Grade 2: Step Up to Grade 3

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Grade 2: Step Up to Grade 3 

Teacher’s Guide 

• Teacher Notes and Answers 

for Step-Up Lessons 

• Practice 

• Answers for Practice 

• Test 

• Answers for Test

A42 E qual 

Parts 

of 

a Whole 

A43 P arts 

of 

a Region 

A47 U sing 

Models 

to 

Compare 

Fractions 

A48 

U sing 

Models 


Find 

Equivalent 

Fractions 

A74 Repeating Patterns 

B45 Using Multiplication 

to Compare 

B48 Multiplying by 9 

B56 Multiplying Three Numbers 

B62 Dividing by 8 and 9 

B63 0 and 1 in Division 

C26 U sing 

Mental 

Math 


Add 

C27 Using Mental Math to Subtract 

C28 A dding 

Two-Digit 

Numbers 

C29 S ubtracting 

Two-Digit 

Numbers 

C37 Adding Three Numbers 

D59 Solid Figures 

D62 Acute, Right, and Obtuse Angles 

D63 Polygons 

D64 Classifying Triangles Using Sides 

and Angles 

D65 Quadrilaterals

© Pearson Education, Inc. 2 

Equal Parts of a Whole 

© Pearson Education, Inc. 

Name 

Name 


Math Diagnosis and 

Intervention System 

Intervention Lesson A42 

Materials rectangular sheets of paper, 3 for each student; 

crayons or markers 

1. Fold a sheet of paper so the two shorter edges 

are on top of each other, as shown at the right. 

2. Open up the piece of paper. Draw a line down the fold. 

Color each part a different color. 

The table below shows special names 

for the equal parts. All parts must be equal 

before you can use these special names. 

3. Are the parts you colored equal in size? yes 

fold 

4. How many equal parts are there? 2 Number of Name of 

Equal Parts Equal Parts 

5. What is the name for the parts you colored? 2 halves 

halves 

3 thirds 

6. Fold another sheet of paper like above. 

Then fold it again so that it makes a long 

slender rectangle as shown below. 

7. Open up the piece of paper. Draw lines down 

the folds. Color each part a different color. 

8. Are the parts you colored equal in size? yes 

9. How many equal parts are there? 4 

10. What is the name for the parts you colored? 

fourths 

4 fourths 

5 fifths 

6 sixths 

8 eighths 

10 tenths 

12 twelfths 

New 

fold 

Old 

fold 

11. Fold another sheet of paper into 3 parts that are 

not equal. Open it and draw lines down the folds. 

In the space below, draw your rectangle and color 

each part a different color. 

Check that students draw unequal parts. 

Intervention Lesson A42 177 

Equal Parts of a Whole (continued) 

Tell if each shows parts that are equal or parts that are not equal. 

If the parts are equal, name them. 

12. equal 13. 

fourths 

14. 15. 

equal 

16. 17. 

equal 

not equal 

equal 

thirds eighths 

twelfths 

18. 19. 

not equal 

20. 21. 

equal 

halves 

22. 23. 

equal 

sixths 

24. Reasoning If 5 children want to equally share 

a large pizza and each gets 2 pieces, will they 

need to cut the pizza into fifths, eighths, or tenths? 

178 Intervention Lesson A42 




not equal 

equal 

fifths 

not equal 

not equal 

tenths 


Teacher Notes 




Ongoing Assessment 

Ask: Looking at the names for shapes divided 

into 4, 5, 6, 8, 10, and 12 equal parts, what might 

be the name of a shape divided into seven equal 

parts? sevenths 

Error Intervention 

If children have trouble understanding the concept 

of equal parts, 

then use A35: Equal parts. 

If You Have More Time 

Have students fold other rectangular sheets of 

paper and circular pieces of paper to find and name 

other equal parts. 

Intervention Lesson A42

Parts of a Region 


Name 

Name 


Materials crayons or markers 

1. In the circle at the right, color 2 of the equal 

parts blue and 4 of the equal parts red. 

Write fractions to name the parts by answering 2 to 6. 

2. How many total equal parts 

does the circle have? 6 

3. How many of the equal parts 

of the circle are blue? 

4. What fraction of the circle is blue? 

2 

6 

____ number of equal parts that are blue 

_____________________________ ____________ 

(numerator) 

total number of equal parts (denominator) 

Two sixths of the circle is blue. 

5. How many of the equal parts of the circle are red? 

6. What fraction of the circle is red? 

4 

6 

____ number of equal parts that are red 

____________________________ ____________ 

(numerator) 

total number of equal parts (denominator) 

Four sixths of the circle is red. 

Show the fraction 3 __ by answering 7 to 9. 

8 

7. Color 3 __ of the rectangle at the right. 

8 

8. How many equal parts does 

the rectangle have? 

8 

9. How many parts did you 

color? 

Parts of a Region (continued) 

Write the fraction for the shaded part of each region. 

10. 11. 12. 

2__ 

3 


2 

3 

1__ 

4 

13. 14. 15. 

1__ 

2 

2__ 

8 

16. 17. 18. 

1__ 

3 

Color to show each fraction. 

19. 3 __ 

4 

20. 5 __ 

6 

3__ 

5 

21. 7 ___ 

10 

22. Math Reasoning Draw a picture to show 1 __ . Then divide 

3 

each of the parts in half. What fraction of the parts does 

the 1 __ represent now? Check students’ drawings. 

3 

23. Ben divided a pie into 8 equal pieces and ate 3 of them. 

How much of the pie remains? 





4 





4__ 

5 

2__ 

5 

5__ 

8 

2__ 

6 

5__ 

8 


Teacher Notes 





Ask: Janet said she ate 4 

of an orange. Explain 

4 

why Janet could have said she ate the whole 

__ 

orange. Sample answer: The orange would be cut 

in 4 pieces and she ate 4 pieces, so she ate the 

whole thing. 


If children have trouble writing fractions for parts of 

a region, 

then use A36: Understanding Fractions to Fourths 

and A38: Writing Fractions for Part of a Region. 


Have students design a rectangular flag (or rug, 

placemat, etc.) that is divided into equal parts. Have 

them color their flag and then on the back write the 

fractional parts of each color. 

© Pearson Education, Inc. 2


Using Models to Compare Fractions 


Name 

Name 

Using Models to Compare Fractions 

Materials fraction strips 

Use , , or to compare 4 __ and 

5 2 __ by answering 1 to 3. 

3 

1. Show 1, 4 __ , and 

5 2 __ with 

3 

fraction strips. 

2. Compare. Which is greater 

in total length, 4 __ or 

5 2 __ ? 

3 

4__ 

5 




1 

1 __ 

5 1 __ 

5 1 __ 

5 1 __ 

5 

1 __ 

3 1 __ 

3 

3. Since 4 __ is longer than 

5 2 __ , 

3 4 __ is greater than 

5 2 __ . Write , , or . 

3 4 __ 

5 2 __ 

3 

Compare 1 ___ and __ 1 

by answering 4 to 6. 

10 4 

4. Show 1, 1 ___ , and __ 1 

with fraction strips. 

10 4 1 

1 ___ 

10 

1 


in total length, 

__ 

4 

1 

1__ 

___ 1 

or __ ? 4 

10 4 

6. Since 1 ___ is shorter than __ 1 

, 

10 4 1 ___ is less than 

__ 1 

. Write , , or =. 

10 4 1 ___ 

10 1 

Compare 

__ 

4 

2 __ and 

5 4 ___ by answering 7 to 9. 

10 

7. Show 1, 2 __ , and 

5 4 ___ with fraction strips. 

10 


in total length, 2 __ or 

5 4 ___ 

10 ? 

They are the same length. 

1 __ 

5 1 __ 

5 

1 ___ 

10 1 ___ 

10 

1 ___ 

10 1 ___ 

10 

9. Since 2 __ and 

5 4 ___ are the same length, 

10 2 __ is equal to 

5 4 ___ . Write , , or . __ 2 

10 5 4 ___ 

10 

Using Models to Compare Fractions (continued) 

Compare. Write , or =. 

10. 1 __ 

4 3 __ 

4 

1 __ 

4 

1 __ 

4 1 __ 

4 1 __ 

4 

12. 2 __ 

3 4 __ 

6 

1 __ 

3 1 __ 

3 

1 __ 

6 1 __ 

6 1 __ 

6 1 __ 

6 

14. 1 __ 

2 1 __ 

5 

1 __ 

5 

1 __ 

2 

16. 2 __ 

6 1 __ 

2 

1 __ 

6 1 __ 

6 

1 __ 

2 

18. Reasoning Give 3 fractions with different 

denominators that are less than 4 __ . 

6 

11. 3 __ 

4 2 __ 

8 

1 __ 

4 1 __ 

4 1 __ 

4 

1 __ 

8 1 __ 

8 

13. 1 __ 

5 5 ___ 

10 

1 __ 

5 

1 ___ 

10 1 ___ 

10 1 ___ 

10 1 ___ 

10 1 ___ 

10 

15. 7 __ 

8 3 __ 

4 

1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 

1 __ 

4 1 __ 

4 1 __ 

4 

17. 3 __ 

5 1 __ 

4 

1 __ 

5 1 __ 

5 

1 __ 

4 

1 __ 

5 

1 


Answers will vary. 

19. Reasoning Two students are writing stories. 

Eric’s story is 2 __ of a page. Alba’s story is 

3 4 __ of 

6 

a page. Whose story is longer? They are equal. 






Teacher Notes 





Make sure children can translate simple number 

sentences such as 7 8, 4 2, and 6 6 into 

words. 


If children have difficulty with the concepts of 

greater than and less than, or with the symbols, 

then use A27: Using , , and to Compare 

Numbers. 


Have students pretend they are each painting 

a board. Have the students say how much they 

have stained. Then use fraction strips to show and 

compare who has stained more. Have each student 

write the comparison on paper. 


Using Models to Find Equivalent 

Fractions 


Name 

Name 

Using Models to Find Equivalent Fractions 

Materials fraction strips 

Find a fraction equivalent to 3 __ by answering 1 to 3. 

4 

1. Show a 1 and 3 __ with fraction strips. 

4 1 

1 __ 

4 1 __ 

4 1 

2. How many 

__ 

4 

1 __ strips does 

8 

it take to equal 3 __ ? 6 

4 

3 __ 

4 6 _______ 

8 

3. So, 3 __ is equal to six 

4 1 __ strips. 

8 

Find the missing number in 1 __ 

2 ? 

____ 

10 , 

by answering 4 to 7. 





1 

1 __ 

4 1 __ 

4 1 __ 

4 

1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 

The denominators of the fractions tell which fraction strips to use. 

4. Show 1 and 1 __ with fraction strips. 

2 1 

1 

5. What is the denominator of 

the second fraction? 10 

__ 

2 

6. Since the denominator of the second 

fraction is 10, find the number 

of 1 ___ strips equal to __ 1 

. 5 

10 2 

7. So, 1 __ is equal to five 

2 1 ___ 

10 strips. 

1 __ 

 

2 5 ____ 

10 

Using Models to Find Equivalent Fractions (continued) 

Complete each number sentence. 

8. 

10. 

12. 

1 __ 

4 

1 __ 

8 1 __ 

8 

1 

9. 

