Number Sense Part 1 - PBworks

1Number Sense 1-

Number Sense Part 1

2 Teacher’s Guide for Workbook 1

Number Sense 1 Part 1

In this unit, students will explore the concept of number. They will count (match numbers with their corresponding quantities and numerals), put numbers in order, and compare quantities (more, less, fewer, as many as). They will also learn to add, subtract, and estimate.

Number Cards Write the numerals 0 through 20 on separate cards. These number cards will be used throughout the unit. BLM Numbers Template (p XXX) provides a template.

Daily RoutinesIncorporate counting into daily routines.

Lining Up. When students line up for recess or lunch, they can each pick a number card and line up in order according to their number. At first, have only as many cards as students; later, there can be more cards than students so that there are gaps in the numbers held by consecutive students.

Ordinal Numbers. When students learn ordinal numbers (NS1-22), use them to identify and call on students. EXAMPLE: Ask the 2nd person in line to open the door.

Counting 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 be finished a task when you say 4 will learn quickly that 5 comes right before 4 when counting back.

Recurring Games. The following games occur often throughout the unit. The rules and materials will vary as students learn more about numbers.

I Have —, Who Has —? Each student will need one card to play (see sample). The student with the card shown in the margin would begin by saying, “I have 3. Who has 7?” The person who has 7 on top would say, “I have 7. Who has [whatever is on the bottom of the card]?” At first, when only numbers 1 to 10 are available, students will have to play in smaller groups so that two people do not have the same number. Sometimes you will be asked to make the cards (see the template on BLM Game Cards, p XXX), sometimes students will be asked to make their own cards, and sometimes cards will be provided on other BLMs. The blank spaces at the top and bottom of each card are to be filled with numerals or other representations of numbers, such as an arrangement of dots, a representation using tens blocks, or an addition or subtraction sentence.

Dominoes. Make domino cards with numbers written in different ways (EXAMPLES: random arrangements of dots, base ten blocks, addition or subtraction sentences, numerals). BLM Blank Domino Cards (p XXX) provides a template for you to create cards. You will need to explain that the cards can be turned around even though the numerals won’t look like

Sample Card I have 3

Who has 000 0 000

33

Go to page 5

THE1

numerals any more. To start, give students 3 or 4 chains of dominoes and ask them to make the longest chain they can using those dominoes. SAMPLE CHAINS: [5,4], [4,6], [6,10], [10,7], [7,3], [3,2] and [6,3], [3,7], [7,8], [8,10] and [7,4], [4,5], [5,6], [6,2]. The second chain can replace domino [6,10] and the last chain can be placed in the opposite direction at the end of the chain, so that only [6,10] is left out. Demonstrate creating a long chain like this before asking students to play.

Go to Page —. First, make sure students can find the page numbers in their JUMP Math workbooks in the bottom left and right corners. Then ask them to turn to different pages, one at a time, in random order. Always ensure that the entire class has found one page before you ask students to turn to another. Students should point to where they see each page number. This will help students to grasp the order of the numbers.

Message Booklet. Create message booklets in which there is only one word on each page and the words are out of order. Instructions at the top of each page tell students which page to turn to next to find the next part of the message. For example, a message booklet for “The pig took a bath in the mud” would need 8 pages. Each page should be one-sided and should look like the sample in the margin.

If you want students to turn the pages in the order 1, 5, 3, 6, 2, 4, 7, 8, then page 5 would say “Go to page 3,” page 3 would say “Go to page 6,” 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 instructions regarding which page to turn to. Provide instructions orally to create an unlimited number of words and messages. Use messages that your class will enjoy.

Solitaire War. Give each student a deck of cards without the face cards (Jack, Queen, King). Tell students to separate the black cards from the red cards and then shuffle both “decks.” Then have students turn over the top card from each pile. If the black card is more than the red one, they can take the cards; if the red card is more than the black card, they lose both cards. If the cards are equal, remove them from each pile, place them face down, and play again, either keeping or losing all the cards involved. VARIATIONS: • War for Less: Players win if the black card is less than the red card. • Addition War: Players play two cards at a time from each deck and keep the cards if the black sum is larger than the red sum. • Difference War: Same as Addition War but players need the black difference to be larger than the red difference. Ensure that students always subtract the smaller number from the larger number. Students might find it helpful to count out the larger number in tokens or counters, and place them on the objects pictured on the smaller card (e.g., clubs, hearts) to see how many are left.

Number Sense 1


Saying the numbers in order from one to ten.

The concept of how many. Have ready six cards with two shapes on each card. Use circles, squares, and stars in different combinations. Vary the shapes on each card so that they are: • sometimes both big, sometimes both small, sometimes one big and one small; • sometimes close together, sometimes far apart; • sometimes black, sometimes white; sometimes one black and one white; • arranged various ways—side by side, one on top of the other, randomly.

Repeat with three shapes on each of six cards, and four shapes on each of six cards. Finally, make six cards with only one shape on each; vary the size, colour, and type of shape as before. (Alternatively, use the cards on BLM How Many?) Then show students sets of seven cards, six of which illustrate the same quantity, and ask students to identify the card that doesn’t belong. Repeat for each quantity (one, two, three, and four) at least once. Discuss what is the same and different about all the cards that do belong. Explain that you made the groups based on how many shapes were on each card. It didn’t matter what the shapes were, how big they were, where they were on the card, or what colour they were.

You must count each object only once. Arrange eight counters in a circle. SAY: I want to know how many counters are in this circle. I’m going to count them. Then demonstrate counting around the circle but keep going so that you count several dots twice. Does anyone notice? ASK: Am I allowed to count the same object twice? Emphasize that if you want to know

CountingNS1-1

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CURRICULUM EXPECTATIONSOntario: 1m1, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20WNCP: kN1, kN3, 1N1, 1N2, 1N3, 1N4, [R, CN, C]

VOCABULARY the numerals 1 to 10 number how many counting

GoalsStudents will use counting to find how many and will associate numbers (spoken) with the corresponding quantities and numerals.

PRIOR KNOWLEDGE REQUIRED

is able to colour and to circle a group of objects

MATERIALS

24 quantity cards (described below) or BLM How Many? (p XXX–XXX)8 counters 5 coloured tokens or paper circles BLM How Many? Part 2 (p XXX–XXX) number cards for 1 to 10 (see BLM Numbers Template (p XXX))

Looking for a pattern

PROBLEM SOLVING

One way to teach this using the song “One, Two, Buckle My Shoe.”

ONLINE GUIDE

how many there are, you have to count each object only once. Then ask students how you can know when to stop. Suggestions might include: • Cover up the first one you count with a small piece of paper. • Move objects already counted to a separate pile.

Change the arrangement of the counters (instead of a circle, perhaps two rows of four or a scattered arrangement) and use students’ suggestions. Does their method work?

Counting in different ways gives the same answer. Arrange seven counters in a row. ASK: Do you think I will get the same answer if I count them starting here (at the left) and then starting over here (at the right). Demonstrate counting in both directions. ASK: Why did we get the same answer?

Use five tokens or paper circles of different colours. Tape them randomly to chart paper or the board and count them, starting with the blue one. Then SAY: This time I am going to count starting with the yellow one. I am counting the same tokens. Who thinks I will get the same answer? Who thinks I will get a different answer? Have students count along with you and demonstrate getting the same answer. Repeat, starting with other colours.

Identifying the numeral with the number (spoken). Draw several capital or lower case letters and ask students to name the letters. Explain to students that just as we have symbols for the letters in the alphabet (E is “ee”), in math we have symbols (called numerals) for the numbers. Write the numerals 1 to 3 in order on the board, then say the numbers in order as you point to them. Erase the numbers, write the same numbers in random order, and have students say the numbers as you point to them. Gradually increase the difficulty by using more numerals.

EXAMPLES: 3 2 1 1 3 2 1 2 3 4 4 1 3 2 1 3 4 2 1 2 3 4 5 6 6 4 2 5 1 3 1 2 3 4 5 6 7 8 9 10 8 9 6 4 2 7 3 4 8 10 9 1 6

Have students put number cards in the correct order. Raise the bar by using more cards.

Identifying the numeral with the quantity. Write the numbers 1 to 4 on the board in order (1 2 3 4), leaving plenty of space below and around each one. Give each student one of the quantity cards used earlier in the lesson and have four volunteers tape a card next to or below the right number. Repeat with more volunteers. Then write the numbers 1 to 4 in random order and repeat with the students who have not yet used their cards. Repeat with the numbers 1 to 7 by adding cards from the first page of BLM How Many? Part 2 to the set (or make your own cards.) Then repeat with the numbers 1 to 10 and the second page of the BLM or your own cards.

Hold up various numbers of fingers, in random order, and ASK: How many fingers am I holding up? (Students should call out the answer.) Then write a numeral on the board and have students hold up the corresponding number of fingers.

5

Bonus

Number Sense 1-1

BLMs similar to Workbook p.1 for numbers 1, 2, 4, 5, 6, 7, 8, and 9.

ONLINE GUIDE


In a two-column chart, draw three different quantities (up to ten) in one column and the same three quantities, arranged differently and using different items, in the second column. (Alternatively, use cards from BLMs How Many? and How Many? Part 2.) For example, draw 4 stars, 5 dots, and 1 checkmark in the first column, and 1 heart, 4 squares, and 5 triangles in the second column. Have students match the items by quantity. Repeat several times, eventually including more quantities in each column and, later, arranging quantities and matching them 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. (You can write the numerals or use pre-made number cards.)

Match by CountingNS1-2

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CURRICULUM EXPECTATIONSOntario: km10, km15, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20 WNCP: kN1, kN3, 1N1, 1N2, 1N3, [R, CN, C]

VOCABULARY The numerals 1 to 10 how many number

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


understands the concept of quantity can join two figures with a line

MATERIALS

number cards from 1 to 10 quantity cards or BLM How Many? (see BLM Numbers Template (p XXX–XXX)), BLM How Many? Part 2 (p XXX–XXX)2-cm grid paper or BLM 2-cm Grid Paper (p XXX)various old magazines and catalogues (e.g. sports, clothing, toys) BLM Game Cards (p XXX)BLM Blank Domino Cards (p XXX)

1. A Counting Game. Pairs start counting at 1 and take turns saying the next number until they reach 5. The pair “wins” if the person who started counting also finishes. Demonstrate by playing the game yourself with a volunteer. Then have students play in partners. Have them repeat the game ending with 6, then 7, 8, 9, and 10. After students have played several times and counted to different numbers, ASK: Was it possible to win every time? What numbers do you need to finish with if you want to win? (5, 7, or 9)

2. Memory. Match quantities to quantities or numerals to quantities up

ACTIVITIES 1–8

Literature— What Comes in 2’s, 3’s, & 4’s? by Suzanne Aker.

One Gray Mouse by Katherine Burton.

Feast for 10 by Cathryn Falwell.

One Hungry Monster by Susan Heyboer O’Keefe.

CONNECTION

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

JOURNAL

77Number Sense 1-2

Extensions1. Hold up pictures of various objects (or the objects themselves) and ask

students to say what number the object rhymes with. EXAMPLES: a pen (10), a zoo (2), sticks (6), a line (9), a tree (3), a beehive (5), a gate (8), a door (4). Give each student one number to focus on, from 1 through 10 (exclude 7). Students draw that number of an object that rhymes with the number (EXAMPLE: three trees). Use the students’ work to build a class poem on a poster. Students can read the poem together as a class, with each student “reading” his or her own line.

2. Have students match by number, but tell them you are going to try to trick them by having groups of the same object. Remind students to match by number, not object.

3. BLM Many Ways to Colour 3 shows one way to colour three of the five given circles and allows students to find five more ways to do the same.

to 10. See BLM How Many? and BLM How Many? Part 2 for pre-made cards.

