Grade 4: Step Up to Grade 5

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Glenview, Illinois • Boston, Massachusetts Chandler, Arizona • Shoreview, Minnesota Upper Saddle River, New Jersey Grade 4: Step Up to Grade 5

Teacher’s Guide• Teacher Notes and Answers

for Step-Up Lessons

• Practice

• Answers for Practice

• Test

• Answers for Test

45096_SLPSHEET_FSD 145096_SLPSHEET_FSD 1 6/6/08 3:57:49 PM6/6/08 3:57:49 PM

F19 Adding Integers

F33 Graphing Points in the Coordinate Plane

F34 Graphing Equations in the Coordinate Plane

F40 Using the Distributive Property

F43 More Variables and Expressions

G60 Divisibility by 2, 3, 5, 9, and 10

G63 Prime Factorization

G65 Least Common Multiple

G73 Dividing by Multiples of 10

G75 Dividing by Two-Digit Divisors

H19 Comparing and Ordering Fractions

H24 Place Value Through Thousandths

H31 Decimals to Fractions

H42 Estimating Sums and Differences of Mixed Numbers

H46 Multiplying Two Fractions

I17 Measuring and Classifying Angles

I20 Constructions

I33 Converting Customary Units of Length

I36 Converting Metric Units

I49 Area of Parallelograms

45096_SLPSHEET_FSD 245096_SLPSHEET_FSD 2 6/6/08 3:57:55 PM6/6/08 3:57:55 PM

Math Diagnosis and Intervention SystemIntervention Lesson F19

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Adding Integers

Teacher Notes

Ongoing AssessmentAsk: Why do you actually subtract the magnitudes when you add integers with different signs? You subtract because you are going in opposite directions on the number line.

Error InterventionIf students have trouble remembering the rules,

then have them use the number line to find the sum and state the rule that would apply right after they find the sum.

If You Have More TimeHave students find a pattern in sets of sums, like the ones below.

�3 � 5 �3 � 1�3 � 4 �3 � 0�3 � 3 �3 � (�1)�3 � 2 �3 � (�2)


Adding Integers

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Intervention Lesson F19 93

Name

Materials scissors, tape

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 10

1. Cut out the figure in the lower right corner of the page. Fold on the dashed line, and tape closed.

2. Place the figure in the starting position, at zero. Adding Integers on the Number Line

• Always start at zero, facing the positive numbers.

• Move forward for positive numbers.

• Move backward for negative numbers.

To add �4 � 7, move the figure backward 4 spaces to �4. Then move it forward 7 spaces to 3. So �4 � 7 � 3.

3. Use the figure to find �2 � 8.

4. To find 3 � (�8), start at zero, move the figure forward 3 spaces to 3. Then move the figure backward 8 spaces to –5.

So 3 � (�8) � .

5. Use the figure to find 5 � (�9).

6. To find �1 � �5, start at zero, move the figure backward 1 space to �1. Then move the figure backward 5 spaces to �6.

So, �1 � (�5) = .

7. Use the figure to find �3 � (�5).

8. How many units is �2 from 0 on the number line?

The magnitude of a number is its distance from zero.

9. What is the magnitude of �8?

10. What is the magnitude of 5?

6

�5

�4

�6

�8

2

8

5

Use the number line to find each sum. Look for a pattern.

11. �2 � (�3) 12. �6 � (�1) 13. �4 � (�2)

14. When you add two integers with the same sign, do you add or subtract the magnitudes of the numbers?

15. When you add two negative integers, what is the sign of the sum?

Use the number line to find each sum. Look for a pattern.

16. �6 � 3 17. �5 � 3 18. 1 � (�6)

19. 9 � (�4) 20. 8 � (�2) 21. �3 � 9

22. When you add two integers with different signs, do you add or subtract the magnitudes of the numbers?

23. Which has a greater magnitude �6 or 3?

24. Is the sum �6 � 3 positive or negative?

25. When you add a positive and a negative integer and the one with the greater magnitude is negative, what is the sign of the sum?

26. Which has a greater magnitude 9 or �4?

27. Is the sum 9 � (�4) positive or negative?

28. When you add a positive and a negative integer and the one with the greater magnitude is positive, what is the sign of the sum?

Add. Use rules for adding integers or a number line.

29. �6 � (�3) 30. �1 � (�5) 31. 2 � (�5) 32. �7 � 5

33. 9 � (�4) 34. �3 � (�6) 35. �8 � (�4) 36. �2 � 7

94 Intervention Lesson F19

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Adding Integers (continued)

Name


�5 �7 �6

add

negative

�3 �2 �55 6 6

subtract

negative

positive

�9 �6 �3 �2

5 �9 �12 5

negative

positive

�6

9

Intervention Lesson F19


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Graphing Points in the Coordinate Plane

Teacher Notes

Ongoing AssessmentMake sure students know the first number in an ordered pair is always horizontal and the second is always vertical. Use (h, v) to help them remember.

Error Intervention If students have trouble plotting points,

then use F30: Graphing Ordered Pairs.

If You Have More Time Have students work in pairs and play Guess My Location. One partner writes down an ordered pair to chose a point. The second student moves a counter on a coordinate grid, one space at a time. The first student says closer or farther for each move until the second student finds the point. Change roles and repeat, as time allows.