1 

1 __ 

2 

1 ___ 

10 1 ___ 

10 1 ___ 

10 1 ___ 

10 1 ___ 

10 


1 

1 __ 

6 1 __ 

6 1 __ 

6 1 __ 

6 

1 __ 

3 1 __ 

3 

1 __ 

4 2 _______ 

8 2 __ 

3 4 _______ 

6 

1 __ 

2 

1 __ 

8 1 __ 

8 1 __ 

8 1 __ 

8 

1 

11. 

1 __ 

5 1 __ 

5 

1 ___ 

10 1 ___ 

10 1 ___ 

10 1 ___ 

10 

1 __ 

2 4 _______ 

8 2 __ 

5 4 _______ 

10 

1 

1 __ 

3 1 __ 

3 

1 ___ 

12 1 ___ 

12 1 ___ 

12 1 ___ 

12 1 ___ 

12 1 ___ 

12 1 ___ 

12 1 ___ 

12 

13. 

1 __ 

4 1 __ 

4 

1 __ 

6 1 __ 

6 1 __ 

6 

2 __ 

3 8 _______ 

12 2 __ 

4 3 _______ 

6 

14. Reasoning On Tuesday, 2 __ of the class time was spent 

3 

on math projects. How many sixths of the class time was 

spent on math projects? 





1 

1 

4__ 

6 


Teacher Notes 





Ask: How many twelfths are equal to 1 

__ 

? 

3 4 ___ 

12 


If students have trouble finding the equivalent 

fraction for Exercise 14, 

then encourage them to use fraction strips. 


Have students use fraction strips to find fractions 

equivalent to 1 __ . Have them record their findings. If 

2 

time allows, do the same for 1 __ and 

4 3 __ . 

4 



Repeating Patterns 


Name 

Name 


Materials pattern blocks or shapes cut out of colored paper 

(10 orange squares, 10 green triangles, 10 red 

trapezoids) for each pair of students; 24 index cards 

(eight labeled 2, eight labeled 3, and eight labeled 4) 

for each pair of students 

Look at the pattern of shapes. 

1. Work with your partner to show the pattern. 

What is the next shape? 

2. Continue the pattern. What is the 14th shape? 

3. What is the 16th shape? 




square 

square 

trapezoid 

4. Work with your partner and use the shapes to make a new 

pattern. Draw the pattern below. Draw the next four shapes. 

Answers will vary. Check that patterns repeat 

consistently. 

Look at the pattern of numbers. 

3 

3 

2 

4 

3 3 

5. Work with your partner to show the pattern. 

What is the next number? 

6. Continue the pattern. What is the 12th number? 

7. What is the 15th number? 

8. Work with your partner and use the numbers to make a 

new pattern. Write the pattern below. Write the next four 

numbers. Answers will vary. Check that patterns 

repeat consistently. 

Repeating Patterns (continued) 

Draw the next three shapes to continue each pattern. 

9. 

10. 

11. 

Write the next three numbers to continue each pattern. 

12. 1, 4, 6, 7, 1, 4, 6, 7, 1, 4, 6 , 7 , 1 

13. 8, 8, 9, 8, 8, 9, 8, 8, 9, 8, 8 , 9 , 8 

14. 3, 2, 0, 0, 3, 2, 0, 0, 3, 2, 0, 0 , 3 , 2 

15. 4, 4, 6, 6, 8, 8, 4, 4, 6, 6, 8, 8, 4, 4 , 6 , 6 

16. Create a pattern using all the shapes shown below. 

2 

4 

3 

4 

2 

3 


Answers will vary. Sample answer: square, circle, 

square, circle, square, circle, square, circle 

17. Create a pattern using all the letters shown below. 

T T T L L W W L W 

Answers will vary. Sample answer: TLWTLWTLW 






Teacher Notes 





Ask: Can a pattern be formed by using only 

circles? Sample answer: Yes, if different size circles 

are used. The pattern could be small circle, small 

circle, big circle. 


If students can recognize the numerical patterns, 

but have trouble recognizing the geometric 

patterns, 

then have students assign/label each type of 

shape with a different number or letter. Have them 

look for a pattern with the numbers. For example, 

the squares could be “1”, triangles “2”, and 

trapezoids “3”. 

If students can not spell the names of the shapes, 

then have students draw the shapes instead of 

naming them. 


Have one student in each pair use the shapes or 

index cards to make a pattern for their partner to 

extend. Change roles and repeat. 


Using Multiplication to Compare 


Name 

Name 

Using Multiplication to Compare 

Materials 12 counters per student 

Alicia has 2 stickers. Pedro has 3 times as many stickers 

as Alicia. How many stickers does Pedro have? 

1. Show Alicia’s stickers 

with counters. 

2. Show Pedro’s stickers 

with counters. 

Intervention Lesson B45 




3. Write a multiplication sentence. 

3 times as many as Alicia has equals number Pedro has 

3 2 6 

4. How many stickers does Pedro have? 

Mia has 4 yo-yos. Flo has twice as many as Mia. How many 

yo-yos does Flo have? 

The word twice in a word problem means 2 times as many. 

5. Show Mia’s yo-yos with 

counters. 

6. Show Flo’s yo-yos with 

counters. 

7. Write a multiplication sentence. 

2 times as many as Mia has equals number Flo has 

2 4 8 

8. How many yo-yos does Flo have? 

Using Multiplication to Compare (continued) 

Solve. You may use drawings or counters to help. 

9. Janos has 3 stickers. Lucy has twice as many stickers 

as Janos. How many stickers does Lucy have? 

6 stickers 

10. Rob has 4 model airplanes. Julio has 3 times as many model 

airplanes as Rob. How many model airplanes does Julio 

have? 

12 model airplanes 

11. Mr. King has 5 apples left in his store. Ruth needs twice as 

many apples to bake apple pies. How many apples does 

Ruth need? 

10 apples 

Use the recipe to answer Exercises 12–15. 

12. The recipe serves 5 people. Joan wants to make 

the recipe for 15 people. How many times more 

is this? 

3 times more 

13. How many bananas will Joan need to make the 

recipe for 15 people? 

3 3 9 bananas 

14. How many cups of strawberries will Joan need 

to make the recipe for 15 people? 

6 cups 

15. Reasoning If Joan wants to make twice as much as the 

recipe in the chart, what will she need to do to all of the 

ingredients? 

double them 

154 Intervention Lesson B45 

8 

6 

Intervention Lesson B45 153 




Fruit Smoothie 

3 large bananas 

2 cups strawberries 

1 cup orange juice 

1 cup cranberry juice 

1 cup ice cubes 

Blend until smooth. 

Makes 5 servings. 


Teacher Notes 





Ask: 12 is twice as many as what number? 6 


If students have trouble figuring out how to draw 

the unknown amount, 

then encourage students to show the first group 

n times. For example, since Wayne has 3 times as 

many as Alicia, show what Alicia has 3 times. 


Have students cut out 9 small squares and label 

them 1 through 9. Have one partner pick a square. 

The other partner calculates 3 times the number 

picked. Do not return the number to the pile. 

Continue until all squares have been picked. Repeat 

the activity by having students calculate 5 times 

each number picked. 



Multiplying by 9 


Name 

Name 


Learn how to multiply by 9 by answering 1 to 5. 

1. Complete the table. 

Fact Product 

Two Digits in the 

Product 




Sum of the Two Digits 

in the Product 

0 9 0 0 and 0 0 0 0 

1 9 9 0 and 9 0 9 9 

2 9 18 1 and 8 1 8 9 

3 9 27 2 and 7 2 7 9 

4 9 36 3 and 6 3 6 9 

5 9 45 4 and 5 4 5 9 

6 9 54 5 and 4 5 4 9 

7 9 63 6 and 3 6 3 9 

8 9 72 7 and 2 7 2 9 

9 9 81 8 and 1 8 1 9 

2. Reasoning Besides the product of 0 9, what pattern do 

you see in the sums of the digits of each product? 

The sum of the digits is always 9. 

3. Look at the number being multiplied by 9 in each product 

and the tens digit of that product. 

When 3 is multiplied by 9, what is the tens digit of the product? 2 . 

When 6 is multiplied by 9, what is the tens digit of the product? 5 . 

Multiplying by 9 (continued) 

4. Reasoning Complete to describe the pattern you see in the 

tens digits of the products when a factor is multiplied by 9. 






The tens digit of the product is 1 less than the other factor. 

5. Complete the following to find 7 9. 

The tens digit is 7 1 6 . 

The ones digit is 9 6 3 . 

So, 7 9 

Find each product. 

63 and 9 7 63 . 

6. 1 7. 9 8. 9 9. 9 

_ 9 _ 2 _ 4 _ 0 

9 18 36 0 

10. 6 11. 9 12. 8 13. 5 

_ 9 _ 9 _ 9 _ 9 

54 81 72 45 

14. 9 15. 3 16. 2 17. 9 

_ 7 _ 9 _ 9 _ 6 

63 27 18 54 

18. Reasoning Joshua and his sister have each saved $9. They 

wish to buy a new game that costs $20. If they put their 

savings together, do they have enough money to buy the 

game? 

No, they only have $18; they are $2 short. 

19. Reasoning Jane said that 7 9 62. Explain how you 

know this is incorrect. 

The sum of the digits in the product does not 

equal 9. 


Teacher Notes 





Ask: Larry said that 6 9 45. Why is this 

incorrect? The tens digit of the product must be 1 

less than the number by which 9 is being multiplied. 

6 1 5, so the tens digit must be 5. The product 

is 54, not 45. 


If students have trouble while using the method 

described in the lesson, 

then show the students how to use their fingers to 

multiply by 9. Put both hands on your desk, palms 

down. Mentally number your fingers and thumbs 

from left to right, starting with 1. To find 3 9, bend 

down finger number 3. The number of fingers to 

the left of the bent finger shows the number in the 

tens place of the product. (2) The number of fingers 

to the right of the bent finger shows the number of 

ones in the product. (7) So, 3 9 27. 


Have pairs play I’m Thinking of a Number. One 

partner writes down a number from 0 to 9, such 

as 7, and says: I’m thinking of a number. When it 

is multiplied by 9, the product is 63. What is the 

number? The other partner says the number. Then, 

students change roles and repeat. 

Intervention Lesson B48

Multiplying Three Numbers 


Name 

Name 






Does it matter how you multiply 5 2 3? Answer 1–8 to 

find out. 

To show the factors you are multiplying first, use parentheses 

as grouping symbols. 

1. Group the first two factors together. ( 5 2 ) 3 

2. Multiply what is in the parentheses first. 5 2 10 

3. Then, multiply the product of what is 

in parentheses by the third factor. 10 3 30 

4. So, (5 2) 3 30 . 

5. Start again and group the last two 

factors together. 5 ( 2 3 ) 

6. Multiply what is in the parentheses first. 2 3 6 

7. Then, multiply 5 by the product of what 

is in parentheses. 5 6 30 

8. So, 5 (2 3) 30 . 

It does not matter how the factors are grouped; the product will 

be the same. 

9. 5 (2 3) ( 5 2 ) 3 

Find 3 2 4 two different ways. 

10. Do the 3 2 first. 

3 2 6 6 4 24 So, (3 2) 4 24 . 

11. Do the 2 4 first. 

2 4 8 3 8 24 So, 3 (2 4) 24 . 

Multiplying Three Numbers (continued) 

Find each product two different ways. 

