Students take turns picking pairs of matching cards and placing them into a common discard pile. When there are no more pairs in the array, more cards are added to it. The goal is to place all the cards into the discard pile. If students have any non-matching cards left at the end, then some of their cards must have been matched incorrectly.


4 TEACHER’S GUIDE

Memory. Students turn over two cards at a time. If the cards match by number, students set these cards aside; otherwise, they turn them face down again and continue playing. Play this first as a whole class, with volunteers taking turns. Students can then play individually or co-operatively in pairs. In either case, the goal is to finish all the cards. If playing with a partner, Player 1 leads by choosing and turning over a card and Player 2 follows by choosing and turning over another card. After all pairs are found, players switch roles and play again. Players can help each other by asking questions or making suggestions (EXAMPLE: “I think I know where both 3s are; should I turn one of them over?”) but they are not allowed to tell each other where specific cards are. (NOTE: It is a good idea for students to play Picking Pairs—to practise making and recognizing matches—before they play Memory.)

Dominoes. Make dominoes with numbers written in different ways (EXAMPLES: random arrangements of dots, base ten blocks, addition or subtraction sentences, numerals). You can use the template on BLM Blank Domino Cards (p XXX). Explain that the dominoes can be turned around even though the numerals won’t look like numerals any more. To play, lay all the dominoes face down and shuffle them. Each player draws 7 dominoes to start. The player with the highest double starts the game by laying that domino face up. On a turn, players play a domino that matches an open end of a domino already in play (there will be only two choices to start). If players cannot make a match, they turn over one of the dominoes that is still face down and play it if possible. Players play as a team and must help each other to place their dominoes; all dominoes in each player’s hand are thus placed face up on the table for all to see. When one player finishes all his or her dominoes, the other players get a chance to put down one domino in turn. Then the game ends. Count the dominoes remaining in all players’ hands; the goal is to have as few as possible. Advanced Variation: Count the “dots” remaining in all players’ hands instead of the dominoes.

I Have —, Who Has —? Each student needs one card to play (see sample in margin). You can make the cards or have students make them using BLM Game Cards (p XXX). The blank spaces at the top and bottom of each card can be filled with numerals or representations of numbers: an arrangement of dots, tens blocks, an addition or subtraction sentence. The student with the card shown in the margin would start by saying, “I have 3. Who has 7?” The students who has 7 on top would respond with, “I have 7. Who has [whatever is on the bottom of the card]?” And so on. Early in the unit, when only numbers 1 to 10 are available, students can play in smaller groups. When they have more numbers, students can play in larger groups or even as a whole class. Ready-made cards (on BLMs) are also available for some lessons.

Group Dominoes. This is a variation of I Have —, Who Has —? Have one student tape his or her card to the board. The person whose top matches the bottom of the card on the board adds his or her card below it, as when you play dominoes. This variation is particularly useful for students who

Sample Card I have 3

Who has 000 0 000

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prefer physical action to verbal answers. You can play with the cards from either Dominoes or I Have —, Who Has —?”

Message booklets. Write one word per page, as shown in the margin. The words should form a sentence, but should be out of order (the first word in the sentence should appear on page 1). Instructions at the top of each page tell students to “Go to page __” to find the next word in a “surprise” message. EXAMPLE: “The pig took a bath in the mud.” would be written over 8 pages. If the words in the sentence appear on pages 1, 5, 3, 6, 2, 4, 7, 8, page 5 would say “Go to page 3” and “pig,” page 3 would say “Go to page 6” and “took,” and so on. As students learn larger numbers, you could make longer books. Variation: Create a 26-page booklet with all the letters of the alphabet in random order but without the “Go to” instructions. (Make a list of the letters and page numbers for yourself.) Give students oral instructions to create an unlimited number of words and messages. Use messages that appeal to your students’ interests or that relate to class activities. EXAMPLE: “Let’s find out where we’re going on our next field trip. Go to page 5. Now go to page...”

Peace. (A co-operative version of the card game War.) Two players sit opposite each other and divide the deck into two equal piles, one on Player 1’s left and one on Player 1’s right. Player 1 begins by turning over the top card of each pile: If the cards are not equal, both cards are placed beside the pile that the greater card came from. If they are equal, they are each placed beside the pile they came from. Player 2 then takes a turn by turning over the top card of each pile. The game ends when all cards have been turned over and played. There will now be two piles on the table. Together, the players must predict, without counting, which pile has more. They count or use one-to-one correspondence to check their prediction. If they are right, they win.

Variations:Peace for Less: Place both cards beside the pile that the lesser card came from. Addition Peace: Turn over the top two cards from each pile and compare the sums of each pair. Difference Peace: Turn over the top two cards from each pile and compare differences instead of sums.

Missing Number Game. Give each student a sheet of paper divided into three equal parts:

Have students write numbers in the first two parts. EXAMPLE:

Then fold the third part over to cover the second part, so that the second number is hidden, and write the sum of the two numbers on the folded-over flap:

Go to page 5

THE1

3 5


6 TEACHER’S GUIDE

(sum)

Play with a partner who has to find the missing number. Players can switch roles and then switch partners to play repeatedly.

Students can exchange and solve each other’s problems. Students can check their own work by unfolding the cards. Students can sign the back of each other’s cards when they solve them. You can ask students to get at least 5 signatures on their cards.

Catch. You will need a small ball or paper object that students can catch in one hand. Throw the ball to a student while saying a number. The student catches the ball with one hand and repeats the number. The student then throws the ball back to you and says whatever “next” number you have asked for (e.g., the next number counting backwards, the next number when skip counting by 5). Ensure that everyone gets a chance to play.

Meeting Your CurriculumAll of the topics covered in this unit are required for students following the WNCP curriculum, either as review or as core curriculum material. The following topics are optional for students in Ontario: creating word problems (NS2-18), solving problems involving missing addends, subtrahends, or minuends (NS2-38 and NS2-39), working with the “not equal” symbol (Workbook page 64).

3 5 3 8

7Number Sense 2-

8 TEACHER’S GUIDE

NS2-1 CountingPage 1

CURRICULUM EXPECTATIONSOntario: 1m13, 1m20; review, 2m1, 2m5, 2m7WNCP: 1N1, 1N3; review, [R, CN, V, C]

VOCABULARY the numbers 0 to 10 number how many count

Review saying the numbers from 1 to 10. Teach a counting song, such as “One two, buckle my shoe.”

The concept of how many. Show students sets of four cards from BLM Quantities, of which three illustrate the same quantity, and ask students to identify the card that doesn’t belong. Point to each card, one at a time, and ask students to raise their hands when you point to the card that doesn’t belong. Repeat for each quantity from zero through nine at least once. Discuss what is the same and what is different about all the cards that do belong. Explain that you made the groups based on how many shapes were on each card. It doesn’t matter what the shapes are, how big they are, where they are on the card, or what colour they are.

Tap your desk a few times and ask students to identify the number of taps. Have all students individually hold up the correct number of fingers. Then hold up various number of fingers and have students say the correct number.

Counting in different ways gives the same answer. Arrange nine counters in a row. ASK: Do you think I will get the same answer starting here (at the left) as I get starting over here (at the right)? Count in both directions. ASK: Why did I get the same answer? (same number of counters) Repeat with different numbers of counters. Occasionally make a mistake by counting a counter twice. Wait for students to discover your mistakes. Discuss strategies to ensure that you don’t count objects twice, for example, move objects already counted to a separate pile or cover up each object that has already been counted.

Identifying the numeral with the sound. Draw several capital or lowercase letters and ask students to name them. Explain to students that just as

GoalsStudents will learn to count and will associate numbers (spoken) with the corresponding quantities and written numerals.

PRIOR KNOWLEDGE REQUIRED

Is able to circle a group of objects Can colour

MATERIALS

BLM Quantities (pp xxx-xxx) 9 counters various old magazines and catalogues (sports, clothing, toys, and so on) packages labelled with numbers BLM 2 cm Grid Paper (pp xxx-xxx) BLM Game Cards (p xxx) BLM Blank Domino Cards (p xxx)

PROBLEM SOLVING

Looking for a pattern

9

we have symbols for the letters in the alphabet (e.g., E is “ee”), we have symbols for numbers. Write some numbers on the board in order, from 0 to 9, and ask students to say the numbers as you point to them. Gradually increase the difficulty by writing more and more numerals that are not in order (4 2 5 3 8 6 1 0 7…). Then write 10 on the board. ASK: Is this a number? (yes) What number is it? (ten)

Identifying the numeral with the quantity. Write the numbers from 0 to 9 across the board, in order, leaving plenty of space between each one. Give each student one of the quantity cards used earlier and ask volunteers to tape their card below the correct number. More than one card will go with the same number. Then write a numeral on the board and have students hold up the corresponding number of fingers.

ACTIVITIES 1-7

1. Five. Give students BLM 2 cm Grid Paper. Ask them to colour any five squares, but only five. Ask one student to count his or her squares, pointing to each square one by one. SAY: I see all of the squares are [describe their arrangement on the page, e.g., in the top corner, in a line]. Did anyone colour five squares in a different way? How is your five different?

2. Posters. Give each student an old magazine or catalogue. Assign each student one number from 2 to 9 and ask students to find and cut out pictures where items are in groups of that many. Students can then form a group with other students who had the same number and pool their cut-outs to make a poster.

3. Numbers on packages. Have students identify the numbers on packages and discuss why numbers are important here. EXAMPLES: puzzle pieces, Lego building blocks, marbles, cookies, pencils, pens, erasers, crayons, chalk, paper, Ziploc bags. Students can also package a product themselves and write how many on the package.

4. I Have —, Who Has —? or Group Dominoes. (See NS Part 1 – Introduction) Use numerals on top and dots on the bottom. Alternatively, use different arrangements of dots on the top and bottom. See BLM Game Cards.

5. Dominoes. (See NS Part 1 – Introduction) Use dots on both sides of the dominoes, but arrange the dots differently for the same quantities. See BLM Blank Domino Cards.

6. Finding page numbers. Have students open their JUMP Math workbook to page 1. Then have them turn and point to the following page numbers in order: 2, 5, 3, 7, 10, 6, 9, 8, 6, 1, 4.

7. Message booklet. Make books with 10 pages. Each page has a word or letter and a page number. Give students various messages to find. The same book can be used for several different short messages, as long as the instructions “Go to page…” are given orally.

PROBLEM SOLVING

Reflecting on other ways to solve a problem

Real world

CONNECTION

Number Sense 2-1

10 TEACHER’S GUIDE

NS2-2 MatchingPage 2

CURRICULUM EXPECTATIONSOntario: 1m11, 1m13, 1m20; review, 2m3, 2m5WNCP:1N1, 1N2, 1N3; review, [CN, T]

VOCABULARY the numbers 0 to 10 how many number

GoalsStudents will practise counting, that is, matching numerals and quantities.

Numbers need to be right side up. Demonstrate that a chair, no matter how you turn it, is still a chair. But letters and numbers are not like chairs; they have to be written “right side up” otherwise they change. Write some lowercase letters, like “j” or “k,” on cards and turn them upside down and sideways to illustrate this. NOTE: Students may identify letters and numbers that don’t change (e.g., 8) or letters that turn into other letters (e.g., “d” becomes “p”) when written on a card and turned upside down. Point out that these are special cases; in general, numbers and letters have only one right side up.

Draw several numbers in two ways, correctly and incorrectly, and have volunteers circle the correct way. Include numbers that are upside down or on their side.

Match by counting. In a two-column chart, draw three different quantities (less than ten) in the first column. Draw the same three quantities, using different items in a different arrangement, in the second column. EXAMPLE: 4 stars, 5 dots, and 1 checkmark in the first column; 1 heart, 4 squares, and 5 triangles in the second column. (Alternatively, use cards from BLM Quantities.) Have volunteers match the items by quantity. Repeat several times, gradually increasing the quantities in each column, up to ten. Then arrange and match quantities by row instead of column. When students can comfortably match quantities, replace the quantities in one column or row with numerals, and have students match numerals to quantities.

ACTIVITY 1

Ask students to walk around the room and look for numbers written the correct way. Have them use the numbers they find to circle numbers written correctly on BLM Circle the Numbers. Some boxes include two correctly written numbers (6 and 9).


Understands the concept of quantity Can join two figures with a line

MATERIALS

BLM Circle the Numbers (p xxx)quantity cards or BLM Quantities (p xxx-xxx) 2 cm grid paper or BLM 2 cm Grid Paper (p xxx)BLM Game Cards (p xxx)BLM Dominoes (p xxx)

NOTE: Technically, a number is the quantity and the symbol for the number is called the numeral. A digit is any symbol from 0 to 9. A numeral can consist of one digit (e.g., 6, which corresponds to the quantity six) or more than one digit (e.g., 12, which corresponds to the quantity twelve). Students do not need to use the word “numeral” at this stage; they can use “number” to refer to both the quantity and the symbol.

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Match two quantities to numerals. Ask students to match dominoes with dots to corresponding dominoes with numbers. EXAMPLE:

Encourage students to check both sides of the dominoes they match to verify their answers. Justifying the solution Repeat with other sets of dominoes where each number appears only once. Then begin to include examples where the same number occurs on one side of two different dominoes. Finally, arrange the dominoes in rows instead of columns and then scatter them.

CONNECTIONLiterature What Comes in 2’s, 3’s, and 4s? by Suzanne Aker One Gray Mouse by Katherine BurtonFeast for 10 by Cathryn FalwellOne Hungry Monster by Susan Heyboer O’Keefe

Extensions1. Have students match objects by number. SAY: It might be tricky. Some

groups have the same objects but you have to match by number, not by object. EXAMPLE:

2. Ask students to think of letters that can be turned around to make other letters. Then ask them to think of numbers that can be turned around to make letters. Give students calculators, and have them push different numbers and then turn the calculators around to see what letters they can make. Ask them to try to make a word. Can they make any of these words: hello, goose, giggles, lego, bees? What other words can they make?

5 4

1 3

2 6

PROBLEM SOLVING


BLM Dominoes

EXTRA PRACTICE ACTIVITY 2

Play Picking Pairs and then Memory (See NS Part 1 – Introduction) using quantity cards. Start with two of each quantity from one to nine. Arrange the 18 cards in 3 rows of 6. Variation: Use one quantity card and one number card for each quantity.

Draw a group of 9 and a group of 10. Have a partner circle the group of 10.

JOURNAL

More Extensions, with BLM Many Ways to Colour

ONLINE GUIDE

Number Sense 2-2


NS2-3 One-to-One CorrespondencePages 3-4

CURRICULUM EXPECTATIONSOntario: 1m11, 1m13, 1m20; review, 2m1WNCP: 1N5; review, [R, CN]

VOCABULARY more less pair enough as many

GoalsStudents will identify which of two sets has more by using one-to-one correspondence.

Adding one to both or removing one from both doesn’t change which has more. Take a pile of 3 red counters and a pile of 4 yellow counters. ASK: Are there more red counters or yellow counters? (yellow) Verify by counting. Emphasize that 4 comes after 3, so there are more yellow counters than red counters. Continue adding one to each pile, asking which pile has more, and verifying. Emphasize that adding one to each pile at the same time doesn’t change which one has more.

Matching chairs to people. Sit in your chair and ask students to do the same so that everyone in the classroom is seated. ASK: Are there more people or chairs in this room? How do you know? (If there are extra chairs, then there are more chairs than people.) Draw several combinations of chairs and stick-people on the board (see suggestions below) and ASK: Are there more people or chairs? How do you know? Did you need to count?

• 5 chairs and 7 people; 2 people are standing • 5 chairs and 7 people, but no one is standing—the first two and last two people are sharing a chair • 9 chairs and 6 people; three chairs are empty

Which group has more? Tell students you want to find out if there are more boys or girls in the class without counting. Ask students to pair up, one boy with one girl. ASK: Are there any boys or girls left without a partner? Are there more boys or girls? How many more?

Find out which pile has more, without counting, by removing one from each pile. SAY: Julie and Teah each have a pile of beads. (Show Julie’s


Understands the concepts of more and less (or fewer) Can count

MATERIALS

lots of objects to count, such as counters and connecting cubes

ACTIVITY

Co-operative musical chairs. Play as you would musical chairs, but no one sits out: Every time a chair is removed, children sit two or more to a chair. Eventually they will all have to fit onto one chair. Play in groups of 7 or 8. Make the connection between having more people than chairs and having to share chairs. VARIATION: Large hula hoops are islands. The water level is rising and islands are disappearing, one by one. People stand inside the hula hoops.

Draw two more hearts than circles. Draw as many pencils as erasers.

JOURNAL

13

pile of 24 yellow counters and Teah’s pile of 26 red counters.) They want to know if they have the same number or not, but counting each pile is too much work. How can they find out without counting? Encourage students to talk over the problem with a partner before sharing ideas with the class. If no one suggests removing one from each pile until only one colour is left, suggest it yourself and then demonstrate. ASK: Which colour is left: red or yellow? (red, so there are more red counters than yellow counters) Who has more counters? (Teah) ASK: If Teah gives a counter to Julie, do you think they will have the same number? Check the prediction. Then let students work in pairs. Give each pair a pile of red and a pile of yellow counters and have them determine if they have more red or yellow counters.

Draw a model for the counters. Draw several squares, some coloured and some uncoloured, scattered on the board. Demonstrate pairing objects by drawing a circle around pairs or by joining pairs with a line. ASK: Are there more coloured or uncoloured squares? How do you know?

Connect one-to-one correspondence with counting. Explain that when you count, you are really pairing up each object with a number. ASK: How many numbers do I say when I count from 1 to 8? (8) Demonstrate by counting 8 cubes. Point out that each cube gets paired up with a number from 1 to 8. Since you know that there are 8 numbers from 1 to 8, there are 8 cubes. Emphasize that it doesn’t matter which cube you pair up with each number, just like it didn’t matter which red counter was paired up with which yellow counter above.

ExtensionStarsweeper. Before they play this game, students should complete BLM Counting Starred Squares (pp XXX–XXX). Over the course of the BLM, students will learn to identify how many starred squares each square in a grid is touching (see examples in margin).

To make a 4 × 4 or 5 × 5 Starsweeper grid, put at most four stars in the 4 × 4 grid and five stars in the 5 × 5 grid. Then write the number of starred squares each square is touching in that square. You (or your students) can use the templates on BLM Blank Starsweeper Grids (p XXX).

Students cover all the squares on the grid with coins or tokens about the size of a penny. Students remove the coin from any square they think does not have a star in it. If they uncover a square with a 0 in it, they know that all the squares around it are star-free and they can uncover all of those too. When students think there are more starred squares still covered than numbered squares, they stop. Students can check if they’re right by putting the pennies left on the board into two piles: one pile for the pennies that cover a starred square and a second pile for the pennies that cover a numbered square. They win if the first pile has more than the second pile. Students can play individually or co-operatively in pairs by taking turns. Players must decide together when to stop uncovering squares.

Real World

CONNECTION

PROBLEM SOLVING

Making a model

1

1 1

0 1

2 2 1

1 1

2 3 1

2 3

1 1 3 2

0 0 1

Number Sense 2-3


NS2-4 Counting with a ChartPage 5

CURRICULUM EXPECTATIONSOntario: 1m11; review, 2m2, 2m5WNCP: 1N1, 1N3; review, [R, CN]

VOCABULARY number line

GoalsStudents will use a chart in place of counting orally.

Make a counting strip for each student. Make strips of paper 2 cm wide and 20 cm long divided into ten numbered squares (or photocopy strips from BLM Counting Cubes).

Count using a chart. Give each student up to ten 2 cm connecting cubes (students should have different numbers of cubes). Ask students to count their cubes. Then have them make a chain with the cubes and place it on the chart, so that each cube covers one square and the chain starts on the 1. Students should exchange cubes with different partners and repeat the exercise several times. Then ASK several students: How many cubes did you count? What is the last number covered on the chart? Does anyone notice a pattern? (the last number covered is always the number of cubes in the chain) Then have students repeat the exercise with this pattern in mind. Does the pattern hold? (yes) ASK: What is an easy way to find out how many cubes there are without counting? (look at the last number covered)

The chart does the counting for you. ASK: How is the chart doing the counting for you? (instead of saying “one, two, three,…” when picking up the cubes, just place a cube on 1, another cube on 2, another on 3, and so on) Demonstrate by picking up a cube, saying “one,” and placing it on the 1. Pick up another cube, say “two,” and place it on the 2. Repeat until all the cubes are counted.

The chart makes sure that each cube is counted once. ASK: How does the chart help to make sure that you don’t count any cube twice? (once a cube is placed on the chart, it’s been counted) How does the chart help to make sure you don’t miss any cubes? (if any cubes are left off the chart, they aren’t counted)


Can say the numbers from 0 to 10 and write the corresponding numerals in sequence Can count to 10

MATERIALS

counting strips (details below) or BLM Counting Cubes (p XXX) lots of 2 cm connecting cubes two-colour counters or coins precut square pieces of paper (details below)

1 2 3 4 5 6 7 8 9 10

PROBLEM SOLVING

Looking for a patternPROBLEM SOLVING

Making and investigating conjectures

15

Demonstrate using the chart incorrectly. Draw the same chart on the board and use square pieces of paper to represent cubes. Place six squares on numbers as shown:

Explain to students that because 8 is the last number covered, you think that you put 8 squares on the chart. ASK: Am I right? (no) Why not? (the squares must cover every number in order; you can’t skip numbers) Then take the squares off and demonstrate counting them incorrectly: 1, 3, 4, 5, 7, 8. SAY: Even when I count them, I still get 8. What did I do wrong now? (you missed two numbers; you didn’t say all the numbers in order) Explain that just as you’re not allowed to miss numbers when counting, you’re not allowed to miss any numbers when using the chart. Repeat with various incorrect placements, always asking students to tell you how this is like missing numbers when counting. EXAMPLE: 2, 3, 4, 5.

Writing numbers. From this lesson forward, students need to be comfortable writing the numerals from 0 to 9.

ExtensionOn BLM Counting Dots, students can count the corners (marked by dots) of various shapes.

1 2 3 4 5 6 7 8 9 10

PROBLEM SOLVING

Connecting

ACTIVITY

Give each student 10 two-colour counters or coins. Have students toss the counters/coins and then use a sequence of numbers to count how many turned up red and how many turned up yellow (or heads and tails). Students could place the red counters (or heads) above the row and the yellow counters (or tails) below the row.

1 2 3 4 5 6 7 8 9 10

Students can practise writing numbers with BLMs Ants, License Plates, Roman Numbers, and Writing Numbers.

ONLINE GUIDE

Number Sense 2-4


NS2-5 More, Fewer, and LessPage 6

CURRICULUM EXPECTATIONSOntario: 1m11, 1m20; review, 2m1, 2m7WNCP: 1N5, 1N8; review, [R, C]

VOCABULARY right left more most less least fewer fewest order

GoalsStudents will understand that the number that means more (less) is said later (earlier) when counting and written to the right (left) when the numbers are written in order.

The concept of more. Ask students to try to explain what “more” means without using the word. Then explain that “more” in math means a larger number. Write “more” on the board. Show lots of pennies in one hand and two or three in the other. ASK: Which hand has more pennies? Then draw lots of little circles on the right side of the board and two big circles on the left. ASK: Are there more circles here or there? Explain that the circles are bigger on one side, but there are more of them on the other side.

The number you say last means more. Show two piles of blocks, one with 8 and one with 9. ASK: Which pile has more blocks? How can we find out for sure? Then count the pile with 8 blocks. Choose a student who said that the pile with 9 blocks has more. SAY: You said that the other pile has more. Do you think I will get to eight when I count the second pile? Emphasize that you should get to eight before finishing the second pile because it has “more.” Then count together and stop at eight. ASK: Was [student’s name] right? Explain that because you were not finished counting the other pile when you said eight, that pile has more.

Show 5 red counters and 7 yellow counters. Count the pile of seven and then check to see if you say seven when you count the other pile. ASK: Are there more red counters or yellow counters? (yellow) How do you know? (when counting the red pile, you didn’t say the number that you got when you finished counting the yellow pile)

It’s easier to count two piles together. SAY: It’s so much work to count each pile separately; let’s try to count two piles at the same time. Show a pile of 6 red cubes and 8 yellow cubes. Taking one of each colour at a time, count up to six; hold up 1 red cube and 1 yellow cube with each number. Explain that you have to stop because you have run out of red cubes. Since there are extra yellow cubes, you know there are “more” yellow than red cubes. Write on the board: red 6. Finish by counting the two extra yellow cubes. Emphasize that you can start at 7 because you already counted 6.


Is able to say the numbers from zero to ten in sequence Can match, and translate between, numbers spoken orally and numerals

MATERIALS

blocks, counters, cubes or other objects to count BLM Who’s Winning? (p xxx)

17

Then write on the board: yellow 8. Give students red and yellow cubes to count in this way. Repeat by having students trade handfuls of cubes with each other.

When numbers are written in order, the number on the right means more. Write the numbers in order on the board. ASK: Are the numbers written in the same order as you say them when counting out loud? (yes) How could you use this order to say if a number is more or less than another number? (the one on the right, or further along in the list, means more, just as the number you say last when counting out loud means more)

Which number means more? Write two numbers on the board. Have students show the larger of the two numbers by holding up the correct number of fingers. Have an ordered list of numbers displayed for reference. Eventually challenge students to indicate which is more without referring to an ordered list.

Which number means the most? Explain that “most” means more than all the others. Write “most” on the board. Write three numbers on the board and have students choose the number that means the most. Start with examples where the numbers are already in order (EXAMPLE: 3, 6, 7), and then give examples where the numbers are not in order (EXAMPLE: 7, 4, 1). Students might at first find it helpful to refer to a list of the ordered numbers. They can circle all three numbers that they are asked to consider on the list and then choose the one furthest right as the most.

Introduce “fewer” and “less” as the opposite of “more.” Have two piles of counters: 5 red and 3 yellow. Tell students there are more red counters than yellow counters; that means there are fewer yellow counters than red counters. Explain that fewer is used for amounts that you can count and less is used for amounts that you cannot count. Show or draw two students with different amounts of cake: One has 2 small pieces, the other has 1 large piece bigger than both small pieces put together. ASK: Who has more pieces? Fewer pieces? More cake? Less cake? Write “fewer” and “less” on the board, spaced apart, and ask students to point to the correct word to finish various sentences (or make cards for the students to hold up). EXAMPLE: I have more coins, so you have coins. (fewer) Repeat with: carrots (fewer), juice (less), pie (less), pizza (less), pieces of pizza (fewer).

Repeat this lesson with “fewer/less.” Go back to “The number you say last means more,” and guide students to decide which pile has fewer by first asking which pile has more. Introduce “least” and “fewest” as the opposite of “most.” Explain that least means less than all the others and fewest means fewer than all the others. Repeat the last exercise above (Which number means the most?) with “fewest” instead of “most”.

PROBLEM SOLVING

Changing into a known problem

BLM Who’s Winning?

EXTRA PRACTICE

PROBLEM SOLVING

Doing a simpler problem first

Number Sense 2-5

Bonus Give students 4 blue, 8 red, and 7 yellow cubes and ask them to count all three piles by saying the counting sequence only one time.

Extension— Introduce the more than (>) and less than (<) symbols using BLM Mr. Hungry.