3. Have students make the numerals 1 through 10 out of clay, playdough, or pipe cleaners.

4. Give students 2-cm grid paper and have them colour any five squares. Discuss the differences between the various answers. Display the various arrangements on a poster titled “5.”

5. Give each student an old magazine or catalogue. Assign each student a number from 2 to 6. Students will find and cut out pictures where items are in groups of that many. Students can then form groups with other students who had the same number and pool their cut-outs to make a poster for each number.

6. Bring in packages that are labelled with numbers. (EXAMPLES: puzzles, marbles, cookies, pencils, pens, erasers, crayons, chalk, paper, Ziploc bags, garbage bags) Have students identify the numbers on the packages. Discuss why numbers are important. Students might wish to package a product themselves and write how many on the package.

7. I Have —, Who Has —? (see NS Part 1 − Introduction). Use the template on BLM Game Cards to make cards with numerals on top and dots on the bottom or different arrangements of dots on the top and bottom.

8. Dominoes (see NS Part 1 − Introduction). Use BLM Blank Domino Cards.

Reflecting on other ways to solve a problem

PROBLEM SOLVING

BLMs for more Tic Tac Toe boards

ONLINE GUIDE

Literacy

CONNECTION

SAMPLE:


There’s Order HereNS1-3

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CURRICULUM EXPECTATIONSOntario: km6, 1m1, 1m3, 1m5, 1m11 WNCP: kN1, 1N1, [R, CN]

VOCABULARY order

GoalsStudents will become familiar with the order of the numbers through exploration.


can associate the numerals 1 to 10 with the corresponding quantities can read the numerals 1 to 10

MATERIALS

number cards for 1 to 10 for each student (see BLM Numbers Template)number cards for 1 to 10 with letters on the other side (details below) JUMP Math Workbook (1 per student)BLM Find the Missing Numbers (p xxx)

Making an organized list.

PROBLEM SOLVING

Reflecting on the reasonableness of an answer.

PROBLEM SOLVING

Using order to find numbers quickly. Start by giving students number cards for 1, 2, and 3 and have them find and hold up the card that matches the number when you say it aloud. Suggest that they order their cards to make it easier. Add cards 4 and 5, then 6 and 7, and finally 8, 9, and 10.

Using order to solve puzzles. Students will work together in small groups for this part of the lesson. Mark the other side of several sets of number cards with the letters shown below (you will need one set with which to demonstrate and one set for each group). Front 1 2 3 4 5 6 7 8 9 10 Back B D E G L N O R U W

Distribute your set on the board with the numerals facing the class in order—spread them as far apart as you can—and have students arrange their cards in the same way. Then tell students to find the 1 and turn it over. What letter do they see? Turn your card over and reattach it to the board in a new row: 2 3 4 5 6 7 8 9 10 B Explain that if students turn over the numbers 5, 9, and 3 in that order, they will make a colour word. Do this together as a class—you with your cards and each group with theirs. 2 4 6 7 8 10 1 5 9 3 B L U E ASK: What word do you see? Have students show you something that is that colour. Have students repeat the task for each of the following groups of numbers: 8 3 2 (red), 1 8 7 10 6 (brown). Encourage students to check

BLM Find the Missing Numbers

EXTRA PRACTICE

9

the words they make against known colour words. Explain how checking that the words are spelled correctly is a way of checking that they have uncovered the numbers in the right order.

Repeat with words and a message instead of letters. (You will need to make new cards.) See the margin for a sample.

Putting the numbers in order. Have cards numbered 1 through 10 arranged on the board in order, but with some cards “missing.” (You can put the missing cards aside or on the ledge in random order.)

Have volunteers move the missing cards into the correct positions. Repeat for increasingly more complex arrangements, first having no two consecutive numbers missing and eventually asking students to order all the cards.

Joining dots in order. Draw numbered dots on the board for students to join in order. You might wish to have the dots spell a word for students to read. (The example in the margin reads “MATH.”)

Bonus

Number Sense 1-3

SAMPLE WORDS: 1 2 3 4 5 sat the pig a hat 6 7 8 9 10 in wig cat big has

SAMPLE MESSAGES: 2 9 3 10 4 7 (the big pig has a wig) 2 8 1 6 4 5 (the cat sat in a hat)

Go to page ----. (see NS Part 1 − Introduction) Use numbers up to 10. Observe students as they work. Do they look in the correct direction? For example, to find the number 2 after finding the number 6, do they know to look left, or do they look right first and then go back to the beginning?

ACTIVITY 1

2 43

1 5

2

1 3

1 2

1 2

2. Message Booklet. (see NS Part 1 − Introduction). Make a 10-page booklet that clearly shows a page number and a letter on each page. You can combine many on the same ten-page book by providing oral instructions instead of having the instruction “Go to page … “ in the booklet. A B E G I L M N R U: 1 8 5 7 1 6 (animal); 2 3 1 9 (bear); 4 9 3 3 8 (green); 8 10 7 2 3 9 (number)

3. Provide pairs of students with cards numbered 1, 2, 3, 4, 5. Player 1 shuffles the 5 cards. Player 2 removes one of the cards. Player 1 orders the remaining cards and Player 2 inserts his or her card in the right place. Progress to cards numbered 1 through 10.

4. On a long piece of thick paper, write the numbers from 1 to 10 equally spaced. Have students make a puzzle by cutting out jagged, curved, or straight lines between each pair of numbers. Partners can then solve each other’s puzzles. Discuss how knowing and using the order of the numbers helped them solve the puzzle.

5. Put a deck of cards in order as though it is brand new.

ACTIVITIES 2–5

Visual Art Students use different kinds of lines to make a puzzle.

CONNECTION

More message ideas.

ONLINE GUIDE


The Number That Means NoneNS1-4

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CURRICULUM EXPECTATIONSOntario: 1m1, 1m3, 1m5, 1m7, 1m11, 1m13, 1m20WNCP: 1N1, [R, CN, C]

VOCABULARY zero (0) none number letter

GoalsStudents will learn that the numeral 0 stands for no objects. Students will distinguish between numerals written correctly and incorrectly.


knows the numerals, sounds and quantities associated with numbers one through ten knows the alphabet

MATERIALS

number cards for 0 to 10 for each student BLM Count and Match (p XXX)BLM Circle the Numbers (p XXX)

Introduce zero. Hold up three fingers and ASK: How many fingers am I holding up? Repeat with different numbers of fingers. Then hold up no fingers and repeat the question. If students say “none,” tell them that mathematicians have come up with a number that means none. Ask if anyone knows what that number is. Does anyone know how to write that number? (0) Does anyone know how to say the number? (Say “zero.”) ASK: How many apples am I holding? (zero) How many grapes am I holding? Draw squares showing groups with different numbers of dots on the board, including zero dots. Ask how many dots are in each group.

Identifying the numeral 0 with the number (spoken). As in NS1-1, but include 0.

Taking away to make zero. Hold up three crayons. Drop one on the floor and SAY: One fell. How many are left in my hand? (two) Repeat until you get to zero crayons. Have three volunteers stand up. Tell each of them to sit down, one at a time, and ask students how many are left standing each time, until you get to zero people standing.

Everyone stands up. You ask a question (EXAMPLE: How many younger sisters do you have?) and all the students who answer “zero” sit down. Play until everyone is sitting down. You ask the first one or two questions, then let students who are sitting down take turns asking the questions. The goal is to try to get everyone sitting down in exactly three turns. If no-one answers zero, it doesn’t count as a “turn.” After each question, remind students how many turns are left. When there is only one turn left, students should try to think of a question that everyone will answer zero to. (EXAMPLE: How many tails do you have?) Challenge students to not repeat questions.

ACTIVITY 1

1111

Where does zero go on the number line? Write the numbers 1 to 10 in order on a number line and ASK: Where should 0 go? How do you know? When we counted from 3 to 0, which way did we go in the numbers—left or right (this way or that way)? Write 0 in the correct place to the left of the 1.

Counting zero objects. Draw several sets of squares and circles on the board. ASK: How many squares? How many circles? Include examples where there are no squares or no circles. Students can hold up the corresponding number of fingers to show the answer. Then write different numerals on the board (including 0) and again have students hold up the corresponding number of fingers.

Drawing zero objects. Have a volunteer draw three circles on the board, then another volunteer draw four stars, and then another volunteer draw zero hearts. Emphasize that drawing zero things is easy—you don’t have to draw any! Repeat with having students colour objects.

Numbers cannot be turned around. Bring a chair to the front of the room. Ask your students what object it is. Then turn the chair around to face the other way. Is it still a chair? Now put it on its side. Is it still a chair? Draw the chair in all three positions on the board. ASK: Are all of these chairs? When all students see that the chair is still a chair, ask them if they can do the same thing with letters. Draw a “c” on the board. Then draw it backward. Is it still a “c”? Then put it on its side. Repeat with “z” which looks like “N” when turned. It might be helpful to have the letters written on cards so that you can physically turn them around. Then draw a 3 on the board or hold it up on a card. ASK: Is 3 still a 3 when you turn it around? On its side? (Demonstrate doing so.) Are there any numbers that are still numbers when you turn them upside down? (8 and 0; 1 when it is drawn as a straight line) Draw several numbers two ways—correctly and incorrectly—and have volunteers circle the correct way.

ExtensionOn BLM Join Dots and Stars, students join dots to dots and stars to stars.


PROBLEM SOLVING

Activity and BLM asking students to identify numbers in postal codes and licence plates.

ONLINE GUIDE

2. Invite students to use numbers around the room to help them identify which numbers are written correctly on BLM Circle the Numbers. Students should carry the BLM with them on a clipboard as they walk around the room.

3. Using pipe cleaners, playdough, or clay, have students make the shape of the numeral 0.

4. Memory, I Have —, Who Has —? and Dominoes. (see NS Part 1 – Introduction) Play as in NS1-2, but include zero.

ACTIVITIES 2–4

Number Sense 1-4

BLM Count and Match

EXTRA PRACTICE


Draw numbers by starting at the big dot and following the arrow. Ask students to watch carefully as you draw a 7 on the board. ASK: Did I start drawing the 7 from the top or the bottom? Draw several more 7s to give every student a chance to see what you are doing. Ask a volunteer to come to the board and draw a big dot to show where you started. Ask for a suggestion on how you could show the direction to move in when drawing the 7. Tell students you will draw an arrow, and do so. Have volunteers draw a 7 the same way you did. Then tell them to watch carefully as you draw a 1. Draw several more 1s before asking a volunteer to add both the dot and the arrow showing where you started and what direction you went in. Repeat with a , emphasizing that it needs two starting points. Then move on to numbers with only curved lines (0, 3, 6, 8, 9) and then numbers with both straight and curved lines (5, 2). Have volunteers draw numbers the same way you did.

How calculators show numbers. Give each student a calculator. Draw the number 2 on the board and have students press the number 2 on their calculators. Compare the two numbers. (On a calculator, all lines are straight and only go up and down or side to side. The number 2 is usually curly or curved, with a more pointy corner at the bottom left. One or the other might be easier to draw.) Repeat with various numbers from 0 to 9. Have a dotted square “8” on the board (see below) that students can trace to show what they see on their calculators.

Writing NumbersNS1-5

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CURRICULUM EXPECTATIONSOntario: km10, 1m1, 1m3, 1m5, 1m7, 1m11, 1m13WNCP: kN1, kN3, 1N1, 1N3, [R, CN, C]

VOCABULARY the numerals from 0 to 10

GoalsStudents will write the numerals, first by tracing, then independently. Students will also write numerals as they appear on digital clocks and calculators (using only straight lines).


can hold a pencil and trace lines can join dots with a straight line

MATERIALS

BLM Calculator Numbers (p XXX) or BLM 2-cm Grid Paper (p XXX)a calculator for each student (to be used during the lesson and when students are completing Workbook pages 18, 19)

ONLINE GUIDE

Technology.