12. (1 3) 6 18 13. (5 2) 4 40 

1 (3 6) 18 5 (2 4) 40 

14. (2 4) 1 8 15. (2 2) 5 20 

2 (4 1) 8 2 (2 5) 20 







16. 2 4 3 24 17. 7 1 3 21 18. 3 3 2 18 

19. 3 2 6 36 20. (4 2) 2 16 21. 3 (0 7) 0 

22. 1 7 9 63 23. 8 (2 3) 48 24. (2 5) 6 60 

25. 9 0 3 0 26. 4 5 1 20 27. (3 6) 1 18 

28. Reasoning When multiplying three numbers, if one 

of the factors is zero, what will the answer be? 

29. A classroom of students is getting ready to take 

a test. There are 5 rows of desks in the room and 

4 students are in each row. Each student is required 

to have 2 pencils. How many pencils are needed? 

Zero 

40 pencils 


Teacher Notes 





Ask: What are three ways to find 1 2 3? 

(1 2) 3; 1 (2 3); and (1 3) 2 


If students forget to multiply the third factor, 

then encourage them to write either “ 4” 

or “4 ”. Where the blank shows the 

product of the first two factors and the number 

is the third factor. 


Have students write problems involving products 

with 3 factors, for a partner to solve. 



Dividing by 8 and 9 


Name 

Name 


Materials Have counters available for students to use. 

You can use multiplication facts to help you divide. 

At the museum, 32 students are divided into 8 equal groups. 

How many students are in each group? 

Find 32 8. 

1. To find 32 8, think about the related multiplication problem. 

8 times what number equals 32? 8 4 32 

2. Since you know 8 4 32, then you know 32 8 4 . 




3. How many students are in each group at the museum? 4 students 

Find 36 9. 

4. To find 36 9, think about the related multiplication problem. 


5. Since you know 9 4 36, then you know 36 9 

Find 8 

4 . 

 

80 . 

6. To find 8 

80 , think about the related multiplication problem. 


7. Since you know 8 10 80, then you know 8 

80 10 . 

8. Reasoning Explain how to find 56 8. 

Think: 8 times what number equals 56. Since 

8 7 56, 56 8 7. 

Dividing by 8 and 9 (continued) 

Use the multiplication fact to find each quotient. 






9. 8 2 16 10. 9 5 45 11. 8 3 24 

16 8 2 45 9 5 24 8 3 

12. 9 6 54 13. 8 4 32 14. 8 6 48 

54 9 6 32 8 4 48 8 6 

15. 9 3 27 16. 9 10 90 17. 8 9 72 

27 9 3 90 9 10 72 8 9 

Find each quotient. 

7 4 4 

18. 9 

63 19. 8 

32 20. 9 

36 

8 9 2 

21. 8 

64 22. 9 

81 23. 8 

16 

5 7 5 

24. 9 

45 25. 8 

56 26. 8 

40 

27. Reasoning If you know that 8 12 96, 

then what is 96 8? 

28. Nine friends go to lunch and split the $54 

ticket evenly. How much does each 

friend pay? 

12 

$6 


Teacher Notes 





Ask: What two division facts can be written 

using 8 9? 72 8 9 and 72 9 8 


If students have trouble remembering the 

multiplication facts for 8 or 9, 

then use G26: Multiplying by 9 and G31: Multiplying 

by 8. 


Have partners make a game like Memory. The 

partners write the expression on one card and 

the quotient on another card for the 8 and 9 

division facts. Have partner A write the eight 8s 

facts beginning with 16 8 2 and ending with 

72 8 9. Have partner B write the eight 9s 

facts beginning with 18 9 2 and ending with 

81 9 9. Shuffle all cards and then place face 

down in a 4 by 8 array. Partner A turns over two 

cards, if they go together the player keeps the two 

cards and goes again. When a match is not made 

the cards are turned back over, and it is the other 

partner’s turn. The game is finished when all cards 

are matched. The partner with the most matches 

wins. 

Intervention Lesson B62

0 and 1 in Division 


Name 

Name 


Think about related multiplication facts to help you divide. 

Find 5 1. 

1. Think: 1 times what number equals 5? 1 5 5 






3. If Karina had 5 oranges to put equally in 1 basket, 

how many oranges would go in each basket? 

Find 9 1. 

5 oranges 

4. 1 9 9 So, 9 1 9 . 

5. What is the result when any number is divided by 1? 

Find 0 7. 



The number 

8. If Karina had 0 oranges to put equally in 7 baskets, 


Find 0 2. 

0 oranges 

9. 2 0 0 So, 0 2 0 . 

10. What is the result when zero is divided 

by any number (except 0)? 

Find 5 0. 

11. Reasoning If Karina had 5 oranges to put equally in 0 

baskets, how many oranges would go in each basket? 

Explain. 

Karina can not put 5 oranges into 0 baskets. 

You cannot divide a number by 0. 

0 and 1 in Division (continued) 

Find 4 4. 




0 





14. If Karina had 4 oranges to put equally in 4 baskets, 


Find 8 8. 

1 orange 

15. 8 1 8 So, 8 8 1 . 

16. What is the result when any number (except 0) 

is divided by itself? 


17. 4 1 4 18. 0 5 0 19. 6 6 1 

0 1 1 

20. 3 

0 21. 9 

9 22. 5 

5 

6 1 0 

23. 1 

6 24. 1 

1 25. 8 

0 

26. Reasoning Use the rule for division by 1 to find 247 1. 

Explain. 

A number divided by 1 equals the same 

number, so 247 1 247. 

27. Larry has 3 friends who would like some cookies but he has 

no cookies to give them. How many cookies can Larry give 

each friend? 

Each friend gets zero cookies. 

1 


Teacher Notes 





Ask: What is 0 245? 0 What is 245 1? 245 


If students have trouble understanding that division 

is actually taking place, 

then encourage them to use counters or draw 

pictures to “see” what is being done. For example, 

5 1 can be 5 counters put into 1 group to find 

how many are in the group. And 0 7 can be 0 

counters put into 7 groups to find how many are in 

each group. 


Place students in groups of 3. One student acts 

as a referee. The referee says a number from 2 to 

9 and then says, “On your mark, get set, go.” On 

go, the referee holds out a fist for 0 or a hand with 

1 finger up for one. The other two students race to 

say the product of 0 or 1 and the number between 

2 and 9. The student who says the product first 

gets a point. The first student to 5 wins. Let 

students play again, until each one has a turn as 

referee. 



Using Mental Math to Add 


Name 

Name 


Materials place-value blocks: 6 tens and 12 ones per pair 

Find the sum of 26 and 42 by breaking apart each addend. 

1. Show 26 with place value blocks. 

2 tens 20 6 ones 6 



3. Add the tens. 20 40 60 

Add the ones. 6 2 8 

4. Add the tens and the ones together. 60 8 

So, 26 42 68 . 

Find the sum of 18 and 34 by breaking apart the second addend. 


1 ten 10 8 ones 8 



7. Take 2 ones from the 34 and add them 

to 18. What sum do you have now? 

18 34 20 32 

8. Add. 20 32 

52 

So, 18 34 52 . 

Using Mental Math to Add (continued) 

Find each sum using mental math. 

108 Intervention Lesson C26 



Intervention Lesson C26 

68 

Intervention Lesson C26 107 




78 61 79 

9. 22 56 10. 37 24 11. 43 36 

87 44 87 

12. 55 32 13. 23 21 14. 43 44 

78 84 49 

15. 44 34 16. 52 32 17. 45 4 

79 88 69 

18. 45 34 19. 37 51 20. 23 46 

87 99 98 

21. 64 23 22. 26 73 23. 35 63 

114 84 73 

24. 88 26 25. 39 45 26. 57 16 

Fill in the blanks to show how to add mentally. 

7 47 120 129 

27. 35 12 40 28. 83 46 9 

15 65 22 102 

29. 49 16 50 30. 78 24 80 

31. Reggie has 25 crayons. Brett gives him 14 more. 

How many crayons does he have now? 

32. Darla bought 32 stickers on Monday. Two days later 

she bought 46 more. How many stickers does she 

have altogether? 

33. Rafael has 41 rocks in his rock collection. His friend gave 

him 18 more rocks. How many rocks did he have then? 

34. Reasoning To add 59 and 16, Juan took one from the 16 

to make the 59 a 60. What number should he add to 60? 

35. Reasoning To add 24 and 52, Ashley first added 24 and 

50. What numbers should she add next? 

39 

78 

59 

15 

74 2 


Teacher Notes 





Ask: How would you break apart 36 to add 

48 36? Change 36 into 2 34. Why? To make 

a ten, 48 2 50. 


If students have trouble remembering what they 

broke each number into, 

then encourage them to write the addition problem 

above each addend. For example, in 23 45, have 

students write 20 3 above the 23 and 40 5 

above the 45. Then they can see the tens and ones 

that need to be added. 


Have students describe situations when they might 

want to add mentally, such as shopping. 

Intervention Lesson C26

Using Mental Math to Subtract 


Name 

Name 

Using Mental Math to Subtract 





20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 

Find the difference of 46 27 one way, by doing the following. 

1. Round the number being subtracted. 

27 rounded to the nearest ten is 30 . 

2. Solve the new problem. 

46 30 

3. Since you rounded 27 to 30, did you 

subtract too much or too little from 46? 

4. How much more is 30 than 27? 

5. Since 30 is 3 more than 27, you subtracted too much. 

You must now add 3 to the difference in Question 2. 

16 3 

16 

19 

6. So, 46 27 19 . 

Find the difference of 46 27 another way, by doing the following. 

7. How much needs to be added to the 27 

so that it forms a ten? 27 3 30 

8. Since you added 3 to 27, you need to 

add 3 to 46. 46 3 

9. Solve the new problem. 49 30 

10. So, 46 27 19 . 

11. How can you change 52 18 to make it easier to subtract 

mentally? 

52 18 54 20 34 

Using Mental Math to Subtract (continued) 

Find each difference using mental math. 


3 

too much 

49 

19 





12. 57 38 13. 32 17 14. 61 26 

15. 85 29 16. 43 28 17. 67 42 

18. 32 18 19. 52 46 20. 41 18 

21. 28 16 22. 55 33 23. 86 23 

24. 39 26 25. 57 28 26. 93 34 

27. 62 47 28. 33 16 29. 84 35 

30. Reasoning To find 56 48, add the same amount to both 

numbers to make it easier to subtract. Explain what you did 

to solve the problem. 

56 48 

19 

31. Lupe has $32. She buys a present for her mother and 

gets $9 in change. How much money did she spend 

on the present? 

15 35 

56 15 25 

14 6 23 

12 22 63 

13 29 59 

15 17 49 

Add 2 to both numbers: 56 2 58; 48 2 50. 

58 50 8; So, 56 48 8. 

32. Reasoning Becca subtracts 73 26 mentally by thinking: 

“73 30 43, and 43 4 39. The answer is 39.” 

What did she do wrong? Explain. 

$23 

Sample answer: Becca added 4 to the 26 to get 30. 

Since she subtracted 4 too much, she should have 

added 4 to the difference. The answer should be 

43 4 47. 


Teacher Notes 





Ask: When solving 38 23, why wouldn’t you 

round the 38 to 40 and then subtract 23? Sample 

answer: Subtracting 40 23 is much more difficult. 

It is much easier to subtract a ten from a number. 


If students continually forget to add the extra to the 

number being subtracted from, 

then encourage the students to say to themselves, 

“What I do to one I have to do to the other.” Then 

have them put the number being added above the 

original numbers. For example, in 23 17, the 

student would write a 3 above both the 23 and 

the 17. That way they know their new problem is 

26 20. 


