Upper Saddle River, New Jersey Grade 1: Step Up to Grade...

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Glenview, Illinois • Boston, Massachusetts Chandler, Arizona • Shoreview, Minnesota Upper Saddle River, New Jersey

Grade 1: Step Up to Grade 2Teacher’s Guide• Teacher Notes and Answers

for Step-Up Lessons

• Practice

• Answers for Practice

• Test

• Answers for Test

45093_SLPSHEET_FSD 145093_SLPSHEET_FSD 1 6/6/08 3:55:50 PM6/6/08 3:55:50 PM

A29 Number Words to Twenty

A32 Numbers to 100 on the Number Line

A41 sa enO gnidnatsrednU a Fraction

A61 Comparing Sets of Coins

A86 Ordering Numbers to 999

B23 Using Doubles to Subtract

B32 Stories about Separating

B33 Stories about Comparing

B44 Arrays and Multiplication

B47 Multiplying by 2 and 5

C8 Adding Two-Digit and One-Digit Numbers

C12 sneT gnitcartbuS

C13 001 fo straP gnidniF

C22 Two-Digit Subtraction

C31 Estimating Di�erences

D25 Inches

D26 Centimeters and Meters

D50 Flat Surfaces of Solid Figures

D51 Properties of Plane Shapes

D89 wohS ot shparG raB gnikaM Outcomes

45093_SLPSHEET_FSD 2 6/6/08 3:56:12 PM

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Intervention Lesson A29

Math Diagnosis and Intervention SystemIntervention Lesson A29Number Words to Twenty

Teacher Notes

Ongoing AssessmentMake sure children can rote count to 20. Encourage them to count and point to each number word and symbol as they say the number.

Error InterventionIf children keep looking at the first page in order to do the matching,

then help them read the number words using phonics.

If You Have More TimeHave pairs of students write the words and the symbols on index cards and then shuffle the deck. Each child takes 7 cards from the deck and makes as many pairs as possible with those cards. Then the children take turns drawing a card from the deck, trying to make a pair, and throwing one card away. The other child may pick up the discarded card or may draw a card from the deck. The game is over when one child pairs up all his or her cards.

Math Diagnosis and Intervention SystemIntervention Lesson A29

Number Words to Twenty

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Intervention Lesson A29 151

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One 1 Eleven 11

Two 2 Twelve 12

Three 3 Thirteen 13

Four 4 Fourteen 14

Five 5 Fifteen 15

Six 6 Sixteen 16

Seven 7 Seventeen 17

Eight 8 Eighteen 18

Nine 9 Nineteen 19

Ten 10 Twenty 20Materials: Two-color counters, 20 per child

1. Have children show one counter. Say the word in the blank beside the word “one” as a class while children point to the word. Then have the children write the number in the blank beside the word.

2. Have children add one more counter. Say the word “two” as a class while children point to the word. Then have children write the number in the blank beside the word.

3. Repeat for each number to twenty.

Match each word to the correct number.

1. twelve 9

2. eighteen 4

3. nine 12

4. fifteen 18

5. four 11

6. eight 15

7. nineteen 19

8. eleven 14

9. twenty 8

10. fourteen 20

152 Intervention Lesson A29

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Number Words to Twenty (continued)

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Numbers to 100 on the Number Line

Teacher Notes

Ongoing AssessmentAsk: Which number is greater, a number left of 50 or a number right of 50, on the number line? The number right of 50 is greater. Numbers increase from left to right on the number line.

Error InterventionIf children have trouble associating numbers with points on a number line,

then use A13: Ordering Numbers to 12 with a Number Line.

If You Have More TimeHave 11 children each write a different number from 70 to 80 on a sheet of paper and line up in any order, facing the class. Have other children take turns telling one child where to move to show where that child’s number would go on the number line. Continue until the numbers are in order.


Numbers to 100 on the Number Line

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1.

2.

3.

4.

1. Say: Every number has its own place on the number line. The numbers go in order from least to greatest. What number comes after 20? Have children write 21 in the box.

2. What number comes between 23 and 25? Have children write 24 in the second box.

3. Have children complete the number lines for Problems 1 and 2. Ask questions like those above for children who have difficulty.

4. For Problem 3, have children find 64 on the number line and circle it and its point. Ask: What number is before 64? After? Have children circle 67 and its point. Ask: Is 67 greater than or less than 64?

5. Have children circle a number that is greater than 53 on the last number line. Then have them circle one that is less than 46.

Sample answers are shown.

Write the missing numbers.

5.

6.

7.

Circle the numbers on the number line.

8. 28, 33

9. 91, 97


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Numbers to 100 on the Number Line (continued)

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Understanding One as a Fraction

Teacher Notes

Ongoing AssessmentAsk: If a pizza is divided into 8 equal slices, how

many slices would it take to equal the whole

pizza? 8 What fraction of the pizza equals a

whole? 8 __ 8

Error InterventionIf children have difficulty writing fractions,

then use A38: Writing Fractions for Part of a Region.

If You Have More TimeHave children name things that come divided into equal parts. State how many equal parts it has and then say a fraction for the whole.


Understanding One as a Fraction

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1. 4

4 parts red

parts in all 4__4 � 1

2. 3

3

parts blue


3. 6

6

parts orange


4. 8

8

parts orange


5. Reasoning 9

___ 9 � 1

Materials: Crayons or markers

1. Have children color all 4 parts of the circle red. Ask: How many parts are red? Have children write 4. How many parts in all? Have children write 4 again. What fraction of the circle is red? Say: Four fourths are red.

2. Ask: Is the whole circle red? Say: So, four fourths equal one whole. Have children write 4__4.

3. Have children color all 3 parts of the square blue. Ask questions like those above.

4. Have children finish the other problems, coloring all 6 parts of the square orange and all 8 parts of the octagon yellow.

Color each shape. Write a fraction equal to 1.

6. 7.

22 � 1

7__7 � 1

8. 9.

5__5 � 1

10__10 � 1

10. 11.

4__4 � 1

12__12 � 1

12. Reasoning Color the whole group.

3__3 � 1


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Understanding One as a Fraction (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson A61Comparing Sets of Coins

Teacher Notes

Ongoing AssessmentMake sure children understand which coins have the same value. For example, make sure they know that two nickels equal a dime and that two dimes and a nickel equal a quarter.

Error InterventionIf children have trouble counting the value of groups of coins,

then use A58: Quarters and A60: Counting Sets of Coins.

If children have trouble with the � and � signs,

then use A27: Using �, �, and � to Compare Numbers.

If You Have More TimeHave children work in pairs. Put about 15 assorted coins in a paper bag. Have each child pull 5 coins from the bag without looking. Each child counts the set of coins drawn. Then they compare to decide which set is worth more. Have them return the coins to the bag and repeat.


Comparing Sets of Coins

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1.

70¢ < 75¢

2.

62¢ > 58¢ Materials: 3 quarters, 5 dimes, 3 nickels, and 3 pennies per child or pair.

1. Have children use the coins to match the ones in the first group. Have them arrange the coins, count on, and write the total value.

2. Have children line up the two groups of coins as shown. Have them cross out the first quarter in each group because they have the same value. Have them continue to cross out coins with the same value, 2 quarters, 2 dimes, and then 2 nickels and the dime. Since the second group of coins has a nickel left, it is greater than the first set. That means and the first set is less than the second. Have children write �.

3. Point out that 70 cents is less than 75 cents, since 70 is less than 75.

4. Repeat for the second group of coins. Tell children to not use coins from their first group.

5. Have children find the value of each set of coins in item 2 and compare.

Write the total amounts and compare them. Write �, �, or �.

3.

48¢ > 43¢ 4.

82¢ > 75¢

5.

95¢ > 85¢


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Comparing Sets of Coins (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson A86Ordering Numbers to 999

Teacher Notes

Ongoing AssessmentMake sure children start by looking at the hundreds.

Error InterventionIf children have difficulty with the concept of ordering,

then use A28: Ordering Three Numbers, A85: Before After, and Between, A84: Comparing Numbers to 999, and A83: Patterns with Numbers on Hundreds Charts.

If You Have More TimePut children in groups of 4. Have 3 children each write a different three-digit number on a half sheet of paper and then physically line up in any order. Have the fourth child reorganize the children to show the numbers in order from least to greatest. Continue until each person in the group gets to be the reorganizer. If two of the students write the same number have the reorganizer put them one in front of the other.


Ordering Numbers to 999

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1.

132 223 124

124 � 132 � 223 least greatest

2. 213 141 236 141 � 213 � 236 least greatest

3. 436 487 243 243 � 436 � 487 least greatest

4. 431 283 281 281 � 283 � 431 least greatest

Materials: Place value blocks, 10 hundreds, 8 tens, 10 ones per pair or group

1. Have children show 132, 223, and 124 with blocks.

2. Ask: Which number has the greatest number of hundreds? 223 Say: If one number has more hundreds than all the others, it is the greatest. Have children write 223 on the line with greatest.