CONNECTION

EXTRA PRACTICE

Copies of the first two worksheets and four new BLMs, for students who need additional practice with counting and writing numbers.

13

Investigate “malfunctioning” calculators. Tell students that your calculator doesn’t work—it’s not showing the numbers properly. Draw for them what you see when you hit 0, 1, 2, 3, and 4 or use a transparency of BLM Calculator Numbers. (See margin)

Ask students what part of each number is missing. Have a volunteer draw it in.

Ask another volunteer to draw how they think your calculator will show 5. Have the dotted square “8” outlined for them to draw on. ASK: Why does the calculator show this number correctly? (Because the 5 doesn’t have the top right line in it.) Which numbers does the calculator show correctly? (5 and 6) Which numbers does the calculator show incorrectly? (0, 1, 2, 3, 4, 7, 8, 9) Are there two numbers that look the same on your calculator? (Yes, 6 and 8, and 5 and 9.)

Tell students that another calculator you have is missing the top left line: Challenge students to draw each number from 0 to 9 as it would appear on this calculator. Students can record their answers on BLM Calculator Numbers or on 2-cm grid paper. ASK: Which numbers does the calculator show correctly? (1, 2, 3, 7) Incorrectly? (0, 4, 5, 6, 8, 9) Are there two numbers that look the same? (Yes, 3 and 9.)

Repeat for other malfunctioning calculators. (When the middle line is deleted, 8 and 0 look the same. When the top line is deleted, 1 and 7 look the same. When the bottom left line is deleted, 5 and 6 look the same, as do 8 and 9. When the bottom right or bottom lines are deleted, no numbers look the same.)

Extensions1. On BLM Roman Numbers, students will count the shapes on playing cards to translate Roman numbers to English numbers.

2. BLM Counting Dots asks students to count the corners (marked by dots) of various shapes.

4. On BLM Missing Numbers, students fill in the missing number in Sudoku-like rows, columns, and boxes.

5. BLM Fractions asks students to count first the shaded squares and then all the squares, and to write the answer as a fraction.

6. Trace a number on a friend’s back. Can your friend guess the number?

13

I Have —, Who Has —? (p XXX). Include numerals as they appear on digital devices.

ACTIVITY

Looking for a pattern.

PROBLEM SOLVING


PROBLEM SOLVING

Using logical reasoning.

PROBLEM SOLVING

BLM How Many Things? (students count two different quantities in the same picture) and BLM Calculator Fun (a sample problem solving lesson which involves malfunctioning calculators)

ONLINE GUIDE

Number Sense 1-5


Counting Using a ChartNS1-6

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CURRICULUM EXPECTATIONSOntario: km6, km10, 1m1, 1m2, 1m5, 1m7, 1m11, 1m21 WNCP: kN1, kN3, 1N1, 1N3, [R, CN, C]

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 numbered squares, as follows: Alternatively, copy and cut strips from BLM Counting Cubes.

Teach students to count using a chart. Provide each student with several 2-cm connecting cubes (different numbers of cubes for each student). 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? Ask students if anyone notices a pattern. (The last number covered is always the number of cubes in the chain.) Have students repeat the exercise with this pattern in mind. Does it hold? ASK: What is an easy way to know 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 “1, 2, 3,…” as I pick up the cubes, I can just place a cube on 1, another cube on 2, another on 3, and so on.) Demonstrate 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.


can say the numbers from 0 to 10 and can 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 pre-cut square pieces of paper (details below) number lines or BLM Number Lines 0 to 10 (p XXX)


PROBLEM SOLVING

Making and investigating conjectures.

PROBLEM SOLVING

1 2 3 4 5 6 7 8 9 10

15

The chart makes sure that you count all the cubes without counting any twice. ASK: How does the chart help to make sure that you didn’t count any cube twice? (By placing a cube on the chart, I can see that I already counted that cube.) How does the chart help to make sure you didn’t miss any cubes? (If any cubes are left off the chart I know I’ve missed them.)

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? (Because you have to put the squares on every number in order—you can’t skip numbers.) Then take the squares off and demonstrate counting them incorrectly: 1, 2, 4, 5, 6, 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 the numbers in order the right way.) 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.

Counting using a number line. Show a number line on the board and introduce the term “number line”. Use the paper squares from the previous exercise to demonstrate counting with a number line. (Place some squares over the numbers in order, starting at 1. What is the last number with a square over it?) Demonstrate counting incorrectly by starting at 0 instead of 1. ASK: When I count the squares and I start counting at 0, will I get the right answer? (no) Demonstrate incorrectly counting the fingers on one hand by starting with 0 and ending with 4. SAY: I get 4 fingers but I really have 5 fingers. How come? Explain that using the number line is just like counting out loud except that we are counting in writing; in either case, you have to start at 1. Provide each student with several (less than 10) counters and have them count the counters using a number line (they can use the number lines on the third worksheet or BLM Number Lines 0 to 10). Students then exchange counters with a partner and check to see if they get the same answer for the same counters.

ACTIVITY

Give each student 10 two-colour counters or coins. Have students toss the counters/coins and then use a chart 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 chart and the yellow counters (or tails) below the chart.

Connecting.

PROBLEM SOLVING

Number Sense 1-6

1 2 3 4 5 6 7 8 9 10


More and LessNS1-7

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CURRICULUM EXPECTATIONSOntario: km6, km7, 1m1, 1m3, 1m5, 1m11, 1m20WNCP: kN5, 1N5, [R, CN]

VOCABULARY right least left fewer more fewest most order less

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


is able to say the numbers from 0 to 10 in sequence can match, and translate between, numbers spoken orally and numerals

MATERIALS

objects to count, such as blocks, counters, and pennies 1-cm connecting cubes BLM Counting Cubes (p XXX)BLM Extra Practice with More and Less (p XXX)

Check that all students understand the concept of more. Show a pile of 5 blocks and a pile of 20 blocks and ASK: Which pile has more blocks? If students don’t know the answer, explain that the word “more” is used to compare how much or how many. EXAMPLE: If you like chocolate, you probably want more chocolate than your parents want to give you.

When the numbers are written in counting order, the number on the right means more. Write the numbers 1-10 in order on the board or refer to a list already posted in the room. Ask students if the numbers are written in the order you say them when counting. Ask students how they could use this order to say if a number is more than another number. (The one on the right, or further along in the list, will mean more, just like the number you say last when counting means more.)

Give each student a handful of 1-cm connecting cubes and ask them to make a chain. Then have students work in pairs to determine who was given more cubes, using the charts on BLM Counting Cubes or on the second worksheet for NS1-6. Students place their chains on the chart starting at 1. Which chain is longer? Which number is under the rightmost cube? Have partners link their chains together and then pair up, so that there are four students in each group. Which pair’s chain has more cubes? Challenge students to find the answer without using numbers. (e.g. by laying the chains side by side)

Which number means more? Write two numbers on the board or on chart paper, and ask a volunteer to circle the number that means more. Have an ordered list of numbers on display for students to refer to at first. Write some pairs out of order and others in order. Then have students show the larger of the two numbers by holding up the correct number of fingers.

Changing into a known problem.

PROBLEM SOLVING

Reflecting on other ways to solve a problem.

PROBLEM SOLVING

17

Which number means the most? Explain that “the most” means which one is more than all the others, just like “biggest” means bigger than all the others. 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 (e.g. 2 5 8) then give examples where the numbers are not in order. (e.g. 4 8 2). Students might at first find it helpful to use a list of ordered numbers. They can circle the three numbers they are asked to consider and then choose the rightmost one.

Introduce “fewer” and “less” as the opposite of “more.” Have two piles of counters: five red and three yellow. Tell students there are more red counters than yellow counters, which means there are fewer yellow counters than red counters. Explain that the number 3 is less than the number 5, but 3 counters is fewer than 5 counters. “Fewer” is used for amounts that you can count; less is used for amounts that you cannot count. Show two people, a girl and a boy, with different amounts of cake. The boy has 2 small pieces and the girl has 1 large piece that is bigger than both of the boy’s pieces put together. ASK: Who has more pieces? Fewer pieces? More cake? Less cake? Write “fewer” on one side of the board and “less” on the other. Tell 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 the exercises for “more” with “less” and “fewer.” At first, guide students to decide which pile has fewer by first asking which pile has more. Explain that “least” means less than all the others and “fewest” means fewer than all the others. Repeat the exercise above (Which number means the most?) with “fewest” instead of “most”.

Adding one to each pile doesn’t change which has more. Show students a pile of 3 red counters and a pile of 4 yellow counters. ASK: Are there more red counters or yellow counters? (yellow) How do you know? (Because 4 comes after 3.) Add one counter to each pile and repeat the question. Have students predict which pile will have more when you add another counter to each pile (the yellow pile will always have more).

Removing one from each pile doesn’t change which has more. Repeat the exercise above but remove one at a time from each pile. Start with 7 red and 8 yellow counters.

ExtensionOn BLM Who’s Winning?, students can compare the scores of two hockey teams and decide who is winning (who has more points).

Doing a simpler problem first.

PROBLEM SOLVING

Bonus Use longer lists of numbers (e.g. 7 6 2 8, 5 6 2 3 8 1)

ACTIVITY

Play Solitaire War (p XXX).

Literature— More, Fewer, Less by Tana Hoban.

CONNECTION

Number Sense 1-7

Individual dart-like game with BLM Target Practice

ONLINE GUIDE

EXTRA PRACTICE

BLM Extra Practice with More and Less.


How to count two piles together. Show a pile of 6 red cubes and a pile of 8 yellow cubes. Demonstrate taking one at a time from each simultaneously, counting the 6 red cubes and 6 of the yellow cubes together. Then finish counting the yellow cubes. Give students piles of red and yellow cubes to count in this way. Repeat by having students trade handfuls of cubes with each other. Give students 4 blue, 8 red, and 7 yellow cubes and ask them to count all three piles by saying the counting sequence only once.

To see which pile has more without counting, you can remove one from each pile. Tell the class that Sayaka and Jenn are playing a game and the person with the most counters wins. Show Sayaka’s pile of 24 yellow counters and Jenn’s pile of 26 red counters (but don’t tell students the number of counters). Explain that you want to know which pile has more without counting. Encourage students to discuss the problem with a partner. Then, demonstrate removing one counter from each pile until only one colour is left. ASK: Which colour is left—red or yellow? (red, so there are more red counters than yellow counters) Who won? (Jenn) Let students work in pairs. Give each pair a pile of red and yellow counters and have them determine if there are more red counters or yellow counters without counting.

Drawing a model for the counters. Draw blank circles and coloured circles scattered on the board. Ask students how you could check, without counting, whether there are more blank circles or more coloured circles. ASK: How could I show removing one of each? If students suggest alternately erasing one of each, explain that it might be hard to remember which one (blank or coloured) they erased first. Take other suggestions, then demonstrate circling pairs of circles (one of each kind) in several examples.

Matching people to determine which group has more. Tell students you want to find out if there are more boys or girls in the class. Ask them how

One-to-One CorrespondenceNS1-8

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CURRICULUM EXPECTATIONSOntario: km7, km16, 1m1, 1m3, 1m5, 1m6, 1m7, 1m11, 1m13, 1m20 WNCP: kN5, 1N5, [R, CN, V, C]

VOCABULARY more less pair enough as many

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


understands the concepts of more and less (fewer) can count

MATERIALS

objects to count, such as counters and connecting cubes

Making a model.

PROBLEM SOLVING

Bonus

Real World

CONNECTION

Draw 2 more hearts than circles. Draw as many pencils as erasers.

JOURNAL

19

you could find out without counting. Then tell the class to pair up, one boy with one girl. Are there any boys or girls left without a partner? Are there more boys or girls? Which group has extra? Repeat with 5-year-olds and 6-year-olds.