Have students tell which method they prefer to use 

and why. 



Adding Two-Digit Numbers 


Name 

Name 

Adding Two-Digit Numbers 





There are 25 boys and 38 girls at the library. How many children total? 

1. Show 25 using place-value blocks. 

2. Show 38 using place-value blocks. 

3. Add 25 38 to find the total children. 

Add the ones. 5 8 

13 

4. Do you have more then 10 ones? 

yes 

5. Since you have 13 ones, regroup them into 

tens and ones 

13 ones 1 ten and 3 ones 

6. Record the 3 ones at the bottom of the ones 

column of the Tens and Ones chart. Record 

the 1 ten at the top of the tens column. 

7. Add the tens. Add the 1 ten that you regrouped, 

the 2 tens from the 25, and the 3 tens from the 38. 

1 ten 2 tens 3 tens 6 tens 

8. Record the tens at the bottom of the tens column of the 

Tens and Ones chart. 

9. So, 25 38 63 

How many children are at the library? 63 . 

10. Use place value-blocks and the Tens and Ones 

chart to add 46 29. 

Adding Two-Digit Numbers (continued) 

Add. 

11. 

Tens Ones 

1 3 

2 8 

4 1 

Add. Use a tens and ones chart if you like. 


12. 

Tens Ones 

2 4 

2 9 

5 3 

Tens Ones 

1 

2 5 

3 8 

6 3 

Tens Ones 

1 

4 6 

2 9 

7 5 





1 

13. 58 14. 56 15. 18 16. 20 

_ 17 

75 

_ 11 _ 19 _ 28 

17. 46 18. 36 19. 17 20. 45 

_ 45 _ 17 _ 49 _ 14 

91 

21. 32 22. 26 23. 22 24. 33 

_ 66 _ 37 _ 65 _ 33 

98 

1 

25. 21 26. 17 27. 36 28. 64 

_ 39 _ 29 _ 16 _ 27 

29. A puppy weighs 15 pounds. His mother 

weighs 65 pounds. How much do the 

puppy and his mother weigh together? 

30. Reasoning What number do you add to 

19 to get 30? 

67 37 48 

53 66 59 

63 87 66 

60 46 52 

91 

1 

80 pounds 

11 


Teacher Notes 





Ask: Does every addition problem need 

regrouping? No, only if there is more than 9 ones. 


If students can not remember the addition facts, 

then use some of the addition fact lessons B8 to 

B15 and B26 to B30. 


Have students write all the two-digit numbers 

that can be added to 46 where regrouping is not 

needed. (10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 

33, 40, 41, 42, 43, 50, 51, 52, 53, 60, 61, 62, 63, 70, 

71, 72, 73, 80, 81, 82, 83, 90, 91, 92, 93) 


Subtracting Two-Digit Numbers 


Name 

Name 

Subtracting Two-Digit Numbers 


There are 34 kittens and 16 puppies. How many 

more kittens than puppies? 

1. Show 34 with place-value blocks. 

2. Do you have enough ones to take away 

6 ones? 

no 

3. Regroup 1 ten into 10 ones. Show this with 

your place-value blocks. 

3 tens and 4 ones 2 tens and 14 ones. 

4. Cross out the 3 tens in the Tens and Ones chart 

and write 2 above it. Cross out the 4 ones and 

write 14 above it. 

5. Now, take away 6 ones and write the difference 

at the bottom of the ones column. 

14 ones 6 ones 8 ones 

6. Subtract the tens and write the difference at the 

bottom of the tens column. 

2 tens 1 ten 1 ten 

7. So, 34 16 

18 

How many more kittens than puppies 

are there? 

8. Use place-value blocks and the Tens and Ones 

chart to subtract 56 27. 

Subtracting Two-Digit Numbers (continued) 

Subtract. 

9. 

Tens Ones 

4 2 

1 9 

2 3 


10. 

Subtract. Use a Tens and Ones chart if you like. 


18 

Tens Ones 

5 0 

2 4 

2 6 




Tens Ones 

2 14 

3 4 

1 6 

1 8 

Tens Ones 

4 16 

5 6 

2 7 

2 9 





11. 35 12. 80 13. 45 14. 61 

_ 17 _ 38 _ 39 _ 13 

18 

15. 74 16. 22 17. 50 18. 48 

_ 45 _ 18 _ 32 _ 20 

29 

19. 95 20. 34 21. 61 22. 90 

_ 69 _ 7 _ 26 _ 74 

26 

3 

12 4 10 

42 6 48 

4 18 28 

27 35 16 

23. Thompson has 32 flowers. If he plants 18 flowers in 

the front yard, how many will he have left? 

24. Reasoning In which problem do you need to regroup to 

subtract, 53 28 or 58 23? Explain. 

14 

53 28; There are not enough ones in 53 to take 

away the 8 ones in 28. However, there are enough 

ones in 58 to take away the 3 ones in 23. 


Teacher Notes 





Ask: What can you do if you forget a subtraction 

fact like 12 8? Think of the related addition fact, 

such as what plus 8 equals 12? 


If students do not recognize the need to regroup 

and simply subtract the smaller ones value from the 

larger ones value such as 4 1 in 31 14, 

then encourage students to circle the greater ones 

value. If the circled number is on the bottom, then 

they need to regroup. 

If students can not remember the subtraction facts, 

then use some of the subtraction fact lessons B19 

to B24 and B34 to B39. 


Have students write a real-world subtraction 

problem for a partner to solve. 



Adding Three Numbers 


Name 

Name 


Materials place-value blocks: 2 hundreds, 6 tens, and 14 ones 

per pair or group 

How many total pieces of fruit are in a box containing 

45 apples, 107 oranges, and 112 bananas? 

1. Show 45, 107, and 112 using place-value blocks. 

2. Add 45 107 112 to find the total pieces of 

fruit in the box. 

3. Do you have more then 10 ones? 

Add the ones. 

yes 

5 ones 7 ones 2 ones 14 ones 

4. Since you have 14 ones, regroup them into 

tens and ones. 

14 ones 1 ten and 4 ones 

5. Record the 4 ones at the bottom of the 

ones column of the Hundreds, Tens, 

and Ones chart. Record the 1 ten at 

the top of the tens column. 

6. Add the tens. 

1 ten 4 tens 1 ten 6 tens 

7. Do you have more than 10 tens? no 




Hundreds Tens Ones 

4 5 

1 0 7 

1 1 2 

2 6 4 

8. Record the tens at the bottom of the tens column of the chart. 

9. Add the hundreds and record the value at the bottom of the 

hundreds column. 

1 hundred 1 hundred 2 hundreds 

10. So, 45 107 112 264 

How many total pieces of fruit are in the box? 

Adding Three Numbers (continued) 

Add. 

11. 

12. 


2 5 4 

1 2 9 

6 2 

4 4 5 


1 1 7 

1 0 6 

7 4 

2 9 7 


264 

1 





13. 123 14. 211 15. 23 16. 322 

365 423 45 43 

_ 50 _ 23 _ 14 _ 16 

538 

17. 335 18. 543 19. 613 20. 851 

125 144 205 32 

_ 32 _ 46 _ 64 _ 40 

492 

1 

1 

1 

657 82 381 

733 882 923 

21. There were 234 books returned to the library on 

Monday, 109 books returned on Tuesday, and 

41 books returned on Wednesday. How many 

books were retuned to the library in the three days? 

22. Reasoning Write the smallest 2-digit number that 

when added to 345 and 133 would require 

regrouping of both the ones and the tens. 

384 

22 


Teacher Notes 





Ask: When adding three numbers, do you always 

have to regroup? No, you only have to regroup if 

you have more than 9 ones or 9 tens. 


If students are having problems with their basic 

facts, 

then use one of the lessons on addition facts, B27, 

B28, or B29. 

If students are having problems regrouping tens. 

then use G9: Adding Two-Digit Numbers. 


Have each student write a two- or three-digit 

number on paper. Then place students into groups 

of 3 and find the sum of the 3 numbers. Continue 

to have students form random groups three more 

times. Have each student share with the class their 

highest and lowest sums. 


Solid Figures 


Name 

Name 

Solid Figures 

Materials power solids arranged in stations around the room 

Find each solid to complete the tables below. 

Solid 

1. Pyramid 

2. Rectangular Prism 

3. Cube 

Number 

of Faces 

Intervention Lesson D59 

Number 

of Edges 

Number of 

Vertices 

5 8 5 

6 12 8 

Objects that roll do not have faces, edges, or vertices. 

Solid 

4. Cone 

Solid Figures (continued) 

Solid 

5. Cylinder 

6. Sphere 




Shapes 

of Faces 

1 square 

4 triangles 

6 

rectangles 

6 12 8 6 squares 

Number of Flat 

Surfaces 

Number of Flat 

Surfaces 

Shape of Flat Surfaces 

1 1 circle 

Intervention Lesson D59 207 

Shape of Flat Surfaces 

2 2 circles 

Name the solid figure that each object looks like. 

7. 8. 9. 

sphere cylinder 

Use the solids in the table above to answer Exercises 10–12. 

10. Which solid figure has 2 flat surfaces that are circles? 

sphere 

11. Which of the 6 solid figures has 6 rectangular faces? 

rectangular prism 

12. Which 3 figures have no vertices? 

cylinder, cone, sphere 

13. Reasoning How are the sphere and cone alike? 

Sample answer: They both can roll. 

208 Intervention Lesson D59 

0 




rectangle 

prism 


Teacher Notes 





Ask: Which two solids are the most alike? Cube 

and rectangular prism; they have the same number 

of faces, edges, and vertices. 


If students have trouble naming the shapes of the 

faces or counting the number of faces, edges, and 

vertices, 

then use D50: Flat Surfaces of Solid Figures, 

D57: Flat Surfaces and Corners, and D58: Faces, 

Corners, and Edges. 


Have a “Solid Bee.” Put solids into a bag, including 

at least one of each discussed in the lesson. Mix 

in real life objects like a ball, piece of chalk, eraser, 

and number cube. Have students stand in line. Say: 

“I need to know the name of this solid.” Then pull a 

solid out of the bag. The first student in line names 

the solid. If the name is correct, the student goes 

to the end of the line. If the name is incorrect, the 

student sits down. Give each student a turn naming 

a solid. Each round, ask a different question such 

as: 

I need to know how many faces (or flat surfaces) 

this solid has; 

I need to know how many edges this solid has; 

I need to know how many vertices this solid has. 



Acute, Right, and Obtuse Angles 


Name 

Name 

Acute, Right, and Obtuse Angles 




Materials 1 inch square piece of paper for each student, 

crayons or markers 

A ray is part of a line. The endpoint is the beginning 

of the ray, and the arrow shows it goes on forever. 

ray 

An angle is made by two rays that have the same 

endpoint. That endpoint is called the vertex. 

vertex 

angle 

1. Color each ray of the angle at the 

right, a different color. 

Check student’s coloring 

Place a side of your square on one ray, and the corner on the 

vertex for each angle in 2 to 4. 

2. Reasoning Right angles are shown below. What do you 

notice about the openings of right angles? 

Sample answer: They are the same size as the 

corner of a piece of paper. 

3. Reasoning Obtuse angles are shown below. What do you notice about 

the openings of obtuse angles? 

Sample answer: They are all larger than the corner 

of a piece of paper. 