3. Ask: Does one number have the fewest number of hundreds? No, 132 and 124 have the same number of hundreds. Say: When two or more numbers have the same number of hundreds, compare the tens. Which number has fewer tens, 132 or 124? 124 Say: So, 124 is the least. Have children write 124 on the line with least.

4. Ask: Which number is between 124 and 223? Have children write 132.

5. Say: So the numbers in order from least to greatest are: 124, 132, 223.

6. Have children order the other sets of numbers, using place value blocks, if they wish.

Write the numbers in order from least to greatest.

5. 188 128 243 128 � 188 � 243 least greatest

6. 465 323 512 323 � 465 � 512 least greatest

7. 342 215 251 215 � 251 � 342 least greatest

8. 767 876 676 676 � 767 � 876 least greatest

9. 809 783 784 783 � 784 � 809 least greatest

10. 645 154 646 154 � 645 � 646 least greatest

11. Reasoning The Lions have 117 points, the Cougars have 112 points, and the Tigers have 121 points. Which team hasthe least number of points? Cougars


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Ordering Numbers to 999 (continued)

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Intervention Lesson B23

Math Diagnosis and Intervention SystemIntervention Lesson B23Using Doubles to Subtract

Teacher Notes

Ongoing AssessmentAsk: What double addition fact can help you find 4 � 2? 2 � 2 � 4

Error InterventionIf children do not know the double addition facts,

then use B12: Adding Doubles

If students have trouble relating addition and subtraction,

then use B19: Relating Addition and Subtraction.

If You Have More TimeHave children draw pictures to show double subtraction facts. Have them write a fact to match each picture.

Math Diagnosis and Intervention SystemIntervention Lesson B23

Using Doubles to Subtract

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Intervention Lesson B23 109

Name

1.

3 � 3 � 6 So 6 � 3 � 3 .

2.

4 � 4 � 8 So 8 � 4 � 4 .

3.

6 � 6 � 12 So 12 � 6 � 6 .

4. 2 � 2 � 4

4 � 2 � 2

Materials: Snap cubes, 12 for each child

1. Have children make 2 trains of 3 snap cubes each. Ask: How much is 3 plus 3? Have children write 6. Have children break the train apart into two trains with 3 each. Ask: Since 3 plus 3 is 6, what is 6 minus 3? Have children write 3.

2. Say: If you know the doubles addition facts, you can use them to subtract. Have children use cubes to find 8 – 4 and 12 – 6.

3. Ask: What doubles addition fact can you use to find 4 minus 2? Have children complete 2 + 2 = 4. Ask: What is 4 minus 2? Have children write 2.

Find the double. Then subtract.Use cubes if you like.

5. 6.

2 � 2 � 4 5 � 5 � 10

So 4 � 2 � 2 . So 10 � 5 � 5 .

Write an addition fact. Then subtract.

7. 1 � 1 � 2 So 2 � 1 � 1 .

8. 3 � 3 � 6 So 6 � 3 � 3 .

9. 4 � 4 � 8 So 8 � 4 � 4 .

10. 6 � 6 � 12 So 12 � 6 � 6 .

11. Carolyn has 6 apples and 3 oranges. How many pieces of fruit does she have in all?

9 pieces of fruit

110 Intervention Lesson B23

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Using Doubles to Subtract (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson B32Stories about Separating

Teacher Notes

Ongoing AssessmentObserve which children can solve the Exercises with pictures and which need to use counters.

Error InterventionIf children have trouble writing number sentences for the separating stories,

then use B2: Subtraction and B17: Separating Stories.

If You Have More TimeHave children work in pairs. One child tells a separating story. The other child writes a number sentence and solves. Then, they change roles and repeat.


Stories about Separating

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1. 12 � 3 � 9 2. 15 � 7 � 8

3. 18 � 9 � 9 4. 13 � 6 � 7

Materials: Counters, 18 for each child

1. Say: Rosa had 12 balloons. Have children put 12 counters in the first box and write 12 in the first line of the number sentence. Say: Rosa gave her sister 3 balloons. Have children move 3 counters to the second box and write 3. Ask: How many balloons did Rosa have then? Have children count how many counters are left in the first box and write 9.

2. Say: Quaid had 15 marbles. Have children put 15 counters in the first box and write 15. Say: Quaidgave his brother 7 marbles. Have children move 7 counters to the second box and write 7. Ask: Howmany marbles did Quaid have then? Have children count how many counters are left in the first box and write 8.

3. Say: What if Rosa had 18 balloons and gave away 9? How many balloons would Rosa have then?Have children write a number sentence and use counters to solve.

4. Say: What if Quaid had 13 marbles and gave 6 away? How many marbles would Quaid have then? Have children write a number sentence and use counters to solve.

Draw a picture to find the difference.Then write the numbers.

5. 11 birds are sitting on the fence.7 birds fly away.How many birds are left?

11 � 7 � 4

6. 13 pigs are in the pen.5 pigs run away.How many pigs are still in the pen?

13 � 5 � 8

7. 16 ducks are in the pond.9 ducks swim away.How many ducks are left?

16 � 9 � 7


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Stories about Separating (continued)

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11

16

13

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Math Diagnosis and Intervention SystemIntervention Lesson B33Stories about Comparing

Teacher Notes

Ongoing AssessmentObserve that children are taking away the counters in pairs, not all from one row. Make sure they understand that they are finding how many more counters are in one row than in the other.

Error InterventionIf children have trouble writing number sentences for the comparing stories,

then use B18: Comparing Stories.

If You Have More TimeHave two different size groups of children come to the front of the class and line up in two rows, one group in each row. Have children in their seats write a number sentence for how many more children are in one group than another. Then, have one child from each group sit down. Continue until there are no children left in the smaller group. Have children count the remaining children to check their number sentences.


Stories about Comparing

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1. 12 � 5 � 7 7 more crayons

2. 16 � 8 � 8 8 more grapes

3. 14 � 5 � 9 9 more apples

4. 15 � 6 � 9 9 more fish

5. 11 � 3 � 8 8 more hair bows

Materials: Counters, 18 for each child

1. Say: Alicia had 12 crayons. Have children show 12 counters in a row and write 12. Say: Max had 5 crayons. Have children show 5 counters in a row below Alicia’s and write 5. Say: How many more crayons did Alicia have than Max? Have children remove 1 counter from each row at the same time. Have them continue removing pairs until all the counters in the top row are gone. Have children complete the number sentence by writing 7.

2. Say: Jaden had 16 grapes. Have children show 16 counters in a row and write 16. Say: Rafel had 8 grapes. Have children show 8 counters in a row below Jaden’s and write 8. Say: How many more grapes did Jaden have than Max? Have children remove 1 counter from each row at the same time. Have them continue removing pairs until all the counters in the top row are gone. Have children complete the number sentence by writing 8.

3. Say: Vero had 14 apples and 5 oranges. How many more apples than oranges did she have? Have children use counters to write and solve the number sentence.

4. Say: Miles had 15 fish. Olivia had 6 fish. How many more fish did Miles have than Olivia? Have children use counters to write and solve the number sentence.

5. Say: Poppy had 11 hair bows. Lora had 3 hair bows. How many more hair bows did Poppy have than Lora? Have children use counters to write and solve the number sentence.

Draw a picture to find the differences.Then write a subtraction sentence.

6. 11 dogs are in a pen. 5 dogs are chasing a cat. How many more dogs are in the pen?

6 more dogs 11 � 5 � 6

7. Paul has 14 dimes. Sue has 6 dimes. How many more dimes does Paul have than Sue?

8 more dimes 14 � 6 � 8

8. 17 apples are in a basket.8 apples are on the ground. How many more apples are in the basket?

9 more apples 17 � 8 � 9


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Stories about Comparing (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson B44Arrays and Multiplication

Teacher Notes

Ongoing AssessmentAsk: If you know 9 � 4 � 36, why can you say you know that 4 � 9 � 36? Sample answer: The arrays are made with the same number of counters, one array is just the other one turned sideways.

Error InterventionIf students get confused on the correct fact for a given array or have difficulty drawing the right number of rows with the right number in each for a given fact,

then encourage the students to read the multiplication fact as “6 rows of 4” instead of “6 times 4”.

If You Have More TimeHave students in pairs. Have one partner draw an array, or make it if counters are available, and write the multiplication sentence. Then have the other partner draw or make the corresponding fact, like 5 � 7 for 7 � 5, and write the multiplication sentence for it.