ONLINE GUIDE

ACTIVITY

Play Peace and Peace for Less. (See NS2 Part 1 – Introduction) Use only the red cards from A to 10 and count A as 1.

Bonus 7, 6, 3, 9; 4, 6, 2, 3, 7, 1


NS2-6 How Many More?Pages 7-9

CURRICULUM EXPECTATIONSOntario: 1m11, 1m14; review, 2m3, 2m5, 2m6, 2m7 WNCP: 1N5; review, [R, CN, C, V]

VOCABULARY extra pair up how many more

GoalsStudents will determine how many more by pairing objects up and counting the extras.

Count the extras to find how many more. Give students two-coloured counters to toss. ASK: Did more counters land with the yellow face up or the red face up? Have students pair up their counters to see which colour has extras. ASK: How many extras are there? Have several volunteers present their answers, showing their pairings. Repeat several times.

Find out how many more by lining up objects above and below a sequence of numbers. Draw the numbers 1 to 10 on the board, then line up eight squares above the numbers and six triangles below the numbers in one-to-one correspondence:

1 2 3 4 5 6 7 8 9 10

Remind students how to pair objects, one square to one triangle. ASK: Are there more squares or triangles? (squares) SAY: If there is more of one shape, I’m going to call the additional number of shapes “extra.” Write the word “extra” on the board. Draw a circle around each extra square and the number below it:

1 2 3 4 5 6 7 8 9 10

ASK: How many extra squares are there? (two) Write the following sentence on the board and ask a volunteer to fill in the blank: There are more than .Repeat with similar pictures.

Counting the extra numbers you say. Write 1 2 3 4 5 and have a volunteer continue writing the numbers until 8. ASK: How many extra numbers did you write? (3) How many more is 8 than 5? (3) Tell students that they can keep track of how many extra numbers there are by counting on their fingers. Tell students you are going to count to 8, but only raise a finger when you say an extra number after 5. Remind students that you want to know how many more 8 is than 5. Count from 1 to 5 with your fist closed,


Understands one-to-one correspondence Understands the concepts of more and less (fewer) Can count

MATERIALS

BLM Counting On (p XXX)BLM How Many Fruits? (p XXX)

Making a model.

PROBLEM SOLVING

19

then raise your thumb and say “6,” raise your index finger and say “7,” raise your middle finger and say “8.” SAY: Because I raised 3 fingers when counting to 8 after I counted 5, I can see that 8 is 3 more than 5.

As a class, use this method to find how many more 9 is than 7. Start counting at 1; students only raise fingers when they get to the extra numbers. Repeat with 8 and 4; 10 and 5; 9 and 6; 10 and 7.

NOTE: Make sure students tuck their thumbs under their other fingers when they make a fist. If the thumb is not tucked under and sticks out, students may start counting the extras with their other fingers but include the thumb when they total the extras. To ensure that students keep their fists closed while saying the first number, you can pretend to throw them the first number which they have to pretend to catch.

Counting on. Show students an easier way to find how many more 10 is than 7. Instead of saying 1, 2, 3, 4, 5, 6, 7, all with their fist closed, they can just say 7 with their fist closed, and count the extra numbers 8, 9, and 10. Discuss why this works. SAY: You are going to get to 7 anyway, by saying all the numbers from 1 to 7, so you might as well save time by starting at 7. Give students lots of practice with this type of question. Eventually include questions where students need to count the extra numbers on both hands, but use only one-digit numbers. EXAMPLE: 9 is how many more than 3?

Counting on with pencil and paper. Tell students that you want to know what number is 4 more than 5. Instead of saying the next four numbers, you can write them. Write on the board: 5 (as on Workbook page 8). Have a volunteer fill in the blanks. ASK: What number is 4 more than 5? Repeat with other numbers, always ending with at most 10. Then write the numbers from 1 to 20 in order on the board, and include problems that require counting to 20. Leave this number sequence visible while students complete Workbook page 8.

Extensions1. BLM More Than. Students discover patterns by changing the order of numbers: 7 is 4 more than 3 but 7 is also 3 more than 4.

2. BLM Keeping Score shows various scores for Red against Blue and asks who’s winning and by how many points.


PROBLEM SOLVING

BLM Counting On

EXTRA PRACTICE

BLM How Many Fruits?

EXTRA PRACTICE

ACTIVITY

Bring in a bed sheet and set up a hiding area at the front of the room. Ask 4 volunteers to hide behind the sheet and ask for 3 more volunteers to stand at the front. ASK: How many children are at the front of the room? SAY: I know there are 4 children hiding even though we can’t see them, so we will count the others starting at 5. Demonstrate doing this and then remove the sheet and count all the students, starting at 1. Repeat with various numbers of volunteers. VARIATION: Hide a known number of counters in a container.

Number Sense 2-6

Literature— More, Fewer, Less by Tana Hoban

CONNECTION


NS2-7 Reading Number Words to TenPages 10-11

CURRICULUM EXPECTATIONSOntario: 1m12; review, 2m3WNCP: 1N4; review, [R]

VOCABULARY one, two, …, ten

GoalsStudents will read the number words from zero to ten.

Sound out number words to read. On the board, write:

two four zero three five one

SAY: These are the number words for 0, 1, 2, 3, 4, and 5, but they are out of order. Write the numbers on the board. Have students say each number out loud. Use sound to match the numerals to the number words in this sequence:

• 4 What sound does it start with? What other words start with the same sound? What letter makes that sound? What sound does the word “four” end with? What letter do you think it ends with? Can you choose the correct word? (When chosen, circle the word “four.”)

• 0 Repeat the questions above. Circle “zero.” Show students how to check their choice using information given. ASK: The word that you circled has an “r” in it—does this make sense?

• 5 There are two ways to see that “five” is 5: first, it’s the only word left that begins with the “f” sound; second, look at all the words in the list and see that “five” is the only one that has a “v” sound as well as an “f” sound.

• 3 Remind students that sometimes two letters make one sound. Ask them which two letters are making one sound in words like throw, thanks, and think. Encourage students to search for the words in a book, point to words on the word wall, or write some of them on the board. Underline the “th.” ASK: Which number word starts with “th”?

• 2 It starts with “t” but not “th.”

• 1 It has an “n” sound; also, it’s the only word left!

Repeat with the words “six” through “ten.” Use the “t” sound at the end of “eight” to help students match it to 8.


Can write the alphabet Knows the sounds associated with each letter of the alphabet

MATERIALS

BLM Match Pictures to Number Words (p xxx)number word cards for zero to ten (one per student) or BLM Number Words to 20 (1) (p XXX)number cards for 0 to 10 (one per student) BLM Reading Numbers

Reflecting on the reasonableness of an answer

PROBLEM SOLVING


PROBLEM SOLVING

BLM Match Pictures to Number Words

EXTRA PRACTICE

21

Find the number word in a sentence. Write the number words from “zero” to “five” on the board and then the sentence, “Four friends played together.” ASK: Can you find the number word in that sentence and say it? Ask a volunteer to write the number above the number word:

4Four friends played together.

Repeat with several more sentences, using “zero” to “five.” Then erase the number words on the board and have students find the number word without the list to refer to. Continue with sentences using number words “six” to “ten,” again starting with a list on the board and then erasing it. Finally, give students sentences using any number from “zero” to “ten.” Start with simple sentences, such as “There are nine monkeys,” and move on to more complex sentences, such as “Rita bought two tennis rackets and three tennis balls.”

EXAMPLES:Four children played hockey. Recess lasts ten minutes. Rita bought three tennis balls. Mary has five erasers. John is seven years old. Karen is five years old. Calli is three years old and Lina is five years old. John has eight fingers and two thumbs. Lucas is two years younger than Sarah.

Ask students to make up their own sentences and have a partner write the number(s) above the number word(s).

A tip for struggling students. When you ask students to write the numbers above the number words, here and on Workbook page 11, some students may find it helpful if you underline the number word first. Once students are able to find and write the number this way, try more sentences without underlining the number word, or photocopy Workbook page 11 and have students redo it.

Extensions1. BLM How Many More Than. Students write how many more one number is than another. Bonus Add the number word above the numeral in the blank. 2.

2. BLM Stars. Students join the dots in order, according to the number words.

3. Give each student number word cards for “zero” to “ten.” Students shuffle the cards and order them. Students can then re-shuffle the cards and exchange with a partner.

Representing

PROBLEM EXPECTATION

More Extensions (with BLMs)

ONLINE GUIDE

Connecting

PROBLEM SOLVING

Number Sense 2-7


NS2-8 AdditionPages 12-13

CURRICULUM EXPECTATIONSOntario: 1m25; review, 2m1, 2m2, 2m5, 2m6, 2m7WNCP: 1N9; review, [R, V, CN, C]

VOCABULARY add plus (+)in total altogether equal (=)addition sentence

GoalsStudents will solve simple addition problems.

Starting with 2 and adding 3 more always gives 5 in total. Draw two circles in a row on the board. ASK: How many circles did I draw? Then ask your students to watch carefully. Draw three more circles. ASK: How many more did I draw? SAY: I started with two circles. I drew three more. How many do I have in total? Repeat with squares in a row and then triangles arranged not in a row, again starting with two and adding three more.

The plus (+) and equal (=) signs. ASK: If you had two apples and someone gave you three more apples, how many would you have in total? Tell students that mathematicians have a way to say that if you have two of something and you add three more, you always have five in total. Ask if anyone knows the way mathematicians write this. If no one does, write 2 + 3 = 5. Ask if students know the way mathematicians say this. Tell them that we say “2 plus 3 equals 5” but what we really mean is “starting with 2 things and adding 3 more is the same number as having 5 things”; point to the corresponding symbol as you say each part. Emphasize that the plus sign (+) means “adding” and the equal sign (=) means “is the same number as.”

Read addition sentences two ways. Write 3 + 4 = 7 on the board. ASK: How could I read this? (“3 plus 4 equals 7” or “starting with 3 things and adding 4 things is the same number as having 7 things”) Say it both ways after volunteers respond. Repeat with more sentences, but don’t include zero yet (students will add and subtract zero in NS2-10). EXAMPLES: 2 + 1 = 3, 2 + 4 = 6, 1 + 5 = 6, 3 + 3 = 6, 4 + 5 = 9, 3 + 5 = 8.

Check with counters that addition sentences are right. Give students two-colour counters or two colours of blocks. Have students make, for example, a pile of 2 yellow counters and another pile of 4 red counters and then see how many they have altogether. Emphasize that starting with 2 counters and then adding 4 more counters is the same number as having 6 counters (i.e., starting with both piles put together). SAY: Notice that we are adding counters, not colours; colour doesn’t matter. Write on the board:


Uses one-to-one correspondence when counting Can count to 10 Know the plus (+) and equal (=) signsUnderstands the concept of addition

MATERIALS

two-colour counters or two colours of blocks dice BLM Game Cards (p xxx) BLM Blank Domino Cards (p xxx) BLM Add the Dots (p xxx)


PROBLEM SOLVING

BLM Add With a Model

ONLINE GUIDE

23

2 + 3 = 5, 3 + 5 = 7, 5 + 4 = 9. Challenge students to find the incorrect sentence and prove that it is incorrect using their counters (when the piles of 3 and 5 counters are put together they do not total 7).

Write the total on the left. Tell students that when you say two things are the same, it doesn’t matter which you say first. For example, “My shirt is the same colour as your crayon” and “Your crayon is the same colour as my shirt” mean the same thing. We can do that with numbers too. Saying 5 + 1 is the same number as 6 (write 5 + 1 = 6 on the board as you say this) means the same thing as saying 6 is the same number as 5 + 1 (write 6 = 5 + 1 on the board). Have students write these addition sentences with the total on the left: 3 + 4 = 7, 2 + 6 = 8, 1 + 4 = 5.

Write on the board: 6 = 3 + 2, 7 = 2 + 5, 8 = 7 +1. Again have students find the incorrect sentence and prove their choice using counters.

Add 3 things together. Tell your students that 3 girls, 2 boys, and 2 adults went on a picnic. Write on the board: 3 girls + 2 boys + 2 adults = people. ASK: How many people went on the picnic? Have one volunteer draw the 3 girls, another volunteer draw the 2 boys, and another draw the 2 adults. ASK: How many people are drawn altogether? Have students find the totals in more such problems by drawing their own pictures or by using counters. EXAMPLES:3 basketballs + 2 volleyballs + 2 soccer balls = balls vehicles = 3 buses + 2 fire trucks + 3 police cars

Bonus animals = 2 lions + 1 bear + 3 cats + 2 dogs + 1 hamster

Write addition sentences another way. Explain that addition sentences can be written up and down too (see margin). Have students practise adding vertically with more problems like those above.

ExtensionsBLM Add Roman Numbers shows playing cards that use Roman numbers. Students use the cards to write and add roman numbers.

BLM I Have — Who Has — Addition Cards has ready-made cards for numbers up to 5. The BLM has 12 cards: the first 6 go together and the next 6 go together. Play in groups of six.

ONLINE GUIDE

ACTIVITIES 1-3

1. If students can count to 12, have pairs of students roll two dice—one each—and add the numbers they roll. Students should add the numbers independently and compare their answers. If students’ answers do not agree, they should add again or count the dots until they do. If students can count to 18, have them work in groups of three.

2. I Have —, Who Has —? (See NS Part 1 – Introduction) Use a number on top and an addition question with a picture on the bottom. Use BLM Game Cards to make cards for numbers up to 10.

3. Dominoes or Group Dominoes. (See NS Part 1 – Introduction) Use BLM Blank Domino Cards to make dominoes with a number on top and an addition problem with a picture on the bottom.

Drawing a picture

PROBLEM SOLVING

Number Sense 2-8

2 apples + 7 bananas= 9 fruits

BLM Add the Dots

EXTRA PRACTICE

Literature— Animals on Board by Stuart J. Murphy. Two trucks of each kind of animal pass by the character’s truck and he adds the numbers together to find the total.

CONNECTION


NS2-9 SubtractionPages 14-15

CURRICULUM EXPECTATIONSOntario: 1m25; review, 2m2, 2m6 WNCP: 1N9; review, [R, V]

VOCABULARY minus (-)take away subtract subtraction sentence

GoalsStudents will understand subtraction as “taking away” and will draw and use pictures to solve subtraction problems.

Taking away 3 objects from 5 always leaves 2 objects. Draw five circles in a row on the board. SAY: I want to remove three circles, but instead of erasing them, I am going to cross them out; please watch carefully and tell me to stop when you think I’ve crossed out enough circles. Cross out the first three circles. If students don’t tell you to stop, ASK: How many have I crossed out? Have I crossed out enough? How many are left? Repeat with five squares in a row, but this time take away the last three squares. Then repeat with five triangles scattered randomly and take away any three. ASK: If you had five apples and someone took three of them away, how many would be left?

The minus sign (−). Explain that if you have five of something and you take away three of them, you always have two left. ASK: Does anyone know how mathematicians write this fact using numbers and signs? Encourage students to come to the board to show you if they want to. If no one volunteers, write 5 - 3 = 2. Ask if students know the way mathematicians say this. Tell them that we say “5 minus 3 equals 2,” or “5 take away 3 equals 2,” or “subtract 3 from 5 to get 2.” Point to the corresponding sign as you say each part. SAY: What we really mean is that when we start with five things, and we take away three of them, we get the same number as if we’d started with only two things.

Write subtraction sentences from a picture. Draw seven circles and tell students you want to remove four. SAY: Tell me when to stop. (Cross out four circles.) Ask a volunteer to write a “take away” sentence on the board for your drawing. (7 - 4 = 3) Write “take away,” “subtract,” and “minus” on the board. Ask another volunteer to read the sentence in two different ways, one using “take away” and another using a different word that means the same thing. Repeat this several times with different numbers, asking students to write the sentence and then read it using “subtract” or “minus.” Do not include examples with 0 yet (students will subtract with 0 in the next lesson).


Uses one-to-one correspondence when counting Can count to 10 Knows the plus (+) and equal (=) signsUnderstands the concept of addition

MATERIALS

counters BLM Colour to Subtract (pp xxx–xxx)

PROBLEM SOLVING


25

Colouring to subtract. Tell students that instead of crossing out circles, you will colour the circles you want to take away and then ask how many are not coloured. Draw on the board the picture shown in the margin. ASK: How many circles did I draw? How many did I colour? How many are not coloured? (Write 5 - 3 = 2.) Repeat for various examples.

Draw a picture to solve the subtraction sentence. Write a subtraction sentence on the board, such as 5 - 2. SAY: Please draw shapes, as I’ve been doing, to show 5 - 2. You might draw circles, squares, triangles, or hearts. Your shapes should be big enough so that the whole class can see them when you hold them up. Have volunteers show their work to the class; emphasize how all the drawings are different and how they are the same. Differences may include shapes drawn, size of shapes, where they are on the page, and colour.

Check with counters that subtraction sentences are right. Give students counters. Have students count out 7 counters, and ask them to take away 3, see how many they have left, and write the subtraction sentence. Repeat for other examples. Then write these subtraction sentences on the board: 8 - 2 = 6, 8 - 3 = 4, 7 - 5 = 2. Challenge students to find the one that’s wrong and to prove it wrong using their counters.

Write the difference on the left. Emphasize that 7 - 3 = 4 (7 take away 3 is the same number as 4) means the same things as 4 = 7 - 3 (4 is the same number as 7 take away 3). Then have students again use their counters to find the incorrect subtraction sentence among these choices: 5 = 9 - 4, 7 = 9 - 2, 3 = 8 - 4.

Another way to write subtraction sentences. Explain that, like addition sentences, subtraction sentences can be written up and down instead of side to side (see margin). Write several subtraction sentences on the board for students to solve using a picture or counters.

Extension

BLM Subtract! shows various models of subtraction

PROBLEM SOLVING

Drawing picture

BLM Colour to Subtract

EXTRA PRACTICE

BLM Subtract Using Dominoes—students write subtraction sentences for pictures of dominoes.

ONLINE GUIDE

ACTIVITIES 1-2

1. Play Difference Peace. (See NS Part 1 – Introduction)

2. a) Give students dominoes. Have pairs play as follows: Player 1 picks a domino, counts the total dots, tells Player 2 how many dots are on the domino, and hides one half. Player 2 guesses how many dots are on the hidden half. Player 1 then reveals the hidden half. Players switch roles. b) Play Missing Number Game (see NS 2 Part 1 – Introduction) but have students draw dots on the first two flaps and write the total number of dots on the third flap. Students might find it helpful to think of the first two flaps as a domino, with the total number dots given on the third flap.

10 cats - 3 cats= 7 cats

Number Sense 2-9


NS2-10 Adding and Subtracting 0Page 16

CURRICULUM EXPECTATIONSOntario: 2m2, 2m6, 2m7, 2m72 WNCP: 2N8, [R, V, C]

VOCABULARY add plus minus take away subtract addition sentence subtraction sentence

GoalsStudents will solve simple addition and subtraction problems involving zero.

Write addition sentences with 0 using dominoes. Tape a large paper domino on the board with a 5 on one side and blank (0) on the other side. Ask students to count the number of dots on each side. SAY: I would like to write an addition sentence for the total number of dots on this domino. Remind students that there is a number that means none (0). Invite answers. Write 5 + 0 = 5 under the domino. Tape a second domino on the board or add dots to the first to show 7 on one side and 0 on the other side. Have a volunteer write the corresponding addition sentence.

Give each student several dominoes, real or paper, that are blank on one side. (You can use BLM Blank Domino Cards to make them.) Have students record the number sentences for their dominoes. ASK: What do you notice? Explain that when students add 0 objects, they don’t add anything, so the result is the same as the number they started with.

Practise adding 0 without dominoes. ASK: If I start with 3 things and add 0 things, how many do I have in total? (3) Write the corresponding addition sentence on the board: 3 + 0 = 3. Repeat with more addition statements. EXAMPLES: start with 5 things and add 0 things; start with 2 things and add 0 things. Invite volunteers to write the corresponding addition sentences on the board: 5 + 0 = 5, 2 + 0 = 2. ASK: What if I start with 0 things and then add 3 things? Now how many do I have? (3) Have a volunteer write the addition sentence on the board: 0 + 3 = 3. Continue with more such questions. Then mix questions with 0 as the first number or the second number. ASK: What do you think 0 + 15 will be? Repeat with 12 + 0, 0 + 18, 10 + 0.

Bonus Use increasingly larger numbers: 20 + 0, 0 + 55, 100 + 0.

Subtract 0 using pictures. Draw 3 circles on the board. ASK: How many circles do I have? (3) Write 3 underneath the circles. ASK: If I want to take away no circles or 0 circles, how many circles would I have left? (3) Count how many are left when no circles are taken away and write the subtraction


Uses one-to-one correspondence when counting Can count from 0 to 10 Knows the plus (+), minus (-), and equal (=) signsUnderstands the concepts of addition and subtraction

MATERIALS

pre-made paper dominoes (see below) BLM Blank Domino Cards (p xxx)BLM Game Cards (p XXX)

PROBLEM SOLVING


27

sentence under the circles, starting with the 3 already written on the board (3 - 0 = 3). Repeat with 5 circles and 1 circle, taking away 0 circles each time. Have volunteers write the subtraction sentences underneath the drawings: 5 - 0 = 5, 1 - 0 = 1. Explain that when you take zero things away, you are left with the number you started with.

Practise subtracting 0 without using pictures. ASK: If I start with 8 things and 0 things are taken away, how many things are left? (8) Have a volunteer write the subtraction sentence on the board: 8 - 0 = 8. Repeat with more subtraction statements. EXAMPLES: start with 7 things and take away 0 things; start with 2 things and take away 0 things. Have volunteers write the subtraction sentences on the board.

Write subtraction sentences that equal 0 using pictures. Draw 7 circles on the board. ASK: How many circles do I have? (7) Write 7 underneath. SAY: I want to take away 7 circles. Then draw an X through all 7 circles. ASK: How many circles do I have left? (0) Write the subtraction sentence under the circles, beginning with the 7 already written: 7 - 7 = 0. Draw 2 circles on the board and cross out 2 circles. Have a volunteer write the subtraction sentence underneath: 2 - 2 = 0.

Practise subtracting without drawing circles. ASK: If we start with 4 things and take away 4 things, how many things are left? (0) Write the subtraction sentence on the board: 4 - 4 = 0. Repeat with 6 things take away 6 things, then 9 things take away 9 things.

Bonus 47 - 47; 312-312.

Subtracting with 0. Have students write the subtraction sentences for pictures in which either all the objects are crossed out (0 is the difference) or none are crossed out (0 is the subtrahand, the number being subtracted).

ExtensionAnother model for subtracting. Draw the model shown in the margin on the board, with the corresponding subtraction sentence. ASK: What number is being subtracted, the shaded part or the white part? (shaded) How would you show 6 - 5 = 1 using this model? Have volunteers draw models for 5 - 2 and 4 - 1. Then have students draw models for 6 - 6 = 0, 4 - 0 = 4, 10 - 10 = 0, 10 - 0 = 10. Instead of crossing out (as with the circles), they should shade the number being subtracted.

BLM I Have — Who Has — Subtraction Cards has ready-made cards for numbers up to 5. The BLM has 12 cards: the first 6 go together and the next 6 go together. Play in groups of six.

ONLINE GUIDE

ACTIVITIES 1-2

1. I Have —, Who Has —? (See NS Part 1 – Introduction) Use a number on top and a subtraction question with a picture on the bottom. Use BLM Game Cards to make cards for numbers up to 10.

2. Dominoes or Group Dominoes. (See NS Part 1 – Introduction) Use cards with a number on top and a subtraction problem with a picture on the bottom. Include 0 in the problems. See BLM Blank Domino Cards.

Number Sense 2-10

7 - 3 = 4


NS2-11 Counting to 20Pages 17-18

CURRICULUM EXPECTATIONSOntario: 1m11, 1m20; review, 2m2, 2m3, 2m5, 2m7 WNCP: 1N1, 1N3; REVIEW, [R, C, CN, V]

VOCABULARY numbers to 20

GoalsStudents will count to 20. Students will learn to keep track of their counting so that they can locate any mistakes and verify their answers with others.

The numbers 14, 16, 17, 18, and 19. Write or tape the numbers from 1 to 20 all in a row and demonstrate counting to 20, pointing to each number as you say it. Then circle the numbers 14, 16, 17, 18, and 19 and ask students to listen carefully as you say them. Then underline the ones digits of those numbers and tell students to listen for those number words as you count again, pointing to each number as you say it. ASK: Do you notice a pattern in how I say those numbers? (the second digit is said first, then the word “teen”) Point to these five numbers in random order and have students say the numbers as you point to them. Then include the numbers from 1 to 10, in random order.

13 and 15. Write these numbers on the board. ASK: Do you know how to say these numbers? Explain that “13” is not “three-teen” but is something close—“thir-teen.” Also, 15 is not “five-teen,” but “fif-teen.” Repeat the exercise above with these numbers included.

11, 12, and 20. Write these numbers on the board. ASK: Do you know how to say these numbers? Explain that these numbers are the hardest to remember because they don’t sound like any number students already know. Teach students how to say these numbers, and repeat the exercise above. Start by focusing only on these numbers, then include all numbers from 11 to 20, and then all numbers from 1 to 20. End by saying the numbers in order from 1 to 20 together as a class.

Count concrete objects. Give each student 4 or 5 cubes to count. Pair up students and ask them to count how many cubes they have together. Then pair up the pairs and ask them to count how many cubes their group of 4 has altogether.

Count objects on paper. Hand out cards with different numbers of objects on them. Ask students to write the number on each object as they count.

PROBLEM SOLVING



Can count to 10

MATERIALS

4 or 5 cubes for each studentnumber cards for 1 through 20 cards with different numbers of objects on them BLM Count the Letters (p xxx) BLM Number Cards Template (p XXX)

29

Explain that this helps keep track of objects already counted and objects that still need to be counted.

Counting on from 10. Draw a basket with 10 apples in it and then draw another apple outside the basket. Count the apples in the basket as a class, then SAY: There are 10 apples in the basket and 1 apple outside the basket. How many apples are there altogether? Emphasize that there is 1 more than 10 apples, so the number of apples is the number that comes right after 10. ASK: What number comes right after 10? (11) Count all the apples together to verify that there are 11. Repeat with 12 apples and 13 apples. Then SAY: 11 is 1 more than 10, 12 is 2 more than 10, and 13 is 3 more than 10. Write 11, 12, and 13 on the board and point to the ones digit as you say how many more than 10. What number do you think is 4 more than 10? (14) Have a volunteer write the number on the board. Draw a basket with 10 apples and 4 more apples outside the basket and count the apples to verify that there are 14 apples altogether. Repeat with 15, 16, and so on up to 20. Then draw pictures with varying numbers of apples outside the basket and ask students to count the apples outside the basket and then determine how many in total without counting. EXAMPLE: “There are 10 apples in the basket and 7 apples outside, so there are 17 apples altogether.” Write the corresponding addition sentence on the board vertically:

Then have students write the answers to more such addition sentences.

Draw pictures like those on Workbook page 18, with one group of 10 and several other objects, and have students count the objects not part of the 10 to say how many there are in total.

Finally, just write vertical addition sentences and have students find the answer. EXAMPLES:

Literature— So Many Cats by Beatrice Shenk de Reigners. Students can count the cats in each part of the story.

CONNECTION

ACTIVITIES 1-3

(Instructions for all Activities are in NS Part 1 – Introduction.)