Acute, Right, and Obtuse Angles (continued) 

4. Reasoning Acute angles are shown below. What do you 

notice about the openings of acute angles? 

Sample answer: They are all smaller than the 

corner of a piece of paper. 

Write ray, vertex, right angle, acute angle, or obtuse angle to 

name each. 

5. 6. 7. 


obtuse angle right angle acute angle 

8. 9. 10. 

vertex right angle ray 

What kind of angle do the hands of each clock show? 

11. 

 

 

 

 

 

 

 

12. 

 

 

 

 

 

 

 

13. 

 

 

 

 

 

 

 

acute angle right angle obtuse angle 






Teacher Notes 





Ask: What type of angle is formed by the hands 

on the clock when it shows the time school 

starts? Answer will vary by school start times. 


If students confuse acute and obtuse, 

then help students by telling them that people often 

say to a baby “Look how little you are. You are so 

cute.” So, a little baby is “acute”. This will help 

them remember that acute is smaller than a right 

angle. You can also say the word “acute” with a 

small, squeaky voice and the word “obtuse” with a 

big, burly voice. 


Have students play a math version of “Simon 

Says”. Have a student be Simon, stand in the front 

of the class room, and say statements such as the 

following: “Simon says make an obtuse angle.” 

Students can show acute, right, and obtuse angles 

with both arms. They can also show a ray by 

pointing with one arm extended in any direction. 

Those who correctly make an obtuse angle 

continue. Those who do not must sit down. 

Students who make the figure when Simon doesn’t 

say “Simon says” must also sit down. 

Intervention Lesson D62

Polygons 


Name 

Name 

Polygons 


Box A Box B 

1. The figures in Box A are polygons. The figures in Box B are not. 

How are the figures in Box A different from those in Box B? 


To be a polygon: 

• All sides must be made of straight line segments. 

• Line segments must only intersect at a vertex. 

• The figure must be closed. 

Polygons are named by the number of sides each has. 

Complete the table. 

2. 

3. 

4. 

5. 

6. 

Polygons (continued) 




Shape Number of Sides Number of Vertices Name 

Tell if each figure is a polygon. Write yes or no. 

7. 8. 9. 

3 3 Triangle 

4 4 Quadrilateral 

5 5 Pentagon 

6 6 Hexagon 

8 8 Octagon 

no yes no 

Name each polygon. Then tell the number of sides and the 

number of vertices each polygon has. 

10. 11. 

hexagon; 6, 6 pentagon; 5, 5 

12. 13. 

triangle; 3, 3 quadrilateral; 4, 4 

14. 15. 

octagon; 8, 8 quadrilateral; 4, 4 

16. Reasoning What is the least number of 

sides a polygon can have? 

17. Reasoning A regular polygon is a polygon 

with all sides the same length. Circle the 

figure on the right that is a regular polygon. 






3 sides 


Teacher Notes 





Ask: Why is a circle not a polygon? A polygon 

must have sides that are line segments. A circle has 

no line segments. 


If students count the same vertex or side twice, 

then have them put an x on each side or vertex 

as they count it. This will help students to avoid 

counting a vertex or side more than once. 


Have students make polygon books. Give each 

student 3 half-sheets of white paper. With all 3 

sheets together, have them fold the papers to 

make a book. Students should title their book 

with something having to do with polygons. The 

first two-page spread should have the heading 

“Triangles.” Let the students use crayons or 

markers to draw examples of different types of 

triangles. Also, let them print pictures from the 

internet or cut out pictures from magazines. 

Make other two-page spreads for quadrilaterals, 

pentagons, hexagons, and octagons. The cover, 

made with construction paper, can be a picture 

drawn by using only polygons. 



Classifying Triangles Using Sides 

and Angles 


Name 

Name 




Classifying Triangles Using Sides and Angles 

Materials 2 yards of yarn, scissors, 6 sheets of construction 

paper, markers for each student and glue 

Create a book about triangles by following 1 to 7. 

1. Put the pieces of construction paper together and 

fold them in half to form a book. Punch two holes 

in the side and use yarn to tie the book together. 

Write “Triangles” and your name on the cover. 

Each two-page spread will be about one type 

of triangle. For each two page spread: 

 

• Write the definition on the left page. 

• Write the name of the triangle near 

the top of the right page. 

 

• Create a triangle with yarn pieces and 

glue the yarn pieces under the name 

of the triangle to illustrate the triangle. 

2. Pages 1 and 2 should be about an equilateral 

triangle. This triangle has 3 sides of equal length. 

So, your 3 yarn pieces should be cut to the same 

length. 

3. Pages 3 and 4 should be about an isosceles triangle. 

This triangles has at least two sides the same length. 

Cut 2 pieces of yarn the same length and glue them 

on the page at an angle. Cut and glue a third piece 

to complete the triangle. 

4. Pages 5 and 6 should be about a scalene triangle. 

This triangle has no sides the same length. So your 

3 yarn pieces can be cut to different lengths. 

5. Pages 7 and 8 should be about a right triangle. 

This triangle has exactly one right angle. Two of 

your yarn pieces should be placed so that they 

form a right angle. Cut and glue a third piece 

to complete the triangle. 

Classifying Triangles Using Sides and Angles (continued) 

6. Pages 9 and 10 should be about an obtuse 

triangle. This triangle has exactly one obtuse 

angle. Two pieces of yarn should be placed so 

that it forms an obtuse angle. Cut and glue down 

a third yarn piece to complete the triangle. 

7. Pages 11 and 12 should be about an acute 

triangle. This triangle has three acute angles. 

Your 3 yarn pieces should be placed so that 

no right or obtuse angles are formed. 

Tell if each triangle is equilateral, isosceles, or scalene. 

8. 9. 10. 

 

 


isosceles scalene equilateral 

Tell if each triangle is right, acute, or obtuse. 

11. 12. 13. 

acute obtuse right 

14 How many acute angles does an acute triangle have? 

15. Reasoning How many acute angles does a right 

triangle have? 

16. Describe this triangle by its sides and by its angles. 

(Hint: Give it two names.) 





acute isosceles 

3 

2 


Teacher Notes 





Ask: What type of angles are in an equilateral 

triangle? acute 


If students have trouble identifying right angles, 

acute angles, and obtuse angles, 

then use I4: Acute, Right, and Obtuse Angles. 


Have students draw a triangle. Trade with a partner 

and have the partner identify the triangle by its 

sides and then by its angles. 

Intervention Lesson D64

Quadrilaterals 


Name 

Name 


Materials Have quadrilateral power shapes available for 

students who want to use them. 

For 1 to 5 study each quadrilateral with your partner. Identify 

the types of angles. Compare the lengths of the sides. Then 

draw a line to match the quadrilateral with the best description. 

Descriptions can be used only once. 

1. Trapezoid 

3. Rectangle 

5. Rhombus 


Four right angles 

and all four sides 

the same length 

All sides are the 

same length 

Exactly one pair of 

parallel sides 

Two pairs of 

parallel sides 

Four right angles 

and opposite sides 

the same length 

6. Reasoning What quadrilateral has four right angles 

and opposite sides the same length, and can also 

be called a rectangle? 

7. Reasoning What quadrilaterals have two pairs of 

parallel sides, and can also be called parallelograms? 

rectangle, rhombus, square 

Quadrilaterals (continued) 

For Exercises 8–13, circle squares red, rectangles blue, 

parallelograms green, rhombuses orange and trapezoids purple. 

Some quadrilaterals may be circled more than once. 

See teachers note page. 

8. 9. 10. 

11. 12. 13. 




2. Parallelogram 

4. Square 

square 


14. I have two pairs of parallel sides, and all of my sides are 

equal, but I have no right angles. What quadrilateral am I? rhombus 

15. I have two pairs of parallel sides and 4 right angles, but 

all 4 of my sides are not equal. What quadrilateral am I? 

16. Name all of the quadrilaterals in the 

picture at the right. 

rectangle, rhombus, 

parallogram, trapezoid 

17. Reasoning Why is the quadrilateral on the 

right a parallelogram, but not a rectangle? 

rectangle 

Sample answer: Both a 

rectangle and a parallelogram 

have opposite sides parallel. A rectangle must 

also have four right angles. This quadrilateral 

does not have four right angles, so it is a 

parallelogram, but not a rectangle. 






Teacher Notes 





Ask: Are all squares rectangles? yes Are all 

rectangles squares? no 


If students list only one name for rectangles, 

squares, or rhombuses, 

then ask students leading questions so they can 

discover that other quadrilateral name(s) can also 

be used. 


Put students in pairs. Each pair needs five index 

cards labeled square, rectangle, rhombus, 

trapezoid, and parallelogram. Have one student 

shuffle and draw a card. Both students then need 

to draw an example of the quadrilateral. Students 

should compare drawings. Tell them to describe 

the different ways a quadrilateral can be drawn. 

Help students to discover that quadrilaterals may 

be different sizes, but they will always have their 

specific characteristics. 

In items 8–13, each quadrilateral should 

be circled with the color listed below 

8. red, blue, green and orange 

9. purple 

10. green 

11. blue, green 

12. orange, green 

13. purple 



Name 


Tell if each shows equal or unequal parts. 


1. 2. 3. 4. 

Name the equal parts of the whole. 

5. 6. 7. 8. 

Use the grid to draw a region showing the number of equal parts 

named. 

9. tenths 10. sixths 

11. Geometry How many equal parts does this figure have? 

12. Which is the name of 12 equal parts of a whole? 

Practice 

A42 

halves tenths sixths twelfths 

Practice A42

Name 


Write the fraction of each figure that is shaded. 

1. 2. 3. 4. 


5. 3 __ 

12 

Practice A43 

6. __ 1 

4 

In 8 and 9, use the information below. 

Three parts of a rectangle are red. Two parts are blue. 

8. What fraction of the rectangle 

is red? 

10. A banner is made of 8 equal parts. 

Five of the parts contain stars. 

Three of the parts contain hearts. 

Draw the banner. 

11. How can you write the fraction 4 __ in word form? 

6 

7. 4 __ 

5 

Practice 

A43 

9. What fraction of the rectangle 

is blue? 

fourth sixth four sixes four sixths fourth six 



Name 

Using Models to Compare 

Fractions 

Compare. Write >,

Name 

Using Models to Find 

Equivalent Fractions 


1. 

3. 

5. 

1 

10 

1 

5 

1 

10 

Practice A48 

1 

1 __ _____ 

5 10 3 __ 

4 

1 

10 

1 

6 

1 

10 

1 

6 

1 

10 

1 

10 

1 

6 

1 

10 

1 

3 __ _____ 

6 10 1 __ 

4 

1 

10 

1 

5 

1 

10 

1 

10 

4 __ _____ 

5 10 

1 

5 

1 

10 

1 

10 

1 

1 

5 

Complete each pattern. 

1 

10 

1 

10 

1 

5 

1 

10 

2. 

4. 

1 

12 

1 

12 

1 

4 

1 

12 

1 

12 

_____ 

12 

1 

4 

1 

12 

1 

12 

_____ 

12 

6. 1 __ , 

3 2 __ , 

6 3 __ , 

9 4 _____ 7. 1 __ , 

2 2 __ , 

4 3 __ , 

6 4 __ , 

8 5 _____ , 6 _____ 

8. Samuel has read 5 __ of his assignment. Judy has read 

6 10 __ 

12 

assignment. Which sentence is true? 