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Arrays and Multiplication

Materials 16 counters per student

1. Show an array of 4 rows with 2 counters in each row.

2. Write a multiplication sentence for the array.

4 � 2 � 8 Number Number of Total of Rows Counters in Number of Each Row Counters

3. How many counters are in the array? 8

4. Show an array of 2 rows with 4 counters in each row.

5. Write a multiplication sentence for this array.

2 � 4 � 8 Number Number of Total of Rows Counters in Number of Each Row Counters

6. How many counters are in this array? 8

7. Both arrays have 8 counters.

So, 4 � 2 � 2 � 4

8. Since both arrays have 8 counters then you can say,

4 � 2 � 8, and 2 � 4 � 8

Knowing one multiplication fact means you know another.

9. If you know 3 � 8 � 24, then you know 8 � 3 � 24 .


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Arrays and Multiplication (continued)

Write a multiplication sentence for each array.

10. 11.

6 � 5 � 30 5 � 7 � 35

Draw an array to find each multiplication fact. Write the product.

12. 3 � 5 � 15 13. 2 � 6 � 12

The array should The array shouldshow 3 rows of 5. show 2 rows of 6.

Fill in the blanks.

14. 4 � 8 � 32, so 8 � 4 � 32 15. 9 � 2 � 18, so 2 � 9 � 18

16. 5 � 7 � 35, so 7 � 5 � 35 17. 3 � 6 � 18, so 6 � 3 � 18

18. 2 � 4 � 8, so 4 � 2 � 8 19. 1 � 6 � 6, so 6 � 1 � 6

20. Reasoning How does an array show equal groups?

Each row has the same number of objects.

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Math Diagnosis and Intervention SystemIntervention Lesson B47Multiplying by 2 and 5

Teacher Notes

Ongoing AssessmentAsk: Since all the multiples of 2 end in either 0, 2, 4, 6, or 8, are multiples of 2 odd or even? Even

Error InterventionIf students are having trouble with problems like 2 � 8,

then have the students think about the doubles addition facts. 2 � 8 is 2 groups of 8, or 8 � 8. Since 8 � 8 � 16, then 2 � 8 � 16.

If You Have More TimeHave 2 students each take 9 index cards and label their cards 1 through 9. Shuffle the cards. The first round is 2s facts. Each student takes a turn drawing a card and finding the product of that number times 2. If correct, the student keeps the card, otherwise it goes back into the pile. After all cards from the pile are used, shuffle and repeat with the 5s facts.


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Multiplying by 2 and 5

1. Continue skip counting by 2s on the number line below.

0 1 2 4 7 9 14 15 16 173 5 6 8 10 12 1311 18 19 20

2 2 2 2 2 2 2 2 2 2

2. Each number that a hop lands on is a multiple of two. Circle each multiple of 2 on the number line. Then list them in the blanks below.

2 4 6 8 10 12 14 16 18 20

3. To find 6 � 2, count by 2s until 2s Facts

0 × 2 = 0 5 × 2 = 10

1 × 2 = 2 6 × 2 = 12

2 × 2 = 4 7 × 2 = 14

3 × 2 = 6 8 × 2 = 16

4 × 2 = 8 9 × 2 = 18

you have said 6 numbers.

2, 4, 6 , 8 , 10, 12

So, 6 � 2 � 12 .

4. Repeat 3 above for eachof the 2s facts in the table. Complete the table.

5. Reasoning What is the pattern in the products of the 2s facts?

All of the multiples of 2 end in 0, 2, 4 , 6 , or 8 .

6. Continue skip counting by 5s on the number line below. Circle each multiple of 5 on the number line.

5 5 5 5 5 5

0 5 10 35 4015 20 25 30 45

5 5 5


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Multiplying by 2 and 5 (continued)

7. Circle each multiple of 5 on the number line. Then list them in the blanks below.

5 10 15 20 25 30 35 40 45

8. To find 7 � 5, count by 5s until 5s Facts

0 × 5 = 0 5 × 5 = 25

1 × 5 = 5 6 × 5 = 30

2 × 5 = 10 7 × 5 = 35

3 × 5 = 15 8 × 5 = 40

4 × 5 = 20 9 × 5 = 45

you have said 7 numbers.

5, 10, 15, 20 , 25 ,

30 , 35

So, 7 � 5 � 35 .

9. Repeat 8 above for each of the 5s facts in the table.

10. Reasoning What is the pattern in the products of the 5s facts?

All of the multiples of 5 end in 0 or 5 .

Complete each multiplication problem.

11. 2 12. 2 13. 2 14. 2 _� 3 _� 6 _� 2 _� 1

6 12 4 2 15. 7 16. 7 17. 5 18. 8 _� 2 _� 5 _� 3 _� 5

14 35 15 40 19. 5 20. 1 21. 2 22. 5 _� 4 _� 5 _� 4 _� 2

20 5 8 10

23. Reasoning Movie tickets are on sale for $5 each. Ross, Emily, and John want to see the movie. Is $18 enough for all of their tickets? Explain.

Yes; 3 � 5 � 15 and $15 � $18.

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Intervention Lesson C8

Math Diagnosis and Intervention SystemIntervention Lesson C8

Adding Two-Digit and One-Digit Numbers

Teacher Notes

Ongoing AssessmentAsk: Which addition problem does not need regrouping?14 � 8, 25 � 5, 53 � 4, 17 � 4 53 � 4

Error InterventionIf children continually reverse the placement of the regrouped ten and the remaining ones, for example if the ones had a sum of 14 and they carry the 4 to the top of the tens column and leave the 1 at the bottom of the ones,

then have children write 14 as tens and ones and put 14 in a place-value chart with nothing else in it. Emphasize that the 1 goes in the tens column and the 4 goes in the ones column.

If You Have More TimePut children in pairs. Give each pair a penny, a copy of a calendar, and a number cube labeled 4 through 9. Have one child flip the penny onto the calendar without looking, while the other child rolls the number cube. Have both children find the sum of the number of the day the penny landed on and the number that was rolled on the cube. Have them change roles and repeat.


Adding Two-Digit and One-Digit Numbers

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Intervention Lesson C8 71

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1. Tens Ones

2 6� 8

Tens Ones

12 6

� 8

4

Tens Ones

1

2 6� 8

3 4

2. Tens Ones

2 3� 4

Tens Ones

2 3� 4

7

Tens Ones

2 3� 4

2 7

3. Tens Ones

1 9� 7

Tens Ones

11 9

� 7

6

Tens Ones

1

1 9� 7

2 6

Materials: Snap cubes, 34 per pair or group

1. Have children show two 10-trains and six individual cubes for 26. Then have them show 8 individual cubes. Ask: How much is 6 ones and 8 ones? 14 ones If you have 14 ones can you regroup? Havechildren snap together 10 ones to make 1 ten-train. Ask: The 14 ones equal how many tens and ones? 1 ten and 4 ones; Have children write a 4 in the bottom of the ones column of the second place-value chart, to show 4 ones, and a 1 in the box at the top of the tens column to show 1 ten. Say: Addthe tens. How much is 2 tens plus 1 ten? Have children write the 3 in the tens column of the last place-value chart. Ask: How much is 3 tens and 4 ones? 34 So, 26 � 8 � 34.

2. Have children show two 10-trains and three individual cubes for 23. Then have them show four individual cubes. Ask: How much is 3 ones and 4 ones? 7 ones If you have 7 ones can you regroup? No; Have children write the 7 at the bottom of the ones column of the second place-value chart. Ask: How many tens? 2; Have children write a 2 in the tens column of the last place-value chart.Ask: How much is 2 tens and 7 ones? 27 So, 23 � 4 � 27.

3. Do Problem 3 similar to Problem 1.

Add.Regroup if you need to.

4. Tens Ones

12 3

� 8

3 1

Tens Ones

13 5

� 7

4 2

Tens Ones

1 6� 3

1 9

Tens Ones

14 2

� 9

5 1

5. Tens Ones

13 5

� 5

4 0

Tens Ones

7 2� 6

7 8

Tens Ones

12 3

� 7

3 0

Tens Ones

14 2

� 9

5 1

6. Tens Ones

16 6

� 6

7 2

Tens Ones

5 4� 5

5 9

Tens Ones

4 1� 6

4 7

Tens Ones

13 8

� 7

4 5

7. Tens Ones

9 2� 3

9 5

Tens Ones

1 4� 4

1 8

Tens Ones

13 9

� 9

4 8

Tens Ones

16 4

� 6

7 072 Intervention Lesson C8

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Adding Two-Digit and One-Digit Numbers (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson C12Subtracting Tens

Teacher Notes

Ongoing AssessmentAsk: How much is 8 tens minus 3 tens? 50

Error InterventionIf children have trouble deciding how much a set of ten is,

then use A7: Counting by 10s to 100.