1. Play Picking Pairs and then Memory. Use cards numbered 11 through 20 (see BLM Number Cards Template) and cards with 11 through 20 pictures or stickers on them. Make 4 rows of 5.

2. Finding page numbers. Have students open their JUMP Math workbook to page 1. Then have them turn and point to the following page numbers: 7, 13, 10, 16, 19, 8, 6, 14, 15, 17, 2, 5, 3, 9, 4, 6, 18, 12.

3. Message booklet. Make books with 20 pages. Each page has a word or letter and a page number. Give students various messages to find. The same book can be used for several different short messages, as long as the instructions “Go to page…” are given orally.

PROBLEM SOLVING


10 + 7 17

10 + 7

10 + 4

10 + 8

Number Sense 2-11


Count letters. Write “the” on the board. Have a volunteer count the number of letters in this word. Then write “the mouse” and demonstrate counting the letters, starting at 1. ASK: Is there an easier way to count all the letters? Is there a way to take advantage of the fact that someone already counted the letters in the word “the”? Challenge the students, working in pairs, to think of a solution. (Since “the” has 3 letters, start at 4 when counting “mouse.”)

Now write on the board: T h e m o u s e a t e t h e a p p l e s.

SAY: I’d like to know how many letters are in the whole sentence. Start by counting the letters in “The” and write 3 just above the end of the word. Continue by counting the letters in “mouse” and write the total 8 on top. Remind students that you are counting each letter from the beginning of the sentence. Ask a volunteer to continue counting the letters up to the end of the next word. Continue with new volunteers. Discuss the advantage of not having to count from the beginning every time.

Why keep track? Tell students you saw two students’ work. It looked like this: 3 8 11 14 20T h e m o u s e a t e t h e a p p l e s. 3 8 11 13 19T h e m o u s e a t e t h e a p p l e s.

ASK: Did the two students get different answers? (yes) What answers did they get? (19 and 20) Which answer is right? (20) Why? (we counted 20) Challenge students to find where the two students first got different numbers. ASK: Which word was counted incorrectly? (the second “the”) How does keeping track make it easy to see who is right? (it’s easier to see that the second student only counted 2 letters for “the” because 13 is only 2 more than 11; the number over “the” should be 3 more than 11). Emphasize that when you keep track, you can look for the first place the numbers start being different; that tells you which word was counted differently. Then re-count that word to see who is right.

Now write the following sentence on the board: A m o u s e r a n u p t h e c l o c k.

Have students write the number of letters after counting each word (1, 6, 9, 11, 14, 19) and compare their answers with a partner. ASK: Did you get the same final answer? Did you get the same numbers all the way through? If not, where do the numbers start to disagree? Can you tell who is correct? Give students lots of practice counting and keeping track and have them compare answers. EXAMPLES: Four dogs ran away. The leaves turned yellow. Today is Eric’s birthday.

Explain that this is called counting on. Write “counting on” on the board. SAY: Even expert mathematicians make mistakes with counting on. This is a way for them to check if they’ve counted correctly.

PROBLEM SOLVING

Reflecting on the reasonableness of an answerPROBLEM SOLVING

Reflecting on what made the problem easy or hard

31

Have students complete BLM Count the Letters then exchange their BLMs with a partner. Did they get the same numbers all the way along in each sentence? Ask students to reflect on any mistakes. Did students make mistakes with longer words or shorter words? At the ends of sentences or at the beginnings? Closer to the end of the page than the beginning of the page?

PROBLEM SOLVING


Number Sense 2-11


NS2-12 The Reading PatternPages 19

CURRICULUM EXPECTATIONSOntario: 1m25, 1m26; review, 2m3, 2m7 WNCP: 1N10; review, [R, C]

VOCABULARY numbers to 100 the reading pattern hundreds chart

GoalsStudents will use the reading pattern to count to 20 using a chart.

Count to 20 using a chart. Give students a long strip of thick paper with 20 squares labeled 1 through 20 and 20 two-coloured counters that fit on the squares. (If your counters are 2 cm wide, make the strip of paper 2 cm wide and 40 cm long.) Have students toss the counters and count the ones that turn up red by placing them on the chart in order, one counter per square. Repeat and have students record how many red counters come up each time.

The reading pattern. Write “cat” on the board and ask students what sound the “c” and the “t” make. Then say “cat.” SAY: Notice that you pronounce the “c” before the “t” (underline both letters). That’s because we read from left to right. Show left to right. Write the following sentence on chart paper, all on one line: “The cat sat on the red rug.” Ask students where the sentence starts and where the sentence ends. Then write “The big black cat sat on the” on one line and SAY: Oh, I’ve run out of paper. How can I finish writing the sentence? (start a new line) On the next line, write “small red rug.” Have students read the whole sentence together as a class. SAY: In English we read from left to right and from one line to the next line below; that’s our reading pattern. Write “reading pattern” on the board. Then write: “The big black cat sat on the small red rug and ate a grey round rat.” SAY: This sentence is very long and hard to read in one breath. Let’s divide the sentence into shorter lines. Show the line breaks in the margin.

ASK: Is this easier to read? Discuss how much easier it is to read the sentence this way. Write the sentence “His name / was Mark.” with the line break indicated. Give each student word cards for: his, name, was, Mark. Tell students to hold up the word they would read first, then the word that comes next, and so on to the end of the sentence. Ask students how they know which order to read the words in. Repeat for these sentences: “Was his / name Mark?” and “Mark was / his name.”


Can count to 20 Can count to 20 using a chart

MATERIALS

a strip of 20 numbered squares and 20 two-coloured counters for each student (see below) 4 word cards for each student: Mark, was, his, name number cards for 1 through the total number of students in your class BLM 2 Cm Grid Paper (p xxx)

PROBLEM SOLVING


Literacy

CONNECTION

The big black cat sat on the small red rug and ate a grey round rat.

33

The reading pattern with numbers. Remind students that counting with a chart from 1 to 10 was pretty easy (see NS2-4), but a chart marked 1 through 20 is harder to work with. ASK: How can we make it shorter and easier to work with? Does this problem remind you of another problem? How did we solve that problem? Help students make the connection to the reading pattern—you can break the long line into smaller lines. Students might suggest starting a new line at different numbers: 5, 10, 4, 6, or 7. Have various long sheets available to demonstrate all their suggestions.

Suggest that if they end the first line at 6, they make every line 6 squares long to make it look nicer. Then have students make their own chart for counting to 20 by cutting, arranging, and taping their long strip of numbered squares.

Use the reading pattern to find the next number. SAY: We read the numbers on a chart like we read text in a book: start at the left, go across the first row, then move to the next line and start at the left again. Because the numbers are not all on one line, it can be tricky to know where the next number is. For example, in the chart above, it’s not too hard to find 5 if I know where 4 is, but finding 7 is a bit harder. It’s not right beside 6 because we moved it. ASK: Where is 7? Can you find the number that comes right after 8, 12, 10, 18, 15, 16, and 19? Which numbers were harder to find: the big numbers or the small numbers? For which numbers was it harder to tell what comes next? (12 and 18) Why? (they are at the end of a row)

Have students copy charts onto BLM 2 Cm Grid Paper. Teach them to do this accurately by counting the squares across and down. Alternatively, draw and photocopy charts for them.

The hundreds chart format. Draw the first two rows of a hundreds chart on the board. Discuss how this chart is different from or the same as the chart with rows of 6 or 7. ASK: How are the rows in this chart the same? (they are all the same length) Refer back to the 6 or 7 chart and ask if this was true there. (yes) Point out two numbers, one on top of the other, and shade them. ASK: What is the same about these numbers? (EXAMPLE: they both have 7’s) Is that the same for any number in the first row? If you look at the number below any number, do you see the same number with a one in front? (yes, except for 10) Refer back to the 6 or 7 chart and ask if this was true there. (no) Explain that rows of 10 are particularly useful because they are convenient for finding numbers. To find 17, look for 7 in the first row and then move down a row. Have students find: 9, 19, 4, 14, 3, 13, 15, 18, 11. Then have students find the numbers that come right after: 4, 14, 9,19, 17.

Count using the hundreds chart. Draw two rows of a hundreds chart and make 20 blank cards to fit. Give 16 cards to a volunteer to tape to the chart so they can be counted. Repeat with different numbers of cards and different volunteers. Emphasize the process for placing the cards: Start at 1; when you reach the end of a line go to the very beginning of the next line. To find how many squares are covered, students uncover the last number covered. Challenge: Predict how many squares are covered without uncovering the last square and then check the prediction.

PROBLEM SOLVING

Looking for a similar problem for ideas

PROBLEM SOLVING


Number Sense 2-12

EXAMPLE:

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20

EXAMPLE:

Bonus 5 rows of 3 6 rows of 2 5 rows of 4 4 rows of 5

Extension— Use logical reasoning to guess numbers, including BLMs Guessing Numbers and BLM Hang Man.

ONLINE GUIDE

Activity— students form a concrete number chart and perform the wave.

ONLINE GUIDE


NS2-13 Adding Using a Chart Pages 20-23

CURRICULUM EXPECTATIONSOntario: 1m25, 1m26; review, 2m1, 2m2, 2m3, 2m7 WNCP: 1N10; review, [R, C]

VOCABULARY reading pattern left right top bottom

GoalsStudents will add using cubes and then a chart.

Add using blocks. Give each student several red and blue 1 cm connecting cubes. Ask them to find 3 red blocks and 4 blue blocks. ASK: How many blocks is that altogether? Write on the board: 3 + 4 = 7. Repeat with various numbers of red and blue blocks, this time having volunteers write the addition sentence on the board.

Add using a chart and paper blocks. Draw the first two rows of a hundreds chart on the board, or use a large hundreds chart if available. Demonstrate how to find 3 + 4 by placing 3 red paper ones blocks and then 4 blue paper ones blocks on the chart in order, so that the last block is on square 7. Count as a class how many ones blocks there are altogether. Do several examples until someone notices that the last number with a block is always the total number of blocks. Then ask students to predict what the last block will be and check using several examples. Demonstrate putting 3 red and then 4 blue blocks on the chart randomly (not covering the first seven squares) and count them individually. Then put them on the chart in order, from 1, and count again. Ask students how the counting is already done for them when they put the blocks on in order. (Putting a card on the “1” is like holding it and saying “one”; the last card covered is like the last number said.)

Give each student a copy of BLM Hundreds Chart, ten red ones blocks, and ten blue ones blocks. Have students find 4 + 5 on their own hundreds charts. ASK: How is the adding done for you on the chart? Repeat using pairs of one-digit numbers that add to more than 10.

Use colouring and circling instead of blocks. Draw the first row of a hundreds chart on the board. Tell students that you want to add 3 + 5. Have a volunteer do so on the chart using the red and blue paper ones blocks.


Can add Can read a hundreds chart Can count using a chart and otherwise

MATERIALS

a large hundreds chart and paper ones and blocks (red and blue) to fit BLM Hundreds Chart (p xxx) BLM Hundreds Charts — Three-Rows (p xxx) BLM Adding and Order (pp xxx–xxx) BLM Hundreds Charts — One-Row (p xxx) BLM Add Larger Numbers (p xxx)

NOTE: If you do not have red and blue ones blocks, you can use small connecting cubes, or else photocopy BLM Base Ten Materials onto red and blue paper.

PROBLEM SOLVING


PROBLEM SOLVING

Reflecting on what made the problem easy or hard, Making an organized list

TEACHING TIP: On Workbook pp. 21, 22 and the BLMs, some students may need to do each step separately; do the first step for all questions first, then go back and do the second step.

35

SAY: Now let’s try something different: instead of putting on 3 red paper blocks, let’s just shade the first 3 squares. (remove blocks and shade the 3 squares) Also, instead of putting on the 5 blue paper blocks, let’s just circle the next numbers. (remove blocks and circle the next 5 squares) We can now see that 3 + 5 = 8 since 8 is the last number circled. ASK: Do you think this way is quicker and easier than using blocks? Discuss.

Practice. Draw the first two rows of a hundreds chart on the board. Use it to add pairs of one-digit numbers that add to more than 10. Invite volunteers, shade the first number of squares, and then circle the second number of squares. As well, have students do problems individually using BLM Hundreds Charts — Three-Rows. Write the problems on the board or on the BLM before photocopying.

Bonus 2 + 7 + 6, 4 + 4 + 4, 6 + 5 + 6.

Shade only the square showing the first number. Draw the first row of a hundreds chart on the board. SAY: I want to add 4 + 3, but this time, instead of colouring the first 4 squares, I’m just going to colour the 4th square. (count out to the 4th square) ASK: What number is in it? Can I tell what square is 4th without counting? (a 4 is in the square) Emphasize that once you’ve coloured the 4th square, you know where to start circling. Have volunteers colour the square showing the first number and then circle the second number of squares to add: 3 + 5, 6 + 2, 4 + 5. Have each student solve more problems, using numbers that add to no more than 10, on BLM Hundreds Charts — One-Row. NOTE: As before, some students may need to do the two steps separately.

Add the second row to the hundreds chart on the board and have volunteers solve 3 + 8 and 5 + 9. Then distribute BLM Hundreds Charts — Three-Rows and have students solve: 7 + 6, 8 + 4, 9 + 5. Bonus 8 + 14, 5 + 8 + 12, 7 + 14 + 6.Bonus BLM Add Larger Numbers

Pretend the blocks are shaded for the first number. SAY: I want to add 2 + 4, but instead of colouring in the first two, I’m just going to pretend the first two squares are coloured and circle the next four. Show this by covering the first two and circling the next four. Emphasize that 2 + 4 is the last number you circled. Repeat with more examples, always emphasizing that you are pretending to have already coloured the first number of squares. If your students have learned how to “count on” to add, ask them how this method relates to counting on.

Extensions1. BLM Adding to the Number 10.

2. If students did BLM More Than in lesson NS2-6, connect the discovery made there with the discovery made on Workbook page 23. For example, the fact that 5 + 3 and 3 + 5 are both 8 corresponds to the fact that 8 is 3 more than 5 and 5 more than 3.

Bonus On BLM Adding and Order, students solve the same questions as on Workbook pages 21, 22, but reverse the numbers they shade and circle. Students can compare their answers in the workbook and on the BLM.

Number Sense 2-13

PROBLEM SOLVING

Connecting Adding two ways.

1 2 3 4 5 6 7 8 9 10

20191817161514131211

2 + 7 + 6 = 15


NS2-14 Tens and Ones BlocksPages 24-25

CURRICULUM EXPECTATIONSOntario: 1m11, 1m20, 1m21; review, 2m2, 2m5, 2m7 WNCP: 1N4; review, [R, CN, C]

VOCABULARY hundreds chart row tens block ones block

GoalsStudents will add numbers on a hundreds chart using tens and ones blocks.

Review adding on a hundreds chart. Trace the first two rows of a hundreds chart from BLM Tens and Ones Blocks onto a transparency and project it on the wall/board. Start with a pile of about 20 ones blocks. Tell students that you’d like to find 10 + 4. Begin to count out 10 ones blocks, then SAY: I could use 10 ones blocks for the first number, but there are so many blocks to count. Another way to count 10 ones is to use something called a tens block. Write “tens block” on the board. Line up 10 ones blocks to show they are the same length as 1 tens block. Also show students that 10 ones blocks and 1 tens block both cover one line on the hundreds chart. Tell students it is easier to use 1 tens block for the first number in 10 + 4. Then use 4 ones blocks for the second number, and cover the next four numbers in the chart. ASK: How can I find the answer to 10 + 4 on the hundreds chart? (uncover the number that the last ones block is covering) Cover 15, with your finger pointing to the 14, while uncovering 14. ASK: What is 10 + 4? Write: 10 + 4 = 14.

Invite a volunteer to find 10 + 5 using a tens block and ones blocks on the hundreds chart. Emphasize that the tens block is like 10 ones blocks, and then you add 5 more ones blocks. You end up with 15 ones blocks, so 10 + 5 = 15, the last number covered. Repeat with different numbers and different volunteers.

Add using a blank chart. Draw the first two rows of a blank hundreds chart on the board and tell students that you want to find the number 12 without the numbers even being there. Ask volunteers to circle the square they think


Can count to 20 Can read numerals to 20 Can add on a hundreds chart

MATERIALS

BLM Tens and Ones Blocks (p xxx)BLM Game Cards (p xxx)BLM 1-Cm Grid Paper (p xxx)tens and ones blocks

ACTIVITY 1

BLM Tens and Ones Blocks. Have students place a tens block and ones blocks on the chart to answer the questions.

37

Should be 12. ASK: If I colour the first 12 squares in order, what will the last number be? (12) Do this while counting out loud, then ASK: Was a whole row coloured before I got to 12? (yes) How many squares does each row have? (10) If a number is bigger than 10, does it have to use up a whole row first? (yes) Is 12 bigger than 10? Is there a way to know how many squares to colour in the second row? (look at the number after the 1—use the term “ones digit” if students know it) Point to the number 2. Demonstrate again with 17. SAY: We had to colour two squares in the second row to get to 12 and seven squares in the second row to get to 17. Then ASK: How many squares in the second row do you think we’ll need to colour to get to 15? Show that you are counting to the number that comes after the 1; point to the 5 in 15. Continue with more examples, including the number 10. For 10, you can ASK: What is the number after the 1, or the “ones digit”? (0) How many ones blocks will we use in the second row? (0) What will the number 10 look like on the chart? (use one tens block) This will help you to emphasize again that a tens block represents the number 10 and covers a full row on the hundreds chart.

Use tens blocks without the hundreds chart to represent a number. On the overhead, show one tens block and three ones blocks, slightly separated so that the outline of each block is clear. ASK: Can you tell me what number these blocks represent without the hundreds chart? How do you know? (the tens block is 10; add three separate ones blocks to get 13) Repeat with another number, asking the same questions. Think of a number (don’t say it!), show it with tens and ones blocks, and ask students to identify it. Check their answers by placing the blocks on a hundreds chart. Then have students work in pairs. Give pairs a tens block, several ones blocks, and two rows of 10 from BLM 1-Cm Grid Paper. One student picks a number and uses the blocks to show the number on the grid paper; the other student identifies the number. Students then switch roles.

PROBLEM SOLVING


ACTIVITY 2

I Have —, Who Has —? or Group Dominoes. (See NS Part 1 – Introduction) Use numbers from 11 through 19 only. Make cards (see BLM Game Cards) with a number on top and a base ten representation on the bottom. See the margin for a sample card.

PROBLEM SOLVING

Connecting

Sample Card I have 18

Who has

?

Number Sense 2-14


NS2-15 Reading Number Words to TwentyPages 26-28

CURRICULUM EXPECTATIONSOntario: 2m2, 2m5, 2m7, 2m12 WNCP: 1N4; review, [R, CN, C]

GoalsStudents will read number words to twenty.

Look for numbers that have sounds in common. Write on the board: 4 5 6. ASK: Which two numbers start with the same sound? Do they start with the same letter too? Write the number words on the board to check. Challenge students to find more numbers that start with the same sound or continue asking students to choose two numbers with the same beginning sounds from a group of three. EXAMPLES: 2 6 10; 6 7 8.

Compare sounds in numbers (to 20). Write 6 and 16 on the board and ask students to say them. ASK: How do they sound the same? How do they sound different? How do they look the same? (they both have the digit 6) How do they look different? Continue with 7 and 17, 9 and 19, 8 and 18, 4 and 14. Repeat with 2 and 12, 3 and 13, 5 and 15. (these don’t have as much in common as 7 and 17, but they do have the first sound the same) Then write 1 and 11 on the board. ASK: Do they sound the same? (no)

Number words for 14, 16, 17, 18, 19. Tell students that they are going to learn the number words from 11 to 20. Write “nineteen” on the board. Ask a volunteer to guess which number it is. ASK: What one-digit number word that you already know is hidden in that word? Write the first digit (1) on the board. ASK: What digit do you think I should write after 1? Why? Repeat with fourteen, sixteen, seventeen, eighteen. Emphasize that we can hear the name of the second digit when we say each number.

Number words for 12, 13, 15. Write “twelve” on the board. Point out the first two letters. ASK: What number word do you already know that starts with the same two letters? Write “two” and underline “tw” in “two” and “twelve.” Repeat with thirteen and fifteen.

The number word for 11. Write “eleven = 11” on the board. Explain that this word does not sound at all like its second digit, “one.”

The number word for 20. Write “two twelve twenty” on the board. ASK: What in the same in all of these words? (the first two letters, “tw”) Underline “tw.” Have volunteers write the numbers for two and twelve (2 and 12) on the board. ASK: What do these numbers have in common? (the digit


Can count to 20 Can read and write number words to 10

MATERIALS

BLM Sounds Like (p xxx)BLM Game Cards (p xxx)BLM Write the Numbers (p xxx)number cards from 11 to 20 number word cards from eleven to twenty

PROBLEM SOLVING

Looking for a similar problem Looking for a pattern

BLM Sounds Like

EXTRA PRACTICE

BLM Write the Numbers

EXTRA PRACTICE

Science— Counting is for the Birds by Frank Mazzola Jr. Animal habitat and adaptation to the environment. Up to twenty birds gather to eat at a feeder while a cat lurks nearby. Number words are in colour.

CONNECTION

39

2) What number do you think the last word says? PROMPT: What other number from one to twenty also has a 2? (20) Have a volunteer write the answer on the board. ASK: Does that number also have a 2?

Number words for 11 through 20 out of context. Make cards for each student with a number word from eleven to twenty (see Number Word Cards in NS2 Part 1 - Introduction). Write a numeral on the board. Ask all students with the corresponding number word to hold up their card. Repeat several times. Then give each student two or three number word cards and repeat. Then give students number cards from 11 through 20, write a number word on the board, and repeat.

Number words in sentences. Invite volunteers to find the number word(s) in sentences and write the numeral(s) above (see examples in margin).

Extensions1. Have students underline common last letters in words like fourteen and

seventeen. Write the corresponding numerals next to each and circle the digits that are the same. ASK: What do you notice? Emphasize that “teen” looks almost like “ten,” so students can think of fourteen as four + ten or 14 = 4 + 10. Verify that this is true by counting on from 4 using both hands.

2. Introduce students to more words that start with “tw” and are connected to the number 2: to do something twice means to do it two times; twins are siblings born at the same time.

ONLINE GUIDE

BLM I Have —, Who Has — ? Number Words, with 12 cards; the first 6 go together and the next 6 go together.

ACTIVITIES 1-5

Instructions for Activities 1–5 are in NS Part 1 — Introduction.

1. Give students number words cards and have students put them in order.

2. Peace. Use number word cards, number cards, or both.

3. I Have — , Who Has — ? Make cards from BLM Game Cards (put a numeral on top and a number word on the bottom) or use the pre-made cards on BLM I Have —, Who Has — ? Number Words. (There are 12 cards on the BLM: the first 6 go together and the next 6 go together. Play in groups of six).

4. Dominoes or Group Dominoes. Use a numeral on one side and a number word on the other.

5. Play Picking Pairs and then Memory. Use cards numbered 11 to 20 and eleven to twenty. Make 4 rows of 5.

6. Electric! (See NS2 Part 1 – Introduction) Match numerals to number words.

Number Sense 2-15

EXAMPLES: • A year has twelve months. • Helen played sixteen soccer games. • Tony has fourteen pets: eleven hamsters, one dog, and two cats. • Conrad scored twenty goals in fifteen games. • The temperature is twelve degrees. • There are thirteen girls in this class. • Patti has eleven toes—six on one foot and five on the other! • Rita has more than twenty teeth. • Bilal lost eleven dimes.


NS2-16 Writing Number Words to TwentyPage 29

GoalsStudents will write number words to twenty.

NOTE: Students will need a list of number words to refer to until they become familiar with them.

Review number words from zero to twenty. Write the number words from zero to ten on the board, and underneath write eleven to twenty (so that eleven is under one and twenty is under ten). Have students write the number words for the following numerals in their notebooks: 7, 17, 4, 14, 9, 19, 6, 16. ASK: What do you notice? (for the two-digit numbers, just write the number for the ones-digit and then “teen”) Tell students that you saw someone write 18 = eightteen. Have them look for the word on the board and ASK: Is this right? What’s wrong? Explain that not all the words are so easy to write. ASK: Is 13 = threeteen? (no) Why not? (we don’t say “threeteen,” we say “thirteen”) Remind students that some words only have the first two letters in common, then have students write the number words for 3, 13, 5, 15. Write the words for 2, 12, and 20. Then challenge students to find the word (eleven) and number (11) that weren’t used yet. Have students write the word and the number together.

Have students write individual answers to various questions using both the numeral and the number word. Keep the previous list of words on the board. EXAMPLES:• How many people in the class have pets? (ask for a show of hands and count together) • How many people in the class are seven years old? • How many people in the class are ten years old? (zero)

Have volunteers make up questions for everyone to answer in their notebooks.


Can read number words to twenty Can write number words to ten

MATERIALS

several tens blocks, pencils, or toothpicks in a resealable bag for each student BLM Writing Cheques (p xxx)BLM Blank Cheques (p xxx)BLM Writing Number Words (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m3, 2m5, 2m7, 2m12WNCP: 2N4, [PS, R, CN, C]

VOCABULARY number words from zero to twenty

ACTIVITIES 1-2

1. Assign each student a different object to count in the classroom. Choose objects which are fewer than 20 in number (EXAMPLES: 11

41

Number word problems. Have students solve the problems below. Explain that the exact number of spaces is given for the answer. Encourage students to use counters as a model to solve the word problems. For the first three questions, students can use the number of blanks and the number of letters in their answer to check if they are right. The last two questions have more than one answer. Challenge students to find as many answers as they can.

a) one + one =

b) three + four =

c) seven - one =

d) + =

(one + eight = nine, two + three = five, one + three = four, two + seven = nine)e) + =

(five + six = eleven, nine + two = eleven)

boys, 5 windows, 8 cupboards). Students should write their answers on large strips of paper which you can display on a bulletin board with the title: In Our Classroom.

2. Buy and Sell. a) Give each student several tens blocks, pencils, or toothpicks in a resealable bag. Have students count the objects and then label the bag with how many items are inside, in words. Also have students write a price on the bag, again in words. ASK: Why do people like to know how many are in a package before they buy it?

b) Draw a blank cheque on the board. Explain that people sometimes write cheques instead of using cash or a credit card to pay for things. Show students where the amount is written in numerals and where it is written in words. Discuss the reason people write the word as well as the numeral on a cheque: the bank wants to be sure they understand the number. EXAMPLE: $16 might look like $6 but using the number word as well as the numeral makes the meaning clear. Explain where to sign and write the payee’s name. Have students first fill in the blanks on BLMs Writing Cheques to practise writing cheques. Then have each student purchase a package made in part a) from another student. Students can use cheques from BLM Blank Cheques to make their purchases. If students are not yet comfortable writing the date, write the date on each cheque before photocopying the BLM.

Real world

CONNECTION

PROBLEM SOLVING


PROBLEM SOLVING

Problem solving

BLM Writing Number Words

EXTRA PRACTICE

ONLINE GUIDE

Instructions and BLM Word Puzzles for teaching students to solve crossword puzzles.

Number Sense 2-16


NS2-17 First Word ProblemsPages 30-34

GoalsStudents will solve word problems involving addition and subtraction by drawing simple models.