1 

12 

1 

4 

1 

12 

1 

12 

1 

1 

of her 

1 

12 

1 

4 

1 

12 

Practice 

A48 

Samuel read more than Judy. Judy read more than Samuel. 

They read the same amount. They will both finish the 

assignment at the same time. 

1 

12 



Name 


Draw the next three shapes to continue the pattern. 

1. 

2. 

Write the next three numbers to continue the pattern. 

3. 4, 6, 2, 8, 4, 6, 2, 8, 4, 6, 2, 8 4. 3, 3, 5, 3, 3, 5, 3, 3, 5 

5. What is the 16th shape in the pattern below? 

6. Mrs. Washington placed students in a line. The order was 

1 boy, 2 girls, 2 boys, 2 girls, 3 boys, 2 girls and continued. 

Was the 15th student a boy or a girl? 

7. Create a pattern using your favorite letters. 

Practice 

A74 

Practice A74

Name 

Using Multiplication 


Find each amount. 

1. 2 times as many as 5 2. 3 times as many as 7 

Practice B45 

× × 


5. twice as many as 8 6. 5 times as many as 3 



11. John has 5 computer games. Julian has twice as 

many computer games as John. How many 

computer games do they have in all? 

12. George Washington is on the $1 bill. Abraham Lincoln is 

on the bill that is worth 5 times as much as the $1 bill. 

What bill is Abraham Lincoln on? 

13. Paula has twice as many guests this week as she did 

last week. Last week she had 7 guests. How many guests 

does she have this week? 

14. John F. Kennedy is on the coin that is worth 5 times as 

much as a dime. What coin is John F. Kennedy on? 

Practice 

B45 

nickel quarter half-dollar dollar 



Name 



1. 4 

× 9 

6. 9 

× 5 

2. 7 

× 9 

7. 2 

× 9 

3. 9 

× 9 

8. 6 

× 9 

4. 8 

× 9 

9. 2 

× 7 

11. Multiply 4 and 9. 12. Find 3 times 9. 

13. Find the product of 14. Multiply 9 and 1. 

9 and 10. 

15. Paula’s hair was put into 9 braids. Each braid used 3 beads. 

How many beads were used in all? 

16. A baseball game has 9 innings. A doubleheader is 

2 games in the same day. How many innings are 

there in a doubleheader? 

17. Write a multiplication story for 9 × 8. Include the product in 

your story. 

18. Which number below is a multiple of 9? 

Practice 

B48 

5. 3 

× 9 

10. 8 

× 9 

35 46 54 65 

Practice B48

Name 


Find each product two diffeent ways. 

Practice B56 

Practice 

B56 

1. 2 × 3 × 3 2. 2 × 2 × 4 3. 8 × 2 × 2 4. 6 × 2 × 3 

5. 3 × 3 × 4 6. 5 × 2 × 5 7. 5 × 4 × 2 8. 4 × 2 × 3 

Find the missing number. 

9. 4 × 5 × 2 10. 5 × 2 × 8 11. 2 × 2 × 5 

12. 2 × 5 × 6 13. 3 × 2 × 5 14. 4 × 9 × 0 

15. Which number makes this number sentence true? 

8 × 2 × 4 = 8 × (☐ × 4) 

2 4 8 64 

16. Which number makes this sentence true? 

(5 × 3) × 4 = 5 × (☐ × 3) 

2 3 4 5 

17. Write three ways to find 3 × 2 × 4. 



Name 



1. 6 8 48 2. 9 2 18 3. 7 7 49 

48 8 18 9 49 7 

4. 8 8 64 5. 9 5 45 5. 6 7 42 

64 8 45 9 42 7 

6. 9 8 72 7. 9 4 36 8. 5 3 15 

72 8 36 9 15 3 


10. 856 11. 981 12. 840 

13. 990 14. 963 15. 832 

16. 390 17. 1199 18. 545 

19. Adam made 19 paper cranes Monday and 8 more Tuesday. 

He gave 9 friends an equal number of cranes. How many 

cranes did each friend receive? Explain how you found 

your answer. 

Practice 

B62 

20. A short story consists of 81 pages. Andrea will read 9 pages each day. 

How many days will it take Andrea to finish the story? 

6 7 8 9 

Practice B62

Name 



1. 0 6 2. 8 8 3. 6 1 

6 0 0 8 1 8 6 1 6 

So, 0 6 

Practice B63 

So, 8 8 

So, 6 1 

Practice 

B63 

4. 5. 6. 7. 8. 

15 40 66 18 13 

9. 10. 11. 12. 13. 

324 642 872 530 763 

14. Find 0 divided by 2. 15. Divide 7 by 1. 16. Find 4 divided by 4. 

Write , , or to compare. 

17. 6 6 8 8 18. 0 5 5 5 19. 9 1 7 1 

20. Tickets for rides cost $1 each at the fair. Bob has $6 

to buy tickets. How many tickets can Bob buy? 

21. Nikki is the goalie on her soccer team. She has allowed 

0 goals in 8 games. How many goals has she allowed 

in each game? 

22. Why is 10 0 10, but 0 10 0? Explain. 

23. Which has the greatest quotient? 

6 6 5 1 0 3 8 8 



Name 


Find the sum by breaking apart each addend. 

1. 53 + 34 

Add the tens. 50 + = 

Add the ones. 3 + = 

Add the tens and the ones together. 

80 + 7 = 

So, 53 + 34 = 

2. 41 + 28 

Find the sum by breaking apart the second addend 

3. 27 + 24 

Take 3 ones from the 24 and add 

them to the 27. 

What sum do you have now? 

27 + 3 = 

Add 30 + 21 = 

So, 27 + 24 = 51 


Practice 

C26 




60 + 9 = 

So, 41 + 28 = 

4. 54 + 19 

Take 1 one from the 54 and add it 

to the 19. 


19 + 1 = 

Add 53 + 20 = 

So, 54 + 19 = 73 

5. 52 + 26 6. 47 + 8 7. 32 + 17 8. 28 + 31 

9. 43 + 38 10. 72 + 7 11. 42 + 33 12. 36 + 14 

Practice C26

Name 

Using Mental Math 

to Subtract 


Practice C27 

Practice 

C27 

1. 38 − 14 2. 42 − 13 3. 55 − 12 4. 62 − 17 

5. 72 − 19 6. 94 − 11 7. 32 − 15 8. 85 − 18 

9. 43 − 16 10. 66 − 15 11. 53 − 19 12. 72 − 16 

13. Gillian started solving 88 − 29. This is what she did. 

88 − 29 = ? 

88 − 30 = 58 

What should Gillian do next? 

14. Tell how to find 81 – 16 using mental math. 

15. Tiffany needs 63 tiles for her art project. She only needs 

17 more tiles. Use mental math to find how many tiles she 

has already. 

16. To solve 35 – 19, Jack used 35 – 20 and then 

added 1. subtracted 1. 

subtracted 9. added 9. 



Name 

Adding 2-Digit Numbers 

Use place-value blocks and the Tens and Ones chart to add. 

1. 

Tens Ones 

2. 

5 2 

1 9 

3. Tens Ones 

4. 

1 6 

4 8 

Add. Use a Tens and Ones chart if you like. 

5. 53 

+ 45 

6. 37 

+ 21 

7. 63 

+ 24 

Tens Ones 

4 7 

3 4 

Tens Ones 

2 8 

2 5 

8. 59 

+ 76 

10. There are 72 people on a train when 25 more people enter. 

How many people are on the train now? 

79 87 97 98 

Practice 

C28 

9. 29 

+ 44 

Practice C28

Name 

Subtracting 2-Digit Numbers 

Subtract. 

1. 

Tens Ones 

2. 

8 2 

4 7 

3. Tens Ones 

4. 

6 3 

3 5 


5. 34 

− 16 

Practice C29 

6. 43 

− 27 

7 76 

− 28 

8. 65 

− 38 

Tens Ones 

8 2 

6 5 

Tens Ones 

7 3 

3 5 

10. The tree farm had 65 shade trees for sale. It sold 39 of the trees. 

How many trees did the farm have left? 

26 36 94 104 

Practice 

C29 

9. 82 

− 47 



Name 


Add. 

1. 

2. 

Find each sum. 

3. 75 

36 

+ 58 


1 4 3 

2 1 9 

4 7 


3 5 6 

1 7 1 

6 3 

4. 142 

297 

+ 116 

5. 524 

97 

+ 176 

8. Kyle has 378 pennies, 192 nickels, and 117 dimes. 

How many coins does he have all together? 

6. 273 

187 

64 

+ 249 

495 570 677 687 

Practice 

C37 

7. 319 

48 

136 

+ 347 

Practice C37

Name 

Solid Figures 

Name the solid figure. 

1. 2. 3. 

4. 5. 6. 


7. 8. 9. 10. 

11. Reasoning What solid figures would you 

get if you cut a cube as shown? 

12. What solid figure does this figure most resemble? 

Practice D59 

Practice 

D59 

Cylinder Cone Pyramid Sphere 

3 

2 

4 



Name 

Acute, Right, and Obtuse 

Angles 


name each. 

1. 2. 3. 

4. 5. 6. 

7. 8. 9. 

Practice 

D62 

10. At what time do the hands of a clock form an acute angle? 

2:00 4:00 6:00 8:00 

Practice D62

Name 

Polygons 

Name the polygon. 

1. 2. 3. 4. 

Is each figure a polygon? If it is not, explain why. 

5. 6. 7. 8. 

9. Juan said that the two figures 

below are quadrilaterals. Is he 

correct? Explain. 

11. How many more sides does an octagon have than a pentagon? 

1 2 3 4 

Practice D63 

Practice 

D63 

10. If two of the line segments of 

a polygon are parallel, what is 

the least number of sides it 

could have? 



Name 

Classifying Triangles Using 

Sides and Angles 


1. 2. 3. 4. 


5. 6. 7. 8. 

9. Can a triangle have 2 right 

angles? Explain. 

11. Which pair of triangle names 

identifies the figure? 

Equilateral triangle, acute triangle 

Equilateral triangle, right triangle 

Scalene triangle, acute triangle 

Isosceles triangle, obtuse triangle 

Practice 

D64 

10. What is the least number of acute 

angles that a triangle can have? 

Practice D64

Name 


Write as many special names as possible for each quadrilateral. 

1. 2. 3. 4. 5. 

In 6–9, write the name that best describes the quadrilateral. 

Draw a picture to help. 

6. A parallelogram with 4 equal 

sides, but no right angles. 

8. A figure that is not a parallelogram, 

with one pair of parallel sides. 

10. Can a rectangle also be a rhombus? 

11. Which of the following correctly names the figure? 

Rhombus 

Trapezoid 

Parallelogram 

Rectangle 

Practice D65 

Practice 

D65 

7. A rectangle with 4 right angles and 

all sides the same length. 

9. A parallelogram with 4 right angles 

and sides of different lengths and 

widths. 




Name 


Tell if each shows equal or unequal parts. 


1. 2. 3. 4. 

equal 

halves 

unequal equal 

eighths 

Name the equal parts of the whole. 

5. 6. 7. 8. 

equal 

fourths 

eighths thirds fifths sixths 

Use the grid to draw a region showing the number of equal parts 

named. 

9. tenths 10. sixths 

4 

Answers 

will vary. 