If You Have More TimePut children in pairs. Give each pair nine 10-trains. Have children work together to write 4 different subtraction sentences starting with 90, such as 90 � 60 � 30; 90 � 40 � 50. If time allows, have them do the same for eight 10-trains.


Subtracting Tens

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7 tens � 5 tens � 2 tens

70 � 50 � 20

2.


70 � 20 � 50

3.


60 � 20 � 40

Materials: Snap cubes, 70 for each pair or group

1. Have children make seven 10-trains. Then have them take five of the 10-trains away and cross out 5 of the ten-trains shown. Ask: Seven tens minus five tens equal how many tens? Have children write 2. Ask: How much is 7 tens? Have children write 70. Ask: How much is 5 tens? Have children write 50. Ask: How much is 2 tens? Have children write 20. Say: So, 70 � 50 � 20.

2. Do the other problems similarly.

Write the numbers. Subtract.

4. 5.

6 tens � 1 ten 6 tens � 2 tens

60 � 10 � 50 60 � 20 � 40

6. 7.

4 tens � 4 tens 8 tens � 7 tens

40 � 40 � 0 80 � 70 � 10

8. 9.

7 tens � 4 tens 7 tens � 7 tens

70 � 40 � 30 70 � 70 � 0

80 Intervention Lesson C12

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Subtracting Tens (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson C13Finding Parts of 100

Teacher Notes

Ongoing AssessmentAsk: One hundred children are in the second grade. Eighty-four of them have already had their picture taken. How many children have not gotten their picture taken yet? 16

Error InterventionIf children have difficulty understanding while using snap cubes,

then use the same process, but with filling partial ten-frames with counters and then adding complete ten frames.

If You Have More TimeHave children work in pairs with 9 ten-trains, ten individual cubes, and a bag. One child hides a combination of 10-trains and individual cubes in the bag. The other child tells how many are in the bag by looking at the ones outside. Then, they change roles and repeat.


Finding Parts of 100

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55, 56 , 57 , 58 , 59 , 60 , 70 , 80 , 90 , 100

55 � 45 � 100

2.

55, 65 , 75 , 85 , 95 , 96 , 97 , 98 , 99 , 100

55 � 45 � 100

Materials: Snap cubes, 100 for each pair or group

1. Have children show five 10-trains and one 5-train of cubes. Ask: How can you find out how many more snap cubes it will take to make 100? Give children time to discuss possible ways. Say: Oneway is to add ones until you make the next ten. Then count by tens until you get to 100. Startwith 55 and add one snap cube at a time until you reach a ten. Have the children add a snap cube to the 5-train, say 56, and write 56. Have them do this until they reach 60. Say: Now count by tens. Have the children add a 10-train down to the pile, say 70, and write 70. Do this until they reach 100. Say: You added 5 ones and 4 tens. How much is 5 ones and 4 tens? Have children write 45. Say: Soyou had to add 45 to 55 to get 100. 55 � 45 � 100.

2. Have children show five 10-trains and one 5-train of cubes again. Say: Another way is to add tens first and then add ones. Start with 55 and add tens until you reach either 100 or a number in the 90s. Have the children add a 10-train to the pile, say 65, and write 65. Have them do this until they reach 95. Say: Now count by ones until you reach 100. Have children add a snap cube to the 5-train, say 96, and write 96. Do this until they reach 100. Say: You added 4 tens and 5 ones. How much is 4 tens and 5 ones? Have children write 45.

3. Ask: Does it matter if you count by ones first or tens first? No

Add on to find the other part of 100.Use mental math or cubes.

3. 4.

25 � 75 � 100 90 � 10 � 100

5. 6.

33 � 67 � 100 64 � 36 � 100

7. 37 � 63 � 100 8. 85 � 15 � 100

9. 56 � 44 � 100 10. 71 � 29 � 100

11. Reasoning The lunchroom holds 100 children.There are 60 children eating in the lunchroom.How many more can join them?

60 � 40 � 100 40 children


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Finding Parts of 100 (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson C22Two-Digit Subtraction

Teacher Notes

Ongoing AssessmentAsk: How do you know you need to regroup to subtract 62 � 14 if you don’t have snap cubes? You need to regroup because 4 is greater than 2.

Error InterventionIf children have trouble regrouping,

then use C19: Subtracting Two-Digit and One-Digit Numbers and C21: Subtracting with Regrouping.

If children have trouble deciding when to regroup,

then use C20: Deciding when to Regroup in Subtraction.

If You Have More TimeHave children make up word problems involving subtracting two-digit numbers. Let them draw a picture to illustrate their problems. Then, have children trade problems with a partner to solve.


Two-Digit Subtraction

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1. Tens Ones

6 167 6

� 2 8

4 8 2. Tens Ones

9 4� 2 2

7 2

Tens Ones

5 176 7

� 1 9

4 8

Tens Ones

2 103 0

� 1 3

1 7

Tens Ones

7 128 2

� 5 5

2 7

3. 8 11 2 18 5 13 4 16 0 13 91 38 63 56 55 13

_� 73 _� 19 _� 36 _� 28 _� 20 _� 5

18 19 27 28 35 8

Materials: Have snap cubes available for children who need them

1. Ask: How many ones are in 76? 6 How many ones are in 28? 8 Does 76 have 8 ones to take away?No Do you need to regroup? Yes How many tens are in 76? 7 If you trade one ten for ten ones, how many tens are left? 6 tens Show this by crossing out the 7 tens in the place-value chart and writing 6 at the top of the tens column. Make sure children record correctly. You had 6 ones and traded one ten for ten ones. How many ones do you have now? 16 Show this by crossing out the 6 ones and writing 16 at the top of the ones column. Make sure children record correctly.

2. Ask: How much is 16 ones minus 8 ones? Have children write 8 in the ones column. Ask: How much is 6 tens minus 2 ten? Have children write 4 in the tens column. Say: How much is 4 tens and 8 ones? 48 So, 76 minus 28 is 48.

3. Do other problems, similarly. When you get to 91 � 73, which is not in a place-value chart, start by asking how many tens and ones are in each number.

Subtract. Regroup if you need to.If you had to regroup, color those shapes red. Color the other shapes blue.


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Two-Digit Subtraction (continued)

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27 _� 13

14

23 _� 4

1997

_� 83

1491

_� 17

74

48 _� 16

32

96 _� 12

84

54 _� 14

40

28 _� 21

7

67 _� 19

48

15 _� 6

9

73 _� 36

37

63 _� 41

22

17 _� 4

13

65 _� 22

4392 _� 34

58

blue

blue

blue

blueblue

blue

blue

blue

blue

red

red

red

red

red

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Math Diagnosis and Intervention SystemIntervention Lesson C31Estimating Differences

Teacher Notes

Ongoing AssessmentAsk: What is the largest number that can be subtracted from 882 so that the difference is 300 when both numbers are rounded to the nearest hundred? 649

Error InterventionIf students are having trouble with rounding the numbers correctly,

then use F2: Rounding to Nearest Ten and Hundred.

If You Have More TimeHave students work with a partner. Each student should write a three-digit number. Then students can estimate the difference of the two numbers by rounding to the nearest hundred.


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Estimating Differences

When Jarvis subtracted 41 � 29, he got a difference of 12. To check that this answer is reasonable, use estimation.

1. Round each number to the nearest ten.

41 rounded to the nearest ten is .

29 rounded to the nearest ten is .

2. Subtract the rounded numbers.

40 � 30 �

Since 12 is close to 10, the answer is reasonable.

DaNitra subtracted 685 � 279 and got a difference of 406. To check that this answer is reasonable, use estimation.

3. Round each number to the nearest hundred.

685 rounded to the nearest hundred is .

279 rounded to the nearest hundred is .

4. Subtract the rounded numbers.

700 � 300 �

Since 406 is close to 400, the answer is reasonable.

40

10

700

30

300

400


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Estimating Differences (continued)

Estimate by rounding to the nearest ten.

5. 47 6. 82 7. 67 � 51 8. 94 � 48 _� 19 _� 34

9. 71 10. 65 11. 89 � 24 12. 51 � 38 _� 12 _� 49

13. 93 14. 88 15. 57 � 18 16. 28 � 17 _� 45 _� 32

Estimate by rounding to the nearest hundred.

17. 586 18. 941 19. 442 � 181 20. 861� 298 _� 195 _� 362

21. 418 22. 546 23. 945 � 119 24 681� 132 _� 125 _� 234

25. 935 26. 322 27. 709 � 649 28. 550 � 214 _� 464 _� 176

29. Reasoning Marlee has collected baseball cards for 3 years. Kin has collected baseball cards for 2 years. Marlee has 845 baseball cards and Kin has 612 baseball cards. About how many more baseball cards does Marlee have than Kin?