Review adding using pictures. Draw a vase with 4 flowers and someone holding 3 flowers. Write “four flowers” and “three more flowers” above the pictures. Have a volunteer write the numbers above the number words. ASK: How many flowers are there altogether? Count together as a class. Have a volunteer write the addition sentence: 4 + 3 = 7.

Gradually simplify the pictures. Draw pictures of flowers with the stems, but no vase or person. Have students solve addition problems written using incomplete sentences. Write each part of the problem on a separate line. EXAMPLES (the slash indicates a line break):

• four flowers / six more flowers / How many altogether? • five flowers / nine more flowers / How many altogether? Bonus three flowers / five more flowers / four more flowers /

How many altogether?

ASK: Which picture do you think is easier to draw: the picture with the vase or the picture with just the stems? Did you find the addition easier, harder, or the same without the vase in the picture? SAY: If the problem doesn’t get harder to solve when you draw less, you might as well draw an easier picture. Continue making the pictures easier to draw; eventually just draw circles. Always ASK: Was the addition any harder to do? Emphasize again that if drawing less doesn’t make the problem harder to solve, students might as well use simpler pictures, even just circles. Have students individually solve many word problems written using incomplete sentences.

Bonus seven flowers / three more flowers / two more flowers / How many flowers altogether?

Solve addition word problems (complete sentences). Write on the board, leaving extra space between each line: Four flies are buzzing. / Five more join them. / How many flies are there in total?

Have one volunteer write the numbers above the number words and another volunteer draw the correct number of circles beside the first two sentences. Have a third volunteer count the total number of circles and write the addition sentence. Repeat with other addition word problems.


Can add Can read number words to twenty Can write numerals

MATERIALS

counters BLM Reading Subtraction Sentences (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m2, 2m3, 2m5, 2m6, 2m7, 2m22, 2m23 WNCP: 1N9; review, [R, CN, V, C]

VOCABULARY join in total altogether how many more left are not take away/took away/went away lost nobody none

PROBLEM SOLVING


PROBLEM SOLVING

Drawing a model

BLM Reading Subtraction Sentences reviews the different ways subtraction sentences are written.

EXTRA PRACTICE

43

Bonus There are eight red marbles. / There are four blue marbles. / There are three green marbles. / How many marbles in total?

What does the word “left” mean? Write on the board: Five children were at the park. Two of them left. How many are left?

Discuss the two different meanings of the word “left” in this word problem (one means the children have gone away; the other means the children are still present). Illustrate the problem using 5 volunteers and then write the subtraction sentence (5 - 2 = 3).

Solve subtraction word problems. Start with subtraction problems written in point form, then use complete sentences. Students can solve the problems by drawing stick people.

Include word problems that involve zero. Use zero either as the amount taken away or the amount left, i.e., “0 children left” or “nobody left” or “There are none left.” Make sure students understand that “nobody” and “none” mean zero.

Connect “how many more than” to taking away. First review pairing objects up to count the extras (see picture in margin). Taking away the objects that are paired up leaves only the extras. In the picture, if you start with 5 dark circles and take away the 3 that are paired up, you have 2 extras; 5 – 3 = 2 is another way of saying that 5 is two more than 3. Draw more pictures to illustrate “how many more than,” and have students write the subtraction sentence and explain how it shows subtraction (what are we taking away?).

Find “how many more.” Use simple sentences and a grid model, as on Workbook pages 33 and 34. Start with the person changing and the object staying the same, and then move to the object changing and the person remaining constant.

Which subtraction sentences make sense? When the smaller number is given first, students might be tempted to reverse the order. For example, if Sara has 2 apples and Ron has 7 apples, students might know the answer is 5 but write 2 – 7 = 5 as their subtraction sentence. Remind students that in addition, order doesn’t matter; 4 + 1 = 1 + 4. However, subtraction is different: order here is very important. Help students make sense of order. Write 4 – 3 = 1 and 3 – 4 = 1 on the board and discuss. PROMPTS: Is 4 – 3 the same as 3 – 4? Can you take away 3 things if you start with 4? Can you take away 4 things if you start with 3? If you start with 3 things and you take some away, can you end up with 1? Emphasize that the first number is the number you start with and the second number is the number being taken away.

ExtensionBLM The Score (p xxx). Students determine the score given that the blue team is leading by 4 points.

Literature— Anno’s Math Games II by Mitsumasa Anno, Chapter 4.Drawings of children become progressively simpler until they are only circles.

CONNECTION

1 2 3 4 5

Number Sense 2-17

EXAMPLES: • nine children / four went away • Seven girls are playing soccer. / Two of them went home. / How many girls are still playing?

ONLINE GUIDE

BLMs Addition Practice and Subtraction Practice provide practice with word problems.


NS2-18 Making Word ProblemsPages 35-40

GoalsStudents will use pictures given to create and solve word problems involving addition and subtraction.

What is being added together? Draw 4 red balls and 2 blue balls on the board. Write the words above the picture, as on Workbook page 35. Discuss what is the same and what is different about the pictures. Have a volunteer underline the words that are the same for both pictures (balls). Explain that this tells you what objects are being added together. There are red balls in one picture and blue balls in the other, but they are all balls. Repeat for green pencils and yellow pencils, new pencils (unsharpened) and used pencils (sharpened), happy faces and sad faces.

Then progress to writing full sentences with the pictures, as on Workbook page 36. Show students 3 red pencils. ASK: What are these? Write: There are 3 red pencils. Show students 4 blue pencils and write the corresponding sentence. Have students circle the words that describe what is being added together. Then have students decide how many there are in total and write it, using both the number and word. (7 pencils) Repeat for 2 new pencils and 4 used pencils, then 3 happy faces and 2 sad faces.

What is different? Write these words on the board: new, used, blue, yellow, empty, full, tall, short. Draw pictures of these objects: 2 new pencils and 4 used pencils; 2 tall trees and 5 short trees; 3 blue circles and 1 yellow circle; 3 full bowls and 2 empty bowls. Have students use the words to fill in blanks to make word problems for each picture.

Do the first problem together, and cross out the words (in the EXAMPLE: “new” and “used”) as you use them. Have students write the remaining problems individually. They should first copy down all the words that haven’t been used yet, and then copy and complete the sentences, crossing out the words as they use them. Discuss the value of keeping track of the words used. Emphasize that, although it may seem like extra work to write the whole list of possibilities at the beginning, it makes it easier when students get to later questions because they will have fewer and fewer words to choose from. Then have students solve the word problems. EXAMPLE: There are pencils altogether.

Combine what is different with what is being added to create addition word problems. See Workbook page 38.


Can add Can read and write simple words Can write numerals

MATERIALS

BLM Apple Trees (P XXX)

CURRICULUM EXPECTATIONSOntario: optional; 2m1, 2m2, 2m7 WNCP: 2N9, [R, C]

VOCABULARY altogether left are not take away/took away/ went away

PROBLEM SOLVING


EXAMPLE:There are pencils.There are pencils. How many pencils altogether?

TEACHING TIP: Remind students that if they don’t know how to spell a word, they can copy from the board, since you have already written the word for them.

45

Create subtraction word problems from pictures. Draw an apple tree with 4 apples on the branches and 5 on the ground. ASK: How many apples are there altogether? How many fell out of the tree? (5) How many are left in the tree? (4) Write the following subtraction problem from the picture: There were 9 apples in the tree. 5 of them fell. How many are left?

Have students write similar word problems for the pictures on BLM Apple Trees. Students can cut the pictures out, paste them in their journals, and write the problem next to each picture. Note that the context is the same in all the problems, so students have to just change the numbers to create the new problems. Then have students write a number sentence and solve their word problems. EXAMPLE: 7 – 2 = 5. There are 5 left.

Creating subtraction word problems with different contexts. Write the number sentence 8 – 2 = 6. ASK: What does the 8 mean? (the number of objects you started with) Write on the board: There were 8 objects. ASK: What does the 2 mean? (2 objects were taken away) Discuss ways that objects can be taken away. ASK: I had pizza for lunch. There were 8 pieces. Now there are only 6 left. What happened to the other two? (you ate them) Write on the board: 2 pieces were eaten. SAY: There were 8 birds in a tree. Now there are only 6. What happened to the other two? (they flew away) Write on the board: 2 birds flew away. Continue in this fashion with other contexts. EXAMPLES: people playing soccer, apples in a tree.

Continue with examples where nothing “happened” to the other two, they are simply of a different sort. EXAMPLES:

• There are 8 marbles. 6 of them are red. What can we say about the other two? (they are not red) • There are 8 people. 6 of them are tall. What can we say about the other two? (they are not tall) ASK: What is another word for “not tall”? (short) Emphasize how this is different from “not red”: Something that is not red can be blue or yellow or green or any number of colours, but something that is not tall must be short, at least in comparison to the tall ones.

Now have students make up subtraction problems from pictures, as on Workbook page 40.

ExtensionHave students create more subtraction word problems from given pictures, with subtraction meaning “how many more than.” EXAMPLE: (see margin for picture)

There are 3 small circles. There are 2 big circles. How many more small circles are there than big circles? Notice that this picture requires students to think about which number is greater, 2 or 3, before they formulate their question.

Number Sense 2-18


NS2-19 Ordinal NumbersPages 41-42

GoalsStudents will use ordinal numbers (1st to 10th) to show position.

Introduce ordinal numbers 1st to 5th. ASK: Have you ever waited in a lineup? Discuss where. Draw 5 people with given names in front of a ticket booth or attach the pictures from BLM Lineup to the board as follows:

ASK: How many people are in the line? (5) Write “1st” under Rosa, “2nd” under Daniel, and so on. SAY: Instead of saying Rosa is number 1 in line, we say Rosa is 1st in line. ASK: Who is 2nd in line? 3rd? 4th? 5th? Where is Mark in line? Daniel? Who are the first two in line?

Then move the ticket booth to the other side of the line so that Rosa is now last and Tegan is first. ASK: How is this line different from the last line? Point to Rosa and ASK: Is she still first? Have a volunteer write 1st under the person who is first (Tegan) and then another volunteer write 2nd under the person who is 2nd (Mark), and so on. Repeatedly rearrange the lineup and ask questions about the people in line. EXAMPLES: Who is 1st in line? 3rd? Who is last? How many people are in front of/behind Bilal?

First and last. Restore the lineup to its original order. ASK: What position is Rosa in? (first) Remove Tegan (she got tired of waiting) and repeat. (Rosa is still first.) Remove Mark (he lost his money) and repeat. (Rosa is still first.) Then put Mark and Tegan back into the lineup in the original order. ASK: What position is Tegan in? (5th) Remove Rosa (she got her tickets) and repeat the question. (Tegan is now 4th.) Remove Daniel (he got his tickets too) and repeat. (Now Tegan is 3rd.) SAY: No matter how many people there are ahead of Tegan, there is still no one behind her. ASK: Does anyone know a word for that? Explain that there is a word that tells us that there is no one behind Tegan, no matter how many people are ahead of her. If no one knows, tell students the word is last and write it on the board. Repeatedly change the order and direction of the lineup, and ask questions. EXAMPLES: Who is first? Who is last?


Can count to ten Understands that numbers have an order or sequence

MATERIALS

5 name cards (see details below) BLM Lineup (p xxx)

CURRICULUM EXPECTATIONSOntario: 1m24; review, 2m7WNCP: 2N3, [C]

VOCABULARY ordinal numbers from 1st to 10th in front of behind last

ONLINE GUIDE

BLM 3rd, 4th, 5th teaches students to differentiate between for example “the first 3” and “the 3rd.”

Tickets

Rosa Daniel Mark TeganBilial

47

Ordinal numbers (positions) up to 20th. SAY: Now that you’ve learned how to say the first 5 positions in a line, it’s easy to learn how to say all the positions up to 20. From 6 to 20, just say the number and then “th,” the way 4 becomes 4th. Draw 20 people on the board lining up for tickets or for the bus. Number them 1 to 20. Have students say the position of each person as you point to them. First point to people in order, and then in random order. Then have 10 volunteers line up at the front of the room. Ask various people to do different things. EXAMPLES: Will the 4th person please clap your hands? Will the 8th person please do a jumping jack? Invite volunteers to name the 2nd person, the 11th person, and so on. Repeat with different volunteers.

More than one type of object is included. Line up a number of boys and girls. ASK: Will the 2nd girl please turn all the way around? Will the 4th boy please raise your hand? And so on. Then draw several circles and squares on the board as follows, using as many different colours as possible:

Write 1st on top of the leftmost shape. ASK: What colour is the 3rd square? The 2nd circle? And so on. Students might raise pencil crayons to show their answers individually. Then ASK: Is the 8th¬¬ shape a square or a circle? Which position is the 3rd square in? The 4th circle? Which comes first: the 3rd square or the 4th circle?

Next, write “mathematics” on the board. Review vowels and consonants. ASK: What is the 3rd vowel in the word? What is the second consonant? What is the last vowel? What is the 5th consonant? What comes first: the last vowel or the 5th consonant?

ONLINE GUIDE

Extensions for counting on to find position, and for sequencing events.

Number Sense 2-19


NS2-20 Writing OrdinalsPages 43-44

GoalsStudents will learn to write ordinal numbers.

Differences between writing ordinals and numbers. Write “1” and “1st” on the board. ASK: What do these symbols mean? (1 tells how many; 1st is a position in a sequence) What is the difference between how we write them? (the “st”) Where do we write the letters “st”? (to the right of the number) SAY: Think of the sounds when we say the word “first.” Are the “s” and “t” sounds at the beginning, at the end, or in the middle? (end) Write on the board: first = 1st.

Use the last two letters in the ordinal word to write the ordinal number. Write “four” on the board and have a volunteer read it. ASK: What do we say if you are number 4 in line? (we say you are fourth in line) Write “fourth” and underline the “th.” Write 4 on the board and have a volunteer complete the ordinal number; if no one volunteers, add the “th” and circle it. ASK: What do you notice about the letters underlined and circled? (they are the same) Have students finish writing the ordinal number given the ordinal number word and the numeral. At first, underline the last two letters of the ordinal number word for them. EXAMPLES: seventh = 7 , eleventh = 11 .

Say the ordinal numbers to write them. SAY: If you say a position out loud, you can hear the letters you need to write: the sound at the end matches the letters you write at the end. Erase any ordinal words on the board and have students add the correct letters to various ordinal numbers from 1st to 10th. EXAMPLES: 2 (answer: nd), 7 (answer: th)


Can write numerals and letters Can read number words

MATERIALS

BLM Ordinal Match (p xxx)BLM Ordinal Practice (p xxx)

CURRICULUM EXPECTATIONSOntario: 1m24; review, 2m2, 2m7 WNCP: 2N3, [R,C]

VOCABULARY ordinal numbers from 1st to 12th

ACTIVITY

Cut out the cards on BLM Ordinal Match to play the following game: Player 1 has the numeral cards. Player 2 has the ordinal ending cards. Players shuffle their cards, place them face down, and play one card from the top of the pile. If the number card matches with the ordinal ending to make an ordinal number, keep the two cards together in a separate pile. If the cards do not match, players create their own discard piles. After all ten cards are played, shuffle the discard piles separately and continue until all the cards are matched. After students play a couple of games, emphasize that “th” is an easy ending to match. Discuss why that is.

49

Write the ordinal numbers on the board, in order. SAY: Look carefully at the last two letters. ASK: Do you notice a pattern? What type of pattern is it, eventually? (repeating pattern) Does it start repeating right away? (no) How does the pattern make it easy to remember how to write the ordinal numbers for 1 to 10? (add “th” to the number for all numbers from 4 to 10) Remind me, what are the only numbers from 1 to 10 that don’t follow the pattern? (1st, 2nd, 3rd)

Reading ordinal words. Teach students to find the number word within the ordinal word. Write “seventh” on the board. ASK: Which number goes with that position word? (7) Why? (the word seven is at the beginning) Have volunteers circle the part of the word that makes them think of the number for these positions: fourth, tenth, sixth, eighth, ninth. Discuss how eighth and ninth are different from the other three. In both cases, it is not exactly the number and then “th”; ninth is not “nineth” and eighth is not “eightth.” Tell students that sometimes it is only part of the word that will remind them of the number. Have students individually write the part of the word that reminds them of the number for third, fourth, ninth, eighth, fifth, tenth, seventh, sixth.

Write “first = 1st” and “second = 2nd” on the board and SAY: The words “first” and “second” are special cases. These are the only two you can’t find at least part of the number hidden inside. Have students write the ordinal numbers for the following in their notebooks: a) seventh b) ninth c) fifth d) third e) second f) first

Writing ordinals in context. Invite ten volunteers to stand in a line. The rest of the class answers questions about the line. (EXAMPLES: Who is first? Who is 7th?) Now have six volunteers line up according to height (tallest to shortest). Write on the board: Height

Have the volunteers write their names on the line in order of height. Then ask the same volunteers to line up according to birthdate (January to December). Underneath the height line, write: Birthdate

This time have students write their names in order of birthdate. Volunteers can sit down. Ask questions, referring to students by name. EXAMPLES: • Who has the first birthday? • Who is the fourth tallest person? • Who is the second tallest boy? • Where is [name a student] in the Height line? • Where is [same student] in the Birthdate line? • In which line is [same student] closer to the front? • Was anyone in the same place in both lines?

Display ten books with different characteristics (size, colour, etc.), including a JUMP Math workbook, on the blackboard ledge. ASK: In which position is the book with the most colours on the cover? The book with no colours? The book that’s open? The thickest book? The JUMP Math workbook?

Patterns

CONNECTION

BLM Ordinal Practice

EXTRA PRACTICE

ONLINE GUIDE

Extensions for adding ordinals

Number Sense 2-20

Bonus eleventh, twelfth


NS2-21 Counting to 100Pages 45-46

GoalsStudents will count orally to 100. Students will check their counting and identify mistakes in counting by keeping track.

Count orally to 30. Review counting to 20. Then write the numbers from 20 to 30 on the board, point to each number, and say it aloud. Repeat, but this time emphasize the last part of the word while underlining the ones digit. ASK: Which two numbers end with the same digit? (20 and 30 both end with 0) Do the words for the numbers sound the same in any way? (they both end with a “tee” sound) Look at the other numbers, from 21 to 29—what are the last digits? (1 to 9) On the board, write 30 and 13. Have students listen carefully while you say the numbers, then ASK: What part sounds the same? (“thir” or “thirt” or “thirtee”) Emphasize that for numbers in the “teens”—thirteen, fourteen, fifteen, and so on—we hear the last digit first. Point to and say “thirteen”: we hear a sound that’s close to “three” and then “teen.” SAY: It’s the same for the number fourteen—we hear “four” and then “teen”—for fifteen, and so on. However, the pattern changes for numbers in the 20s. First we hear a sound that’s close to “two” and then the ones digit. Say the numbers again to demonstrate.

Continue counting orally to 100. Write 31 on the board and say it aloud. Then write 32. ASK: How would you say this? Continue through the 30s, first in numerical order and then in random order. Repeat with the 40s, 50s,..., 90s. Emphasize the connection between how we say 40 and 14, 50 and 15, and so on (just take the “n” sound off “teen” to get the other number). Ask students to say 20, 30, 40, 50, 60, 70, 80, and 90, first in numerical order and then in random order.

The number after numbers ending in 9. SAY: The numbers you say after 29, 39, and 49 are the hardest to remember. Once you remember that 30 comes after 29, you can easily count to 39 (count from 30 to 39 together). It’s remembering what comes after 39 that’s hard. Look at a hundreds chart together or give one to each student (see BLM Hundreds Chart). Point to the 2 and 3 in the 20s and 30s. SAY: We know the 20s start with a sound that’s close to “two” (“tw”). The thirties start with a sound that’s close to “three” (“th”); remember how it sounds more like 13 than 3 (take off the “n”


Can count on Can count to 20

MATERIALS

ball or paper object (for Activity 1) hundreds chart BLM Hundreds Chart (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m2, 2m3, 2m5, 2m7, 2m11, 2m13WNCP: 1N1; 2N4, 2N7, [R, C, CN]

VOCABULARY numbers to 100 keep track

PROBLEM SOLVING


PROBLEM SOLVING


ACTIVITY 1

Catch. (See NS Part 1 - Introduction) Do not include numbers ending in 9.

Literature and Nature— The Wildlife 1 2 3: A Nature Counting Book by Jan Thornhill Pictures of 1 to 20 animals in their habitats, then 25, 50, 100, and 1000.

CONNECTION

Art— On Workbook page 46, students discover how mixing colours can make brown.

CONNECTION

51

sound). ASK: What comes after 3? What should the numbers after the 30s sound like? (PROMPT: Think of the number that comes after 13, but “n” sound.) Then chant the numbers from 40 to 49 as a class. Continue to 100.

We count by grouping in tens. Tell students that you heard someone count like this: “one, two,…, twenty,…, twenty-nine, twenty-ten, twenty-eleven,… twenty-twenty.” ASK: Is this right? What’s different about this counting? Why do you think the person counted like this? Explain that in English we start counting over at ten and groups of ten numbers sound the same. That’s why numbers twenty to twenty-nine have twenty in common; thirty to thirty-nine have thirty in common, and so on.

Say and write two-digit numbers. Display a large hundreds chart and ask students to first say, and then write, numbers as you point to them. Point to numbers that look or sound similar one after the other.

Say the number given groups of tens and ones. Draw or present various objects grouped by 10s and 1s (e.g. crayons or dots). Have students say what number is represented. Connect to tens and ones blocks.

Count by keeping track. Remind students how to count and keep track of all the letters in a sentence, as they did in NS2-11, but use longer words and sentences. EXAMPLES (see margin for subtotals):

1. Sara likes to jump rope with her sister.

2. John likes to bake chocolate chip cookies with his father.

3. Matt likes to jump rope with his brother and bake chocolate chip cookies

with his mother.

Students can compare their answers. As before, discuss how counting letters in this way gives students an opportunity to check their work and find mistakes.

Extensions1. Teach students to count to 200, or even 1000.

2. Which is longer? Measure a chain of 100 paper clips against the height of one school floor. Students can hang the chain from the top of a stairway.

PROBLEM SOLVING

Splitting into simpler problems

Number Sense 2-21

ACTIVITIES 2-3

2. Have students stand in a line. The first person in line says “one,” the next person says “two,” and so on to 100, with one catch: any student who says a word that has the sound “four” in it (EXAMPLES: 14, 24,40–49) has to move to the front of the line. (EXAMPLE: I say 14 and move; the student who stood next to me before I moved says 15.) Repeat with the sound “five.” (NOTE: 50–54 and 56–59 have a “fif” sound, not a “five” sound) VARIATION: Students stand in a circle and whisper the next number to the next person; special numbers are said out loud.

3. Play Catch again, but include two-digit numbers ending in 9.

EXAMPLES: 23, 32; 6, 16, 60; 65, 55, 95

SUBTOTALS:1. 4, 9, 11, 15, 19, 23, 26, 32. 2. 4, 9, 11, 15, 24, 28, 35, 39, 42, 48 3. 4, 9, 11, 15, 19, 23, 26, 33, 36, 40, 49, 53, 60

PROBLEM SOLVING


NOTE: Some languages group numbers differently.

Measurement

CONNECTION


NS2-22 Hundreds ChartsPage 47

GoalsStudents will use patterns to find numbers on a hundreds chart.

Review finding numbers in the first row of a hundreds chart. Give each student ten tokens and a large strip of paper with the first row of a hundreds chart (e.g., from BLM Hundreds Chart – One Row). Ask students to place a token on each number from 1 to 10 as you say the numbers in random order. Stop when the row is full.

Review finding numbers in the second row of a hundreds chart. Draw the first two rows of a hundreds chart on the board and review how to find numbers in the second row using the first row as a guide, e.g., to find 17, find 7 and move down a row. Have volunteers use this method to find various numbers in the second row. Hand out BLM Hundreds Chart. Have students find and colour lightly the first two rows. Ensure that all students choose the correct rows. SAY: I will call out numbers only in the first two rows. Please place a token on each number as I say it. Verify that each student has the correct numbers covered.

Find numbers on the entire hundreds chart. Tell students to look at the third row. ASK: How can we find 27 if we know where 7 is? (find 7, then move down until you find 27) How can we find 57 if we know where 7 is? (move down from 7 until you find the 57) Repeat with various numbers, including numbers that end in 0. Then have students place a token on: 35, 75, 95, 85, 15, 65, 25, 55; then 17, 67, 87, 97, 47, 57; then 30, 60, 50, 90, 10, 70, 80, 20; then 53, 46, 81, 42, 75, 90, 45, 33, 77.

Use the reading pattern to find the next number, the previous number and the number in between. Tell students to find the number 37 and place a token on that square. ASK: What is the next number? Write on the board: 37 . Have a volunteer fill in the blank. Repeat with various numbers. Have students write the number you say and the number that comes next in their notebooks. Repeat with numbers that come before a given number, and then with numbers that come in between two given numbers.


Knows how to use the reading pattern Can count to 10 using a hundreds chart

MATERIALS

tokens BLM Hundreds Chart (p xxx)BLM Hundreds Chart Pieces (p xxx) BLM A Larger Hundreds Chart (p xxx)BLM Hundreds Charts – One Row (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m7, 2m11, 2m13, 2m19 WNCP: 2N4, [R, C]

VOCABULARY reading pattern hundreds chart

PROBLEM SOLVING


ONLINE GUIDE


53

Find groups in a hundreds chart. Arrange cut-out “pieces” of a hundreds chart on the board. Label each piece with a colour. Have students find and colour the pieces on BLM Hundreds Chart. EXAMPLES:

Blue Red Yellow Green Purple Orange

Find missing numbers in a hundreds chart. Create part of a hundreds chart with cards. Withhold three cards. See the margin for an example.

Give each missing card to a volunteer to put in the correct place. Remove different cards from the chart, shuffle them, and have volunteers put them back. Repeat with a different part of the hundreds chart. Remove more and more cards from the chart. Finally, have volunteers write the missing numbers in the empty spaces instead of referring to the cards. Eventually, you should have no cards on the board—only numbers written in by students.

Extensions1. Give students BLM Hundreds Chart – 5 Rows Have students use the

hundreds chart to add: 5 + 3, 15 + 3, 25 + 3 (EXAMPLE: shade 5 and circle the next 3 numbers). ASK: What pattern is there in the answers? Can you predict 65 + 3? 75 + 3? 85 + 3? Verify the prediction on a large hundreds chart. Repeat with 19 + 3, 29 + 3, 39 + 3.

2. The reading pattern in Japanese is bottom to top and then right to left. Together, fill out a hundreds chart using this reading pattern.

i n e

t o c

e p n

m a u O

ONLINE GUIDE


ONLINE GUIDE

BLM Hundreds Chart Practice

12 13

22 23

27 28 29

37 38 39

35

45

55

41 42

51 52

61 62

71 72

67 68 69 70

77 78 79 80

87 88 89 90

92 93 94

ACTIVITY

Students cut out the pieces from BLM Hundreds Chart Pieces and glue them in the correct place on BLM A Larger Hundreds Chart.

15 16 18 19

25 26 27 29

35 37 38 39

45 46 47 48 49

Number Sense 2-22


PROBLEM SOLVING


NS2-23 More Tens and Ones BlocksPages 48-50

GoalsStudents will use tens and ones blocks to represent numbers and to find numbers on a hundreds chart.