11. Geometry How many equal parts does this figure have? 

12. Which is the name of 12 equal parts of a whole? 

Practice 

A42 

halves tenths sixths twelfths 

Practice A42 

A42 A43 

45094_Practice_A42-D65.indd A42 6/30/08 12:00:45 PM 


Name 

Using Models to Compare 

Fractions 

Compare. Write >, __ 

__ < 

2 __ 

4 1 

3 3 

8 1 __ 

2 

3. 1 

1 

1 4. 

1 

8 

 

3 __ 

4 6 __ 

8 1 __ 

5 2 __ 

8 

5. 1 

1 

1 

1 6. 

6 

< 

__ 

__ > 

4 __ 

6 2 

3 3 

10 1 __ 

6 

7. 1 

8. 

5 

1 

6 

> 

4 

4 

1 

3 

1 

8 

1 

3 

6 

1 

8 


 

1 __ 

5 1 __ 

6 2 __ 

6 1 __ 

3 

9. Give 3 fractions with denominators 

that are less than 6__ 8 . 

4 

4 

1 

8 

6 

1 

3 

1 

8 

6 

4 

1 

8 

1 

8 

1 

5 

1 

8 

1 

10 

1 

6 

1 

6 

1 

10 

1 

8 

1 

8 

1 

3 

1 

2 

1 

10 

1 

6 

1 

8 

Practice 

A47 

10. Which fraction is the same as 1__ 2 ? 

1 __ 

4 3 __ 

6 3 __ 

8 3 __ 

4 

Practice A47 

Name 


A47 A48 


Answers for Practice 

A42, A43, A47, A48 

Write the fraction of each figure that is shaded. 

1. 2. 3. 4. 

1 _ 

6 2 _ 

5 1 _ 

2 7 __ 

12 


5. 3 __ 

12 6. 1__ 4 7. 4__ 5 

Sample Answers. 

Practice A43 

Practice 

A43 

3 _ 

5 2 _ 

In 8 and 9, use the information below. 

Three parts of a rectangle are red. Two parts are blue. 

8. What fraction of the rectangle 9. What fraction of the rectangle 

is red? 

is blue? 

5 

10. A banner is made of 8 equal parts. 

Five of the parts contain stars. 

Three of the parts contain hearts. 

Draw the banner. 


11. How can you write the fraction 4__ in word form? 

6 

fourth sixth four sixes four sixths fourth six 


Name 

Using Models to Find 

Equivalent Fractions 


1. 

1 

1 

10 

1 

5 

1 

10 

2 9 

__ 1 _____ 

5 10 3 __ _____ 

4 12 

3. 

1 

4. 

1 

6 

1 

10 

1 

10 

5 3 

8 

1 

6 

1 

10 

3 __ _____ 

6 10 

5. 

1 

10 

1 

5 

1 

10 

1 

10 

1 

5 

Practice A48 

1 

10 

1 

10 

1 

6 

1 

10 

1 

10 

1 

1 

5 

1 

10 

1 

10 

1 

5 

1 

10 

12 10 12 

2. 

1 

4 

Practice 

A48 

1 1 1 1 1 1 1 1 1 

12 12 12 12 12 12 12 12 12 

1 

4 

1 1 1 

12 12 12 

__ 1 _____ 

4 12 

4 __ _____ 

5 10 

Complete each pattern. 

6. 1 __ , 

3 2 __ , 

6 3 __ , 

9 4 _____ 7. 1 __ , 

2 2 __ , 

4 3 __ , 

6 4 __ , 

8 5 _____ , 6 _____ 

8. Samuel has read 5 __ of his assignment. Judy has read 

6 10 __ of her 

12 

assignment. Which sentence is true? 

Samuel read more than Judy. Judy read more than Samuel. 

They read the same amount. They will both finish the 

assignment at the same time. 


Answers: A42, A43, A47, A48 

1 

4 

1 

1 

1 

4 




Name 


Draw the next three shapes to continue the pattern. 

1. 

2. 

Write the next three numbers to continue the pattern. 

3. 4, 6, 2, 8, 4, 6, 2, 8, 4, 6, 2, 8 4. 3, 3, 5, 3, 3, 5, 3, 3, 5 

4, 6, 2 3, 3, 5 

5. What is the 16th shape in the pattern below? 

6. Mrs. Washington placed students in a line. The order was 

1 boy, 2 girls, 2 boys, 2 girls, 3 boys, 2 girls and continued. 

Was the 15th student a boy or a girl? 

boy 

7. Create a pattern using your favorite letters. 

Answers will vary. Students should show 

at least 4 repetitions of the pattern. 

Answers: A74, B45, B48, B56 

Practice 

A74 

Practice A74 

A74 B45 



Name 



1. 4 

× 9 

36 63 81 72 27 

6. 9 

× 5 

2. 7 

× 9 

7. 2 

× 9 

45 18 54 14 72 

36 27 

9 

90 

27 beads 

18 innings 

3. 9 

× 9 

8. 6 

× 9 


4. 8 

× 9 

9. 2 

× 7 

11. Multiply 4 and 9. 12. Find 3 times 9. 

13. Find the product of 14. Multiply 9 and 1. 

9 and 10. 

15. Paula’s hair was put into 9 braids. Each braid used 3 beads. 

How many beads were used in all? 

16. A baseball game has 9 innings. A doubleheader is 

2 games in the same day. How many innings are 

there in a doubleheader? 

17. Write a multiplication story for 9 × 8. Include the product in 

your story. 

18. Which number below is a multiple of 9? 

35 46 54 65 

Practice 

B48 

5. 3 

× 9 

10. 8 

× 9 

Practice B48 

Name 

Using Multiplication 


Find each amount. 

B48 B56 

45094_Practice_A42-D65.indd B48 6/30/08 12:00:55 PM 


A74, B45, B48, B56 


2 5 10 3 7 21 

24 27 

16 15 

28 30 

12 48 

Practice B45 

× × 


5. twice as many as 8 6. 5 times as many as 3 



11. John has 5 computer games. Julian has twice as 

many computer games as John. How many 

computer games do they have in all? 

12. George Washington is on the $1 bill. Abraham Lincoln is 

on the bill that is worth 5 times as much as the $1 bill. 

What bill is Abraham Lincoln on? 

13. Paula has twice as many guests this week as she did 

last week. Last week she had 7 guests. How many guests 

does she have this week? 

Practice 

B45 

15 games 

$5 bill 

14 guests 

14. John F. Kennedy is on the coin that is worth 5 times as 

much as a dime. What coin is John F. Kennedy on? 

nickel quarter half-dollar dollar 


Name 


(2 3) 3 18 

2 (3 3) 18 

(3 3) 4 36 

3 (3 4) 36 

(2 2) 4 16 

2 (2 4) 16 

(5 2) 5 50 

5 (2 5) 50 

(8 2) 2 32 

8 (2 2) 32 

(5 4) 2 40 

5 (4 2) 40 

40 80 20 

60 30 0 

17. Write three ways to find 3 × 2 × 4. 

(3 2) 4, 3 (2 4), (3 4) 2 

Practice B56 

Practice 

B56 

Find each product two diffeent ways. 

1. 2 × 3 × 3 2. 2 × 2 × 4 3. 8 × 2 × 2 4. 6 × 2 × 3 

(6 2) 3 36 

6 (2 3) 36 

5. 3 × 3 × 4 6. 5 × 2 × 5 7. 5 × 4 × 2 8. 4 × 2 × 3 

Find the missing number. 

9. 4 × 5 × 2 10. 5 × 2 × 8 11. 2 × 2 × 5 

12. 2 × 5 × 6 13. 3 × 2 × 5 14. 4 × 9 × 0 

15. Which number makes this number sentence true? 

8 × 2 × 4 = 8 × (☐ × 4) 

2 4 8 64 

16. Which number makes this sentence true? 

(5 × 3) × 4 = 5 × (☐ × 3) 

2 3 4 5 

(4 2) 3 24 

4 (2 3) 24 







Name 



1. 6 8 48 2. 9 2 18 3. 7 7 49 

48 8 18 9 49 7 

4. 8 8 64 5. 9 5 45 5. 6 7 42 

64 8 8 45 9 5 

42 7 

6. 9 8 72 7. 9 4 36 8. 5 3 15 

72 8 


36 9 15 3 

10. 856 11. 981 12. 840 

6 2 7 

9 4 5 

7 9 5 

10 7 4 

13. 990 14. 963 15. 832 

30 9 9 

16. 390 17. 1199 18. 545 

19. Adam made 19 paper cranes Monday and 8 more Tuesday. 

He gave 9 friends an equal number of cranes. How many 

cranes did each friend receive? Explain how you found 

your answer. 

Practice 

B62 

3 cranes; 19 8 27; 27 9 3 

20. A short story consists of 81 pages. Andrea will read 9 pages each day. 

How many days will it take Andrea to finish the story? 

6 7 8 9 

6 

Practice B62 

B62 B63 



Name 


Find the sum by breaking apart each addend. 

1. 53 + 34 

2. 41 + 28 

30 80 

4 7 




80 + 7 = 

87 

87 

So, 53 + 34 = 

So, 41 + 28 = 

Find the sum by breaking apart the second addend 

3. 27 + 24 

4. 54 + 19 

Take 3 ones from the 24 and add 

them to the 27. 


27 + 3 = 

69 

69 

30 19 + 1 = 20 

51 73 

Add 30 + 21 = 

So, 27 + 24 = 51 


Practice 

C26 

78 55 49 59 

81 79 75 50 

20 60 

8 9 




60 + 9 = 

Take 1 one from the 54 and add it 

to the 19. 


Add 53 + 20 = 

So, 54 + 19 = 73 

5. 52 + 26 6. 47 + 8 7. 32 + 17 8. 28 + 31 

9. 43 + 38 10. 72 + 7 11. 42 + 33 12. 36 + 14 

Practice C26 

Name 


C26 C27 

45094_Practice_A42-D65.indd C26 6/30/08 12:01:02 PM 


B62, B63, C26, C27 

0 1 6 

5 0 1 8 3 

8 7 9 6 9 

0 7 1 


Practice B63 

Practice 

B63 


1. 0 6 2. 8 8 3. 6 1 

6 0 0 8 1 8 6 1 6 

So, 0 6 So, 8 8 So, 6 1 

4. 

15 

5. 

40 

6. 

66 

7. 

18 

8. 

13 

9. 10. 11. 12. 13. 

324 642 872 530 763 

14. Find 0 divided by 2. 15. Divide 7 by 1. 16. Find 4 divided by 4. 

Write , , or to compare. 

17. 6 6 8 8 18. 0 5 < 5 5 19. 9 1 > 7 1 

20. Tickets for rides cost $1 each at the fair. Bob has $6 

to buy tickets. How many tickets can Bob buy? 

21. Nikki is the goalie on her soccer team. She has allowed 

0 goals in 8 games. How many goals has she allowed 

in each game? 

22. Why is 10 0 10, but 0 10 0? Explain. 

23. Which has the greatest quotient? 

6 6 5 1 0 3 8 8 

6 tickets 

0 goals 


Name 

Using Mental Math 

to Subtract 


24 29 43 45 

53 83 17 67 

27 51 34 56 

Answers will vary. Sample answer: 

Change 81 to 80; So, 80 16 64; 

64 1 65. 

46 tiles 

Practice C27 

Practice 

C27 

1. 38 − 14 2. 42 − 13 3. 55 − 12 4. 62 − 17 

5. 72 − 19 6. 94 − 11 7. 32 − 15 8. 85 − 18 

9. 43 − 16 10. 66 − 15 11. 53 − 19 12. 72 − 16 

13. Gillian started solving 88 − 29. This is what she did. 

88 − 29 = ? 