30. Reasoning What is the smallest number that can be subtracted from 723 so that the difference is 200 when both numbers are rounded to the nearest hundred? Explain.

40

Sample answer: 450, Since 723 will round to 700, 500 would need to be taken away from it. The smallest number that rounds to 500 when rounded to the nearest hundred is 450.

20

1070

1040

600200

600800

400100

200

30 50

60 20

40 60

400 500

300 300

400 100

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Intervention Lesson D25

Math Diagnosis and Intervention SystemIntervention Lesson D25Inches

Teacher Notes

Ongoing AssessmentMake sure children can use and read a ruler correctly. Some common errors to watch for include not starting at the zero and not measuring in a straight line parallel to the object being measured.

Error InterventionIf children have trouble comparing a unit length to a given length,

then use D22: Unit Size and Measuring.

If You Have More TimeHave children estimate and then measure objects in the classroom to the nearest inch.

Math Diagnosis and Intervention SystemIntervention Lesson D25

Inches

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Intervention Lesson D25 139

Name

1. estimate inches 2. estimate inches

measure 3 inches measure 2 inches

3. estimate inches 4. estimate inches

measure 4 inches measure 1 inches

Materials: Inch rulers, 1 for each child

1. Show children an inch on a ruler. Ask them to find the line numbered 1 on the boat. Ask: About how many inches long do you think the line is? Have children write their estimates.

2. Draw a line on the board or overhead and demonstrate how to measure its length. Tell children to line up the zero on the ruler+ with one end of the line and read the number that is closest to the other end. Have children measure the line numbered one on the boat and write the measure.

3. Have children compare their measures to their estimates.

4. Have children estimate and then measure the other lines.

1.

2.

3.

4.

Check that students’ estimates are reasonable.

Use a ruler. Measure each dotted line on the house.Color the lines to show how long each line is.

red � 1 inch green � 3 inchesblue � 2 inches yellow � 4 inches

140 Intervention Lesson D25

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Inches (continued)

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yellow

red

red

redred

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Math Diagnosis and Intervention SystemIntervention Lesson D26Centimeters and Meters

Teacher Notes

Ongoing AssessmentAsk: Would you use centimeters or meters to measure the width of the classroom? meters

Error InterventionIf children have trouble estimating,

then let them use a pencil and a piece of yarn cut to the width of the door to measure real objects.

If You Have More TimeGive children two pieces of construction paper and old magazines. Let them cut out and glue pictures to the construction paper. One piece should have pictures of things they would measure in centimeters and the other should have pictures of things they would measure in meters.

1. about 1 centimeter 2. about 1 meter

Check that children’s estimates are reasonable. 3. 4.

about centimeters about meters

Materials: meter stick and feather for demonstration

1. Show children one centimeter on the meter stick. Tell them a pencil is about one centimeter wide. Ask them to draw pictures in the first rectangle to show objects that are about one centimeter long or wide.

2. Tell children the meter stick is one meter long and a door is about one meter wide. Ask them to draw pictures in the second rectangle to show objects that are about one meter long or wide.

3. Show the feather. Ask: Would you use centimeters or meters to measure the length of the feather?centimeters About how many centimeters long is the feather? Have children write their estimates. Discuss the estimates.

4. Ask: Would you use centimeters or meters to measure the length of the bulletin board? metersAbout how many meters long is the bulletin board? Have children write their estimates. Discuss the estimates.


Centimeters and Meters

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About how long or tall might the real object be?Circle the better estimate.

5. 6.

about 1 centimeter about 30 centimeters

about 1 meter about 3 meters

7. 8.

about 10 centimeters about 1 centimeter

about 1 meter about 1 meter

9. Reasoning Would it take more centimeters or meters centimetersto measure your height? Circle your answer. meters

Centimeters and Meters (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson D50Flat Surfaces of Solid Figures

Teacher Notes

Ongoing AssessmentAsk: What shape is the flat surface on a can of soup? circle

Error InterventionIf children have trouble relating a solid to the shape of its flat surface,

then let them trace the bottoms of the geometric solids onto a piece of paper.

If You Have More TimeGive children a cube and either a cone or a cylinder. These can be real objects or shapes made out of poster board. Also, provide paint so that children can make a picture by putting the solids in the paint and pressing them onto a piece of paper.


Flat Surfaces of Solid Figures

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4.

Materials: Cylinder, cube, sphere, and cone geometric solids

1. Show the cylinder and ask children its name. Ask: Does a cylinder have any flat surfaces? It has two. Ask: If you traced one of the flat surfaces, what shape would you get? Hold the cylinder against the board or overhead and trace around the bottom to make a circle. Have children ring the circle.

2. Repeat with the cube and the cone similarly.

3. Show the sphere. Ask: Does a sphere have any flat surfaces? no

Look at each shape.Circle the object that has the flat surface.

5.

6.

7.

8.

9.


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Flat Surfaces of Solid Figures (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson D51Properties of Plane Shapes

Teacher Notes

Ongoing AssessmentAsk: What does a corner feel like on the triangle? Possible Answer: The corner is sharp.

Error InterventionIf children count one side of a shape twice,

then have them color each side in their tracing as they count.

If You Have More TimeHave children work in pairs and play “Guess My Shape.” Place the set of attribute blocks on the table between the two children. One partner describes a shape using words like, “It has 3 corners and 3 sides.” The other partner chooses the attribute block that fits the description. Have children change roles and repeat until all the blocks have been chosen.

1. Square 2. 3 corners

44 3

3. 0 corners 4. 6 sides

Materials: Attribute blocks, one triangle, one square, one rectangle, one circle, and one hexagon for each child or pair

1. Show a corner and a side of an attribute block. Have children touch one of each on a block.

2. Ask the children to choose the square and trace it in the first space on their paper. Ask: How many sides does a square have? Have children write 4 inside the square they drew. Ask: How many corners does a square have? Have children write 4 inside the square again.

3. Ask the children to choose the shape with 3 corners, trace it in the second space, and write the number of sides. Ask: What is the name of the shape with 3 corners? triangle

4. Ask the children to choose the shape with zero corners and trace it in the third space. Ask: What is the name of the shape with 0 corners? circle

5. Reasoning Ask the children to choose the shape with 6 sides, trace it in the last space, and write the number of corners.


Properties of Plane Shapes

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Trace each side in a different color.Draw an X on each corner.Write how many sides and corners.

5. 6.

4 sides 4 corners 4 sides 4 corners

7. 8.

4 sides 4 corners 3 sides 3 corners

9. Color

Properties of Plane Shapes (continued)

x x x x

x x x x

x x

x

x

x

x x

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Making Bar Graphs to Show Outcomes

Teacher Notes

Ongoing AssessmentAsk: How can you tell which color on a spinner covers the most area by looking at a bar graph? The color that has the longest bar probably has the largest area on the spinner.

Error InterventionIf students have trouble make or reading bar graphs,

then use D84: Reading and Making a Bar Graph, D71: Reading Bar Graphs, and D75: Making Bar Graphs.

If You Have More TimeHave students repeat the activity, but with the word “COMPUTER”. Pick one letter from the bag 40 times. After the students have drawn their bar graph, ask: Will it be easy to predict what letter would be drawn next? Sample answer: No, all the letters were drawn about the same amount of times. It could be any of the letters. Then ask: Why do you think all the letters were drawn about the same number of times? There are only 1 of each letter. So they are all equally likely to be drawn.


Making Bar Graphs to Show Outcomes

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Materials 3 index cards (cut in half vertically), bag

1. Write each letter in the word “MUMMY” on an index card. Use the extra index card to make a tally chart for the possible outcomes: M, U, and Y.

2. Place the letters in a bag. Shake them and without looking pick a letter. Tally the letter. Replace the letter, shake, pick, and tally. Do this 20 times.

Answer 3 to 8 to make and use a bar graph of the results.

3. Write the title: Letters Picked from Letters Picked from Bag

M U Y

1614121086420

Nu

mb

er o

f Tim

es

Outcome

Bag above the graph and label the axes: Outcome and Number of Times.

4. Complete the scale. Make the scale by 2s.

5. Draw a bar for each letter. For every 2 tally marks for the letter M, color in one square above the letter M. After coloring a square for every 2 tallies, if you have a tally left over, color half of a square. Do this for U and Y.

6. Which two letters were picked about the same number of times?

U and Y

7. Which bar is the longest? MThe lengths of the bars will vary, the bar for M should be the tallest.

Since the bar above M is the longest, M is the outcome that occurred most often.

8. Reasoning Predict the next letter picked. Explain how you made your prediction.

M; it is the outcome that occurred most often.