Count past 20 using the hundreds chart. Review the reading pattern and counting to 20 using the first two rows of a hundreds chart. Then give each student at least 30 ones blocks and BLM Hundreds Chart. Have students count their blocks by using the chart. ASK: How many blocks did you count? How many full rows did your blocks cover? How many blocks in the next row did you need? Record answers on the board (EXAMPLE: 35 blocks, 3 rows and 5 more blocks). Have students predict how many full rows they will fill and how many more blocks they will use to make these numbers: 28, 32, 23, 31, 13, 30, 36. Verify their predictions on an enlarged hundreds chart.

Tens blocks. ASK: How many full rows and how many more blocks would we need to show 74? Record the students’ predictions. To verify them, begin placing ones blocks in order on the hundreds chart on an overhead projector. After you finish a few rows, SAY: I’m tired of placing so many ones blocks in order. Does anyone remember what we used before? (a tens block) Show students a tens block. Count again the individual ones blocks that they are visible within a tens block to verify that there are ten. Then cover one full row with a tens block. ASK: Do we need to cover another full row or is 74 in the next row? (Repeat until 74 is in the next row.) How many ones blocks do we need in the next row? (4) How many full rows did we cover? (7) Record the answer on the board: 74 is 7 full rows and 4 more blocks. Repeat with various numbers, using tens blocks for full rows.

Find numbers on a hundreds chart. SAY: How many full rows do I have to cover before I get to 63? (6) Where is 63 in the next row? (the third one) Count 6 full rows using tens blocks and then count 3 in the next row using ones blocks to demonstrate finding 63. Invite volunteers to find various numbers, then have students find numbers on their own hundreds chart.


Knows how to use the reading pattern Can count to 20 using a chart

MATERIALS

lots of ones and tens blocks BLM Hundreds Chart (p xxx)BLM Hundreds Chart and Base Ten Materials (p xxx) BLM Game Cards (p xxx)

CURRICULUM EXPECTATIONSOntario: 1m11; 2m1, 2m2, 2m3, 2m7, 2m11, 2m13 WNCP: 2N4, 2N7, [R, C]]

VOCABULARY reading pattern ones digit tens digit

PROBLEM SOLVING


PROBLEM SOLVING

Reflecting on other ways to solve the problem

ACTIVITY 1

Assign each student a number up to 49. Students display their number on a hundreds chart by cutting the correct blocks from BLM Hundreds Chart and Base Ten Materials.

55

Compare two methods of finding numbers on a hundreds chart. Compare the first method students learned with the method they learned in this lesson. Use the number 45 as an example: • Find 5 in the first row, then move down until you find 45. • Move down or cover 4 full rows and then count across 5 squares. Point out that you’re really doing the same two steps but in different order. Whether you move across then down, or down then across, you end up in the same place.

Show numbers using tens and ones blocks without a chart. SAY: You can use blocks without the hundreds chart to represent a number. Show students 3 tens blocks and 7 ones blocks. Draw a T-chart on the board and label the columns “tens” and “ones.” ASK: How many tens blocks do I have? (write 3 in the tens column) Repeat for ones blocks and the ones column. ASK: If we placed these on the hundreds chart, what number would we get? (37) Check by counting each cube, including the 10 in each tens block. Then place the blocks on a hundreds chart and emphasize that 37 is the last square covered. Repeat with various numbers, this time having students fill in the chart and write the number. Finally, have students show various numbers using tens and ones blocks. Do not give students more than 9 ones blocks so that they use the fewest blocks possible.

Tens digits and ones digits. Write 27 on the board. ASK: Which digit shows me the number of tens blocks I need to make 27—the 2 or the 7? (the 2) Which digit shows me the number of ones blocks I need to make 27—the 2 or the 7? (the 7) Explain that the 2 is called the tens digit and the 7 is called the ones digit. Ask students to tell you the tens digit and the ones digit in various numbers. Then write 25, 34, and 35 on the board and ask a volunteer to circle the two numbers with the same tens digit and underline the two numbers with the same ones digit. Repeat with similar sets of numbers. EXAMPLES: 74, 89, 84; 51, 58,18; 3, 37, 7.Bonus 51 12 35 48 50 84 25

PROBLEM SOLVING


ONLINE GUIDE

BLM Tens and Ones (1)

EXTRA PRACTICE

ACTIVITIES 2-4

Instructions for Activities 3–4 are in NS Part 1 — Introduction.

2. Play I Have —, Who Has—? Use BLM Game Cards to make cards with numerals and base ten models. EXAMPLE: 38 on the top and 2 tens blocks with 5 ones blocks on the bottom (I have 38, who has 25?).

3. Electric! Match numerals to base ten models.

4. Have students stack as many ones blocks as they can in a given time interval. Then ASK: Did you stack more than 10 or less than 10? How can you tell? (compare to a tens block) More than 20 or less than 20? (compare to two tens blocks) Have students determine how many ones blocks they stacked by counting the number of tens blocks and then the number of extra ones blocks they need to build an equivalent stack. Repeat several times.

Number Sense 2-23


NS2-24 Ordering Numbers to 100Pages 51-56

GoalsStudents will compare and order numbers to 100.

Use tens and ones blocks to compare numbers to 100. Write 29 on the board in blue and 34 in red. Give students more than enough tens and ones blocks to make 29 using blue and 34 using red. Have students place the blue blocks into one-to-one correspondence with the red blocks. Emphasize that students must place tens blocks with tens blocks and ones blocks with ones blocks. ASK: Do you have more red or blue blocks left over? (red, because I have 10 left over in red and only 5 left over in blue) Emphasize that a tens block is counted as 10 and a ones block is counted as 1. Which number is more, 29 or 34? Repeat with 42 (blue) and 37 (red). ASK: Do you have more red or blue blocks left over? (blue) Which number is more? (42) Repeat with various numbers. EXAMPLES: 83 or 38; 74 or 38.

Use tens and ones blocks symbolically to compare two numbers. Write two numbers on the board, say 36 and 43. Ask students to predict which number is bigger. Draw the base ten representation for the majority vote on the board. Then have a volunteer try to make the other number by colouring the picture on the board. For example, if students predict that 43 is bigger, the volunteer will colour 3 tens blocks and 6 ones blocks.

If students predict that 36 is bigger, the volunteer will not be able to colour 4 tens blocks and 3 ones blocks; there won’t be enough blocks drawn on the board. Repeat with various numbers. Then have students answer similar questions individually.

Use a number line to order numbers. Give students a long number line to 100 (to make one from BLM Hundreds Chart, see NS Part 1 – Introduction) and challenge them to find these numbers: 38, 12, 25. ASK: Which is the smallest number? Which is the largest number? How do you know? Repeat with increasingly more difficult groups of three numbers (see margin).

Discuss how ordering numbers using a number line is harder or easier than using blocks (possible answers: it is harder to find numbers on the number line than to make them using blocks, but once we find the numbers, it is easier to compare them; it is much easier to compare many numbers on a number line).


Knows how to use the reading pattern Can count to 20 using a chart Can find numbers in a hundreds chart

MATERIALS

lots of tens and ones blocks (red and blue) BLM Hundreds Chart (p xxx)tokens or counters

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m5, 2m7, 2m11, 2m13 WNCP: 2N5, 2N7, [R, C, CN]

VOCABULARY reading pattern hundreds chart larger, largest smaller, smallest

EXAMPLES: 28, 24, 31; 41, 39, 40; 78, 29, 56. Bonus

Put these numbers in order: 42, 14, 74, 41, 32, 73.


PROBLEM SOLVING

57

Use a hundreds chart to order numbers. Review finding numbers on a hundreds chart using the reading pattern. Students can compare many numbers at a time by first finding each number on the chart and then writing them in order. Give each student a copy of BLM Hundreds Chart. Students can place tokens or counters on the numbers and then write them in order on a separate sheet of paper.

Compare numbers with the same number of tens. Tell each student to take 3 red blocks and 5 blue blocks. ASK: Which is more, 3 or 5? Have a volunteer show the answer by using one-to-one correspondence. Repeatedly have students add a tens block to each group, and after each addition ask students what numbers they have and which number is bigger. Emphasize that by adding a tens block to each, we never change which number is bigger. When two numbers have the same number of tens, the number with more ones is bigger.

Ask students to choose the largest number among a set of three numbers, all with the same number of tens. Then have students order lists of numbers, all with the same number of tens.

Compare numbers with the same number of ones. Tell each student to take 2 red tens blocks and 3 blue tens blocks. Repeatedly have students add a ones block to each group, and after each addition ask students what numbers they have and which number is bigger. Emphasize that if the number of ones is the same, the number with more tens blocks is bigger. Repeat the previous exercises with numbers that have the same number of ones.

Compare numbers with different numbers of tens and ones. Tell each student to take 3 red ones blocks and 6 blue ones blocks. ASK: Which is more? How do you know? Tell each student to add 2 red tens blocks and 1 blue tens block. Repeat the questions. This time, the colour of the larger number changed: even though there are more blue ones blocks, there are more red blocks altogether. ASK: How can a number with 3 ones blocks be more than a number with 6 ones blocks? (it has more tens blocks) Repeat with more numbers. EXAMPLES: 31 and 26; 37 and 45. Emphasize that if both the tens and ones are different, the number with more tens is bigger. Repeat the previous exercises with numbers that have different tens and ones.

ExtensionFind a number between 42 and 81 that can be represented using exactly 9 base ten blocks. Challenge students to find as many correct answers as they can.

ACTIVITY

Find page numbers. (See NS Part 1 – Introduction) Have students open their JUMP Math workbooks to page 1. Then have them turn and point to the page numbers in the following order: 24, 29, 26, 21, 28, 20, 25, 27, 30, 34, 31, 38, 36, 39, 35, 37, 41, 48, 46, 45, 49, 42, 47, 44.

PROBLEM SOLVING


Number Sense 2-24

EXAMPLES: 34, 21, 26, 19, 7, 45 21, 12, 33, 9, 41, 14, 50 31, 62, 77, 80, 43, 52

EXAMPLES: 42, 45, 40; 36, 35, 39.

Bonus 342 348 345

PROBLEM SOLVING

Problem Solving


Trade tens blocks for ones blocks. Give each student 6 tens blocks and 30 ones blocks. Have students make the number 28 using their blocks. (2 tens and 8 ones) Then ask them to trade a tens block for ten ones blocks. ASK: How many tens and ones blocks do you have now? (1 ten and 18 ones) Was it a fair trade? (yes) How do you know? (there are 10 ones in 1 tens block; verify this by counting) Can we say that you still have 28? (yes) How do you know? (it was a fair trade) Count the blocks to verify that students still have 28, by counting on from the 10 (11, 12, 13,…, 28). Write on the board: 28 = 2 tens + 8 ones = 1 ten + 18 ones. Then have students trade their last tens block for 10 more ones blocks. Now what do they have? (0 tens blocks and 28 ones blocks). Add “= 0 tens + 28 ones” to the expression on the board. Illustrate this on a hundreds chart:

NS2-25 Many Ways to Write a NumberPages 57-58

GoalsStudents will show numbers using different combinations of tens and ones blocks. Students will make organized lists to show all the possible combinations.


Can find numbers on a hundreds chart Knows ten ones blocks are equivalent to one tens block

MATERIALS

6 tens blocks and 30 ones blocks for each student BLM Many Ways to Show a Number (p xxx)BLM Hundreds Chart (p XXX)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m7, 2m11, 2m13 WNCP: 2N4, [R, C]

VOCABULARY hundreds chart

28 = 2 tens + 8 ones

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

29 3021 24 2723 2622 25 28

28 = 1 ten + 18 ones

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

29 3021

11

24

14

27

17

23

13

26

16

22

12

25

15

28

18 19 20

28 = 1 ten + 18 ones

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

29 3021

11

1

24

14

4

27

17

7

23

13

3

26

16

6

22

12

2

25

15

5

28

18

8

19

9

20

10

59

Make an organized list. Give each student a hundreds chart (e.g. from BLM Hundreds Chart) to use with tens blocks and ones blocks (i.e., each square is 1 cm2). Have students make the number 43 in as many ways as they can. Guide students to record their answers in an organized way, on a chart with headings “tens” and “ones.” ASK: Can you find a way to make sure you include all possible combinations? How many tens are in 43? (4) Start with 4 in the tens column and ASK: How many ones do I need to put in the ones column? (3) I want to make sure that I have all the possibilities—how can I make sure I don’t leave anything out? What other numbers can go in the tens column? Can I have 5 tens? 3 tens? 8 tens? 0 tens? (only 4 tens or less can be in the tens column because there are only 4 tens in 43) SAY: To make sure we write every possible number in the tens column, let’s write the numbers in order. Then write the numbers from 4 to 0 in the tens column.

ASK: If I have 3 tens, how many ones (blocks) do I need to make 43? (13) Have students add this to their chart. Repeat for 2 tens, 1 ten, and 0 tens.

Create and complete another tens and ones chart for the number 36. Next, have students make their own tens and ones charts for other two-digit numbers. EXAMPLES: 23, 28, 49, 62, 71. Allow students to use tens and ones blocks and a hundreds chart if they wish.

Have students take 3 tens blocks and 12 ones blocks. ASK: What number do these blocks represent? Suggest that students trade 10 ones blocks for a tens block until they have less than 10 ones blocks. This will make it easier to see the answer. Repeat with 4 tens blocks and 18 ones blocks, then 2 tens blocks and 21 ones blocks.

ACTIVITY 1

Students can use BLM Many Ways to Show a Number with tens and ones blocks to make different numbers; they will see that the same number can be made in various ways. Then students determine how many more ones blocks they need to make 45, given various numbers of tens blocks.

PROBLEM SOLVING

Making an organized list

ACTIVITY 2

Have students design any shape or object they want using tens and ones blocks from their collection (6 tens and 30 ones). ASK: How many tens blocks did you use? How many ones blocks? What number does that represent? Then have students make another shape using a different number of blocks. Students can determine the numbers represented by other students’ shapes.

Number Sense 2-25

Tens Ones

4 3

3

2

1

0


Use the length of a model to add. Draw the model used on Workbook page 59 and start by having volunteers add two numbers, then three or four. Give students BLM 1 Cm Grid Paper and show them how they can use two alternating colours to add different numbers (see margin).

What it means when two addition sentences have the same total. Show an example of two addition sentences with the same answer (EXAMPLE: 5 + 4 and 7 + 2) using the model on Workbook page 61. Colour the squares for each number.

5 + 4 = 9

7 + 2 = 9

SAY: 5 + 4 and 7 + 2 both have the same number of squares coloured, so they are equal. Instead of writing 5 + 4 = 9 and 7 + 2 = 9, we can just write 5 + 4 = 7 + 2. We often compare things using words: for example, Tom’s shirt is red and Karen’s pants are red. We can shorten this to Tom’s shirt matches Karen’s pants or Tom’s shirt is the same colour as Karen’s pants. Just as we can say that two things are the same colour without

NS2-26 Using Length to Add and Subtract Pages 59-61

GoalsStudents will use the length of concrete materials and models to add and subtract and to combine addition and subtraction sentences.


Can add and subtract numbers up to 10 Can write addition and subtraction sentences

MATERIALS

BLM 1 Cm Grid Paper (p XXX)BLM Using Tens and Ones Blocks to Add (p XXX)paper sticks (see NS Part 1 – Introduction)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m3, 2m5, 2m6, 2m7 2m68, 2m69 WNCP: 2N9, [R, C, CN, V]

VOCABULARY length long equal

PROBLEM SOLVING

Making a modelACTIVITY

Give each student two paper sticks of each length from 2 cm to 10 cm. Have students write the length in squares on the back of each stick. They should check that they have two of each length and that the two sticks with the same number are in fact the same length.

Show students how to use the sticks to solve 2 + 3 + 4 = . Write the addition statement on the board. Place the sticks end to end. Then find the single stick that has the same length.

Have students repeat for many addition statements (2 numbers, 3 numbers, then 4 numbers). EXAMPLES:2 + 4 = 3 + 2 = 4 + 3 = 6 + 2 + 2 = 2 + 3 + 5 = 2 + 2 + 2 + 3 =

PROBLEM SOLVING

Connecting

2 3 4

?

3 + 4 + 2

Give each student 1 tens block, 9 ones blocks, and BLM Using Tens and Ones Blocks to Add. Students line the blocks up to add.

EXTRA PRACTICE

61

saying which colour that is, we can say that two things are the same number without saying which number that is. Since “=” means “is the same number as” it makes sense to write 5 + 4 = 7 + 2.

Now write two more addition statements on the board: 4 + 3 and 6 + 1. Have a volunteer draw the model for each and have another volunteer write one sentence for both. Repeat with more addition statements.

Chains of equal signs. SAY: Instead of writing 4 + 1 = 3 + 2 and 2 + 3 = 3 + 2, we can take a shortcut and write: 4 + 1 = 3 + 2 = 2 + 3. Have volunteers continue the chain to make it as long as they can. Read the math sentence aloud with “=” as “is the same number as.” Then have students make a chain with numbers that add to 8. Start with 1 + 7 = 7 + 1 = .

Use the length of concrete materials to subtract. SAY: Just as we used our paper sticks to add, we can use them to subtract. Write 8 – 3 on the board. Start with a stick 8 squares long. Show students how to fold back the number of squares being subtracted—in this case, 3. SAY: The number of squares we have left after the fold mark shows 8 – 3. ASK: How many squares are left? (5) Subtract more numbers this way. EXAMPLES: 9 – 2, 7 – 3.

Use the length of a model to subtract. SAY: You can fold back a stick to subtract a number but it’s hard to fold back a drawing of a stick. How can we “take away” squares in a drawing? Show students how to mark an X through squares to subtract. Write 9 – 4 on the board and draw a stick 9 squares long. Compare two ways of marking 4 Xs on the squares: mark the first 4 squares and the last 4 squares (see margin).

ASK: Do these models give the same answer? (yes) Is one easier to draw or use? (not really) Now tell students that you want to compare 9 – 4 to 7 – 2 and show these two models.

ASK: Which way of crossing out squares makes it easier to compare 9 – 4 to 7 – 2? (crossing out from the right) Why? (because the ones not crossed out are lined up) How does 9 – 4 compare to 7 – 2? (they are equal) Repeat with more EXAMPLES: 7 – 2 and 8 – 1; 10 – 5 and 9 – 7.

Combine the models for subtraction and addition. Write an addition sentence on the board and challenge students to find a subtraction sentence with the same answer. Students can use their sticks to help them. Record several answers on the board and circle one of them. Have a volunteer come to the board and prove using models that the subtraction sentence has the same answer (draw the grid outline for students). Then ask a volunteer to combine the addition and subtraction sentences into one sentence. Ask the volunteer to write the sentence on the board (EXAMPLE: 2 + 1 = 8 – 5). Have volunteers draw models for pairs of addition and subtraction sentences with the same answer and have all students combine the two sentences into one (see examples and bonus in margin).

PROBLEM SOLVING


Number Sense 2-26

EXAMPLES: 4 + 3 and 10 – 3, 6 – 1 and 2 + 3.

Bonus 10 – 2 and 4 + 4 and 9 – 1. Have students draw the model and write a chain of equal signs. Challenge students to extend the chain.


Addition sentences and a number can be equal or not equal. SAY: If an addition sentence and a number are the same, then they are equal; if they are different numbers (not the same), they are not equal. Give an example: 5 + 3 and 8. ASK: Are this addition statement and number equal or not equal? (equal) Are 5 + 2 and 6 equal or not equal? (not equal) Have students write “equal” or “not equal” for more such problems. EXAMPLES:4 + 2 and 6 are 7 and 3 + 3 are

Students may wish to use their paper sticks from the last lesson to solve these questions. Review how to do so: line sticks up end to end (to represent the addition sentence) and compare their length to the single stick the length of the number.

Subtraction sentences and a number can be equal or not equal. Repeat the above for subtraction. EXAMPLES: 9 – 2 and 6 are 10 – 1 and 8 are 5 and 7 – 2 are 6 and 9 – 3 are

Two addition sentences can be equal or not equal. Write 3 + 6 and 5 + 4 on the board. SAY: I want to know if these addition sentences are equal. Write “equal” on the board. Place sticks 3 squares long and 6 squares long end to end on an overhead projector. Find the single stick that is the same length (9). ASK: How can we tell if they are equal in length to 5 + 4? (place sticks that are 5 squares and 4 squares long end to end and find the single stick that is the same length) ASK: Are the two additions sentences the same? (yes) How do you know? (the are both the same as 9) Do we have to use the single stick or can you think of another way to see if the length of 3 + 6 equals the length of 5 + 4? (line up the sticks for 3 + 6 and 5 + 4 using the same starting point) SAY: If both lines are the same length (or number of squares) they are equal. Now write 2 + 5 and 6 + 3 on the board. Have volunteers place the sticks for 2 + 5 and 6 + 3 end to end. ASK: Are these two equal? (no) How do you know? (they’re different lengths) Have students use sticks to determine whether other addition sentences are equal or not equal. Students should complete sentences in their notebooks. EXAMPLES: 6 + 2 and 2 + 5 (not equal); 9 + 2 and 4 + 6 (not equal).

NS2-27 Equal or Not Equal Pages 62-64

GoalsStudents will know whether addition and/or subtraction sentences are equal or not equal.


Can add and subtract numbers up to 10 Can write addition and subtraction sentences

MATERIALS

paper sticks (see NS Part 1 – Introduction) 2 cm grid paper to colour or use with counters

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m6, 2m7, 2m68, 2m69 WNCP: 2PR4, [R, V, C]

VOCABULARY equal (=)not equal (≠)

PROBLEM SOLVING

Making a model

NOTE: Workbook page 64 is optional for students in Ontario.

63

Two subtraction sentences can be equal or not equal. SAY: We can also compare two subtraction sentences. Using your paper sticks, tell me if the following subtraction sentences are equal: 8 – 3 and 7 – 2 (equal); 10 – 5 and 5 – 1 (not equal) ASK: Why are they not equal? (the sticks when folded back are different lengths) Have students solve more such problems independently. EXAMPLES: 10 – 2 and 9 – 3; 3 – 1 and 4 – 2; 5 – 2 and 7 – 3.

Addition and subtraction sentences can be equal or not equal. Write on the board: 6 – 2 and 2 + 1 are . After students have manipulated and compared their sticks as necessary, have a volunteer write in the answer. Repeat with 4 + 5 and 10 – 1. Have students solve more such problems independently. EXAMPLES: 10 – 5 and 3 + 2; 7 + 2 and 10 – 3.

Equal or not equal using models. Take away the concrete materials and give students 2 cm grid paper to colour or use with counters. Review how to draw models for addition and subtraction problems. Emphasize that models need to be lined up the same way concrete materials were lined up. SAY: Just as you lined up sticks in the same place to start, you have to draw your models starting at the same place and look to see if they end at the same place. If the models end at the same place we say they are equal; if they end at a different place we say they are not equal. Have students solve more questions like those above. Start with two addition sentences, then two subtraction sentences, and then one addition and one subtraction sentence. Some students might need you to draw the outline of a grid that is 2 squares tall so that they automatically start at the right place. EXAMPLES: 4 + 6 and 5 + 6 are 10 – 3 and 8 – 1 are 7 – 6 and 1 + 2 are 8 + 3 and 1 + 4 are

The sign for not equal. Show students the equal sign (=). ASK: How would you make a sign that means “not equal”? Take various answers and show the symbol that mathematicians use (≠). Provide more numbers and number sentences (addition and subtraction) and have students write = or ≠ between them. Students can draw models or use grid paper. EXAMPLES: 3 2 + 1; 4 + 2 3 + 5; 8 – 2 5 + 1; 7 – 6 3 – 1

ExtensionA new model for addition and subtraction. For addition, draw the first number as circles, draw a line, then draw the second number as circles. For subtraction, draw the first number as circles and cross out circles for the second number. Then have students write = or ≠ in between the two number sentences. For practice, provide BLM Equal or Not.

4 + 2 = 9 – 3

PROBLEM SOLVING

Drawing a model

ONLINE GUIDE

Other ways to use “=”

Number Sense 2-27


Equal and not equal. ASK: What does it mean when we say two things are equal? (they are the same in some way) Explain that equal objects could have the same mass, length, or colour, for example, but in math, when we say equal, we usually mean the same number. Write “equal” and “=” on the board. ASK: What do we mean when we say two things are not equal? (they are not the same number) Write “not equal” and “≠” on the board.

Explain how pan balances work. Tell students that you are going to put five connecting cubes in one pan and three in the other. Ask students to predict which side will go down and why. Check predictions. ASK: What do I have to do in order to balance the two pans? Test students’ answers. Repeat with different numbers of cubes. Emphasize that if equal numbers of cubes are on both sides, the pans will balance. NOTE: If you do not have pan balances, use a teeter-totter to review the concept of a balance, then work through the same examples with pictures of cubes and balances (see the Workbook for examples).

NS2-28 Equality and Inequality with Balances Pages 65-69

GoalsStudents will use pan balances to illustrate equalities and inequalities and solve simple equations.


Can count to 20 Recognizes numbers and quantities to 20 Is familiar with how a balance works Can add Knows the concepts of more and less

MATERIALS

pan balances connecting cubes BLM Equal or Not Equal? (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m2, 2m3, 2m5, 2m7, 2m70 WNCP: 2PR3, [R, C, CN]

VOCABULARY balance equal (=)not equal (≠)addition sentence subtraction sentence

PROBLEM SOLVING


ACTIVITIES 1-2

1. Students will need pan balances, connecting cubes, and a copy of BLM Equal or Not Equal? Students can work independently or in pairs to predict and check which groups of connecting cubes are equal and which are not equal. They join the cubes as shown in the pictures. Have students explain their results to the class. (This is a good explanation for the second problem: These [child holds up one cube and a train of three cubes] and these [child holds up two trains of two cubes] are the same because they are both 4 cubes.) Students can also line up the connecting cube trains to verify that the total lengths are equal or not equal.

2. Students work in groups of three: two students create sets that

Have students choose two groups that are not equal and explain in their journals how they know they are not equal.

JOURNAL

PROBLEM SOLVING

Connecting

65

Balance the pans by adding cubes. Place a train of two cubes in one pan. ASK: How many cubes do we need to put in the other pan in order to balance the pans? Do so. Then add one more cube to the train. ASK: How many cubes must be in the other pan to balance the pans? (3) How many are there now? (2) How many cubes should we add to the other pan? (1) Balance the pans again. Add two cubes to the original train (for a total of five) then add one more; balance the pans after each addition. Always ask students how many cubes need to be on the other side and how many need to be added to the other side in order to balance the pans.

Balance the pans by adding cubes and solve addition sentences. Empty the balance pans and put a train of three cubes in one pan and one cube in the other. Tell students that you want to write an addition sentence to match what you are doing. Write 3 = 1 + on the board. ASK: How many cubes must be added to the pan with one cube in order to balance the pans? Show this on the balance. Write that number in the blank space and have students explain how the addition sentence matches the balance.

Now place four cubes in one pan and two in the other. Have a volunteer write the corresponding addition sentence using what is known so far (4 = 2 + ). Prompt students to tell how many more cubes must be added to the pan with two cubes to make both sides equal. Another volunteer may fill in the missing number.

Balance the pans by removing cubes and solve subtraction sentences. Repeat the above for subtraction: instead of asking students how many cubes they need to add to balance the pans, ask them how many cubes they need to remove (and from which side). Then write and solve the subtraction sentences corresponding to different balance models.