As many as. Draw three hearts and three circles and ASK: Are there more hearts or circles? Tell students that since there are the same number of each, we say there are as many hearts as circles. Have students draw on a separate piece of paper a different example of “as many hearts as circles” and then discuss the various ways of doing so. ASK: If you draw 4 hearts, how many circles do you have to draw? If you draw 1 heart, how many circles do you have to draw? If someone decides to draw no circles and no hearts, have they drawn as many hearts as circles? (yes)

Have students take one pencil and one workbook and get into groups of four. ASK: Are there as many people as pencils? How do you know? (Yes, because each person has a pencil.) Are there as many people as workbooks? (Yes, because each person has a workbook.) As many workbooks as pencils? (Yes, because there are the same number of workbooks as people and the same number of pencils as people, so there are the same number of workbooks as pencils.)

Build a set that has more, fewer, or as many elements as a given set. Give each student five connecting cubes of each colour: red, white, blue, green. Ask students to build a set of connecting cubes so that there are more red than white, fewer blue than white, and as many green as red (give these criteria one at a time). ASK several students: How many green cubes do you have? Do you have more green or white? Why did everyone get the same answer to the second question but not to the first? (Students could choose different numbers of green cubes, but if there are more red than white and as many green as red, everyone’s set will have more green than white.) Are there more green or blue? How do you know? (There are more green than white, and more white than blue, so more green than blue.)

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 10? (10) When I count from 1 to 5? (5) When I count from 1 to 8? (8) Demonstrate counting 7 cubes, while explaining that each cube gets paired up with a number from 1 to 7. Since you know that there are 7 numbers from 1 to 7, there are 7 cubes.

ExtensionDraw the Olympic rings on the board (see margin) and show students 4 chalks of different colours. ASK: Can I colour each circle a different colour? Do I have enough colours?

Match chairs to people and then play Cooperative Musical Chairs.

ONLINE GUIDE

Using logical reasoning.

PROBLEM SOLVING

Using logical reasoning, Reflecting on the reasonableness of an answer.

PROBLEM SOLVING

Goldilocks. In this story, were there enough beds for both Goldilocks and the three bears?

CONNECTION

Number Sense 1-8


Counting the extras to find how many more. Give students two-colour counters. Have them toss their counters. ASK: Did more counters land with the yellow face up or the red face up? Have students pair up their counters. Are any counters left unpaired? What colour are the extras? Have several volunteers present their answers and show their pairings. Repeat several times.

Draw the following picture on the board:

ASK: Are there more circles or squares? How many more? (i.e., How many extras are there?) Remind students how to pair objects up in drawings by joining them with a line. Students can colour any shapes not joined to identify the extras and then count the extras to find how many more.

Students can complete BLM Pairing Them Up for additional practice.

Counting extras when objects are lined up in grids. Display the following picture on the board:

How Many More?NS1-9

Page xxxx

CURRICULUM EXPECTATIONSOntario: km2, km16, 1m1, 1m7, 1m11, 1m14WNCP: kN5, 1N5, [R, C]

VOCABULARY extra how many more

GoalsStudents will determine how many more by pairing objects up and counting the extras. Students will also understand how much more one number is than another.


understands one-to-one correspondence understands the concepts of more and less (fewer) can count

MATERIALS

two-colour counters BLM Pairing Them Up (p XXX)BLM 2-cm Grid Paper (p XXX) OR BLM Counting Cubes (p XXX)2-cm connecting cubes

Changing into a known problem.

PROBLEM SOLVING

21

ASK: Are there more circles or triangles? How many more? Explain to students that the grid does the pairing for them. Have a volunteer colour the extra triangle (the one that isn’t paired up). Repeat with more examples. Have the triangles sometimes in the top row and sometimes in the bottom row. Then draw only the triangles and have volunteers add the circles so that there are: 2 more circles than triangles; 3 more triangles than circles; 1 fewer triangle than circles; 2 fewer circles than triangles. Then give students connecting cubes of two colours and ask them to use BLM 2-cm Grid Paper or BLM Counting Cubes to determine which colour of cubes they have more of and how many more. You could then have students choose a combination of cubes (e.g., 3 more red than blue) and use the grid to show that they have done so correctly.

How much more is one number than another? Display three circles and four squares in a grid as shown:

ASK: How many circles are there? How many squares are there? How many more squares than circles are there? Summarize as follows:

1 more than

Draw several similar grids using different shapes but always 3 of one and 4 of the other. Write the summary statements one below the other, so that “1 more” and “than” create clear columns. ASK: What is always the same? Emphasize that the group of 4 always has one extra, so 4 objects is always 1 more than 3 objects. Explain that mathematicians shorten this to saying 4 is 1 more than 3. Repeat with 5 shapes and 3 shapes and have a volunteer fill in the blank: 5 is more than 3.

Find the number that is 2 more than another number by drawing circles and triangles. Draw 4 triangles in a grid and have a volunteer draw 2 more circles than triangles. ASK: How many circles did she/he draw? What number is 2 more than 4? Repeat with other numbers of triangles. Then have students draw 5 triangles and 2 more circles than triangles on grid paper or BLM Counting Cubes. ASK: How many circles did you draw? What number is 2 more than 5? Repeat with various examples of “2 more than” and then ask for examples of “1 more than” and “3 more than.”


PROBLEM SOLVING

3

4

Number Sense 1-9

Activity with BLMs based on popular computer game Minesweeper.

ONLINE GUIDE


Counting OnNS1-10

Page xxxx

CURRICULUM EXPECTATIONSOntario: km13, 1m1, 1m3, 1m7, 1m11, 1m14WNCP: 1N5, [R, C]

VOCABULARY extra how many more counting on

GoalsStudents will determine how many more by counting on.


understands one-to-one correspondence understands the concepts of more and less (fewer) can count can determine how many more

MATERIALS

counters bedsheet BLM Counting On (p xxx)

Counting extras when objects are lined up with numbers. Draw or display the following picture on the board. 1 2 3 4 5 6 7 8 1 2 3 4 5 ASK: How many circles are there? How many squares? Are there more circles or squares? Have a volunteer circle the extra circles. ASK: How many extras are there? Have a volunteer fill in the blanks in this sentence: There are more than . Repeat with similar pictures.

How many more than another number? Draw the numbers in between the rows, as shown, but with all the numbers dotted for the students to trace. 1 2 3 4 5 ASK: How many circles are there? How many squares? Have a volunteer trace the extra numbers. ASK: How many numbers did you trace? How many more squares than circles are there? Repeat with pictures of different objects but with the same numbers, 3 and 5. Emphasize that the group of 5 always has 2 extra, so 5 objects is always 2 more objects than 3 objects. Mathematicians say that 5 is 2 more than 3.

Write on the board: 1 2 3 4. Have a volunteer continue writing the numbers up to 7. ASK: How many numbers did the volunteer write? Explain that 7 is 3 more than 4 because the volunteer had to write 3 more numbers after 4 to get to 7. Repeat with various examples.

23

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 than 5 is 8? (3) Tell students that there is a way to keep track only of the extra numbers by counting on your fingers. Tell students you are going to count to 8, but only raise a finger when you say a number after 5. Remind students that you want to know how many more 8 is than 5. Count to 5 with your fist closed, then raise your thumb when you say 6, raise your index finger when you say 7, and raise your middle finger when you say 8. Explain that because you raised 3 fingers when you counted to 8 after counting to 5, we can see that 8 is 3 more than 5.

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

Counting on. Then show students an easier way to find how many more 10 is than 7. Instead of counting from 1 to 7 with their fist closed, they can just say 7 with their fist closed and then count the extra numbers (8, 9, and 10). Discuss why that works. Emphasize that saying all the numbers from 1 to 7 is going to get them to 7 in the end, so they might as well save time and just start at 7. Give students lots of practice with this type of question. Eventually give examples where students need to count the extra numbers on both hands. EXAMPLE: 9 is how many more than 3?

To ensure that students keep their fist closed while saying the first number, you could pretend to throw them the first number which they have to pretend to catch—then their fists will automatically be closed when they say that number. Students then count the extra numbers using their fingers as above.

Extensions1. BLM More Than gives students an opportunity to discover patterns in changing the order of numbers: 6 is 4 more than 2 and 2 more than 4.

2. On BLM Who is Winning? (Advanced), students will decide who’s winning and by how much.


PROBLEM SOLVING

Reflecting on other ways to solve a problem.

PROBLEM SOLVING

1 2 3 4 5 6

7 8

Bring in a bedsheet and set up a hiding area at the front of the room. Ask 4 volunteers to hide behind the sheet and 3 more volunteers to stand at the front of the room. ASK: How many children are at the front of the room? Explain that you know there are 4 children hiding even though you can’t see them, so you can count the others starting from 5. Demonstrate doing this and then remove the sheet and count everyone, starting at 1. Repeat with various numbers of volunteers. This game can also be played with counters hiding under a sheet of paper.

ACTIVITY

Number Sense 1-10

EXTRA PRACTICE

BLM Counting On


Counting to 20NS1-11

Page xxxx

Provide lots of oral practice counting to 20.

Count concrete objects. Give each student four or five cubes to count. Then have partners count how many cubes they have altogether. Then have partners pair up and count how many the group has altogether.

Count objects on paper. Teach students to write the numbers on pictures as they count, to help them keep track of which objects they have already counted and which objects they still need to count.

Counting letters. Write “the” on the board. Have a volunteer count the number of letters in the word. Then write “the mouse” and demonstrate counting the letters, starting at 1. ASK: Is there an easier way to count the letters? Is there a way to take advantage of the fact that someone already counted the letters in “the”? Challenge students, working in pairs, to think of

CURRICULUM EXPECTATIONSOntario: 1m1, 1m3, 1m5, 1m6, 1m7, 1m13, 1m20WNCP: 1N1, 1N3, [R, CN, C]

VOCABULARY numbers to 20

GoalsStudents will count concrete objects to 20. Students will verify the correctness of their counting with other students and learn how to find mistakes in their counting by keeping track.


can count to 10 can count on from a number

MATERIALS

4 or 5 connecting cubes for each student number cards for 11 to 20 quantity cards for 11 to 20 (you can draw shapes or use stickers to make these) JUMP Math workbook (1 per student)BLM Count the Letters (p XXX)

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

CONNECTION

1. Memory. Use number and quantity cards for 11 through 20. Make 4 rows of 5.

2. Go to page —. Have students turn to the following pages in order: 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. The same book can be used for several different short messages, as long as the instructions “Go to page …” are given orally.

ACTIVITIES 1–3

Using an organized list, Representing

PROBLEM SOLVING

Learning to say 1 – 20.

ONLINE GUIDE

25

a solution. (Since “the” has 3 letters, start at 4 when counting the letters in “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.

Count the letters in “The” and write 3 above the word. Continue counting the letters in “mouse” and then write 8 above that word. Have a volunteer continue counting the letters up to the end of the next word. Continue with new volunteers. How many letters are in the whole sentence? 3... 8... 11... 14... 20. Count from the beginning to verify the answer. Discuss the advantage of not having to count from the beginning every time.

How keeping track helps you find mistakes. Tell students you saw two people’s work and it looked like this: 3 8 11 14 20 T 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 the same answer? (no) What answers did they get? (19 and 20) Who do you think is right? (the person who said 20) Why? (because we counted 20) Challenge students to find the mistake in the other person’s answer. Then ask a volunteer to point out where the two students first got different numbers. Which word did the person count wrong? (The second “the”; the second student counted only 2 letters since 13 is only 2 more than 11, but “the” has 3 letters.) ASK: How does keeping track like this make it easy to see who is right and to find mistakes? Emphasize that when you keep track, you can look at the first place the numbers start being different and that’s how you know which word was counted differently. By re-counting that word, you can then 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 total number of letters after counting each word (1, 6, 9, 11, 14, 19). Have students compare their answers with a partner. Did they get the same final answer? Did they get the same numbers all the way through? If not, where do they start to disagree? Can they tell who is correct? Give students lots of practice with this type of counting and keeping track and have them compare their answers with a partner. (EXAMPLE sentences: Four people had a picnic. The leaves turned red. Today is Joe’s birthday.) There are more sentences for students to practise with on BLM Count the Letters. Have students exchange their completed BLMs with a partner. Did they get the same numbers all the way along? ASK: Did you make mistakes more with longer words or with shorter words? Explain that even expert mathematicians make mistakes with counting on, so it’s nothing to be embarrassed about. The difference between experts and other people is not that the experts get it right more often—it’s that they know how to check if they’re right.