88 − 30 = 58 

What should Gillian do next? 

14. Tell how to find 81 – 16 using mental math. 

15. Tiffany needs 63 tiles for her art project. She only needs 

17 more tiles. Use mental math to find how many tiles she 

has already. 

16. To solve 35 – 19, Jack used 35 – 20 and then 

added 1. subtracted 1. 

subtracted 9. added 9. 

Sample answer: 

58 1 59 


Answers: B62, B63, C26, C27 




Name 

Adding 2-Digit Numbers 

Use place-value blocks and the Tens and Ones chart to add. 

1. 

Tens Ones 

2. 

1 

5 2 

1 9 

7 

1 

6 

1 

3. Tens Ones 

4. 

1 6 

4 8 

4 

Add. Use a Tens and Ones chart if you like. 

5. 53 

+ 45 

6. 37 

+ 21 

7. 63 

+ 24 

Tens Ones 

98 58 87 135 73 

Answers: C28, C29, C37, D59 

1 

4 7 

3 4 

8 

1 

5 

8. 59 

+ 76 

10. There are 72 people on a train when 25 more people enter. 

How many people are on the train now? 

79 87 97 98 

1 

Tens Ones 

2 8 

2 5 

3 

Practice 

C28 

9. 29 

+ 44 

Practice C28 

C28 C29 



Name 


Add. 

1. 

2. 

1 1 

1 4 3 

2 1 9 

4 7 

4 0 9 

1 

6 3 

5 9 0 

Find each sum. 

3. 75 

36 

+ 58 



1 

3 5 6 

1 7 1 

4. 142 

297 

+ 116 

5. 524 

97 

+ 176 

6. 273 

187 

64 

+ 249 

169 555 797 773 850 

8. Kyle has 378 pennies, 192 nickels, and 117 dimes. 

How many coins does he have all together? 

495 570 677 687 

Practice 

C37 

7. 319 

48 

136 

+ 347 

Practice C37 

Name 

Subtracting 2-Digit Numbers 

Subtract. 

1. 

Tens Ones 

2. 

7 12 

8 2 

4 7 

C37 D59 


3 

2 

5 

3. Tens Ones 

4. 

5 13 

6 3 

3 5 

8 


5. 34 

− 16 


C28, C29, C37, D59 

7 12 

18 16 48 27 35 

Practice C29 

6. 43 

− 27 

7 76 

− 28 

1 

3 

8. 65 

− 38 

Tens Ones 

8 2 

6 5 

7 

Tens Ones 

6 13 

7 3 

3 5 

8 

Practice 

C29 

9. 82 

− 47 

10. The tree farm had 65 shade trees for sale. It sold 39 of the trees. 

How many trees did the farm have left? 

26 36 94 104 


Name 

Solid Figures 

Name the solid figure. 

1. 2. 3. 

rectangular 

prism 

cube square 

pyramid 

cone cylinder 

4. 5. 6. 


7. 8. 9. 10. 

sphere 

sphere rectangular cylinder cube 

Practice D59 

prism 

11. Reasoning What solid figures would you 

get if you cut a cube as shown? 

12. What solid figure does this figure most resemble? 

Practice 

D59 

rectangular prisms 

Cylinder Cone Pyramid Sphere 

45094_Practice_A42-D65.indd D59 6/30/08 12:01:12 PM 

3 

2 

4 






Name 

Acute, Right, and Obtuse 

Angles 


name each. 

1. 2. 3. 

acute angle ray obtuse angle 

4. 5. 6. 

vertex right angle acute angle 

7. 8. 9. 

obtuse angle vertex ray 

Practice 

D62 

10. At what time do the hands of a clock form an acute angle? 

2:00 4:00 6:00 8:00 

Practice D62 

D62 D63 



Name 

Classifying Triangles Using 

Sides and Angles 


1. 2. 3. 4. 

equilateral isosceles scalene scalene 


5. 6. 7. 8. 

right acute obtuse right 

9. Can a triangle have 2 right 

angles? Explain. 

No. Sample Answers: 

2 right angles 180° 

(90° 90°). A triangle 

must have 3 angles 

which equal 180° 

11. Which pair of triangle names 

identifies the figure? 

Equilateral triangle, acute triangle 

Equilateral triangle, right triangle 

Scalene triangle, acute triangle 

Isosceles triangle, obtuse triangle 

2 

Practice 

D64 

10. What is the least number of acute 

angles that a triangle can have? 

Practice D64 

Name 

Polygons 

Name the polygon. 

D64 D65 



D62, D63, D64, D65 

1. 2. 3. 4. 

hexagon octagon pentagon triangle 

Is each figure a polygon? If it is not, explain why. 

5. 6. 7. 8. 

No; not 

a closed 

figure 

9. Juan said that the two figures 

below are quadrilaterals. Is he 

correct? Explain. 

Yes. Quadrilaterals 

have 4 sides and 

4 angles 

Practice D63 

Yes No; some 

sides are 

curves 

11. How many more sides does an octagon have than a pentagon? 

1 2 3 4 

4 

Practice 

D63 

Yes 

10. If two of the line segments of 

a polygon are parallel, what is 

the least number of sides it 

could have? 


Name 


Write as many special names as possible for each quadrilateral. 

1. 2. 3. 4. 5. 

trapezoid rectangle, 

parallelogram 


rhombus 

trapezoid 

parallelogram square, 

rectangle, 

rhombus, 

parallelogram 

In 6–9, write the name that best describes the quadrilateral. 

Draw a picture to help. 

6. A parallelogram with 4 equal 

sides, but no right angles. 

8. A figure that is not a parallelogram, 

with one pair of parallel sides. 

10. Can a rectangle also be a rhombus? 

square 

rectangle 

rhombus, 

parallelogram 

Yes, if it has 4 equal sides, and 2 pairs 

of equal angles. 


11. Which of the following correctly names the figure? 

Rhombus 

Trapezoid 

Parallelogram 

Rectangle 

Practice D65 

Practice 

D65 

7. A rectangle with 4 right angles and 

all sides the same length. 

9. A parallelogram with 4 right angles 

and sides of different lengths and 

widths. 


Answers: D62, D63, D64, D65 




Name 

1. 

2. 

3. 

4. 

1 

6 

1 

5 

1 

3 

1 _ 

5 3 __ 

10 

Grade 2 

Step Up to Grade 3 Test 

fi fths sixths 

eighths tenths 

4 _ 

8 5 _ 

8 

6 _ 

8 7 _ 

8 

$ 

1 

6 

1 

10 

1 __ ____ 

3 6 

5 _ 

6 4 _ 

6 3 _ 

6 2 _ 

6 

5. 5, 5, 7, 7, 8, 9, 5, 5, 7, 7, 8, 9, _ , _ , _ , 

1 

10 

1 

10 

5, 5, 7 9, 5, 5 7, 7, 9 5, 7, 7 

Directions Mark the best answer. 1. Which word names the equal parts of the whole? 2. What is the fraction 

for the shaded part of this region? 3. Which sign completes this number sentence? 4. 1 _ is equal to _____ (how 

3 

many) sixths? 5. What are the next three numbers in this pattern? 

T1

Name 

6. 

7. 4 9 

8. 8 3 3 

9. 48 8 

10. 8 1 

11. 53 24 

T2 



12 14 18 28 

13 27 36 45 

72 24 14 9 

24 12 6 3 

1 8 18 81 

53 24 50 3 24 

50 20 3 4 50 10 3 4 

Directions Mark the best answer. 6. What is four times as many as three? 7. Find the product. 8. Find the 

product. 9. Find the quotient. 10. Find the quotient 11. Which shows the best way to find the sum with mental 

math? 



Name 

12. 

13. 

14. 

15. 

 

 

 

43 dollars 27 dollars 


Tens Ones 

7 9 

1 2 

Tens Ones 

6 2 

2 6 


4 1 2 

3 2 1 

3 0 



67 77 

81 91 

26 36 

44 56 

736 763 

836 863 

Directions Mark the best answer. 12. Todd has 50 dollars. He spends 37 dollars on a used bike. How much does 

he have left? 13. Add. Use the workspace to help you solve. 14. Subtract. Use the workspace to help you solve. 

15. Add. 

T3

Name 

16. 

17. 

18. 

19. 

20. 

T4 



cube sphere 

square pyramid cone 

acute obtuse 

right straight 

rectangle rhombus 

parallelogram trapezoid 

Directions Mark the best answer. 16. Name this figure. 17. What kind of angle is shown? 18. Which polygon is 

not a quadrilateral? 19. Which triangle is not isosceles? 20. What is not a name for this quadrilateral? 




Name 

1. 

2. 

3. 

4. 

1 

6 

1 

5 

1 

3 

1_ 5 

3__ 

10 

T1 T2 

T3 



fi fths sixths 

eighths tenths 

4_ 8 5_ 8 

6_ 8 7_ 8 

$ 

1 

6 

1 

10 

1 

10 

1 

10 

1 __ ____ 

3 6 

5_ 6 4_ 6 3_ 6 2_ 6 

5. 5, 5, 7, 7, 8, 9, 5, 5, 7, 7, 8, 9, _ , _ , _ , 

5, 5, 7 9, 5, 5 7, 7, 9 5, 7, 7 

Directions Mark the best answer. 1. Which word names the equal parts of the whole? 2. What is the fraction 

for the shaded part of this region? 3. Which sign completes this number sentence? 4. 1_ is equal to _____ (how 

3 

many) sixths? 5. What are the next three numbers in this pattern? 

45094_T1-T4.indd T1 7/1/08 2:05:11 PM 


Name 

12. 

13. 

14. 

15. 

 

 

 



Tens Ones 

7 9 

1 2 

Tens Ones 

6 2 

2 6 


4 1 2 

3 2 1 

3 0 



67 77 

81 91 

26 36 

44 56 

736 763 

836 863 

Directions Mark the best answer. 12. Todd has 50 dollars. He spends 37 dollars on a used bike. How much does 

he have left? 13. Add. Use the workspace to help you solve. 14. Subtract. Use the workspace to help you solve. 

15. Add. 

45094_T1-T4.indd T3 7/1/08 2:05:13 PM 

T1 

T3 

Name 

6. 

T2 

Answers for Test 

T1, T2, T3, T4 

T4 



12 14 18 28 

7. 4 9 

13 27 36 45 

8. 8 3 3 

72 24 14 9 

9. 48 8 

24 12 6 3 

10. 8 1 

1 8 18 81 

11. 53 24 

53 24 50 3 24 

50 20 3 4 50 10 3 4 

Directions Mark the best answer. 6. What is four times as many as three? 7. Find the product. 8. Find the 

product. 9. Find the quotient. 10. Find the quotient 11. Which shows the best way to find the sum with mental 

math? 

45094_T1-T4.indd T2 7/1/08 2:05:12 PM 

Name 

16. 

17. 

18. 

19. 

20. 

T4 



cube sphere 

square pyramid cone 

acute obtuse 

right straight 

rectangle rhombus 

parallelogram trapezoid 

Directions Mark the best answer. 16. Name this figure. 17. What kind of angle is shown? 18. Which polygon is 

not a quadrilateral? 19. Which triangle is not isosceles? 20. What is not a name for this quadrilateral? 

45094_T1-T4.indd T4 7/1/08 2:05:14 PM 

Answers: T1, T2, T3, T4

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