Unbalance the pans. Have students create two equal sets using a pan balance and then change one of the sets (by adding or subtracting) to unbalance the pans. Discuss different strategies.

are equal and the third creates a set that is unequal to the other two. Groups then switch sets with another group and determine which of the other group’s sets are unequal (and explain how they know)

ONLINE GUIDE

EXTRA PRACTICE BLM Balances asks students to choose how the pan balance should look with different numbers of cubes on each side (i.e. which side will go up and which will go down).

PROBLEM SOLVING

Making a model

ACTIVITY 3

Give each group of three students a pan balance and about 40 connecting cubes. Player 1 creates a balance problem: he or she places some cubes on each pan so that the balance is unbalanced. Player 2 has to write the addition sentence (with a blank) that represents the unbalanced pans. Player 3 has to balance the pans and fill in the blank. Players then exchange roles. Repeat until all students are comfortable with the concept of balance in addition sentences. Advanced Variation: Change the order: Player 1 writes an addition sentence with a blank, Player 2 creates the corresponding balance model, and Player 3 has to balance the pans and fill in the blank.

PROBLEM SOLVING

Making a model

Number Sense 2-28


Use a calculator to find missing numbers by guessing and checking. Write on the board: 3 + = 9. Take guesses as to which number fits in the blank. Then give each student a calculator and have all students try one of the guesses, say 5. ASK: Is 3 + 5 equal to 9? (no) What is 3 + 5? (8) Is that more than 9 or less than 9? (less) SAY: 5 is too little because 3 + 5 is only 8. Let’s try a larger number. Take guesses again and repeat the process until 6 is tried and agreed to work. Repeat for several addition sentences. Then do subtraction sentences.

Emphasize that if a guess gives an answer that is too big, students didn’t take away enough, so they should try taking away more. Encourage students to record each guess with the answer it gives and to ask themselves whether the answers are getting closer to or further from the number they want. EXAMPLES:for 15 – = 11: 1st guess: 15 – 3 = 12; 2nd guess: 15 – 2 = 13

13 is further from 11 than 12, so 3 is closer than 2 to the number that goes in the blank. My next guess will be 4, so we get 15 – 4 = 11. It works!

Next, combine addition with subtraction. For example, 5 + 4 = 17 – . First calculate the side that doesn’t have a missing number: 5 + 4 = 9. Then rewrite the problem to change it into one the students already know how to solve: 9 = 17 – . Now solve the problem as before.

Use paper sticks to find the missing addend. Have students find missing addends by lining up sticks against a known sum. Start by adding two numbers, with one missing, then increase to three numbers with one missing. Also, change the position of the missing number. Do a problem together to start: 2 + = 7. Use the paper sticks to model it. Turn the sticks with numbers around to show the grid marks (see margin).Now the “?” is aligned with 5 squares, so 2 + 5 = 7. EXAMPLES: 3 + = 8; + 2 = 6; 2 + + 2 = 7.Bonus 2 + + 4 + 2 = 10

NS2-29 Missing Numbers Pages 70-74

GoalsStudents will find missing numbers in addition and subtraction sentences.


Can add and subtract numbers up to 10

MATERIALS

Paper sticks (see NS Part 1 – Introduction a calculator for each student BLM 1 cm Grid Paper (p XXX)BLM The Number in the Middle (p xxx) BLM Missing Number Practice (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m4, 2m6, 2m7, 2m70 WNCP: 2N4, [R, C, V, T]

VOCABULARY addition sentence subtraction sentence missing number middle number

PROBLEM SOLVING

Guessing, checking and revising, Technology

PROBLEM SOLVING

Using logical reasoning, Making an organized list

PROBLEM SOLVING


2 ?

7

?

EXAMPLES: 2 + = 10; 18 + = 12; 4 + = 19; 15 + = 11; 8 + = 13; 13 + = 4;

67

Use a model instead of sticks. Give each student a copy of BLM 1 cm Grid Paper. Write 3 + 5 + = 10 on the board. Have students solve this problem using their sticks and then explain that we don’t always have sticks when we add. Draw ”sticks” on grid paper by outlining the length of the sticks and have students do the same on their grid paper. Suggest that students colour each of the two known “sticks” using different colours, so that it is easy to see the parts that are left (2):

ASK: Is this (2) the same answer as before? (yes) Repeat with more questions that have only the last number unknown. Ensure that the bottom line has the same number of squares as the total.

The middle number missing. Repeat the exercises above, but this time, colour the first and last squares on the top grid and leave the middle part blank. EXAMPLES: 3 + + 4 = 8, 2 + + 1 = 6.

Find the missing number to make two addition sentences equal. Write 3 + 2 = 1 + on the board. Using the same model as on Workbook page 72, colour the three known parts. ASK: How many squares do I have to colour to make the length of the bottom line equal to the length of the top line? (4) Fill in the blank. Repeat, finding missing numbers in addition sentences with up to three addends.

Find the missing number to make a subtraction sentence and a number equal. Write on the board: 8 – 2 = . Review the model on paper: cross out the last 2 squares starting on a grid 8 squares long. The number of squares left is the answer (6). Then write on the board: 9 – = 7. ASK: How is this question different? (we don’t know how many squares to cross out) What do we know? (the answer is 7; the length that we start with is 9) SAY: Since we know how many squares are not crossed out, let’s count that many and then cross out the rest. That number will tell us how many to subtract. Have students try this on grid paper. Outline a stick for the total number (9), leave the “answer” number of squares (7) blank, and cross out the rest. How many did students cross out? (2)

Find the missing number to make addition and/or subtraction sentences equal but do not include addition and subtraction in one sentence, e.g., 3 + 4 = 8 – 1, but not 3 + 4 – 1 = 5 + 1.

The advantage of models on paper over concrete materials. Have students solve this problem using their sticks: 7 + 3 = 4 + . Then have them try 12 + 5 = 8 + . They won’t be able to solve this one using sticks because they don’t have a stick that is 12 squares long. Emphasize that models are better for larger numbers.

Students use the model from BLM Equal or Not (NS2-27) to complete BLM Missing Number Practice. They can create concrete models for numbers up to 18 using counters and toothpicks. Students may create their own problem and then exchange with a partner to solve.

?53

10

EXTRA PRACTICE BLM The Number in the Middle

Number Sense 2-29

PROBLEM SOLVING

Making a model

EXAMPLE: 3 + 2 + = 8

EXAMPLES:

6 + 3 = + 8

3 + 2 + = 1 + 7

2 + + 4 = 3 + 3 + 3

EXAMPLES:

6 – = 4

10 – = 3

5 – = 1.

EXAMPLES:

6 – 2 = 1 +

4 + = 10 – 3

3 + + 2 = 9 – 2

8 – = 7 – 5

PROBLEM SOLVING

Selecting tools and strategies

NOTE: Allow students to use sticks to do the worksheets.


Switch objects between hands to show that the total stays the same. Make sure students can correctly identify their left and right hands. Hold 3 objects in your left hand and 4 in your right hand. ASK: How many do I have in each hand? How many do I have in total? Write on the board:

+ +

Left hand right hand total

Have a volunteer fill in the correct numbers. Then switch hands and have the volunteer write the new corresponding addition sentence (left hand first again). ASK: What is the same about the two addition sentences? (the same three numbers and the total) What is different? (the order of the other two numbers) Repeat with several examples. Then have students solve examples independently, recording their number sentences in their journals.

Add three numbers and switch the order. Students find a partner. One partner picks up some counters with one hand and some with the other hand. The other partner picks up some counters only with the non-writing hand. The person with a free hand records different number sentences to show the total number in all three hands by counting different hands first. Challenge students to find at least 3 different number sentences. NOTE: If two of the numbers are the same (e.g., 2, 3, 3), there will only be three number sentences. If all numbers are the same, there will only be one number sentence. In most cases, there will be a total of six number sentences.

Turn dominoes around and add. Tape a blank paper domino to the board. Have a volunteer put dots on the domino to show 6 + 4. ASK: What could I do to this domino to make it show 4 + 6 instead of 6 + 4? (turn it around) Does turning the domino change the total number of dots? (no) How does turning the domino change the addition sentence? (6 + 4 = 10 becomes 4 + 6 = 10)) What stays the same? (the three numbers used and the total)

NS2-30 Adding, Subtracting, and Order Pages 75-77

GoalsStudents will see that changing the order of the addends does not change the total; however, changing the order of numbers in subtraction sentences does change the situation.


Knows the plus (+) and minus (–) signsCan count Can distinguish between right and left

MATERIALS

counters dice large blank paper domino real or paper dominoes BLM Cubes (p XXX)

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m5, 2m6, 2m7, 2m71 WNCP: 2N9, [R, CN, V, C]

VOCABULARY addition sentence subtraction sentence total take away from

PROBLEM SOLVING


PROBLEM SOLVING

Making a model

69

What is different? (the order of the other two numbers) Give students dominoes. Have them turn the dominoes around to write two addition sentences.

Order doesn’t matter in addition. Students have seen that the order of numbers does not matter in addition. As a reminder, write on the board: 6 + 2 = 2 + 6. Emphasize that we always read from left to right, so 6 + 2 means start with 6 and add 2. Also, 2 + 6 means start with 2 and add 6. Verify that these are equal with a picture (EXAMPLE: Draw 6 circles and then add 2 more, then draw 2 circles and add 6 more, for a total of 8 both times).

Does order matter in subtraction? Write on the board: 6 – 2 = 2 – 6. SAY: 6 – 2 means start with 6 and take away 2. What does 2 – 6 mean? Emphasize that we start from the left, so we have to start with 2 things and try to take away 6 of them. Show 2 objects. Ask a volunteer to take away 6 of them. Explain that the question doesn’t even make sense: if you start with 2 things, you can’t take away 6 of them. Give students counters and have them decide whether they can subtract the following: 3 – 4 and 4 – 3. Have volunteers show and explain their answers using the counters.

Subtract using circles. Have students use the subtraction model on Workbook page 77 to solve more subtraction problems like those above, and ask volunteers to say what each subtraction means. Tell students that you are going to try to trick them by including some that don’t make sense.

ExtensionHave students count the number of letters in each sentence by adding the number of letters in each word:

Joe’s birthday is today. (4 + 8 + 2 + 5 = 19)Today is Joe’s birthday. (5 + 2 + 4 + 8 = 19)Is today Joe’s birthday? (2 + 5 + 4 + 8 = 19)

ASK: What do you notice? (the total is always 19, the same 4 numbers are in all the sentences) Do you know why the answer is always the same? (the same 4 words are in all the sentences, just rearranged)

ACTIVITIES 1-2

1. Toss 8 two-colour counters. ASK: How could the colours show an addition sentence? Could we count red first and then yellow? What number sentence would we get? What if we counted yellow first and then red—what number sentence would we get?

2. Pairs of students roll 3 dice and add the numbers together. Each student privately writes a number sentence. If they get the same total, they get one point. If they get the same numbers in the same order, they get two points. If you don’t have dice, either make egg-carton dice or red, blue, and yellow dice from coloured paper (see NS Part 1 – Introduction; use BLM Cubes).

Number Sense 2-30

MORE EXAMPLES: 5 – 2;2 – 7;10 – 5;3 – 9;6 – 7.

EXAMPLES:

7 – 3 =

7 – 9 =

Literacy— Domino Addition by Lynette Long Reinforces addition skills for numbers 0–12 using dominoes.

CONNECTION

ONLINE GUIDE

More Extensions: investigate symmetry in addition tables and order in subtraction. Includes BLM Addition Tables and BLM Subtract Two Ways.

More sentences:The blue hat is big The big hat is blue. Is the big hat blue? Is the blue hat big?


Locating numbers on a number line. Draw a partial number line from 34 to 41:

34 35 36 37 38 39 40 41

Tell students that you want to find 39. Start at 34 and ASK: Is this it? (no) Try 35, 36, and 37. SAY: I wonder if we missed 39. I’m at 37 now and we haven’t found it yet. How can we be sure we didn’t miss it? (39 is greater than 37) PROMPT: What comes first, 37 or 39? Emphasize that as long as you’re still at numbers that come before 39, then you know you didn’t miss it. Continue searching one at a time for 39 until you find it. Repeat with other numbers on partial number lines.

Introduce the strategy of starting in the middle. Draw a number line from 46 to 56 and tell students you want to find 53. Explain that instead of starting at 46 and checking all the numbers until you get to 53, you’re going to take a shortcut. Start in the middle of the number line (at 51) and decide whether to go right or left. ASK: Is 53 more than 51 or less? (more) Which way should I go on the number line: right or left (this way or that way)? Look to the right of 51 because 53 is more than 51. Explain that now you have fewer numbers to check. Repeat for various number lines and numbers.

Adding 1 on a number line. Remind students that to find 3 + 1, they can find the number they say after 3—it is the number that is one more than 3. Draw a number line on the board and tell students that instead of counting on from 3 and saying the next number, they can draw a leap from 3 to the next number. Cut the frog out of BLM Frog. Place the frog on the 3 and move it one leap forward to the 4.

The frog ends up at the next number after 3, or 3 + 1. Write: 3 + 1 = 4. Add 1 to several other numbers. Use partial number lines that begin at larger numbers. EXAMPLE: on a number line from 34 to 47, find 37 + 1. At first, place the frog on the number line where students need to start and have them just add 1. Then have students both locate the starting number and add 1. Students can draw a dot (instead of a frog) at the starting number and draw arrows for the leaps.

NS2-31 Adding with a Number Line Pages 79-81

CURRICULUM EXPECTATIONSOntario: 1m25; 2m1, 2m2, 2m3, 2m5, 2m6, 2m7, 2m21WNCP: 2N9, [R, CN, V, C]

VOCABULARY number line leap

GoalsStudents will locate numbers on a partial number line and then use number lines to add.


Can count to 100 Can order numbers Understands the concept of more

MATERIALS

BLM Frog (p XXX)BLM Finding Missing Numbers (p XXX) BLM Blank Number Lines (p xxx)

Using an organized list.

PROBLEM SOLVING

0 1 2 3 4 5 6 7

Literature— Rock It, Sock It, Number Line by Bill Martin Jr. and Michael Sampson. Counting to 10 and back again—silly rhyming verses and lots of fun!

CONNECTION

71Number Sense 2-31

Adding 2 or 3 on a number line. Start by drawing two leaps in order to add 2. EXAMPLES: 4 + 2, 27 + 2, 72 + 2, 38 + 2, 46 + 2. Then draw three leaps in order to add 3. EXAMPLES: 5 + 3, 17 + 3, 26 + 3, 39 + 3. At first, draw a big dot where students need to start for them, then have students do both steps (finding the place to start and drawing the leaps).

Then mix up examples that require adding 1, 2, or 3. Students need to decide how many leaps to add—1, 2, or 3—depending on the second addend.

Connect adding on a number line to adding by counting on. Draw a number line from 0 to 10 on the board and tell students that you want to add 5 + 3. ASK: What number should I start at (5)? Draw a big dot at the 5. ASK: What part of counting on to add is this like? (saying 5 with your fist closed) How many leaps should I draw starting at the 5? (3) What part of counting on is this like? (saying the next three numbers after 5)

Connect the number sentence to the number line. Write the addition sentence (5 + 3 = 8) below the number line. Point out that leaps start and end at numbers that we see in the addition sentence. Show that 5 is where the leaps start and 8 is where they end. Connect the numbers in the number sentence to the numbers on the number line.

Repeat with several examples, having volunteers join the numbers. Then draw number lines and have students fill in the missing numbers in the number sentences based on the number lines.

Find the missing number. Draw more number lines that show addition but leave out the second number in the addition sentence. Include examples that require more than 3 leaps.

Have students practise writing addition sentences for models and vice versa. Copy BLM Blank Number Lines onto overheads, mark the starting point, draw the leaps, and have students write the corresponding addition sentences. Or write number statements on the board (EXAMPLE: 24 + 5) and have students draw the corresponding models and solve the addition on laminated (re-usable) copies of the BLM.

ExtensionHave students compare adding 3 + 4 and 4 + 3 on the same number line. They can do 3 + 4 above the line and 4 + 3 below it. Give several examples of this sort. ASK: What do you notice?

PROBLEM SOLVING

Connecting

PROBLEM SOLVING

Making a model.

BLM Word Problems

ONLINE GUIDE

Matching games with BLM Addition Sentence Memory and BLM Adding Cards

ONLINE GUIDE

EXTRA PRACTICE

BLM Finding Missing Numbers.

4 5 6 7 8 9

5 + 3 = 8

4 5 6 7 8

+ 2 =

EXAMPLES:

43 + = 48

51 + = 57

58 + = 63


NS2-32 Adding by Counting OnPages 82-87

CURRICULUM EXPECTATIONSOntario: 1m26; 2m1, 2m2, 2m3, 2m4, 2m5, 2m7, 2m70 WNCP: 1N10; 2N9, [R, C, CN]

VOCABULARY next

GoalsStudents will add by counting on. Students will discover that adding by counting on is easier when starting from the larger number.

Add 1 by finding the next number. Draw three circles on the board. Count the circles one at a time and write the numbers above the circles as you count.

Then add one more circle and ASK: Now how many circles are there? Erase the numbers above the circles and count again. Rewrite 1, 2, and 3, and add 4 above the last circle. Repeat for several examples. Then, instead of erasing the original counting, SAY: I might as well leave the numbers there and just write the next number above the new circle. Draw 5 circles on the board and count them, writing the numbers above the circles as you count.

Add another circle and ASK: What is the next number after 5? Write 6 over the last circle and the addition sentence.

Repeat with several examples where students add 1 to a number, but have volunteers finish the model. Emphasize that the answer is just the next number you say when counting. Write on the board the sequence of numbers from 0 to 10. Emphasize that the numbers are written in order and have students add 1 to more one-digit numbers without drawing pictures. EXAMPLES: 4 + 1, 8 + 1, 0 + 1. Continue writing the numbers up to 20 and have students add: 15 + 1, 18 + 1, 12 + 1, 17 + 1. Bonus 73 + 1, 52 + 1, 65 + 1, 39 + 1

Count the number of boys in the class together. SAY: Pretend we have one new boy in the class. Then how many boys would there be in the class? Repeat for girls.

Add 2 by finding the next two numbers. Draw the picture in the margin on the board. Repeat the lesson for adding 1, but add 2, first to numbers from 0 to 10, then to numbers up to 20. EXAMPLES: 4 + 2, 8 + 2, 13 + 2, 16 + 2.


Can order numbers to 20 Can count to 20 orally and in writing Can add Knows that “next” means “right after” Knows that numbers can be added in any order

MATERIALS

pencil case pencil crayons a paper domino (modelling 2 + 7)ball or paper object (for Activity 1)

Real World

CONNECTION

1 2 3

1 2 3

1 2 3 4 5

1 2 3 4 5 6

5 + 1 = 6

On BLM Next, students move game pieces to the next square on a game board.

ONLINE GUIDE

73

Add by saying the next several numbers. Start by adding 5. Draw the following picture on the board:

1 2 3

SAY: The first 3 circles are already counted. Have a volunteer say the next 5 numbers to add 3 + 5. Pose the problem as a challenge; SAY: 5 is a lot of numbers to keep track of! Check the volunteer’s answer by writing the next 5 numbers above each of the white circles. If the volunteer is incorrect, invite another volunteer to do it. If the volunteer is correct, have another volunteer add 8 + 7 using the same method. SAY: 7 is a lot of numbers to keep track of. Who thinks they can keep track of 7 numbers to find 8 + 7? Repeat with other volunteers, all adding 7 to a number. Discuss the strategies you observe. (EXAMPLES: Write a mark for each number said, hold up a finger for each number said, keep track of both numbers all along (9 is 8 + 1, 10 is 8 + 2, and so on until 15 is 8 + 7), write the numbers after 8 and stop when 7 numbers are counted)

Review counting on your fingers. Have students count to 10 on their fingers, starting with the thumb. Then hold up several fingers at once as though you counted this way and ask students what number you counted to.

Use your fingers to keep track of how many numbers you said. SAY: I would like to add 6 + 8, but saying 8 numbers after 6 is a lot of numbers to keep track of. I am going to use my fingers to help keep track. I can hold up one finger for every number I say after 6. Demonstrate and ASK: What is the first number that comes after 6? (hold up your thumb when students say 7) And the next number? (hold up your thumb and forefinger when they say 8) Continue in this way. After 10, ASK: How many numbers have I said after 6 so far? (4) How do you know? (you’re holding up 4 fingers) How will I know when to stop? (8 fingers will be up) Continue to count. When you have 8 fingers up, ASK: What was the last number we said? (14) Write on the board: 6 + 8 = 14. Verify by drawing 6 coloured circles and 8 blank circles all in a row. Write 6 on top of the last coloured circle, then write the next eight numbers on top of the blank circles. Count the blank circles to show eight numbers are counted after you said 6. Have students solve more addition problems individually using their fingers. Gradually increase the difficulty. EXAMPLES: 4 + 5, 13 + 6, 11 + 8, 38 + 9.

Model mistakes in counting on to add. EXAMPLES: count faster or slower than you hold fingers up (i.e., only hold up 2 fingers while adding 3); skip or repeat numbers; say some numbers in the wrong order. Challenge students to say what you do wrong each time. Then have students work in pairs to

ACTIVITY 1

Catch. (See NS Part 1 – Introduction) Students say the next number after the one you say. Repeat with students saying the next two numbers. Finally, students just say the number plus 2.

Literature— Two Too Many by Jo Ellen Bogart One Monkey Too Many by Jackie French Koller

CONNECTION

PROBLEM SOLVING


PROBLEM SOLVING


Number Sense 2-32

BLM Add to Find the Picture, Apples and Missing Addends.

ONLINE GUIDE


add by counting on: 7 + 3, 6 + 5, 8 + 3, 9 + 6, 7 + 7, 10 + 5. One person writes the question, the other adds by counting on and writes the answer. Then they switch roles.

Compare adding by counting on to adding with a hundreds chart. Write on the board: 5 + 3. Colour only square 5 on a hundreds chart. SAY: Starting at 5 is like saying 5 with your fist closed. Then circle the next 3 squares and SAY: Circling the next numbers is like saying 6, 7, 8 while raising 3 fingers one at a time. Instead of seeing how many numbers you have circled, you see how many fingers you have up.

Order in addition doesn’t matter (review). Tape a paper domino showing 2 and 7 to the board. SAY: I want to know how many dots there are.

Cover the 2 and SAY: I know there are 2 dots here, so I can count on from 3. Demonstrate doing so while pointing to each of the 7 dots on the right side: 3, 4, 5, 6, 7, 8, 9. Write: 2 + 7 = 9. Now turn the domino around. Cover the 7 on the left side and SAY: I know there are 7 dots here, so I can count on from 8. Demonstrate doing so while pointing to each of the 2 dots on the right side: 8, 9. Write: 7 + 2 = 9. ASK: I added 2 + 7 by counting on and I added 7 + 2 by counting on—did I get the same answer both ways? (yes) Why did that happen? (because order doesn’t matter in addition)

Choosing which number to count on from. Write on the board: 2 + 9 = 9 + 2 =

ASK: Will these questions have the same answer? (yes) How do you know? (note what happened before with the domino) Explain that since you know that both problems have the same answer, you want to do the easier one. SAY: Let’s try it both ways and find out which one is easier. ASK: How would I solve 2 + 9? How many numbers would I count? What number would I start at? (count 9 numbers starting at 3) Demonstrate doing so. How would I solve 9 + 2? (count 2 numbers starting at 10) Demonstrate doing so. ASK: What is easier—to count 9 numbers starting at 3 or to count 2 numbers starting at 10? (Demonstrate both again.) Which would be faster? (counting 2 numbers starting at 10) Emphasize that when mathematicians see two problems that they know have the same answer, they can be smart and pick the easier one to do.

Have students predict which will be faster to do: 3 + 7 or 7 + 3. Have students try it both ways and have volunteers circle the faster and easier way. Repeat with the examples in the margin. Tell students to look at the questions they circled as being easier. Point to the first number of each circled question and ASK: Is this number the bigger number or the smaller number? What do students notice? (the first number is always the bigger number) Explain to students that they can make 4 + 9 into an easier problem just by writing the bigger number first: 9 + 4. Demonstrate adding by counting on both ways.

Challenge volunteers to try adding more numbers both ways using blanks. At first, give volunteers the numbers to count from and the number of blanks. EXAMPLE:

PROBLEM SOLVING

Connecting

PROBLEM SOLVING

Selecting tools and strategies, Reflecting on other ways to solve a problem

PROBLEM SOLVING


3 + 7 7 + 3

8 + 4 4 + 8

1 + 9 9 + 1

2 + 10 10 + 2

5 + 1 1 + 5

8 + 3 3 + 8

Bonus 65 + 2, 48 + 3

75Number Sense 2-32

6 + 3 6

3 + 6 3

Then have volunteers write the numbers and blanks, and discuss how they know how many blanks to draw (start at the first number and draw the second number of blanks or vice versa). Have students do similar questions individually in their notebooks. EXAMPLES: 3 + 8 or 8 + 3; 9 + 1 or 1 + 9; 14 + 2 or 2 + 14. Bonus 23 + 4 or 4 + 23

ASK: Which is easier—to count starting from the bigger number or the smaller number? (from the bigger number) Why do you think that is? (there are fewer numbers to count).

Counting on to find missing addends. This time, students count on from the first number until the total. They find the second number by seeing how many fingers are up.

ExtensionIn the game Scrabble, players make words from letters. Some letters are worth more points than others, and the points are written right next to the letter. Tell students that you have the following letters: A1 B3 I1 T1 S1 H4 Y4

Have students determine how many points various words are worth: HI (4 + 1 = 5)IS (1 + 1 = 2) BY (3 + 4 = 7) Bonus SHY, BAY, SAY, THIS

Students who finish quickly can make their own words using the same letters and count the total points for each word.

Then show these letters: A1 C3 E1 H4 O1 B3 F4

How many points is each of these words worth? CAT, BET, HAT, THEBonus BATH, CHAT, BOAT, COAT, TEACH

Again, students who finish quickly can make their own words from the letters and count the total points for each word.

NOTE: Students who spell incorrectly should not be discouraged; simply ensure that students are adding correctly. Only correct spellings if students request you do so.

PROBLEM SOLVING


ACTIVITY 2

Missing Number Game. (See NS2 Part 1 – Introduction) Use single–digit numbers only. Partners count on using fingers to see how many numbers they say after the first number to get to the second number.


NS2-33 Subtracting with a Number LinePages 88-92

CURRICULUM EXPECTATIONSOntario: 1m26; 2m1, 2m2, 2m3, 2m5, 2m6, 2m7, 2m70WNCP: 1N10; 2N9, [R, C, CN, V]

VOCABULARY number line remaining leftover subtract minus take away forwards backwards

GoalsStudents will subtract by drawing leaps on a number line.

Draw circles in a row to subtract. Draw 7 circles in a row (because circles are easy to draw) and count them by writing the numbers above the circles. Cross out the fourth circle and then count the remaining (leftover) circles by writing the numbers underneath the circles:

1 2 3 4 5 6 7 1 2 3 5 6 7

Write the subtraction sentence: 7 - 1 = 6.