PROBLEM SOLVING

Reflecting on what made the problem easy or hard.

PROBLEM SOLVING

Number Sense 1-11


Using a Chart to Count to 20NS1-12

Page xxxx

Counting to 20 using a chart. Give students or small groups a long strip of thick paper (if your two-colour counters are 1 inch in diameter, make the paper 1 inch wide and 20 inches long) with 20 squares labeled 1 through 20. Give students 20 two-colour counters and have students toss them and count the ones that turned up red by placing them on the chart in order, one counter per square. Students could repeat this activity and record how many counters came up yellow each time.

The reading pattern. Write the word “bat” on the board and ask students what sound the “b” and the “t” make. ASK: How do you say the word bat? How do you know to pronounce the “b” before the “t”? (We read from left to right.) Write a short, familiar sentence on chart paper, all on one line. (EXAMPLE: The cat sat on the rug.) Ask students where the sentence starts and where the sentence ends. Then write a long sentence in one line on the board, such as “The orange cat sat on the blue rug and ate a big rat.” Draw a rectangular page on the board. Ask for suggestions on how to fit the sentence on the page. Divide the sentence into shorter lines, such as “The orange cat / sat on the blue rug / and ate a big rat.” Discuss how much easier it is to read this way.

The reading pattern with numbers. Tell students that counting with a chart marked 1 through 10 is pretty easy, but a chart marked 1 through 20 is harder to work with. ASK: How can we make a chart for counting to 20 that is shorter and easier to work with? ASK: Does this problem remind you of another problem? How did we solve that problem? Some students might suggest starting a new line at 5, others at 10, and others might even say 4,

CURRICULUM EXPECTATIONSOntario: 1m1, 1m2, 1m3, 1m5, 1m7, 1m20, 1m21WNCP: 1N4, [R, CN, V]

VOCABULARY the reading pattern hundreds chart

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


can count to 10 using a chart knows how to read from one line to the next (the reading pattern)

MATERIALS

two-colour counters long strips of paper with numbered squares (1 per student or group, details below) 20 pre-made paper ones blocks (squares) to fit on a hundreds chart drawn on the board BLM 2-cm Grid Paper (p XXX)BLM Reading Pattern Practice (p XXX)

Looking for a similar problem for ideas.

Literacy

CONNECTION

PROBLEM SOLVING

27

6, or 7. Have various long sheets of paper available to demonstrate all these options. For example, with 6, you might have a chart like the following: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Suggest that if students end the first line at 6, they should make every line 6 squares long to make it look nicer. Then have students make their own chart for counting to 20 by cutting, rearranging, and taping their long strip of numbered squares.

Using the reading pattern to find the next number. Tell students that we “read” the numbers in charts like these the same way we read text in English: start at the left, go across a row, move to the next row. We call this the reading pattern. Explain that because the numbers are not all in a line, it can be tricky to know where the next number is. For example, in the chart above, it’s easy 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? Have students 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? (because they are at the end of a row)

Ask them to write the numbers in order, starting at 1, in the following charts:

Bonus 5 rows of 3, 5 rows of 2, 5 rows of 4, 4 rows of 5.

Students could copy these and other charts onto BLM 2-cm Grid Paper. Teach them to do this accurately by counting the squares across and the squares 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 a chart with rows of 6 or 7. ASK: How are the rows in this chart the same as the rows in our charts? (They are all the same length.) 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 a 3 in them) Is that the same for any number in the first row—if you look at the number below, do you see the same number with a 1 in front? Refer back to a chart with rows of 6 or 7 and ASK: Does this happen in this chart? Explain that rows of 10 are used so often 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 these numbers and then the numbers that come right after in the hundreds chart: 7, 5, 17, 10, 6, 19, 4.


PROBLEM SOLVING

Use the reading pattern to do the wave.

ONLINE GUIDE

Extension: Use logical reasoning to guess numbers with BLMs Hangman and Guessing Numbers.

ONLINE GUIDE

Number Sense 1-12

Bonus

BLM Reading Pattern Practice

EXTRA PRACTICE


Tens and Ones BlocksNS1-13

Page xxxx

Display the first two rows of a hundreds chart.

Place 17 paper ones blocks on the chart. ASK: How many blocks are on the chart. How many full rows of blocks are there? (1) How many blocks after the full row are there? (7) Repeat with different numbers of blocks, ending with 12 blocks.

The number of squares in the second row is the digit after the one. ASK: Was a whole row covered before we got to 12? How many squares does a row have? (10) Explain that since 12 is more than 10, 12 takes up more than a whole row. SAY: We had to cover 2 squares in the second row to get 12. How many squares do you think we will have to cover in the second row to get 13? (3). Have a volunteer check this by covering the squares in the second row until they get to 13 and counting as they cover them. Repeat with various numbers, such as 15, 17, 16, and 19.

Tens blocks and ones blocks. Use an overhead projector if available. Show students a tens block and several ones blocks. Copy the two rows on the second worksheet for this lesson onto a transparency and demonstrate how the bigger block (the tens block) fills a whole row but the smaller block only fills a square. ASK: How many squares does the big block cover? (10) How many squares does the little block cover? (1) Explain that the bigger block is called a “tens block” and the smaller block is called a “ones block”. Write on the board: 14 = tens block and ones blocks. Have students predict how many of each type of block they will need, then record and check their predictions. Have a volunteer fill in the blanks. Explain that you are using only 5 blocks (count the blocks together to see this) to show 14. Because one of the blocks is bigger, you can still cover the 14 squares using only 5 blocks.

CURRICULUM EXPECTATIONSOntario: 1m1, 1m3, 1m6, 1m20, 1m21WNCP: 1N4, [R, CN]

VOCABULARY the reading pattern tens block ones block tens digit ones digit

GoalsStudents will use tens and ones blocks on a hundreds chart to represent the last number covered.


knows how to use the reading pattern can count using a chart

MATERIALS

pre-made paper ones and tens blocks to fit on a hundreds chart tens and ones blocks BLM Game Cards BLM Finding Numbers


PROBLEM SOLVING

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

29

ASK: Could we have used only ones blocks and no tens blocks at all? How many ones blocks would we need then? (14) Count out 14 ones blocks and have a volunteer demonstrate placing them on the chart in order. Explain that you could use 14 ones blocks to count to 14, but you find it easier to work with fewer blocks. Have volunteers solve several problems using tens and ones blocks on the projector: 15 = tens block and ones blocks11 = tens block and ones blocks

Tens digits and ones digits. Write the number 17 on the board. ASK: Which digit shows the number of tens blocks I need to make 17—the 1 or the 7? (the 1) Which digit shows the number of ones blocks I need to make 17—the 1 or the 7? (the 7) Explain that the 1 is called the “tens digit” and the 7 is called the “ones digit”.

NOTE: When doing the first two worksheet pages, students can place actual tens and ones blocks on the chart and count how many of each they used – the charts match the size of the blocks.

More than one answer. When students have completed the second worksheet, discuss any differences between answers to the last question (20 = tens blocks and ones blocks). Some students might have used 2 tens blocks and 0 ones blocks while others might have used 1 tens block and 10 ones blocks. ASK: Did both combinations fit perfectly? Is there another way to make the blocks fit perfectly? What if I don’t want to use any tens blocks at all—how many ones blocks would I need? (20) Then explain to students that you want them to use as many tens blocks as they can. Have students answer the question again with that in mind. Then ASK: What digit shows the number of tens blocks? (the tens digit) The number of ones blocks? (the ones digit) Have students answer many similar questions (for numbers with tens digit 1) without using blocks. EXAMPLE: 19 = tens block and ones blocks.

Showing numbers using tens and ones blocks without the hundreds chart. Explain to students that sometimes we use tens and ones blocks alone to represent numbers (without the chart). We would show 14 as 1 tens block and 4 ones blocks because that’s what we would need to fill up a hundreds chart to 14. Take 1 tens block and 4 ones blocks and count how many ones altogether, including the 10 ones that make up the tens block.

Have students practise showing various numbers (up to 20) using only tens and ones blocks. Occasionally have them count the number of ones, including the 10 on the tens block, to emphasize the connection between the number the set represents and the blocks.

Reflecting on other ways to solve a problem

PROBLEM SOLVING

Representing

PROBLEM SOLVING

I Have —, Who Has —? (see NS1 Part1 − Introduction). Use tens and ones blocks to represent numbers. See BLM Game Cards.

ACTIVITY

Number Sense 1-13

EXTRA PRACTICE

On BLM Finding Numbers, students can use tens and ones blocks to locate numbers on a blank chart.


Ordering Numbers NS1-14

Page xxxx

Using tens and ones blocks to order numbers. Give each student a copy of BLM Frames to Model Numbers, 2 tens blocks, and 9 ones blocks. Have each student make 15 using tens and ones blocks and place the blocks on the frame (2 rows of a hundreds chart) at the top of the page. Students then copy the model onto a blank frame in the left-hand column by colouring the squares that are covered in the first frame. Students should write the number 15 above the frame that models it. Repeat with 18 in the right-hand column. ASK: Which frame is coloured more—the one showing 15 or the one showing 18? Which number is larger—15 or 18? (18 is larger than 15 because it covers more of the frame.) Repeat with other pairs of numbers (to 20). EXAMPLES: 14 and 20; 14 and 9; Students will need several copies of the BLM to do many examples. Then give students similar questions in the form of simple word problems. EXAMPLE: The red team has 15 points and the blue team has 9 points. Who is winning? Have students model the two numbers to determine which is more.

Using tens and ones blocks to find how many more. Have students repeat the exercises above, but this time saying how many more one number is than the other. Use numbers that are less than 10 apart.

Comparing and ordering many numbers using tens and ones blocks. Have students compare 3, 4 or 5 numbers using BLM Frames to Model Numbers. ASK: Why is it harder to compare many numbers than to compare two numbers? (because we still have to compare them two at a time).

Using a number line to order numbers. Show an incorrect number line on the board by labelling the markings, in order, 2, 4, 1, 5, 6, 0, 3. ASK: Have I labelled this number line correctly? What is the smallest number on the number line? At which end should that number go? What is the biggest

CURRICULUM EXPECTATIONSOntario: 1m1, 1m3, 1m4, 1m6, 1m7, 1m11, 1m20WNCP: 1N4, 1N5, [R, V, C]

VOCABULARY more less ones digit tens digit

GoalsStudents will represent, compare, and order whole numbers to 20, using a variety of tools and contexts.


can show numbers using tens and ones blocks knows how to use the reading pattern can count to 20 using a chart understands the concepts of more and less (fewer)

MATERIALS

tens and ones blocks hundreds charts and number lines drawn on the board BLM Frames to Model Numbers (p XXX)

Making a model.

PROBLEM SOLVING


PROBLEM SOLVING

Alternative lesson using two colours of tens and ones blocks, instead of BLM Frames to Model Numbers.

ONLINE GUIDE

31

number on the number line? At which end does it go? Ask a volunteer to come to the board and fix your mistakes. Explain that a number line doesn’t have to start at 0. Ask a volunteer to draw a number line from 5 to 10. Have a blank number line with 6 markings on the board for the volunteer to complete. Draw more labelled partial number lines, for numbers up to 20, and have volunteers decide which number is biggest/smallest. EXAMPLE: 13–17. ASK: What are the two biggest numbers? The two smallest? Bonus Include numbers up to 100, or even 3-digit numbers.