Kendra spun a spinner 20 times. She recorded the number of times each color was spun. Use the data for Exercises 9 to 13.

Spinner ResultsOutcome Tally Number

Purple 11

Green 4

Orange 4

Yellow 1

9. Make a bar graph in the grid on Spinner Results

Nu

mb

er

of

Tim

es

Outcome

the right to show the data.

10. Which color occurred most often? least often?

purple; yellow

11. Reasoning What can you tell from the orange and green bars?

Sample answer: Orange and green were spun the same number of times.

12. Reasoning Which color do you predict would be spun next?

purple

13. Reasoning Draw what you think the spinner looked like that Kendra used.

Purple

Orange

Green

Yellow

Sample spinner is shown.


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Making Bar Graphs to Show Outcomes (continued)

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Practice A29

Practice

A29Number Words to TwentyWrite the number.

1. four 4 2. seven

3. five 4. eight

5. twelve 6. eleven

7. fourteen 8. twenty

9. seventeen 10. nineteen

11. thirteen 12. sixteen

Write the number word.

13. 1 one 14. 2

15. 3 16. 6

17. 10 18. 9

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Practice A32

Practice

A32Numbers to 100 on the Number LineUse the number line below. Write the numbers in order.

1. 45, 32, 59, 51

32 45

2. 35, 45, 60, 30

3. 49, 37, 68, 55

4. What is the missing number?

38 44

42 60


15 21

17 23

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Practice A41

Practice

A41

1. 2.

Understanding 1 as a FractionColor to show 1 whole.Write the fraction that equals 1 whole.

= 133

= 1

3. 4.

7. Which fraction is equal to 1 whole?

1 _ 4 2 _

4 3 _ 4 4 _

4

= 1 = 1

5. 6.

= 1 = 1

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Practice A61

Practice

A61Comparing Sets of CoinsWrite the total amounts and compare them.Write >, <, or =.

1.

65¢

2.

3.

Choose the correct symbol.

4.

> < = ¢

5.

> < = ¢

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Practice A86

Practice

A86Ordering Numbers to 999Write the numbers in order from least to greatest.

1. 207 , 267 , 276 least greatest

2. , , least greatest

Write the numbers in order from greatest to least.

3. , , greatest least


5. Which number is the least?

529 531 560 528

6. Which number is the greatest?

120 102 110 100

7. Tell how you would decide which number is the greatest. Then circle it.

572, 570, 576

276 267 207

16 600 60

986 789 892

377 737 773

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Practice B23

Practice

B23Using Doubles to Subtract Subtract. Write the doubles fact that helped you.Use cubes if you need to.

1. 2.

3. 4.

5. 16 − 8 = 6. 18 − 9 =

+ = + =

7. 6 − 3 = 8. 8 − 4 =

+ = + =

4− 2

2

12− 6 +

2+ 2

4

14− 7 +

10− 5 +

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Practice B32

Practice

B32Stories About SeparatingDraw a picture to find the difference. Write a subtraction sentence.

1. Pete has 16 stickers. He uses 9 of them. How many stickers does he have left?

7 stickers 16 − 9 =

2. Hong has 10 stamps. She gives 6 stamps to Joe. How many stamps does she have left?

4 stamps 6 stamps

5 stamps 7 stamps

3. James has 12 rocks. He puts 7 rocks in Maria’s garden. Which subtraction sentence tells how many rocks he has left?

7 − 2 = 5 12 − 5 = 7

7 − 4 = 3 12 − 7 = 5

16

10

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Practice B33

Practice

B33Stories About ComparingDraw a picture to find the difference. Write a subtraction sentence.

1. A pond has 11 weeds and 7 lily pads. How many more weeds than lily pads does the pond have?

4 more weeds 11 − 7 = 42. A vine has 8 red leaves and

5 brown leaves. How many fewer brown leaves does the vine have?

fewer brown leaves − =

3. Mike plants 6 trees. Faye plants 4 trees. How many fewer trees does Faye plant than Mike?

2 fewer trees 6 fewer trees


4. Write a math story about comparing to go with the picture.

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Practice B44

Practice

B44Arrays and MultiplicationComplete the sentence for each grid.

1.

3 × 4 = 12 × = rows in each product rows in each product row row

2.

× = × = rows in each product rows in each product row row

Which number sentence fits the grid?

3.

2 × 5 = 10 2 × 7 = 14

2 × 6 = 12 3 × 6 = 18

4. Write multiplication sentences.

× = × =

Do both grids show the same number?

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Practice B47

Practice

B47

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20.

Multiplying by 2 and 5Multiply. Use cubes if you need to.

2s Facts

0 × 2 = 0 5 × 2 = 10

1 × 2 = 2 6 × 2 = 12

2 × 2 = 4 7 × 2 = 14

3 × 2 = 6 8 × 2 = 16

4 × 2 = 8 9 × 2 = 18

5s Facts

0 × 5 = 0 5 × 5 = 25

1 × 5 = 5 6 × 5 = 30

2 × 5 = 10 7 × 5 = 35

3 × 5 = 15 8 × 5 = 40

4 × 5 = 20 9 × 5 = 45


2× 0

5× 1

2× 4

2× 2

5× 3

5× 0

2× 1

2× 7

5× 2

2× 5

6× 3

5× 4

5× 7

5× 8

2× 6

4× 3

2× 9

2× 8

5× 9

5× 6

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Practice C8

Practice

C8Adding Two-Digit and One-Digit NumbersAdd. Regroup if you need to.

1. 2. 3. 4.

5. 6. 7. 8.

9. Bessie has 25 flowers. Then she picks 9 more flowers. How many flowers does Bessie have in all?

33 34 35 36

10. Tell how you know when to regroup.

Tens Ones

+ 7 6 7

8 3

Tens Ones

+

6 4 3

Tens Ones

+

8 3 6

Tens Ones

+

3 7 9

Tens Ones

+

7 5 7

Tens Ones

+

5 0 8

Tens Ones

+

7 6 4

Tens Ones

+

8 3 5

1

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Practice C12

Practice

C12


4. 5.

6 tens � 2 tens tens � tens

60 � 20 � 40 � �

6. 7.

tens � tens tens � tens

� � � �

8. 9.


� � � �

Subtracting Tens

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Practice C13

Practice

C13

Add on to find the other part of 100.

1. 2.

54 � � 100 89 � � 100

3. 4.

43 � � 100 72 � � 100

5. 29 � � 100 6. 18 � � 100

7. 37 � � 100 8. 65 � � 100

9. The lunchroom holds 100 children. There are 50 children eating in the lunchroom. How many more can join them?

� � 100 children


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Practice C22

Practice

C22Two-Digit SubtractionWrite the subtraction problem. Find the difference.

1. 64 � 39 2. 65 � 16 3. 72 � 31 4. 56 � 29

5. 84 � 25 6. 34 � 16 7. 96 � 48 8. 43 � 27

Subtract. Regroup if you need to.

9.

Tens Ones

−

6 43 9

2 5

5 14Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

92− 18

36− 25

64− 47

18− 5

86− 33

77− 69

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C31

Practice C31

Estimating DifferencesEstimate by rounding to the nearest ten.

1. 92 2. 63 3. 43 � 32 4. 94 � 28 _ � 56 _ � 48

5. 89 6. 75 7. 48 � 18 8. 51 � 28 _ � 48 _ � 32

9. 23 10. 37 11. 76 � 53 12. 28 � 16 _ � 18 _ � 12


13. 820 14. 421 15. 637 � 231 16. 861 � 375 _ � 205 _ � 196

17. 794 18. 679 19. 916 � 593 20. 681 � 232 _ � 512 _ � 199

21. 909 22. 726 23. 694 � 203 24. 550 � 414 _ � 287 _ � 204

25. Marlee has 845 baseball cards and Kin has 612 baseball cards. About how many more baseball cards does Marlee have than Kin?

26. Reasoning What is the smallest number that can be subtracted from 723 so that the difference is 200 when both numbers are rounded to the nearest hundred?

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Practice D25

Practice

D25InchesEstimate the length of each object.Then use a ruler to measure.

1.

Estimate: inches

Measure: 4 inches

2. Estimate: inches

Measure: inches

3. Estimate: inches

Measure: inches

4. Measure the length of the straw in inches. About how long is the straw?

5 inches 7 inches

6 inches 8 inches

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Practice D26

Practice

D26Centimeters and MetersEstimate the length of each item. Then measure to the nearest centimeter. Write about how many centimeters long.

1.

Estimate: cm long

Measure: 16 cm long

2.

Estimate: cm long

Measure: cm long

3.

Estimate: m long

Measure: m long

4. What is the best estimation for the length of the rope?

2 m 5 m 15 cm 25 cm

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Practice D50

Practice

D50Flat Surfaces of Solid FiguresCircle the solid figure or figures that have flat surfaces you can trace to make the plane shape.