Taking away the last circle(s) makes it easier to count the leftover circles. Draw several rows of 7 circles on the board with a different circle crossed out in each row:

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

Have volunteers count the remaining circles by writing the numbers underneath. ASK: Did we always get the same answer? (yes, 6) Where are the numbers under the circles the same as the numbers above the circles? (before the crossed out circle) Why did that happen? (once a circle is crossed out, the count changes) How is counting the leftover circles easier when you take away the last circle? (just look at the numbers above the circles; the numbers underneath will be the same as the numbers above)

Have students count how many circles are left over:

1 2 3 4 5 6 7 8


Can count to 10 Understands the concept of more Understands arrows and direction Understands addition on a number line Knows to say the number before to subtract 1 Knows to say the number before two times to subtract 2

MATERIALS

BLM Blank Number Lines (p xxx)BLM Which Way Does the Frog Leap? (p xxx) BLM Adding and Subtracting (p xxx)

PROBLEM SOLVING

Drawing a picture, Reflecting on what makes the problem easy or hard

77Number Sense 2-33

ASK: How did you count the leftover circles? Emphasize that when you take away 1 circle, you just have to move back 1 number to find the number of leftover circles. To demonstrate, draw a leap from 8 to 7.

Subtract 1 using a number line. Draw a number line from 0 to 8. Discuss how you can subtract 1 using the number line by drawing a leap going backwards from the 8. SAY: We don’t need to draw circles; we can just use the number line to find the number before. (If you create a large number line on the floor with masking tape, students can act out the leap.)

Show students several number lines with a leap drawn backwards and ask them to solve the subtraction problems. EXAMPLES:

5 - 1 = 43 - 1 = 66 - 1 =

Repeat the exercise, but this time draw a number line that ends at 10 and a dot on the starting number. Have students draw leaps and complete subtraction sentences. EXAMPLES: 7 - 1 = 10 - 1 = 4 - 1 = 9 - 1 =

Subtracting larger numbers. Repeat the above for subtracting 1 but use 2 leaps to subtract 2. Then subtract larger numbers. Ensure students understand that the number of leaps is the number being subtracted. Use the same process for subtracting on a number line as for adding:

Literature— The Shopping Basket by John Burningham How many objects are left after subtracting 1? Students can subtract by counting back and then count to check.

CONNECTION

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 40 41 42 43 60 61 62 63 64 65 66

Literature and Social Studies

CONNECTION ACTIVITY 1

Monster Musical Chairs by Stuart J. Murphy Mathematically, you could discuss why the number of chairs is always one less than the number of monsters. You could count how many monsters are playing in each round and emphasize the connection between subtracting 1 and how many are left or the connection between adding 1 and how many are on the side. Emotionally, you could discuss how each monster is feeling. Before starting the game, do the monsters expect it to be fun? Are they excited about winning or worried about losing? What happens when one of the monsters is out—how does he or she feel? After the second one is out, ASK: How is the second one out feeling? How is the first one out feeling? Why do you think the first one out is smiling? As you continue reading, ask students to make connections to their own experiences playing musical chairs: how did they feel when they lost, or watched a friend lose early? ASK: How can we change the rules so that the game is more fun for everyone—so that everyone gets to play and no one has to worry about winning or losing? (accept all answers) Play through their ideas. See also Co-operative Musical Chairs (NS2-3).


• Use a big dot to show where to start subtracting from (find the first number on the number line). • Decide how many leaps to draw by looking at the subtraction sentence (the number being subtracted tells how many leaps to draw). • Decide how to find the answer to a subtraction sentence from a number line (where the leaps end).

How to find the answer. ASK: Which number on the number line tells you how many circles are left? (the number that the last leap points to) Use pictures of number lines to emphasize the answer. Then have students individually answer questions with dots drawn on the number line and have volunteers explain their work.

Choosing between adding and subtracting. Tell your students that you want to find 7 - 3. ASK: How can I use a number line to help me? Take answers and then draw a number line on the board. Invite a volunteer to put a big dot where you should start drawing leaps. Then ASK: How many arrows should I draw on the number line? Should I go forwards or backwards? How do you know? What symbol shows us that the arrows go backwards instead of forwards? Repeat with more addition and subtraction problems. Then give students BLM Which Way Does the Frog Leap? Finally, have students solve the following problems individually on a blank number line (BLM Blank Number Lines): a) 6 - 2 b) 6 + 2 c) 27 + 3 d) 27 - 3 e) 15 + 4 f) 15 - 4 g) 29 - 3

BLM Adding and Subtracting. Students add and subtract at the same time, e.g., 5 - 3 + 2. To help keep track, students might use a different colour to draw the leaps for different numbers. Remind students that we

ACTIVITY 2

Have students form a human number line (from 1 to however many students are in the class). Each student has a number, which they need to remember; ensure that everyone knows their number by asking in random order. Give the student with the highest number a ball. This student says a subtraction sentence starting with his/her number and students use the ball to count off “leaps” on the line to solve the subtraction sentence. EXAMPLE: Player 17 might say 17 - 4. Player 17 then tosses the ball to Player 16 and the class counts 1, 16 tosses to 15 and the class counts 2, and so on to 4. When the class counts 4, the player who caught the ball says “17- 4 is 13” (that’s the player’s number). Player 13 then says a new subtraction sentence and play continues until the ball reaches player 1.

ACTIVITY 3

Students form a human number line as in Activity 2 and play the same game, but they have the option of adding or subtracting. Start with a middle player. The goal is to make sure everyone plays in as few turns as possible. Students must stay within the limits (e.g. if there are 17 players, Player 15 is not allowed to say 15 + 3).

More Activities: sorting games and matching games with BLM Adding Cards, BLM Subtracting Cards, and BLM Subtraction Sentence Memory.

ONLINE GUIDE

EXTRA PRACTICE

79Number Sense 2-33

read from left to right, so we do 5 - 3 first because it is the first one we see. Then we add 2 to the answer.

Extensiona) Have students make subtraction sentences from groups of numbers that are not in order: i) 6 2 8 ii) 7 8 1 iii) 5 3 8 iv) 3 9 6

b) Have students make subtraction sentences using three of the four numbers given: (in order) i) 9 8 2 1 ii) 5 3 4 2 iii) 7 6 4 3 (not in order) iv) 8 10 1 2 v) 4 3 7 10

c) Isobel’s phone number is 633 7523. Her older brother, Soren, remembers their phone number this way: 6 - 3 = 3, 7 - 5 = 2, and 5 - 2 = 3. Can you find subtraction sentences in these phone numbers?i) 532 8624 ii) 871 4312 iii) 963 9725 iv) 853 9817 v) 880 9909 Bonus 209 1192 (20 - 9 = 11 and 11 - 9 = 2)


NS2-34 Subtracting by Counting BackwardsPage 93

CURRICULUM EXPECTATIONSOntario: 1m26, review; 2m1, 2m2, 2m3, 2m5, 2m7 WNCP: 1N10, review; [R, CN, C]

VOCABULARY counting on counting back backwards subtract minus take away

GoalsStudents will subtract by counting back from 20.

Practise counting back from 5 to 0. Write 0 1 2 3 4 5 on the board and tell the students to say the numbers out loud together, but backwards. Point to each number as the students say it.

Then erase 2 and leave a space or replace it with a blank line: 0 1 3 4 5. Point to each number and the space as students count backwards from 5, remembering to say 2. Repeat several times with different missing numbers. EXAMPLE: 0 1 2 3 5.

Continue to have students say the numbers in order backwards, but with more missing: • Two numbers, but not two in a row. EXAMPLE: 0 1 3 5• Two numbers in a row. EXAMPLE: 0 1 4 5• More than two numbers. EXAMPLES: 0 2 5, 3 5• All numbers. .

Always point to each number or space starting at the right.

Count back from 10 to 0. Repeat the sequence of exercises above, starting from 7, then from 9, and finally from 10.

Count back from any number up to 20. Repeat the sequence of exercises above, starting from 13, then 15, then 18, and finally 20.

Make the connection between counting forwards and counting backwards. For example, if students are not sure if 8 comes after 9 when


Can count forwards Can find the missing number in a list Understands the concepts of more and less Understands that subtraction means “take away” Understands that 5 - 3 is always 2, no matter how you solve itKnows the minus sign (-) Understands that quantity is the last number you say when counting Can identify first and last in a group or list Can identify leftovers Can count forwards and backwards Can count on using fingers

MATERIALS

BLM Number Cards Template (p xxx)BLM Number Chains (p xxx)BLM Number Trains (p xxx)

81Number Sense 2-34

counting backwards, they can count forwards from 8 and check to see if 9 comes right after 8.

Count backwards between any two given numbers from 0 to 100. Have the class count forwards from 40 to 49 and then backwards from 49 to 40. Do the same (count forwards and backwards) for 70 to 79, 60 to 69, and 90 to 99. Then have students count forwards from 38 to 42 and then backwards from 42 to 38. Repeat for 29 to 33 and 67 to 71. Then ASK: What group of numbers comes after the thirties? (forties) What group of numbers comes before the forties? (thirties) What group of numbers comes before the sixties? (fifties) Before the nineties? (eighties) Before the twenties? (teens or 10 to 19) Then have students count back five numbers from: 43, 81, 92, 60, 22.

Ask students where people use counting back. Examples may include traffic lights (the number of seconds before you have to finish crossing the street), the countdown to the launch of a space shuttle, the countdown on New Year’s Eve, clocks counting down to the end of a game or match, time left on a microwave oven, and so on.

Spelling Backwards. Challenge students to spell words backwards (to develop the same type of memory skill as counting backwards). EXAMPLES: of, to, in, is, he, on, as, at, the, for, bat, hat, lip, bit, pit, zip, top, mop, zig, and zag. (If they are having trouble, have students spell the words forwards first and then backwards.) When one person has correctly spelled a word backwards, you can still ask other students to spell the same word backwards—this will allow more students to participate. Bonus Have students spell their own name backwards. Bonus Challenge students to think of words that are spelled the same

forwards as backwards such as pop, mom, dad, wow, and bib. Give Hints: What do babies wear when they eat? What do you call your mother? And so on. The following picture books involve counting backwards. You can read them aloud to the class or make them available for independent reading.

PROBLEM SOLVING

Connecting, Changing into a known problem, Reflecting on the reasonableness of an answer

Real world

CONNECTION

Games, activities, and discussions about real-life connections for counting backwards.

AT HOME ACTIVITIES 1-2

1. Prepare a set of cards marked 1 through 10 (see BLM Number Cards Template). Shuffle and place the cards face down in two rows of 5. Turn over one card at a time. If the card is a 10, place it face up in a separate pile. If it is not a 10, try to remember it then turn it over. Repeat with 9, 8, 7, and so on until 1. The goal is to finish as soon as possible. VARIATION: Play with numbers up to 20.Bonus Play with numbers up to 50.

2. Pairs put number cards (to 10, 20, or even 100) in a pile face down. Player 1 turns up the top card and Player 2 says the number that comes before. Players then switch roles.

Language Arts

CONNECTION

Interactive website for counting back from 20 to 0

ONLINE GUIDE

Literature

CONNECTION


One Less Fish by Kim Michelle Toft Ten Sly Piranhas: A Counting Story in Reverse by William Wise Mouse Count by Ellen Stoll Walsh Smokejumpers One to Ten by Chris L. Demarest Ten Seeds by Ruth Brown| Ten, Nine, Eight by Molly Bang

Review subtraction. Remind students how they subtracted 1 from a number by finding the number that comes before and how they subtracted 2 by finding the two numbers that come before.

Subtract any number by counting back. Write the numbers from 1 to 10 on the board. Then write: 7 7 - 3 =

Guide students to fill in the blanks with the next three numbers they would say when counting back from 7 and the answer to the subtraction sentence (which is the last number you say when counting back). Emphasize that in a subtraction sentence, the first number (7) tells us what to subtract from and the second number (3) tells us how many numbers to say when counting back. Have students do more problems individually. EXAMPLES:6 6 - 2 = 8 8 - 4 = 7 7 - 4 = 6 6 - 3 =

Then have students draw the correct number of blanks before solving a subtraction sentence.

Finally, have students decide both which number to start counting back from and how many blanks to draw.

Does it matter which number you count back from? Remind students about adding and order using 6 + 2 as an example. Students can start at 6 and draw 2 blanks or start and 2 and draw 6 blanks: 6 7 8 or 2 3 4 5 6 7 8

ASK: Does it matter which number you subtract from and how many blanks you draw for 6 - 2? Have students explain their answers. Then draw on the board: 6 5 4 or 2 1 0 ? ? ? ?

Explain that we can’t count back 6 times starting at 2 because there aren’t 6 numbers that are less than 2. We must start with the bigger number (6) and draw the smaller number of blanks (2).

Subtract by counting backwards on your fingers. Write 8 - 2 on the board. SAY: I am going to count back from 8 and I want you to tell me to stop when I have 2 fingers up. Then say “8” with a closed fist (thumb tucked under fingers), “7” with 1 finger (your thumb) up, and “6” with 2 fingers up. If students don’t tell you to stop, ASK: How many fingers am I holding up? Tell students that since you are holding up 2 fingers, you can stop counting, so 8 - 2 = 6. Demonstrate subtracting more numbers from 8 in this way. Repeat until all students actively identify when you have enough fingers up.

PROBLEM SOLVING

Revisiting conjectures that were true in one context

83Number Sense 2-34

Tell students you want them to find 39 - 4. ASK: How many fingers will you be holding up when you get to the answer? (4) Remind students to concentrate on both the numbers they say when counting back and the number of fingers they are holding up. Then ask a volunteer to count back from 39 to find 39 - 4. Repeat with other subtraction sentences starting at 39. Ask how the volunteers knew to start at 39.

Finally, have students subtract from different numbers individually in their notebooks. EXAMPLES: 15 - 3, 48 - 5, 64 - 2.

Potential mistakes in counting back to subtract. Model several incorrect ways of counting back, such as counting faster or slower than you hold fingers up (EXAMPLE: hold up 2 fingers while subtracting 3), skipping or repeating numbers, saying some numbers in the wrong order or counting forwards to start (EXAMPLE: I get 8 - 4 = 6 because I counted 8 9 8 7 6). Challenge students to tell you what you are doing wrong each time. Then have volunteers subtract by counting back: 7 - 3, 6 - 1, 18 - 3, 49 - 2, 37 - 4, 80 - 5.

On BLM Number Chains and BLM Number Trains, students can add and subtract the same number in turn to discover that adding and subtracting the same number results in no change. This prepares students to learn about the connection between addition and subtraction.

Connect subtraction on a number line to subtraction by crossing out circles. Write 6 - 2 and draw a number line from 0 to 6 with 6 circles underneath it. ASK: Which number in the subtraction sentence tells you how many leaps to draw? (the second number) Which number tells you how many circles to take away? (the second number) Emphasize that we draw a leap for every circle we take away. Every time you remove a circle, you move back one number:

ExtensionASK: What pattern is in the answers to these questions: 7 - 1, 8 - 2, 9 - 3, 10 - 4, 11 - 5, 12 - 6? Why did that happen? Find another set of subtraction problems that all have the same answer.

BLM In the Bag

ONLINE GUIDE

PROBLEM SOLVING

Making a model

0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6

EXTRA PRACTICE


NS2-35 Comparing Number SentencesPages 94-95

CURRICULUM EXPECTATIONSOntario: 2m2, 2m5, 2m6, 2m7, 2m22, 2m23 WNCP: 2N10, [CN, R, V, C]

VOCABULARY leaps forwards backwards number line plus sign (+)minus sign (-)

GoalsStudents will use number line representations and models to compare addition and subtraction sentences from the same fact families.

Compare number lines representing subtraction sentences. Draw three number lines on the board from 0 to 10. Show 8 - 3 = 5, 8 - 2 = 6, and 8 - 7 = 1 with a dot to start and arrows for the leaps back. Write the corresponding number sentences underneath the number lines. ASK: What is the same about all three number lines? (They all go from 0 to 10; they are the same length; the big dot is always at the 8; the leaps/arrows all go back.) What is different about them? (The number of leaps changes; the number where the arrows/leaps stop is different.)

Compare subtraction sentences. ASK: What is the same about all three number sentences? (They all include 8; 8 is always the first number; 8 is always the number you’re taking away from; they are all subtraction sentences; they all have three numbers; they all have an equal sign; the answer is always on the right side.) What is different about them? (The answers are different; the number you take away from 8 is different.)

Relate the subtraction sentences to their number lines. • The number sentences all start with 8 and 8 is always the number that you’re taking away from. ASK: What’s the same about the number lines because of this? (the big dot is always at the 8; the leaps start at the 8) • The arrows point back (left) in all of the number lines (the leaps go backwards). ASK: What’s the same about the number sentences because of this? (they are all subtraction sentences) • The answers are all different in the number sentences. ASK: What’s different about all the number lines because of this? (where the arrows stop) • The number of leaps is different in all the number lines. ASK: What’s different about all the number sentences because of this? (the number you are taking away)

PROBLEM SOLVING

Connecting


Can read a number line Can draw number line representations for number sentences and vice versa Can count on to add Can count back to subtract Can draw models to add and subtract Can identify different attributes (e.g., shape, size, colour)

MATERIALS

(none)

85

Compare addition and subtraction sentences to their number line representations. Draw two number lines on the board. Show 8 - 3 = 5 and 5 + 3 = 8. Have volunteers write the corresponding number sentences. First compare the number lines—how are they the same and different?—and then compare the number sentences.

Relate the number sentences to their number lines. • On the number lines, the leaps go in different directions. ASK: What’s different about the number sentences because of this? (the sign: it’s minus (-) when the leaps go back and plus (+) when the leaps go forwards) • The number of leaps is the same in each picture. ASK: What’s the same about the number sentences because of this? (the second number in each number sentence) • The big dot is at different places in both pictures. ASK: What’s different about the two number sentences because of this? (the first number in each number sentence) • The leaps go between the numbers 5 and 8 in both pictures. ASK: What can you say about the number sentences because of this? (the same three numbers are in both number sentences)

Generalize with different examples. Write the number sentences 3 + 6 = 9 and 9 - 6 = 3 on the board. ASK: How are the number sentences the same and different? How will the number lines be the same and different? PROMPTS: How many leaps will there be? What direction will the arrows point in? What two numbers will the leaps go between? Other than where you put the big dot, what is the only difference between the two number lines? (the direction of the arrows) Draw the two number lines.

The same picture can represent different number sentences. Draw:

ASK: How does this picture show 3 + 6 = 9? (3 dark squares + 6 white squares = 9 squares altogether) How does it show 6 + 3 = 9? (6 white squares + 3 dark squares = 9 squares altogether) How does it show 9 - 6 = 3? (Take away the 6 white squares from the 9 squares and you have 3 dark squares left. You can demonstrate by covering up the 6 white squares.) How does it show 9 - 3 = 6? (Take away the 3 dark squares from the 9 squares and you have 6 white squares left. Demonstrate by covering up the 3 dark squares.) Draw more pictures and ask volunteers to write a number sentence and explain their choice. Continue prompting for more addition or subtraction sentences until students find all the possibilities for each picture. Then have students find number sentences from pictures individually (see margin for examples). EXAMPLES: 4 number sentences

8 number sentences

Number Sense 2-35

PROBLEM SOLVING

Connecting

PROBLEM SOLVING

Revisiting conjectures that were true in one context

PROBLEM SOLVING

Drawing a picture

Bonus 12 number sentences

(ANSWER: size: 3 + 6 = 9, etc.; shape: 5 + 4 = 9, etc.; colour: 1 + 8 = 9, etc.)


NS2-36 Subtracting by Counting OnPages 96-97

CURRICULUM EXPECTATIONSOntario: 2m4, 2m7, 2m22, 2m23WNCP: 2N10, [R, C]

VOCABULARY more fewer solve

GoalsStudents will use addition to subtract.

Review adding by counting on. Tell students that you want to find 4 + 5 by counting on. ASK: What number tells you the number to start at, the 4 or the 5? What number tells you how many fingers to be holding up when you stop? Tell students to stop you and start counting; say “4” with your fist closed (thumb tucked under), “5” with one finger up (the thumb), and so on until you have five fingers up. If students don’t stop you when you have five fingers up, ASK: How many fingers do I have up? Is that the number that I’m supposed to be holding up when I stop? What number did I say when I held up my fifth finger? If they don’t remember, SAY: Listen carefully for the number I say when I hold up my fifth finger. That will be the answer to 4 + 5. Then repeat the counting on process. Repeat with more examples.

Review finding the missing addend by counting on. Write on the board: 4 + = 9. ASK: How is this problem different from finding the answer to 4 + 5 = ? How can I use counting on to solve the first problem? Explain that instead of knowing that you have to have five fingers up when you stop, you know what number you need to say to stop. ASK: Does anyone know what that number is? (9) Tell students to listen carefully as you count on from 4 and to stop you when you say “9.” Then count on using your fingers and when students tell you to stop, ASK: How many fingers am I holding up? Fill in the blank: 4 + 5 = 9. Repeat with more questions, always asking students to tell you when to stop. Next, have volunteers write the answer on the board after students tell you to stop. Finally, have volunteers count on and write the answer to more missing addend problems.

Subtract by counting on. ASK: How does finding the missing number in 4 + = 9 help you find the answer to 9 - 4 = ? Draw this picture as a reminder:


Can find the missing addends in addition problems Can count back to subtract Can count on to add Understands the relationship between addition and subtraction sentences

MATERIALS

(none)

PROBLEM SOLVING


87

ASK: How could you use counting on to subtract 9 - 4? If no one answers, SAY: You could count on from 4 and see how many fingers you are holding up when you say “9.” Remind students that what they are really doing is finding the missing number in 4 + = 9, but that’s okay because 9 - 4 = has the same answer. Repeat with several examples.

Compare counting on and counting back to subtract. Ask a volunteer to find 10 - 1 by counting on. Ask another volunteer to find 10 - 1 by counting backwards. ASK: Which way is easier—counting on or counting back? (answers may vary) Which way is faster? (counting back) Why? (When counting back, you only have to say, “10, 9” and see that you are holding up one finger, whereas when counting on from 1, you have to count from 1 to 10 and see that you are holding up nine fingers.) Explain that there are often many ways to solve a math problem, so you should use your brain to pick the best way. Have students solve the following problems using both methods, to decide which is faster: 9 - 8 = 9 - 2 = 8 - 1 = 8 - 7 = 10 - 1 = 10 - 8 =

Then use larger numbers: 38 - 2 = , 76 - 73 = , 99 - 4 = , 82 - 79 = .

Number Sense 2-36

PROBLEM SOLVING


ACTIVITIES 1-2

1. Missing Number Game. (See NS Part 1 – Introduction) The first number should have 2 digits and the second number should have 1 digit. The partner can count up after the first number. EXAMPLE:

2. Number Balance. If you have a number balance available, have students play with it to discover the pattern for which weight goes down if you put one on each side in different places (the one further out with the higher number will go down). Then have students put two cubes on one side of the number balance and determine where to put a third cube on the other side to balance. Students record their findings and make a discovery (the distance of the third cube from the centre is equal to the sum of the distances of the other cubes from the centre). Then have students use the number balance to solve missing addend problems. For example, students can solve 3 + = 9 by placing a cube on 3 on one side, a cube on 9 on the other side and seeing where they need to put another cube for the number balance to balance.

PROBLEM SOLVING

Problem Solving

27 5 27 32

Drawing to be done


NS2-37 Subtracting in Word ProblemsPages 98-99

CURRICULUM EXPECTATIONSOntario: 2m5, 2m26WNCP: 2N9, [CN]

VOCABULARY how many and joined altogether in total more take away are left not left/went away still more/longer…than

GoalsStudents will solve word problems involving the addition and subtraction of two-digit numbers.

How many more does Sara have than Ron (or vice versa)? Write on the board: “Sara has 12 marbles” and “Ron has 8 marbles”.

ASK: How are the two sentences the same? (they are both talking about marbles) How are they different? (Sara and Ron are different; the number of marbles is different) Who has more marbles? (Sara) How many more marbles does Sara have than Ron? (4) Count up from 8 to verify this. Write on the board: Sara has 4 more marbles than Ron.

Repeat with other questions, but have students individually write the sentence saying who has more objects and by how many. Emphasize that if they don’t know how to spell a word, they should look for it on the board. EXAMPLES: Sara has 5 candies. Ron has 7 candies.

How many more apples than oranges (or vice versa)? Now write on the board: “Sara has 8 apples” and “Sara has 5 oranges”. ASK: How are the two sentences the same? (they are both talking about what Sara has; they are both talking about fruit) How are they different? (apples and oranges are different; the number of each is different) Does Sara have more apples or oranges? (apples) How many more? (3) Write on the board: Sara has 3 more apples than oranges.

Have students do several problems individually. EXAMPLES:Sara has 6 apples. Bonus Ron has 62 apples.Sara has 10 oranges. Ron has 58 oranges.

Combine both types of problems. Use different objects and contexts. See Workbook page 98.


Can add Can subtract

MATERIALS

2 dice for each student 1 two-colour counter for each student BLM How Many Fewer? (p XXX)BLM How Many More and Fewer? (p XXX)

89

Associate vocabulary with addition or subtraction. Write several word problems on the board and read them to the class, and ask students to identify key words and phrases that tell you whether to add or subtract. Students might make a plus or minus sign with their hands to show their answer. Create a T-chart with the headings + and -. Take each word or phrase, one at a time, and place it in the + column or the - column as the students tell you.

EXAMPLES:Problems and key words/phrases

+ -

There were 10 children playing hide and seek. Three more joined them. How many are there now? Replace “more joined them” with “left,” then “went away.”

more joined

left went away

There are 3 big balls. There are 7 little balls. How many balls in total?

Replace “balls in total” with “more little balls than big balls” (emphasize the difference between this use of “more” and “three more joined”), then “fewer big balls than little balls.”

in total

more ... than

fewer ... than

Ron picked 6 flowers. His mother gave him 4 more flowers. How many flowers does Ron have altogether?

altogether

Ron picked 6 flowers. His mother took 4 flowers away. How many flowers does Ron have now?

took ... away

ExtensionOn BLM The Score (p XXX), students will have to determine when to add and when to subtract to find the scores. Bonus Redo the BLM with different instructions: Red is leading by 3.

Number Sense 2-37

Sorting

CONNECTION

NOTE: “More” can indicate addition or subtraction. (How many more are there? How many more … than …? Four more joined.) Put the word in both columns. Do the same with other vocabulary as necessary. Note also that “three left” and “how many are left” both indicate subtraction, but for different reasons.

ACTIVITY

Give each student a pair of dice and a coin or two-colour counter. Have them create word problems using the numbers they roll on the dice and the coin toss (heads means addition, tails means subtraction). Students should illustrate their problems in their journals and say them aloud or act them out.

JOURNAL

BLM How Many Fewer? and BLM How Many More and Fewer?

ONLINE GUIDE


NS2-38 More Missing NumbersPages 100-101

CURRICULUM EXPECTATIONSOntario: 2m1, 2m3, 2m7, optional WNCP: 2N9, [V, R, C]

VOCABULARY number line count on count back missing number

GoalsStudents will find missing numbers in subtraction sentences.