Using a number line to order many numbers. Draw a number line from 1 to 20. Ask volunteers to find and circle the numbers 17, 6, and 13. Have another volunteer put the numbers in order. Repeat with 5 numbers: 12, 9, 7, 18, 16. ASK: What is easier to use when comparing many numbers—a number line or tens blocks? (a number line) Why? (We don’t need to compare the numbers two at a time—we just read the numbers in order.)

Review using the reading pattern to show numbers. Explain that you find the line from 1 to 20 too long to work with. ASK: How did we solve a similar problem before? (broke up the rows in a chart into smaller rows) Show students 2 rows of a hundreds chart. Remind students how to show a number on a blank hundreds chart (e.g. ,you can show 17 by colouring the first row completely and then 7 squares in the second row). Emphasize that students should always use the reading pattern when colouring squares.

Using the reading pattern to order numbers on the same grid. Review the reading pattern with your students. Tell them that even if the numbers are not all on a number line, as long as they are in order, you can use the reading pattern to tell which number is biggest. Draw a blank chart with 2 rows of 3 squares and have a volunteer write the numbers from 1 to 6 in the chart using the reading pattern order. Then make an identical chart, but fill it with bigger numbers, such as 8 to 13. ASK: Which is the smallest number? (8) Which is the largest number? (13) Which is bigger—10 or 11? 8 or 10? 11 or 9? 12 or 10? 11 or 13? Then draw a chart, 3 rows of 4 squares, numbered 9 through 20. Shade numbers 12, 14, and 19. Ask a volunteer to write the three shaded numbers in order.

A strategy for finding given numbers on a chart. Draw two ten-frames (charts with 2 rows of 5 squares) on the board, one numbered 1 to 10 and the other numbered 11 to 20. Ask a student to find and circle the number 2 in the first chart and then the number 12 in the second chart. Do this with several similar pairs: 3 and 13, 9 and 19, 6 and 16. ASK: If you know where 7 is in the first chart, how can you find 17 in the second chart? Repeat with a hundreds chart format, where the second row is below the first row (e.g., once I know where 3 is, I can find 13 by moving down).

ExtensionHave students use a ruler as a number line to order numbers.

Selecting tools and strategies. Reflecting on what made the problem easy or hard.

PROBLEM SOLVING


PROBLEM SOLVING


PROBLEM SOLVING

Number Sense 1-14


Comparing to 5 or 10NS1-15

Page xxxx

Counting extra fingers to compare numbers more than 5 to 5. Hold up 7 fingers, 5 on one hand and 2 on the other. ASK: How many fingers am I holding up? (7; count these together) Am I holding up more than 5 fingers or less than 5? (more than 5) How can you tell? How many fingers are on one hand? (There are 5 fingers on one hand, and I am holding up one full hand plus some on the other hand.) How many more than 5 am I holding up? (2) Write on the board: 7 is 2 more than 5. Repeat with 6, 9, and 8.

Counting fingers not up to compare numbers less than 5 to 5. Hold up 3 fingers on one hand and ask the same questions. This time, the number of fingers not up tells you how many less than 5. Since 2 fingers are not up, 3 is 2 less than 5. Repeat with 4, 1, and 2.

Using fingers on both hands to compare numbers less than 10 to 10. Repeat the exercise above, but use both hands to say how many less than 10.

Introduce five-frames. Draw a five-frame on the board and tell students what it’s called. ASK: How many squares are in a five-frame? (5) Why do you think it is called a five-frame? (because there are 5 squares)

Numbers less than 5 on a five-frame. Give students five-frames (see BLM Five-Frames) and counters. Have students place 3 counters on the frame (each counter should be in one square). Discuss various ways of doing so. ASK: How many squares are not covered? Is 3 more than 5 or less than 5? How many less than 5? How can you tell?

CURRICULUM EXPECTATIONSOntario: km12, 1m1, 1m3, 1m6, 1m7, 1m14WNCP: kN5, 1N3, 1N4, 1N5, 1N8, [R, V, C]

VOCABULARY more less pair five-frame ten-frame

GoalsStudents will relate numbers to the anchor numbers of 5 and 10.


understands one-to-one correspondence can pair things up understands the concepts of more and less (fewer)

MATERIALS

BLM Five-Frames (p XXX)BLM Ten-Frames (p XXX)lots of counters

Have students determine if the number of letters in their first name is more or less than 5 by using their fingers.

ACTIVITY

Modelling

PROBLEM SOLVING

Five - frame:

33

Numbers more than 5 on a five-frame. Give each student a handful of counters (more than 5 but less than 10). Ask students to place their counters on the frame. ASK: Did they all fit? Do you have more than 5 or less than 5? How do you know? (More than 5, because they don’t all fit.) How many extras don’t fit? How many more than 5 do you have? ASK: Who has 2 more than 5? How many is that? Demonstrate counting on from the 5 already in the frame and then counting the 2 extras as 6 and 7. Repeat with other numbers. Ask volunteers to count their counters and say how many more than 5 they have.

Introduce ten-frames. Introduce ten-frames in the same way as five-frames.

Numbers less than 10 but more than 5 on a ten-frame. Give students ten-frames (see BLM Ten-Frames) and counters. Tell students to fill in the first 6 squares (using the reading pattern) with counters. Have a volunteer draw the counters on a ten-frame on the board. Repeat with various numbers.

Ask a volunteer to draw 5 counters in a ten-frame using the reading pattern. Then have a volunteer draw 6 counters in a ten-frame using the reading pattern and ASK: Can you tell without counting whether there are more than 5 or less than 5? Draw a third ten-frame and add 6 counters in random squares:

ASK: Can you tell if there are more than 5 or less than 5 in the last ten-frame without counting? How does using the reading pattern to arrange the counters make it easier to tell whether there are more than 5 or less than 5? How does it make it easy to tell exactly how many there are? Ensure that students realize they don’t have to count the counters in the first row—they can start at 5 and count on in the second row. Ask students how they can figure out how many more than 5 there are. Ensure that students realize that 6 is 1 more than 5 because there is 1 in the second row. Repeat for other numbers between 5 and 10.

Numbers less than 5 on a ten-frame. Ask students to show 3 using the reading pattern on their ten-frames and have a volunteer show the answer on the board. ASK: Are there more than 5 or less than 5 counters? How many less than 5? How can you tell? (There are 2 blank squares in the first row.) Emphasize that when using the reading pattern, the blank squares in the first row tell how many less than 5.

Numbers more than 10 on a ten-frame. Ask students to show 14 on a ten-frame. Is 14 more than 10 or less than 10? How do they know? How many more than 10? (4, because there are 4 that don’t fit) Repeat with various numbers.


PROBLEM SOLVING

Using logical reasoning

PROBLEM SOLVING

Ten - frame:

Number Sense 1-15

34

AddingNS1-16

Page xxxx

Starting with 2 and adding 3 more always gives 5 in total. Draw two circles in a row on the board or on chart paper. ASK: How many circles did I draw? Then ask your students to watch carefully while you draw more circles so that they can say how many more you drew. Draw three more circles. SAY: How many more circles did I draw? I started with two circles and I drew three more. How many do I have in total?

Draw two squares in a row. Tell students that you want to draw three more squares, and have them tell you when to stop. Ask how many you now have in total, again emphasizing that you started with two and added three more. Repeat with triangles, but arrange them randomly (not in a row).

The plus sign (+) and equals sign (=). 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 come up with a way of saying that if you have two “anythings” and you add three more of them, you always have five in total. Ask if anyone knows the way mathematicians write this. Encourage students to come to the board and show it if they want to. If no one does, write “2 + 3 = 5” on the board for them. Ask students if they know how to read this addition sentence. Tell them that it says “2 plus 3 equals 5” but what it really means is that “starting with 2 things and adding 3 more is the same number of things as having 5 things” (point to the corresponding symbol as you say each part.) Emphasize that + means “adding more things” and = means “is the same number as.”

Read addition sentences both ways. Ask volunteers to read addition sentences both ways. EXAMPLE: 3 + 4 = 7 is “3 plus 4 equals 7” or “starting with 3 things and adding 4 things is the same number of things as

CURRICULUM EXPECTATIONSOntario: 1m1, 1m5, 1m25WNCP: 1N9, [R, CN]

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

GoalsStudents will solve simple addition problems, including problems involving 0.


uses one-to-one correspondence when counting can count to 10

MATERIALS

two-colour counters or two colours of blocks dice playing cards BLM I Have —, Who Has —? Addition Cards (p XXX–XXX)BLM Blank Domino Cards (p XXX)


PROBLEM SOLVING

Teacher’s Guide for Workbook 1

35

having 7 things.” More number sentences to read: 2 + 1 = 3, 2 + 4 = 6 1 + 5 = 6, 3 + 3 = 6.

Check that addition sentences are right. Give students two-colour counters or two colours of blocks and display the addition sentence 2 + 4 = 6. 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 and then adding 4 more is the same number as having 6 things (that is, starting with both piles put together). Have students find the incorrect sentence and verify the rest: 2 + 5 = 7; 8 + 1 = 9; 6 + 2 = 7; 5 + 3 = 8.

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” say 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 math sentences the other way, with the total on the left: 3 + 4 = 7, 2 + 6 = 8, 1 + 4 = 5.

Adding 0. ASK: Can we add zero to a number? If we start with three things and add zero things, how many do we have in total? Have students write the corresponding addition sentence. Repeat with other examples, such as 5 + 0 or 2 + 0, and then SAY: What if I start with zero things and then add three things? Now how many do I have? Have a volunteer write the addition sentence. Continue with examples such as 0 + 4, 0 + 2, or 0 + 7. Ask students to predict what 0 + 17 will be. What about 12 + 0?

Connecting

PROBLEM SOLVING


PROBLEM SOLVING

1. Have pairs of students each roll a die and find the total number they rolled together. Students should add separately and compare their answers until they agree on the answer. If there are not enough dice for everyone in the class, this can be done as a station.

2. I Have —, Who Has —? (see NS Part 1 − Introduction). Students can play in groups of 6 with cards from BLM I Have —, Who Has —? Addition Cards. There are 2 sets of cards on the BLM: the first 6 go together and the next 6 go together. Make as many copies as required for your class.

3. Addition War (see NS Part 1 − Introduction). Use only cards 1 (ace) through 5 to start.

4. Dominoes (see NS Part 1 − Introduction). Students can play with the cards from Activity 2 or you can make dominoes (see BLM Blank Domino Cards) with a number on top and an addition problem with a picture on the bottom.

ACTIVITIES 1–4

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. At the end, all the animals go together on a merry-go-round.

CONNECTION

Number Sense 1-16


More AddingNS1-17

Page xxxx

Explain that “+” can mean “and.” Ask 3 girls and 2 boys to stand up. ASK: How many children are there altogether? Point out that the plus sign can be read as “and”: 3 girls and 2 boys equals 5 children altogether.

Using counters to solve addition problems. Write the sentences below and read them aloud for your students, using the word “and” for “+.”