1.

2.

3. Dionne traces a square using a solid shape.Which solid shape does he have?

4. Which object did Maggie use to trace the rectangle?

5. Circle the block or blocks Vincent can trace to draw the bug.

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Practice D51

Practice

D51

Write how many sides and corners.

1. 2.

4 sides 4 corners sides corners

3. 4.

sides corners sides corners

5. 6.


7. 8.



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Practice D89

Practice

D89Making Bar Graphs to Show OutcomesJoey had a bag of animal erasers. He recorded the number of times he drew each animal eraser out of the bag.

1. Fill in the missing numbers and tally marks.

Animal Erasers

Outcome Tally Number

Cow 2

Duck

Pig

Sheep 6

2. Make a bar graph with the data.

Animal Erasers

Num

ber

of A

nim

als

Outcome

0

1

2

3

4

5

6

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A29 A32

A41 A61Answers: A29, A32, A41, A61

Answers for Practice

A29, A32, A41, A61

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Practice A29

Practice

A29Number Words to TwentyWrite the number.

1. four 4 2. seven

3. five 4. eight

5. twelve 6. eleven

7. fourteen 8. twenty

9. seventeen 10. nineteen

11. thirteen 12. sixteen

Write the number word.

13. 1 one 14. 2

15. 3 16. 6

17. 10 18. 9

5 8

7

14 20

12 11

13 16

17 19

two

sixthree

nineten

45093_Practice_A29-D89.indd A29 6/30/08 11:59:33 AM

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Practice A32

Practice

A32Numbers to 100 on the Number LineUse the number line below. Write the numbers in order.

1. 45, 32, 59, 51

32 45

2. 35, 45, 60, 30

3. 49, 37, 68, 55


38 44

42 60


15 21

17 23

51 59

30 35 45 60

37 49 55 68


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Practice A41

Practice

A41

1. 2.

Understanding 1 as a FractionColor to show 1 whole.Write the fraction that equals 1 whole.

= 133

= 1

3. 4.

7. Which fraction is equal to 1 whole?

1 _ 4 2 _

4 3 _ 4 4 _

4

= 1 = 1

5. 6.

= 1 = 1

6

6

5

5

4

4

8

8

2

2


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Practice A61

Practice

A61Comparing Sets of CoinsWrite the total amounts and compare them.Write >, <, or =.

1.

65¢

2.

3.

Choose the correct symbol.

4.

> < = ¢

5.

> < = ¢

56¢>

20¢ 36¢<

60¢ 60¢=


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A86 B23

B32 B33Answers: A86, B23, B32, B33


A86, B23, B32, B33

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Practice A86

Practice

A86Ordering Numbers to 999Write the numbers in order from least to greatest.

1. 207 , 267 , 276 least greatest

2. , , least greatest

Write the numbers in order from greatest to least.



5. Which number is the least?

529 531 560 528

6. Which number is the greatest?

120 102 110 100

7. Tell how you would decide which number is the greatest. Then circle it.

572, 570, 576

276 267 207

16 600 60

986 789 892

377 737 773

570, 572, 576 Answers will vary.

16 60 600

986 892 789

773 737 377


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Practice B23

Practice

B23Using Doubles to Subtract Subtract. Write the doubles fact that helped you.Use cubes if you need to.

1. 2.

3. 4.

5. 16 − 8 = 6. 18 − 9 =

+ = + =

7. 6 − 3 = 8. 8 − 4 =

+ = + =

4− 2

2

12− 6 +

2+ 24

14− 7 +

10− 5 +

6

6

6

12

8 8 16 9 9 18

8 9

7

7

7

145

5

5

10

3 3 6 4 4 8

3 4

45093_Practice_A29-D89.indd B23 6/30/08 11:59:43 AM

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Practice B32

Practice

B32Stories About SeparatingDraw a picture to find the difference. Write a subtraction sentence.

1. Pete has 16 stickers. He uses 9 of them. How many stickers does he have left?

7 stickers 16 − 9 =

2. Hong has 10 stamps. She gives 6 stamps to Joe. How many stamps does she have left?

4 stamps 6 stamps

5 stamps 7 stamps

3. James has 12 rocks. He puts 7 rocks in Maria’s garden. Which subtraction sentence tells how many rocks he has left?

7 − 2 = 5 12 − 5 = 7

7 − 4 = 3 12 − 7 = 5

16

10

7


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Practice B33

Practice

B33Stories About ComparingDraw a picture to find the difference. Write a subtraction sentence.

1. A pond has 11 weeds and 7 lily pads. How many more weeds than lily pads does the pond have?

4 more weeds 11 − 7 = 42. A vine has 8 red leaves and

5 brown leaves. How many fewer brown leaves does the vine have?

fewer brown leaves − =

3. Mike plants 6 trees. Faye plants 4 trees. How many fewer trees does Faye plant than Mike?



4. Write a math story about comparing to go with the picture.

Pictures will vary.

Answers will vary.

3 8 5 3

Pictures will vary.

Pictures will vary.


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B44, B47, C8, C12

B44 B47

C8 C12Answers: B44, B47, C8, C12

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Practice B44

Practice

B44Arrays and MultiplicationComplete the sentence for each grid.

1.

3 × 4 = 12 × = rows in each product rows in each product row row

2.

× = × = rows in each product rows in each product row row

Which number sentence fits the grid?

3.

2 × 5 = 10 2 × 7 = 14

2 × 6 = 12 3 × 6 = 18

4. Write multiplication sentences.

× = × =

Do both grids show the same number?

4 3 12

4 2 82 4 8

yes

3 5 155 3 15


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Practice B47

Practice

B47

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20.

Multiplying by 2 and 5Multiply. Use cubes if you need to.

2s Facts

0 × 2 = 0 5 × 2 = 10

1 × 2 = 2 6 × 2 = 12

2 × 2 = 4 7 × 2 = 14

3 × 2 = 6 8 × 2 = 16

4 × 2 = 8 9 × 2 = 18

5s Facts

0 × 5 = 0 5 × 5 = 25

1 × 5 = 5 6 × 5 = 30

2 × 5 = 10 7 × 5 = 35

3 × 5 = 15 8 × 5 = 40

4 × 5 = 20 9 × 5 = 45


2× 0

5× 1

2× 4

2× 2

5× 3

5× 0

2× 1

2× 7

5× 2

2× 5

6× 3

5× 4

5× 7

5× 8

2× 6

4× 3

2× 9

2× 8

5× 9

5× 6

0

5

8

4

15

0

2

14

10

10

18

20

35

40

12

12

18 16 45 30


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Practice C8

Practice

C8Adding Two-Digit and One-Digit NumbersAdd. Regroup if you need to.

1. 2. 3. 4.

5. 6. 7. 8.

9. Bessie has 25 flowers. Then she picks 9 more flowers. How many flowers does Bessie have in all?

33 34 35 36

10. Tell how you know when to regroup.

Tens Ones

+ 7 6 7

8 3

Tens Ones

+

6 4 3

Tens Ones

+

8 3 6

Tens Ones

+

3 7 9

Tens Ones

+

7 5 7

Tens Ones

+

5 0 8

Tens Ones

+

7 6 4

Tens Ones

+

8 3 5

1

6 7 8 9 4 6

1

8 2 5 8 8 0 8 8

11

Answers will vary.

45093_Practice_A29-D89.indd C8 6/30/08 11:59:52 AM

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Practice C12

Practice

C12


4. 5.

6 tens � 2 tens tens � tens

60 � 20 � 40 � �

6. 7.


� � � �

8. 9.


� � � �

Subtracting Tens

6 3

60 30 30

8 4 9 7

80 40 40 90 70 20

7 5 5 5

70 50 20 50 50 0


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C13, C22, C31, D25

C13 C22

C31 D25Answers: C13, C22, C31, D25

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Practice C13

Practice

C13

Add on to find the other part of 100.

1. 2.

54 � � 100 89 � � 100

3. 4.

43 � � 100 72 � � 100

5. 29 � � 100 6. 18 � � 100

7. 37 � � 100 8. 65 � � 100

9. The lunchroom holds 100 children. There are 50 children eating in the lunchroom. How many more can join them?

� � 100 children


11

57 28

71 82

63 35

50 50 50

46


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Practice C22

Practice

C22Two-Digit SubtractionWrite the subtraction problem. Find the difference.

1. 64 � 39 2. 65 � 16 3. 72 � 31 4. 56 � 29

5. 84 � 25 6. 34 � 16 7. 96 � 48 8. 43 � 27

Subtract. Regroup if you need to.

9.