Use addition to find the number being subtracted from. Review the connection between adding and subtracting using the models on Workbook page 95. Then introduce the models on page 100:

Addition: 5 + 3 = 8

Subtraction: 8 - 3 = 5

Have volunteers circle the total number of boxes in each number sentence: 5 + 3 = 8 8 - 3 = 5

Explain how to turn the model for one sentence into the model for the other:

ASK: Did we change the total number of boxes by changing the model? (no) Write on the board: 2 + 7 = . Have a volunteer draw the model and write the answer. Then write: - 7 = 2. ASK: Can we get a model for - 7 = 2 by using the model [the volunteer] drew? Have another volunteer do this. ASK: Did we change the total number of boxes? Emphasize that the number of boxes is still the same, so the total number is still the same. ASK: Where in the subtraction sentence is the total number of boxes? (in the blank) Write 9 in the blank.

Have students individually solve more problems with, and then without, models. EXAMPLES: 7 + 2 = so - 2 = 73 + 4 = so - 4 = 35 + 5 = so - 5 = 5

Bonus 17 + 3 = so - 3 = 17 4 + 15 = so - 15 = 4

Use number lines to find the number being subtracted from. Write on the board: 27 + 4 = and - 4 = 27. Draw a number line from 26 to 33 and have a volunteer use it to find 27 + 4. Then ASK: How would you


Understands the relationship between addition and subtraction Can add and subtract on a number line Can count backwards to subtract and forwards to add

MATERIALS

sheet of paper to use as place marker

91

use the number line to find 31 - 4? Draw the 4 leaps going backwards from 31 underneath the number line. Explain that since you moved forwards 4 from 27 to get to 31, you know that you have to start at 31 and go backwards 4 places to get back to 27. You can find the number to start moving back from by moving forward from where you want to end up.

Illustrate this with another model. Put a place marker, such as a sheet of paper, on the floor. Tell a volunteer that this is where you would like him or her to end up after taking 4 steps in a particular direction (point in the direction). Invite suggestions for finding the volunteer’s starting point. Students might recommend guessing and checking. Emphasize the merits of this strategy; students will get closer to the right place every time, and this is a good strategy that mathematicians use often. But you’re thinking of another strategy. ASK: How can I start from the sheet of paper to find the starting point? (walk 4 steps in the opposite direction—walking 4 steps back will get you to the sheet of paper again)

Transfer this back to the number line: If I want to take 4 steps in that direction (point to the students’ left) to get to 27, I need to move 4 steps from 27 in the other direction (point to the students’ right) to find my starting point. Repeat with various examples, and then have students work individually. EXAMPLES: - 2 = 37 - 3 = 58 - 5 = 29

Counting forwards to find the number being subtracted from. Explain that by using number lines, students are counting forwards to find the missing number. EXAMPLES: - 5 = 33 - 4 = 28 - 6 = 47

Write on the board: - 38 = 4. Explain that to do this question, you should start at 4 and count out 38 numbers. Begin doing so, and then say that you lost track of how many numbers you said. ASK: Can I do this an easier way? Remind students that when counting forwards they will get the same answer whether they start from the bigger number or the smaller number. You would get the same answer counting 4 numbers after 38 as counting 38 numbers after 4. ASK: Do you think that will be easier? Let a volunteer try it. Write on the board: 38 + 4 = 42 so 4 + 38 = 42. But then 42 - 38 = 4. Write 42 in the blank. Repeat for various subtraction sentences. EXAMPLES: - 38 = 1 - 47 = 4 - 25 = 3

Now have students decide whether they need to switch the order of the numbers or not. EXAMPLES: - 28 = 4 - 4 = 49 - 2 = 19 - 28 = 3

Different strategies. When students finish Workbook page 101, have volunteers explain to the class how they found the missing number in - 26 = 5. Emphasize that there are often many ways of solving the same problem. The methods shown in this lesson include: use a number line starting at 26, count 5 numbers forwards after 26, use the fact that - 5 = 26 was already done and - 26 = 5 will have the same answer. Other methods: use a hundreds chart or count forwards 26 numbers after 5 (although the latter will take a while).

Number Sense 2-38

PROBLEM SOLVING

Working backwards

PROBLEM SOLVING


PROBLEM SOLVING



NS2-39 Missing Numbers in Word ProblemsPages 102-106

CURRICULUM EXPECTATIONSOntario: 2m1, optionalWNCP: 2N9, [R]

VOCABULARY altogether joined left not went still

GoalsStudents will write number sentences for stories and find the missing number.

Missing numbers in addition stories. Write several addition stories with a missing number (as on Workbook page 102) on the board. Vary the position of the missing number. Have students write the corresponding number sentence, with a blank or box in place of the missing number. Demonstrate with one example.

Review how to find the missing number in addition sentences such as + 4 = 7, 3 + = 8, or 2 + 7 = .

Then explain that if students know how to write the number sentence for the story and can fill in the blank, then they can find the missing number in any story. Demonstrate doing so by doing each step separately. Emphasize that even though the story involves addition, students might need to subtract to find the missing number. Let students practise this with the questions on Workbook pages 102 and 103.

Missing numbers in subtraction stories. Repeat with subtraction stories. You may need to spend more time reviewing how to find the missing number in subtraction sentences such as - 3 = 4 or 8 - = 6. In the first case, add (4 + 3); in the second case, subtract (8 - 6).

Again, emphasize that while the number sentence involves subtraction, students might need to add to find the missing number. Students can practise with the questions on Workbook pages 103 and 104.

Missing numbers in addition and subtraction stories. Write missing number stories with three number sentences and have students determine which number sentence matches the story. EXAMPLES:

Tegan has 5 stickers.

Daniel has stickers.

Together, they have 11 stickers.

5 + = 11 11 + = 5 5 - = 11


Can find missing numbers in addition and subtraction sentences Can read simple words

MATERIALS

BLM Number Words in Word Problems (p XXX)

Splitting into simpler problems

PROBLEM SOLVING

93

There are 9 people.

5 of them are girls.

of them are boys.

9 + 5 = 9 - 5 = 5 - = 9

Bonus

Ahmed ate 53 peas.

Rosa ate 57 peas.

Rosa ate more peas than Ahmed.

53 + 57 = 53 - 57 = 57 - 53 =

Now mix up stories that require addition with those that require subtraction and have students decide which symbol is required (+ or -), write the appropriate sentence, and then find the missing number. Remember: depending on where the missing number is in a number sentence, addition sentences may be solved by subtraction and subtraction sentences may be solved by addition.

BLM Number Words in Word Problems. Students will write the numbers above the number words before they solve the problems.

Number Sense 2-39

EXTRA PRACTICE


NS2-40 Making 10 Pages 107-109

CURRICULUM EXPECTATIONSOntario: 2m1, 2m7, 2m22WNCP: 2N10, [R,C]

VOCABULARY making 5 making 10 fingers up fingers down fingers altogether

GoalsStudents will find many combinations of numbers that add to 5 or 10.

Find the second addend (to 5) using your fingers. Hold up all your fingers on one hand and ASK: How many fingers do I have up? Then hold up 1 finger and ASK: Now how many fingers do I have up? (1) And how many are down? (4) What is 1 + 4? (5) How do you know? (we have 5 fingers on each hand; 1 up plus 4 down is 5 altogether) Repeat with several examples, including 0 up or all 5 up. SAY: I want to know what number with 3 makes 5. Write on the board: 3 + = 5. ASK: How could I use my 5 fingers on one hand? How many fingers should I hold up? (3) Show 3 fingers up. ASK: What does the number of fingers I’m not holding up tell me? (what to add to 3 to make 5) Add labels to the number sentence and have a volunteer fill in the blank: 3 + 2 = 5

fingers up fingers down

Students should recognize that the total number of fingers up and fingers down equals 5. Complete more addition sentences this way, including sentences with 0 as an addend. Then write similar sentences on the board for students to complete individually. EXAMPLES: 2 + = 5, 5 = 0 + .

Find the second addend (to 10) using your fingers. Repeat the above using both hands, and pairs adding to 10.

Find the first addend using all fingers on one or two hands. Review with students that if numbers add up to 5, they use all the fingers on one hand; if numbers add up to 10, they use all the fingers on both hands. Write on the board: + 7 = 10. Remind students that the first number shows the number of fingers up and the second number shows the number of fingers down. Show students how, if you start with 10 fingers up and then put down 7 fingers for the second number, the 3 fingers remaining will be the first number. Have students individually solve more such problems.


Understands having 5 fingers on each hand and 10 on two hands Can find missing addends

MATERIALS

pre-made dice with top and bottom numbers adding to 5 (or 10) a deck of cards BLM Ten-Dot Dominoes (p xxx)BLM Ten Wins! (pp XXX–XXX)BLM Cubes (p xxx)

BLM Pairs Adding to 5BLM Five-Dot Dominoes

ONLINE GUIDE

EXTRA PRACTICE BLM Ten Wins!

EXTRA PRACTICE BLM Ten-Dot Dominoes

95Number Sense 2-40

More activities to practice finding pairs that add to 10- a card game and a dice game.

ONLINE GUIDE

Check for pairs in an organized way. Write three numbers on the board: 4, 5, 6. SAY: I want to circle the pair of numbers that add to 10. ASK: Does 4 make 10 with either of the next two numbers? (yes, the 6) Students may use their 10 fingers to check; if they hold 4 fingers up, they can easily see that 6 fingers are down. Circle the 4 and the 6.

Repeat with 2, 3, and 7. ASK: Does 2 make 10 with either of the next two numbers? (no) If students hold up 2 fingers they can see that the number of fingers they have down (8) is not in the list. Then cross out the 2.

Then SAY: look at the last two numbers. ASK: Do they make 10? (yes) Circle the 3 and the 7. Repeat with more groups of three numbers where two total 10: either circle the first number with one of the other two, or cross out the first number and circle the other two.

Then write four numbers on the board: 3, 4, 5, 6. Check whether each number in turn makes 10 with another number in the list: 3 does not so cross it out, 4 does so circle 4 and 6. Finally, move on to lists of 5 or 6 numbers. ExtensionUse a partner and your fingers to find ways to add to 10 that involve more than two addends. EXAMPLE: first 3 up, next 3 down, next 1 up, next 2 down, last 1 up, gives: 3 + 3 + 1 + 2 + 1 = 10. One partner holds up fingers, the other partner writes the addition sentence.

Next, using a model of 10 dots in a row with vertical lines between them, find many ways of adding to 10 using two or more addends. Note the advantage of a model that does not involve your fingers: you can write the answer while looking at the model.

Let everyone in the class individually write as many sentences as they can in one minute (the time it takes the “fast” hand to move all the way around the clock), each on a separate strip of paper. Then build the poster: Select random students to place one of their strips on the poster, then ask for volunteers who have a different number sentence to add it. When no more volunteers step forward, ASK: Did anyone find as many number sentences as this on their own? Emphasize the value of working together: a group can do more, and sometimes more quickly, than an individual.

Have students sort a set of dominoes into “totals 10” and “doesn’t total 10.” Discard the pile that doesn’t total 10 and turn the remaining dominoes upside down. Students use these dominoes to play a game in pairs. Player 1 picks a domino, covers one half, and shows Player 2 the other half. Player 2 guesses the hidden number of dots. Player 1 informs Player 2 whether the guess is correct, too low, or too high. Player 2 continues guessing until the answer is correct. Players then switch roles. Play until all students consistently guess correctly without hints.

ACTIVITY

Making an organized list

PROBLEM SOLVING

4 5 6

2 3 7

EXAMPLES: 2 + 8;3 + 3 + 4;1 + 2 + 3 + 4; 2 + 2 + 1 + 5.


Add 10 on a hundreds chart by moving down one row. Draw the first two rows of a hundreds chart on the board. Shade the squares showing 3. Have a volunteer circle the next 10 numbers after 3 the reading pattern. Then point to each circled number and say, in turn, 3 + 1, 3 + 2, 3 + 3, until you reach the 10th circled number and say 3 + 10. ASK: What is 3 + 10? (13) Repeat to find the next 10 numbers after 7. Have students look at the shaded number and the number they get by adding 10. Compare the locations of 7 and 17 on the hundreds chart. ASK: If you know where 9 is, how can you find 9 + 10? (just look directly underneath) Have a volunteer verify this by circling the next 10 numbers using the reading pattern.

Then add 10 to larger numbers using other rows from the hundreds chart, such as 31 to 50 or 61 to 80. ASK: When you go down a row in the hundreds chart, what digit stays the same? (the ones) What digit changes? (the tens) How does it change? (the tens digit goes up by 1) Does this make sense? (Yes, when you add 10 to a number, the number of tens goes up by 1, but the number of ones stays the same.)

Have the first three rows of a hundreds chart visible for all students to see (for example, on an overhead projector). Review ways of finding a number in the first two rows (7 is closer to 10 than to 1; 17 is right under 7). Then have students add 10 by finding the number directly under the number you are adding to. EXAMPLES: 6 + 10, 14 + 10, 12 +10, 9 + 10, 18 + 10.

Add 10 to larger numbers. Students first need to find the number they are adding to and then move down a row. Review strategies for finding larger numbers. EXAMPLE: To find 38, find the ones digit (8) in the first row and then move down the column to find 38. Once you find 38, add 10 by moving down a row.

NS2-41 Adding 10 and Subtracting 10 Pages 110-113

GoalsStudents will add and subtract 10 by moving up or down on a hundreds chart. Students will understand that the tens digit changes while the ones digit does not.


Can count on to add Can count back to subtract Knows the reading pattern Can identify the tens and ones in two-digit numbers Can find numbers on a hundreds chart

MATERIALS

the first 3 rows of a hundreds chart (for overhead projector) several tens and ones blocks

CURRICULUM EXPECTATIONSOntario: 2m20, 2m26WNCP: 2n9, 2n10

VOCABULARY hundreds chart reading pattern previous numbers


PROBLEM SOLVING

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

97

Subtract 10 on a hundreds chart by moving up a row. Draw the first three rows of a hundreds chart. Remind students that a hundreds chart is like a number line divided into rows. If you were to cut the rows of a hundreds chart and put them beside each other, you would get a number line. ASK: How could I subtract 10 on a number line? (move back 10 leaps) How could I subtract 10 on a hundreds chart? (move back 10 squares) Write 23 - 10. Shade the square with 23. Explain that you will move back 10 squares by circling the 10 squares that come before 23. Demonstrate this, and explain that when you get to the beginning of a row, you have to start at the end of the row above it. Then ASK: What is 23 - 10? (13) Subtract 10 from more numbers this way, but have volunteers circle the 10 squares. Leave the hundreds charts on the board if possible. ASK: Where is the answer compared to the number you started with? Is there an easy way to find the answer? PROMPT: When adding 10, we could just move down a row; what can we do to subtract 10? (move up a row) Have students try this for several questions and then check by circling the 10 previous numbers. Does it work? Show a large hundreds chart and have students subtract 10 by moving up a row. Again, students will first need to find the number on the hundreds chart and then move up a row.

Add 10 using base ten blocks. Write on the board: 36 + 10. Have a volunteer show 36 using a model of tens and ones blocks. Then add another tens block to the volunteer’s blocks. Explain that you started with 36 and added 10. ASK: What number is that? (46) Repeat with various numbers. ASK: When I add 10, which digit changes? (the tens digit) How does it change? (It goes up by one; note that the ones digit stays the same because you didn’t add any ones blocks.) Have volunteers do several similar questions by drawing tens and ones blocks (don’t add 10 to any number in the nineties). EXAMPLES: 45 + 10, 68 + 10, 70 + 10, 31 + 10.

Subtract 10 using base ten blocks. Write on the board: 35 - 10 = . Have a student model 35 using tens and ones blocks. Demonstrate removing a tens block. ASK: What is left? (25) ASK: When we take away a ten, how many tens are left? (2) How many ones are left? (the same amount, 5) Which digit changed? (the tens digit) How did it change? (it’s one less) Which digit stayed the same? (the ones digit) Have students subtract 10 from more two-digit numbers by drawing the tens and ones blocks and then crossing out a tens block. Then ask again which digit changed and how.

Then have students subtract 10 from multiples of 10 by simply subtracting 1 from the tens digit (i.e., without drawing the tens and ones blocks and crossing out a tens block). EXAMPLE: 40 - 10. ExtensionSubtract 20 using two tens blocks. Write on the board: 26 - 20. Show 2 tens blocks and 6 ones blocks. ASK: How many tens blocks will I take away to subtract 20? (2) How many blocks are left? (6 ones blocks) Subtract 20 from more numbers.


PROBLEM SOLVING

Number Sense 2-41

Bonus Subtract 30 using three tens blocks. EXAMPLES:38 - 30, 35 - 30, 53 - 30.


Review adding 10 to a number. Have students solve several questions in the following progression:

a) Fill in the tens digit only, for EXAMPLE: 47 + 10 = 7.b) Fill in the ones digit only, for EXAMPLE: 14 + 10 = 2 . c) Fill in either missing digit (mix up which digit is missing). d) Add 10 by filling in both digits. Remind students that when adding 10 to a number only the tens digit changes; the ones digit remains the same.

Review subtracting 10 from a number. Have students solve several questions in the following progression:

a) Fill in the tens digit only, for EXAMPLE: 47 - 10 = 7.(Emphasize that if the tens digit is 0, you don’t write it, for EXAMPLE: 17 - 10 = 7, not 07.) b) Fill in the ones digit only, for EXAMPLE: 14 - 10 = , 36 - 10 = 2 . c) Fill in either missing digit (mix up which digit is missing). d) Subtract 10 by filling in both digits.

Remind students that when subtracting 10 from a number only the tens digit changes; the ones digit remains the same.

Group piles of counters that make 10. Give each student 20 counters. Tell students to make a pile of 3 counters, a pile of 5 counters, and a pile of 7 counters. Write on the board: 3 + 5 + 7 = . ASK: Which two piles together make 10? (3 and 7) Tell students to put those piles together and verify that they make 10. ASK: How many are in the other pile? (5) How many altogether? (15) How do you know? (10 + 5 = 15) Count all the counters to make sure there are 15. Repeat with various triples. EXAMPLES: 2, 4, and 8 (group 2 and 8), 1, 3, and 9 (group 1 and 9). Emphasize that

NS2-42 More Adding and Subtracting 10 Pages 114-116

GoalsStudents will add and subtract 10 to a number without using concrete materials. Students add three numbers by grouping the two that make 10.


Can count on to add Can count back to subtract Knows the reading pattern Can identify the tens and ones in two-digit numbers

MATERIALS

20 counters for each student

CURRICULUM EXPECTATIONSOntario: 2m1, 2m2, 2m7, 2m26WNCP: 2N10, [R, V, C]

VOCABULARY hundreds chart reading pattern previous numbers

99Number Sense 2-42

it doesn’t matter which two piles make 10. Remind students that order doesn’t matter when adding: 2 + 4 + 8 = 2 + 8 + 4 = 10 + 4 = 14.

Draw a model. Draw three groups of circles, similar to piles of counters, on the board: 7 circles, 4 circles, 3 circles. ASK: Which two groups make 10? (7 and 3) Colour those two groups. ASK: How many are in the other group? (4) How many circles altogether? What is 10 + 4? (14) Repeat with various triples, but this time have volunteers colour the two groups that make 10. Finally, give students similar problems and have them draw the model themselves.

Add three numbers by circling two numbers that make 10. Have students solve 4 + 5 + 6 by drawing a model and finding two groups that make 10. Circle the two numbers that were combined into the group of 10:

4 + 5 + 6

ASK: What number is not circled? (5) Write 4 + 5 + 6 = 10 + 5. Explain that 4 and 6 make 10 and 5 is left over, so 4 + 5 + 6 is 10 + 5.

Repeat with more examples, this time having volunteers circle the two numbers that are grouped to make 10. Then point out that if students know the pairs that make 10, they don’t even need a model. Give students questions where the two numbers that make 10 are circled (see margin for example). Then leave out the circles and let students circle the two numbers that make 10 themselves.

Extensions1. Add and subtract with three-digit numbers. Have students add 10 to

numbers such as 97 or even 397 by counting the number of tens in the number. (There are 9 tens and 7 ones in 97, so adding 10 will result in 10 tens and 7 ones, or 107; there are 39 tens and 7 ones in 397, so adding 10 will result in 40 tens and 7 ones.) Be sure that students can read the number of tens in a number first, even for three-digit numbers. You might introduce three-digit numbers by telling them that the first two digits count the number of tens and the last digit counts the number of ones. Later, you can relate this to the hundreds digit, which is the number of hundreds (or groups of ten tens); a hundreds digit of 3 and a tens digit of 9 mean 3 hundreds (or 30 tens) plus 9 tens, or 39 tens altogether.

Have students subtract 10 from three-digit numbers, such as 108, by looking at the total number of tens rather than the tens digit. (There are 10 tens and 8 ones in 108, so when I subtract 10, there are only 9 tens and 8 ones, so 108 - 10 = 98.) Have students predict how they would add 100 to three-digit numbers.

2. Teach students to skip count by 10 from any number (EXAMPLE: 3, 13, 23, 33...) by repeatedly adding 10. Teach students to skip count back by 10 from any number less than 100 (EXAMPLE: 74, 64, 54...) by repeatedly subtracting 10.

Drawing a model, Visualizing

PROBLEM SOLVING

Using logical reasoning

PROBLEM SOLVING

EXAMPLE: 2 + 3 + 8 = 10 + =


Find the next number on a hundreds chart by adding 1. Remind students that they can find the next number on a hundreds chart by adding 1. Have volunteers find 23 + 1, 34 + 1, 16 + 1, and 8 + 1 on the first four rows of a hundreds chart. ASK: When adding 1, which digit changes and which digit stays the same? (the ones digit changes and the tens digit stays the same) Challenge students to find a two-digit number where both digits change when adding 1 (EXAMPLE: 19 + 1 = 20).

Have students find the missing number by adding 1 and then check their answer using the large hundreds chart:

7 34 18 29 31 12

Find the number below a number on the hundreds chart by adding 10. Draw the first two rows of a hundreds chart on the board as a reference. ASK: If we know 13 is in one box, what is the number that goes in the box right below it? (23) Going down one row in a hundreds chart is like doing what? (adding 10) What digit changes when we add 10 to a number? (the tens digit) What digit stays the same? (the ones digit) Remind students how to add 10 to a one-digit number, such as 7. ASK: How many tens are there in 7? (0) How many ones? (7) If we add 1 ten, how many tens will there be? (1) SAY: If we start with 0 tens and 7 ones and we add 10, we have 1 ten and 7 ones or 7 + 10 = 17.

Have a large hundreds chart available for viewing. Draw the following small pieces from the chart and ask students to find the missing numbers by adding 10:

NS2-43 Hundreds Chart Pieces Pages 117-119

GoalsStudents will add and subtract 1 and 10 from given numbers on pieces of a hundreds chart.


Can add and subtract 1 by finding the “right after” or “right before” number Can add and subtract 10 by moving down and up on the hundreds chart Can add and subtract 1 by changing the ones digit Can add and subtract 10 by changing the tens digit

MATERIALS

a large hundreds chart hundreds charts for each student (see BLM A Larger Hundreds Chart (p xxx)) BLM Missing Numbers (p xxx)BLM What’s Wrong (p xxx)BLM The Secret Number (p xxx)

CURRICULUM EXPECTATIONSOntario: 2m3, 2m5, 2m6, 2m26WNCP: 2N9, [R, V]

VOCABULARY ones digit tens digit row column reading pattern

101

4 7 9 10 8 6 3 5 1 12 17 16

Have students check their answers by looking at the hundreds chart. This will help them connect going down a row in the hundreds chart and adding 10.

Repeat with higher numbers. Give several examples between 10 and 30, 30 and 50, 50 and 70, and finally 70 and 90. Show students which rows to look in before having them verify their answers on the hundreds chart.

Then have students add 10 to find these missing numbers, but let students decide which rows to check to verify their answers themselves.

5 18 29 30 23 76 83 55

Find the next number and the number below (add 1 and 10). Have students find the missing numbers in these and similar hundreds chart pieces:

13 27 39 46 71

Use only examples that will fit onto a hundreds chart (e.g., do not ask students to find a number to the right of a multiple of 10 or a number below any number in nineties). Don’t let students refer to a hundreds chart while they work; give them a hundreds chart after they have finished the puzzles and have them find and outline their answers to check them. EXAMPLE:

13 14

24

Find the number before and the number above (subtract 1 and 10). Use the process for adding 1 and 10, as shown above.

Do we add or subtract 1 or 10? Have students decide whether they need to add or subtract and by how much (1 or 10):

37 18 20 15 55 40 74

48 90

Finally, have students add and subtract to complete these hundreds chart pieces:

25 23 89

54 50 74

Connecting. Reflecting on other ways to solve a problem

PROBLEM SOLVING

Visualizing, Representing

PROBLEM SOLVING

EXTRA PRACTICE BLM Missing Numbers

Number Sense 2-43


19 70

59 88

25 52

93

Students should check their answers at every stage using hundreds charts. This will help them see the connection between adding and subtracting 1 or 10 and positions in the hundreds chart.

Extensions1. Give students a copy of a hundreds chart. Have them use a blue

pencil crayon to colour all the squares with a digit 3 and a red pencil crayon to colour all the squares with a digit 5. ASK: Which squares are purple? (35 and 53) Why? (they have both 3 and 5) Then give students a blank hundreds chart (e.g. from BLM Blank Hundreds Chart) with no numbers and have them guess where the numbers are that have a digit 1. They should colour those squares red, and then guess where the numbers are that have a digit 0 and colour those squares blue. Then have them put an actual transparent hundreds chart the same size (e.g. from BLM A Larger Hundreds Chart) over their blank hundreds chart to see if they were correct.

2. Give students partially completed rows, columns, and then diagonals from a hundreds chart and have them fill in the missing numbers:

3. Give students BLM Hundreds Chart Puzzles (p xxx).

EXTRA PRACTICEBLM What Is Wrong? BLM The Secret Number

23 26 27

57

56

67

86 7711

22

45

54

103

Introduce number crossword puzzles. Show the following grid and clues:

Across Down 1. 53 + 10 1. 4 more than 572. 9 + 5 2. 44 - 10

Show students how to complete such puzzles by doing this one together. SAY: Each answer has two digits. ASK: What is the answer for 1 Across? (63) SAY: We start at the square marked 1 on the left side and go across. Write the two-digit number in the 2 squares. ASK: What is the answer for 2 Across? (14) SAY: We start at the square marked 2 on the left side and go across. Have a volunteer write the number as you did for 1 Across. SAY: You can check your answers for the Across questions by doing the Down questions. If the Down numbers match the Across numbers in the each square, you know your answers are correct. Then do 1 Down and 2 Down to check the Across answers (start at the square marked 1 or 2 at the top and move down). Explain that students may also solve the Down questions first and then see if they match the Across answers.

Solve many such puzzles. Questions should never include 2 two-digit numbers unless one of them is 10.

Extensions1. Include puzzles where students need to use the answer to a previous

clue to obtain another answer:

Across Down 1. 73 + 10 1. 4 more than 782. 20 + 5 2. 10 more than 2 Across

2. Include puzzles where the grids are different shapes:

3. BLM What Do They Make? asks students to decide which number statements make given numbers.

4. BLM Word Puzzle

NS2-44 Problems and Puzzles Page 120

Extension: Reading number words past twenty, with BLM Number words to 100 and BLM Number Word Serach to 100. On the word search some words are diagonal.

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Number Sense 2-44

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Number Sense 2 Part 1 − Introduction

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Transcript of Number Sense 2 Part 1 − Introduction