4 red crayons + 3 blue crayons = crayons altogether3 boys + 1 girl = children altogether4 bike helmets + 2 hockey helmets = helmets altogether

Explain to students that we can solve the problems by using counters. Show a set of 4 counters. SAY: These 4 counters represent the 4 red crayons. Show a set of 3 counters beside the set of 4. SAY: These 3 counters represent the 3 blue crayons. ASK: How many counters are there altogether? How much is 4 + 3? How many crayons is 4 red crayons plus 3 blue crayons? Then have students use counters to solve problems such as the following: 3 dolls + 2 stuffed animals = toys altogether Adding 3 things. Challenge your students with the following problem: I saw 3 girls, 2 boys, and 2 adults on a picnic. How many people were on the picnic altogether? Write on the board: 3 girls + 2 boys + 2 adults = people. Have a volunteer use counters to model the problem. ASK: How many counters are there altogether? Explain that we can add three or more groups of things, not just two. Have students find totals such as the following using counters:

3 basketballs + 2 volleyballs + 4 footballs = balls trees = 2 maple trees + 1 birch tree + 6 cedar trees animals = 2 lions + 1 beaver + 3 cats + 2 dog + 1 hamster

CURRICULUM EXPECTATIONSOntario: 1m1, 1m5, 1m6, 1m25WNCP: 1N9, [R, V, CN]

VOCABULARY add plus (+)equals (=)

GoalsStudents will solve addition problems by drawing pictures. Students will add more than two numbers and will see the vertical notation for adding.


knows the plus sign (+) and equals sign (=) and what they mean understands the concept of addition

MATERIALS

counters BLM Game Cards (p XXX)BLM Practice Adding (p XXX)

Modelling

PROBLEM SOLVING

Bonus

These are counters:

37

Notation: up and down addition instead of side to side. Explain that addition sentences can be written vertically (to save space) and demonstrate with several examples. Let students practise adding this way with more problems like the ones above.

Adding 10. Draw a basket with 10 apples, so that the 10 apples are visible:

Draw 3 apples outside the basket and have students count the total number of apples. Write on the board: 10 apples in the basket + 3 apples outside = apples altogether. Repeat with various other numbers of apples (1–9) outside the basket. Guide students to notice two things—first, that they do not need to keep counting the 10 apples but can start at 11 for the apples outside; and second, that the number of apples outside is just the ones digit of the total number of apples. Discuss how this is similar to counting with a tens block (instead of ten apples in a basket) and ones blocks (for the apples outside the basket). Show the first two rows of a hundreds chart and remind students that when they use 1 tens block and 3 ones blocks, they end up at 13 on the hundreds chart. Once students see the pattern (10 + any number is written as that number to the right of 1), have students solve many problems without using a picture. EXAMPLES: 10 + 4 = , 10 + 7 = , 10 + 8 = . Include vertical sums, but do not yet include examples like 3 + 10 = .

Extensions1. Tell students that objects do not have to be facing the same direction to be counted together. ASK: How many arrows are there altogether in this picture? (See margin) Write “7 =” on the board. ASK: How many arrows are in each group? Have a volunteer finish writing the addition sentence. Then give students several similar problems to solve independently.

2. Students can try adding Roman numbers on BLM Add Roman Numbers (p XXX).

Connecting

PROBLEM SOLVING

EXAMPLE:

1 book 4 books + 3 books

___ books

Number Sense 1-17

Repeat the activities from NS1-16. Activity 1 can be done in groups of 3 instead of 2, so that students add the results of 3 dice. Students can use BLM Game Cards to make their own cards for I Have —, Who Has—? Play Addition War using cards 1 (Ace) through 10.

ACTIVITYEXTRA PRACTICE

BLM Practice Adding


Addition and OrderNS1-18

Page xxxx

Order doesn’t affect the total. Review the words “right” and “left” with your students. Hold three objects in your left hand and four in your right hand. Ask students how many you have in each hand. Then ask how many you have in total. Write on the board:

+ = Have a volunteer fill in the right numbers. Then switch the objects in your hands and repeat. ASK: What is the same about the two addition sentences? What is different? (Same: the same three numbers are used, the total is the same in each case. Different: the order of the two numbers being added is different.) Repeat with several examples.

Then write “4 + 6 = 10” on the board and ASK: How could I show this addition sentence using ten objects and both hands? What if I wanted to show 6 + 4 = 10? How could I show that? Demonstrate switching the groups of objects in your hands and ask if doing this changed the total.

CURRICULUM EXPECTATIONSOntario: 1m1, 1m5, 1m6, 1m7, 1m25, 1m26WNCP: 1N9, [R, CN, V, C]

VOCABULARY addition sentence right left

GoalsStudents will see that changing the order in which you add numbers does not change the total.


knows the plus sign (+)can count

MATERIALS

counters dice paper dominoes and real dominoes BLM Snowman (p XXX)

Looking for a pattern, Miodelling

PROBLEM SOLVING

Have students pick up some counters with their left hand and some more with their right hand and then record the corresponding number sentence on paper. Have them switch the counters in their hands and record the new number sentence.

Partner up to make addition sentences with three numbers. One partner picks up some counters with each hand and the other partner picks up some counters with only their non-writing hand. The person with a free hand records different

ACTIVITY 1

Bonus

39

Turning dominoes around to change the order. Have a blank paper domino taped to the board.

Ask a student to put dots on the domino to show 6 + 4. Then ask how you could use the same domino to show 4 + 6. ASK: What could I do to this domino to make it show 4 + 6 instead of 6 + 4? Demonstrate turning it around. ASK: Does turning the domino around change the total number of dots on it? How does turning the domino around change the addition sentence? What stays the same and what changes? How do those numbers change? Distribute dominoes and have students turn them around to write two addition sentences.

Provide students with the dominoes that appear on the worksheets, so that they can literally turn the dominoes around as they answer the questions. Bonus BLM Snowman asks students to add three different kinds

of buttons in six ways.

ExtensionCount letters in sentences that have the same words in different orders. EXAMPLE: Joe’s birthday is today. The blue hat is big. Today is Joe’s birthday. Is the big hat blue? ANSWERS: 4 + 8 + 2 + 5 = 5 + 2 + 4 + 8 = 19; 3 + 4 + 3 + 2 + 3 = 2 + 3 + 3 + 3 + 4 =15

number sentences as ways of showing the total number in all three hands, by counting different hands first. Challenge students to find at least three different number sentences.

Literature— Domino Addition by L. Long. Games using dominoes that reinforce addition skills for numbers 1 to 12.

CONNECTION

2. If you have two-colour counters, toss eight of them up in the air and write an addition sentence for the colours that face up when they land. ASK: Does anyone see another addition sentence that we could make for the colours? What if we counted the counters that showed red first and then yellow? What number sentence would we get? What if we counted the counters that showed yellow first and then red—then what number sentence would we get? Give students two-colour counters to toss up and record two number sentences for each result.

3. Play in pairs. Students roll three dice. Each student independently adds the numbers and writes a number sentence. If pairs get the same total, they get one point. If they get the same numbers in the same order, they get two points.

ACTIVITIES 2-3

Learn how to make your own dice.

ONLINE GUIDE

Number Sense 1-18

NOTE: If two of the numbers are the same, as in 2, 3, and 3, there will be only three possible number sentences. If all numbers are the same, there will be only one possible number sentence. In most cases, there will be a total of six possible number sentences).


SubtractingNS1-19

Page xxxx

Taking away 3 objects from 5 always leaves 2 objects. Draw 5 circles in a row on the board or on chart paper. Tell students you want to remove 3 of them, but instead of erasing them, you will cross them out. Tell students to watch you carefully and tell you to stop when you’ve crossed out enough circles. Cross out the first 3 circles. (If students haven’t told you to stop yet, ask them how many you’ve crossed out. Then ASK: Have I crossed out enough?) ASK: How many are left? Repeat with 5 squares in a row, but this time cross out the last 3 squares. Then repeat with 5 triangles scattered randomly and cross out any 3. ASK: If you had 5 apples and someone took 3 of them away, how many would be left?

The minus sign (−). Explain that if you have five “anythings” and you take away three of them, you always have two left. Explain that mathematicians invented a way to write this fact using numbers and symbols and ask if anyone knows how to do this. Encourage students to come to the board and show it if they want to. If no one volunteers, write “5 – 3 = 2” on the board for them. Ask students if they know the mathematician’s way of reading this sentence. Tell them that we can say “5 minus 3 equals 2,” “5 take away 3 equals 2,” or “subtract 3 from 5 to get 2.” What we really mean by this is that when we start with five things, and we take away three of them, we get the same number as if we started with only two things.

CURRICULUM EXPECTATIONSOntario: 1m1, 1m6, 1m7, 1m25WNCP: 1N9, [R, V, C]

VOCABULARY minus minus sign (−) take away subtract

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


understands conservation of number (number does not depend on the attributes of what you count) uses one-to-one correspondence when counting can count to 10 can add two or three quantities

MATERIALS

counters BLM 0 in Subtraction (p XXX)BLM Colour to Subtract (p XXX–XXX)BLM I Have —, Who Has —? Subtraction Cards (p XXX–XXX)BLM Game Cards (p XXX)BLM Black Domino Cards (p XXX)


PROBLEM SOLVING

41

Writing subtraction sentences from a picture. Draw seven circles and tell students you are going to remove four. Tell them to tell you when to stop. Ask them what “take away” sentence you would write for this picture. Have a volunteer come to the board to write it. Ask another volunteer for two different ways to say it, one using “take away” and another using a different word that means the same thing (subtract or minus). Repeat this several times with different numbers.

Subtracting with 0. Have students write the subtraction sentences for pictures in which either no objects are crossed out (such as 3 − 0) or all objects are crossed out (such as 3 − 3), so that 0 is either the difference or the number being subtracted. Students can complete BLM 0 in Subtraction for more practice.

Using counters to solve subtraction sentences. Write a subtraction sentence on the board, such as 5 − 2 = and have students use counters to represent it. Repeat with a few more simple subtraction sentences. Then, show 2 counters and ASK: Can I take 5 counters away? (no) Why not? (because there are only 2 counters). Explain that in subtraction, the bigger number needs to go first.

Subtraction sentences can be vertical too. Explain that, like addition sentences, subtraction sentences can be written up and down instead of side to side. Write several subtraction sentences on the board for students to solve using a picture.

ExtensionThe problems on BLM Subtract! (p XXX) use various models of subtraction.

Drawing a picture.

PROBLEM SOLVING

Modelling

PROBLEM SOLVING

1. I Have —, Who Has —? (see NS Part 1 − Introduction). Students play in groups of 6 with BLM I Have —, Who Has —? Subtraction Cards. There are 2 sets of cards on the BLM: the first 6 go together and the next 6 go together. Make as many copies as required for your class. Students could also make their own cards with BLM Game Cards.

2. Difference War (see NS Part 1 − Introduction).

3. Dominoes (see NS Part 1 − Introduction). Use the cards from Activity 1 or make up your own cards (see BLM Blank Domino Cards) with a number on top and a subtraction problem with a picture on the bottom.

ACTIVITIES 1–3

Number Sense 1-19

EXTRA PRACTICE

On BLM Colour to Subtract, students will use colouring, instead of crossing out, as a model for subtraction.


Closer and FartherNS1-20

Page xxxx

Introduce closer and farther. Ask a volunteer to stand close to the door. Then ask another volunteer to stand far from the door. Then ask questions of all the students: Who is closer to the window? Who is farther from the window? Who is closer to the chart paper? Who is farther from the chart paper? Continue for other objects in the classroom, such as a bookcase, desk, or filing cabinet. Then ask the two volunteers to stand close to each other and then far apart.

Determine which pair of dots is closer together. Ask students to decide which pair of dots on either side of a line is closer together. Tell students that “closer” means “more close.” Repeat with more examples. Volunteers can come to the board and circle the pair that is closer together.

We can compare how close or far apart numbers are by looking at a number line. Draw a number line from 0 to 6 on the board and ask if 3 is closer to 1 or to 2.

0 1 2 3 4 5 6 Repeat the same question (Is 3 closer to 2 or 1?) with more number lines, some with the numbers far apart and some with the numbers close together, but always with numbers that are equally spaced.