Tens Ones

−

6 43 9

2 5

5 14Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

Tens Ones

−

92− 18

36− 25

64− 47

18− 5

86− 33

77− 69

74 11 17 13 53 8

5

4 9

156 51 6

56

4 1

7 23 1

4

2 7

165 62 9

65

7

5 9

148 42 5

482

1 8

143 41 6

438

4 8

169 64 8

693

1 6

134 32 7

34

45093_Practice_A29-D89.indd C22 6/30/08 12:00:00 PM

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Practice

C31

Practice C31

Estimating DifferencesEstimate by rounding to the nearest ten.

1. 92 2. 63 3. 43 � 32 4. 94 � 28 _� 56 _� 48

5. 89 6. 75 7. 48 � 18 8. 51 � 28 _� 48 _� 32

9. 23 10. 37 11. 76 � 53 12. 28 � 16 _� 18 _� 12


13. 820 14. 421 15. 637 � 231 16. 861 � 375 _� 205 _� 196

17. 794 18. 679 19. 916 � 593 20. 681 � 232 _� 512 _� 199

21. 909 22. 726 23. 694 � 203 24. 550 � 414 _� 287 _� 204

25. Marlee has 845 baseball cards and Kin has 612 baseball cards. About how many more baseball cards does Marlee have than Kin?

26. Reasoning What is the smallest number that can be subtracted from 723 so that the difference is 200 when both numbers are rounded to the nearest hundred?

6010

2030

1030

500400

500300

200500

200

30 10

40 50

0 30

600 200

300 500

600 500

450

45093_Practice_A29-D89.indd C31 6/30/08 12:00:02 PM

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Practice D25

Practice

D25InchesEstimate the length of each object.Then use a ruler to measure.

1.

Estimate: inches

Measure: 4 inches

2. Estimate: inches

Measure: inches

3. Estimate: inches

Measure: inches

4. Measure the length of the straw in inches. About how long is the straw?

5 inches 7 inches

6 inches 8 inches

Answers will vary.

Answers will vary.

2

Answers will vary.

3

45093_Practice_A29-D89.indd D25 6/30/08 12:00:04 PM

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D26, D50, D51, D89

D26 D50

D51 D89Answers: D26, D50, D51, D89

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Practice D26

Practice

D26Centimeters and MetersEstimate the length of each item. Then measure to the nearest centimeter. Write about how many centimeters long.

1.

Estimate: cm long

Measure: 16 cm long

2.

Estimate: cm long

Measure: cm long

3.

Estimate: m long

Measure: m long

4. What is the best estimation for the length of the rope?

2 m 5 m 15 cm 25 cm

Answers will vary.

Answers will vary.

Answers will vary.1

12


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Practice D50

Practice

D50Flat Surfaces of Solid FiguresCircle the solid figure or figures that have flat surfaces you can trace to make the plane shape.

1.

2.

3. Dionne traces a square using a solid shape.Which solid shape does he have?

4. Which object did Maggie use to trace the rectangle?

5. Circle the block or blocks Vincent can trace to draw the bug.


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Practice D51

Practice

D51

Write how many sides and corners.

1. 2.

4 sides 4 corners sides corners

3. 4.


5. 6.


7. 8.



8 8

6 6 4 4

6 60 0

3 3 5 5


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Practice D89

Practice

D89Making Bar Graphs to Show OutcomesJoey had a bag of animal erasers. He recorded the number of times he drew each animal eraser out of the bag.

1. Fill in the missing numbers and tally marks.

Animal Erasers

Outcome Tally Number

Cow 2

Duck

Pig

Sheep 6

2. Make a bar graph with the data.

Animal Erasers

Num

ber

of A

nim

als

Outcome

0

1

2

3

4

5

6

45

Cow Duck Pig Sheep


50 5149 53 54 56 57 58 59 60

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T1

Name Grade 1

Step Up to Grade 2 Test

1. 11

twelve eleven ten one

2.

50, 51 50, 55 52, 55 51, 55

3.

1 _ 4 2 _ 4 3 _ 4 4 _ 4

4.

5. 462, 264, 626 462, 626, 264

264, 626, 462 264, 462, 626

Directions Mark the best answer. 1. What is the word number for 11? 2. Which two numbers are missing? 3. Which fraction is equal to 1 whole? 4. Which set of coins is worth the most? 5. Which group shows the numbers in order from least to greatest?

14

?

Name Grade 1


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T2

Directions Mark the best answer. 6. 6 + 6 = 12 so 12 – 6 equals? 7. In the morning, 14 books were on the shelf. In the afternoon, 6 books were checked out. How many books are left on the shelf? 8. Linda has 12 new pencils. Rachel has 7 new pencils. How many more new pencils does Linda have than Rachel? 9. 6 rows with 5 in each row. How many in all? 10. 2 rows with 8 in each row. How many in all?

6. 6 � 6 � 12 so 12 � 6 � ____

12 9 6 4

7.

8 7

6 5

8.

8 7 6 5

9.

30 33

35 37

10. 2� 8 13 14

15 16

Linda Rachel

6 � 5

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T3

Name Grade 1


Directions Mark the best answer. 11. Add these two numbers. Use the workspace. 12. Which number sentence matches this picture? 13. Add on to find the other part of 100. 14. Subtract. 15. Estimate the answer by rounding to the nearest ten.

11. 44 45

46 47

12. _____ tens � _____ tens

40 � 10 � 30 40 � 20 � 20

40 � 30 � 10 40 � 40 � 0

13. 75 � _____ � 100

20 25 30 35

14.

24 25

26 27

15. 89 � 22

70 65 60 55

Tens Ones

�

25

52

Tens Ones

�

3 9 6

Name Grade 1


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T4

Directions Mark the best answer. 16. About how long is the pencil? 17. About how long is this toothbrush? 18. Which solid figure has this flat surface? 19. How many corners? 20. How many students liked oat cereal best?

16.

1 inch 2 inches

6 inches 15 inches

17.



18.

19. 7 6

5 4

20. Favorite CerealsOutcome Tally Number

Rice 5

Corn 11

Oat ___

Wheat 3

3 5

7 11

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Answers for Test

T1, T2, T3, T4

T1 T2

T4T3Answers: T1, T2, T3, T4

50 5149 53 54 56 57 58 59 60

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T1

Name Grade 1


1. 11

twelve eleven ten one

2.

50, 51 50, 55 52, 55 51, 55

3.

1_4 2_4 3_4 4_4

4.

5. 462, 264, 626 462, 626, 264

264, 626, 462 264, 462, 626

Directions Mark the best answer. 1. What is the word number for 11? 2. Which two numbers are missing?3. Which fraction is equal to 1 whole? 4. Which set of coins is worth the most? 5. Which group shows the numbers in order from least to greatest?

45093_T1-T4.indd T1 7/1/08 2:02:19 PM

14

?

Name Grade 1


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T2

Directions Mark the best answer. 6. 6 + 6 = 12 so 12 – 6 equals? 7. In the morning, 14 books were on the shelf. In the afternoon, 6 books were checked out. How many books are left on the shelf? 8. Linda has 12 new pencils. Rachel has 7 new pencils. How many more new pencils does Linda have than Rachel? 9. 6 rows with 5 in each row. How many in all? 10. 2 rows with 8 in each row. How many in all?

6. 6 � 6 � 12 so 12 � 6 �� ____

12 9 6 4

7.

8 7

6 5

8.

8 7 6 5

9.

30 33

35 37

10. 2�� 8 13 14

15 16

Linda Rachel

6 � 5

45093_T1-T4.indd T2 7/1/08 2:02:21 PM

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T3

Name Grade 1


Directions Mark the best answer. 11. Add these two numbers. Use the workspace. 12. Which number sentence matches this picture? 13. Add on to find the other part of 100. 14. Subtract. 15. Estimate the answer by rounding to the nearest ten.

11. 44 45

46 47

12. _____ tens �� _____ tens

40 � 10 �� 30 40 � 20 �� 20

40 � 30 �� 10 40 � 40 � 0

13. 75 � _____ �� 100

20 25 30 35

14.

24 25

26 27

15. 89 �� 22

70 65 60 55

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45093_T1-T4.indd T3 7/1/08 2:02:23 PM

Name Grade 1


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Directions Mark the best answer. 16. About how long is the pencil? 17. About how long is this toothbrush? 18.Which solid figure has this flat surface? 19. How many corners? 20. How many students liked oat cereal best?

16.

1 inch 2 inches

6 inches 15 inches

17.



18.

19. 7 6

5 4

20. Favorite CerealsOutcome Tally Number

Rice 5

Corn 11

Oat ___

Wheat 3

3 5

7 11

45093_T1-T4.indd T4 7/1/08 2:02:24 PM

Upper Saddle River, New Jersey Grade 1: Step Up to Grade...

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