CURRICULUM EXPECTATIONSOntario: 1m1, 1m6, 1m7, reviewWNCP: 1N6, [R, V C]

VOCABULARY close closer far apart farther estimate about exactly

GoalsStudents will understand that numbers that appear close to one another on an evenly spaced number line are considered to be close together, and that numbers that are close together have only a few numbers between them.


understands the concept of distance (even without the vocabulary) can count to 20 knows what a number line is

MATERIALS

large number cards for 0 to 10 (could write the numbers on sheets of paper) BLM Number Lines 0 to 5 (p XXX), BLM Number Lines 0 to 10 (p XXX)

Modelling

PROBLEM SOLVING

EXAMPLE:

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0 1 2 3 4 5 6

0 1 2 3 4 5 6

What do students notice? Explain that no matter how we draw the number line, 3 is always closer to 2 than to 1. Mathematicians say that 3 is closer to 2 than to 1 because that’s how it is on any number line.

Which number is closer to 3? Ask if 3 is closer to 4 or to 6 and draw the corresponding number line and dots. Then draw another number line from 0 to 6 and have a volunteer draw the dots in the right place to see whether 3 is closer to 4 or 5. Do several examples with both numbers on the same side of 3 and then switch to examples where one number is less than 3 and the other number is more than 3.

Is the number closer to 0 or to 5? To 0 or to 10? Give each student a number line from 0 to 5 (see BLM Number Lines 0 to 5) and ask students to determine which numbers are closer to 0 than to 5, and which numbers are closer to 5 than to 0. Then provide a number line from 0 to 10 (see BLM Number Lines 0 to 10) and ask students to determine which numbers are closer to 10 than to 0 and which numbers are closer to 0 than to 10. Which number is equally close to both?

Closer to 10 than to 0 means fewer numbers away from 10 than from 0. Have eight volunteers stand in line at the front of the room and identify the front of the line. ASK: Is Ajoy closer to the front of the line or to the back? How do you know? How many people are in front of him? Behind him? (Possible answer: There are more people behind him than in front of him, so he is closer to the front.) Is Wei closer to Hamide or to Mina? (Possible answer: Wei is closer to Mina, because there is only one person between him and Mina but three people between him and Hamide.)

Have 11 students stand in a line, each holding a number card from 0 to 10, to form a number line. ASK: Is the person holding 3 closer to the person holding 7 or to the person holding 1? How do you know? How many people are between them? Is 7 closer to 0 or to 10? Is 8 closer to 5 or to 10? Is 5 closer to 3 or to 8? Draw a number line from 0 to 10 on the board and ask similar questions. Explain that two numbers are closer together if there are fewer numbers between them.


PROBLEM SOLVING

Number Sense 1-20


Estimating How ManyNS1-21

Page xxxx

Is the number of objects closer to 0, 5, or 10? Draw a 0 − 10 number line with just 0, 5, and 10 marked. Then draw 6 stars on a number line as follows:

0 5 10

Ask if the number of stars is closer to 5 or 10. Repeat with different numbers of stars.

Using arrangements of 5 and 10 to estimate. Draw on the board: 5 10

Ask if students think the number of dots in the middle is closer to 5 or 10. Ask for strategies. (Possible strategies: count and then decide whether 6 is closer to 5 or 10; compare the arrangements of dots to each other and notice that the middle one has only 1 more than 5, but several fewer than 10.)

Estimating means finding “about how many.” Explain to students that we can say there are about 5 dots in the middle because the number of dots is not exactly 5 (like the number of dots on the left) but really close to 5. Tell students that when they don’t find the exact number of something, but only what number it’s close to, they are estimating. Show another example of 5, 10, and an unknown number of dots arranged in a special way:

CURRICULUM EXPECTATIONSOntario: 1m1, 1m6, 1m7, optionalWNCP: 1N6, [R, V, C, ME]

VOCABULARY estimate closer to

GoalsStudents will estimate the number of objects and check to see if their estimate is close to the count.


understands that a number is “closer” to one number than another number if there is less distance between them on a number line, or if there are fewer numbers between them

MATERIALS

counters BLM 5, 10, or 20.

Drawing a picture.

PROBLEM SOLVING

Mental math and estimation

PROBLEM SOLVING

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5 10

Again ask students for strategies to determine which set the middle one is closer to. ASK: If we want to estimate how many dots are in the middle, should we estimate 5 or 10? Why?

Then do examples where you provide the examples of 5 and 10 dots, but the unknown set is not a subset of the 10 (in other words, it is arranged very differently). EXAMPLE:

Then continue with examples where you do not show sets of 5 or 10 at all; students will look at only the unknown set of dots and estimate either 5 or 10. Finally, create different arrangements of between 5 and 10 dots on large sheets of paper or cardboard. EXAMPLES:

Hold up each quantity for only a few seconds—long enough for students to estimate the number of dots but not count them. Then have students hold up the number of fingers (either 5 or 10) they think is the better estimate, and then count together as a class.

Estimating larger quantities. Repeat the lesson for larger numbers and quantities. Start by comparing numbers on a number line from 10 to 20. ASK: Is the number closer to 10 or 20? Then use a longer number line and compare numbers to 5, 10, or 20. Finally, estimate larger quantities (arrangements of dots): Is the number less than 5, between 5 and 10, or more than 10? Is the number closer to 10 or 20? Create different arrangements of between 10 and 20 dots on large sheets of paper or cardboard and repeat the exercise above. EXAMPLES:

You might tell students to pretend their fingers are tens blocks and to hold up 1 finger to indicate 10 and 2 fingers to indicate 20. You may need to remind students with a hundreds chart that two tens blocks make 20.

Number Sense 1-21

EXTRA PRACTICE

BLM 5, 10, or 20


First, Last, and In BetweenNS1-22

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CURRICULUM EXPECTATIONSOntario: km11, 1m24WNCP: optional

VOCABULARY ordinal numbers from 1st to 20th

GoalsStudents will learn that ordinal numbers show position.


can count to 10 understands that numbers have an order, or sequence

MATERIALS

5 name cards (details below) BLM 3rd, 4th, 5th (p XXX)

Use a lineup to introduce ordinal numbers 1st to 5th. Ask students if they ever had to wait for tickets in a lineup. Discuss such situations. Then draw 5 people in line in front of a ticket booth and put a name card above each one (use any names you like).

ASK: How many people are in this line? (5) Write “1st” under Calli, “2nd” under Mayah, an so on. Explain that instead of saying “number 1 in line,” we say “first”, and so on. ASK: Who is 4th in line? 2nd? 3rd? 1st? 5th? Where is Mayah in the line? Where is Soren? And so on. ASK: Who are the first two in line? Who is second in line?

Then move the ticket booth to the other side, so that Soren is first and Calli is last. ASK: How is this line different from the last line? Point to Calli and ASK: Is she still first? Have a volunteer write “1st” under the person who is first (Soren) and then another volunteer write “2nd” under the person who is 2nd (Isobel), and so on. Repeatedly change the order in the lineup (by moving the name cards) and ask questions such as: Who is 1st? Who is 4th? Who are the first two people in line? Who is second in line? How many people are in front of/behind Calli? Where is Calli in line? Students can complete BLM 3rd, 4th, 5th for extra practice.

First and last. Restore the original order of the lineup. ASK: What position is Calli in? (first) Remove Soren (you could say that he got tired of waiting) and repeat. (Calli is still first.) Remove Isobel and repeat once more. Then put Isobel and Soren back into the lineup. ASK: What position is Soren

Tickets

Calli Mayah Isobel SorenBilial

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in? (5th) Remove Calli (you could say that she got her tickets) and repeat the question. (Now Soren is 4th.) Remove Mayah and repeat. (Now Soren is 3rd.) Explain that no matter how many people are ahead of Soren, there is still no one behind him. ASK: Does anyone know a word for that? Explain that there is a word that tells us that there is no one behind Soren, no matter how many people are ahead of him. If no one knows, tell them (last). Repeatedly change the order in the lineup (and have it face different directions as well) and ask questions such as: Who is first? Who is last?

Ordinal numbers up to 20th. Explain to students that now that they know how to say the first 5 positions in line, it’s easy to learn how to say all the positions up to 20. Tell them that from 6 to 20, they just say the number and add “th” to the end, the same way 4 becomes 4th. Draw 20 people on the board lining up for tickets or for a bus. Number them 1 to 20. Have students say the position of each person as you point to them. First point to people in numerical order, and then in random order. Then have 10 volunteers line up at the front. Ask various people to do different things. EXAMPLES: Will the 2nd person please clap your hands? Will the 4th person please do a jumping jack? Then invite volunteers to name the 7th person in line, the 9th person, and so on. Repeat with different volunteers.

When there is more than one type of object. Have a number of students line up and ASK: Will the 3rd girl please turn all the way around? Will the 4th boy please raise your hand? Who is the last girl? Who is the first boy? Draw several circles and squares on the board as follows, using as many different colours as possible:

ASK: What colour is the 3rd square? The 2nd circle? Students might raise pencil crayons to show their answers individually.

ExtensionTeach students how to find various letters by counting on their fingers. Demonstrate how to find the fourth letter of the alphabet by counting on your fingers.

Repeat with different letters. Emphasize the importance of saying only one letter at a time while holding up each finger. Demonstrate doing it incorrectly and ask what you did wrong. Possible things to do wrong include holding up fingers more quickly or slowly than you are saying the letters, saying the letters in the wrong order, or missing a letter. Then ask volunteers to find certain letters of the alphabet (3rd, 7th, 9th, 8th, and so on) by counting on their fingers. 17th, 14th, 20th. Bonus

A B C D

Number Sense 1-22

BLM Ordinal Numbers asks students to finish writing the ordinal given the number.

ONLINE GUIDE


Problems and PuzzlesNS1-23

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MATERIALS

BLM 2-cm Grid Paper (p XXX)BLM Finding Letters (p XXX–XXX)

On the worksheet for this lesson, students will use their understanding of numbers and the reading pattern to decode words.

Extensions1. Draw a chart (5 rows of 4 squares) and write the numbers from 1 to 20 in

the squares. Write this list of numbers next to the chart: 1, 4, 10, 3, 9, 11, 17, 5, 2, 13. Invite volunteers to shade those numbers in the chart. ASK: What letter do the unshaded squares form? (F) Invite students to create similar puzzles on grid paper. Assign each student a letter or let students choose their own letter. Partners can then solve each other’s puzzles.

2. Counting on to find the alphabet positions of various letters. Explain that you know the fourth letter of the alphabet is D. ASK: How can I find the sixth letter without starting at A? ASK: What letter do I say when I hold up four fingers? Hold up four fingers and say: “D”. What letter do I say next? Hold up your fifth finger and say, “E.” Hold up a finger on the other hand and say, “F.” ASK: How many fingers do I have up? What letter did I say when I held up my sixth finger? What is the sixth letter of the alphabet? Repeat with several letters (to J). EXAMPLES: The 5th letter is E—what is the 9th letter? The 3rd letter is C—what is the 7th letter? The 6th letter is F—what is the 8th letter? Challenge students to find the 15th letter knowing the 10th letter. Explain that they do not have 15 fingers, so they can’t hold up 10 fingers and then 5 more. ASK: Does this remind you of something we’ve done before? How did we use counting on when we wanted to find how many more 8 is than 5? Did we have to hold up all 5 fingers and then start counting to 8? Explain that if they know the 10th letter, they can just say the 10th letter and keep track of how many they say after the 10th one. Have students find: the 3rd letter after M, the 5th letter after T. (Students may find it easier to start at A, but only start holding up fingers after M or T.) Students can practise counting on to find letters on BLM Finding Letters.

3. Have students make up their own word or message for a partner to decode using the letters chart on the worksheet. Students need to decide on a word that uses only the letters in the chart, write the corresponding numbers in the order they occur in the word, and then make a grid using those numbers. (Students can use BLM 2-cm Grid Paper to make their puzzle).


PROBLEM SOLVING

Using an organized list.

PROBLEM SOLVING

Number Sense Part 1 - PBworks

Documents

Transcript of Number Sense Part 1 - PBworks