Graphing Points in the Coordinate Plane

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Name

Materials red and blue crayons, markers, or colored pencils

To graph a point in the coordinate plane always start at the origin. You can use a red crayon to show negative numbers and a blue crayon to show positive numbers.

Plot point A at (3, �4) by doing the following.

1. Since the x-coordinate, 3, is positive, draw a blue line from the origin right 3 units on the x-axis to (3, 0).

2. Since y-coordinate, �4, is negative, draw a red line from (3, 0) down 4 units and plot a point. This point is (3, �4). Label it A.

Find the coordinates of point B, by doing the following.

3. From the origin, you must go left, so use the red crayon. Draw a red line from the origin, along the x-axis, to the point directly below point B.

4. How many units

10�1�1

�2

�3

�4

�5

�6

�7

�2�3�4�5�6�7

1

2

3

B

A

4

5

6

7

2 4 5 6 7 x

y

x-axis

y-axis

Origin

3

did you move left from the origin?

5 5. So, what is the

x-coordinate of point B?

�5 6. Since you need to

move up from (�5, 0) to get to point B, use the blue crayon. Draw a blue line from (�5, 0) to point B.

7. How many units did you move up from the x-axis to point B?

2 8. So, what is the

y-coordinate of point B? 2

9. What are the coordinates of point B? (�5, 2)

Write the ordered pair for each point.

0 1

1

�1

2

�2

3

�3

4

�4

5

�5

�1�2�3�4�5 2 3 4 5 x

y

E

I

HF

J

K

G

L

10. E 11. F

12. G 13. H

Name the point for each ordered pair.

14. (4, 0) 15. (1, �2)

16. (1, 4) 17. (�4, �2)

18. Reasoning What is the y-coordinate for any point on the x-axis?

Write the ordered pair for each point.

0 1

1

�1

2

�2

3

�3

4

�4

5

�5

�1�2�3�4�5 2 3 4 5 x

y

N

S

V

QP

T

R

M

19. M 20. N

21. P 22. Q


23. (1, 3) 24. (4, 4)

25. (0, �2) 26. (�3, 4)

27. Reasoning What is the x-coordinate for any point on the y-axis?

0

28. Is the point (�3, �4) located above, below, or on the x-axis? below

29. Is the point (0, �8) located above, below, or on the x-axis? below


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Graphing Points in the Coordinate Plane (continued)

Name


(�3, 2)

(3, 3)

(�1, �4)

(4, �3)

L I

K J

(3, 0)

(�2, �3)

(�2, 1)

(2, �4)

0

T R

V S




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Graphing Equations in the Coordinate Plane

Teacher Notes

Ongoing AssessmentAsk: The graph of y � x � 1 seems to go though the point (3, 2). How can you verify that (3, 2) is a point on the line y � x � 1? Check if y � x � 1 is true when x � 3 and y � 2.

Error Intervention If students add, subtract, or multiply integers incorrectly

then use F19: Adding Integers, F20: Subtracting Integers, or F21: Multiplying and Dividing Integers.

If students plot points incorrectly,

then use F33: Graphing Points in the Coordinate Plane.

If You Have More TimeHave students work in pairs. One partner graphs a line and the other partner tries to guess the equation by creating a table of ordered pairs and looking for a pattern. Change roles and repeat.


Graphing Equations in the Coordinate Plane

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Graph the equation y � x � 1 by doing the following.

1. Find y when x � �2, x � 0, and x � 4. Complete.

When x � �2: When x � 0: When x � 4:

y � x � 1 y � x � 1 y � x � 1

y � �2 � 1 y � � 1 y � � 1

y � �2 � (�1) y � � (�1) y �

y � y �

2. Complete the table of ordered pairs.

0

2

�2

4

�4

�2�4 2 4x

y

x y

�2 �3

0

4

3. Plot each ordered pair.

4. Draw a line through the points. If the points are not on a line, check your work above.

Graph y � � 2x by doing the following.

0

2

�2

4

�4

�2�4 2 4x

y

5. Complete the table of ordered pairs for the equation y � �2x.

x y

�2

0

2

6. Plot each ordered pair.

7. Draw a line through the points. If the points are not on a line, check your work above.

�3 �1

00

43

�13

40

�4

Complete each table of ordered pairs. Then graph the equation.

8. y � x � 2 9. y � 2x

x y

�4

0

2 0

2

�2

4

�4

�2�4 2 4 x

y

x y

�2

0

2 0

2

�2

4

�4

�2�4 2 4 x

y

10. y � �3x 11. y � 2 � x

x y

�1

0

1 0

2

�2

4

�4

�2�4 2 4 x

y

x y

�2

0

3 0

2

�2

4

�4

�2�4 2 4 x

y

12. Reasoning Is the point (6, �1) on the graph of y � 5 � x? Explain.

13. Reasoning Is the point (2, �8) on the graph of y � 4x? Explain.


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Graphing Equations in the Coordinate Plane (continued)

Name


�224

�404

30

�3

42

�1

The point (6, �1) is on the graph of y � 5 � x,because y � 5 � x is true when x � 6 and y � �1.

No, the point (2, �8) is not on the graph of y � 4xbecause y � 4x is not true when x � 2 and y � �8.



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Using the Distributive Property

Teacher Notes

Ongoing AssessmentAsk: Does 3 � (4 � 7) � (3 � 4) � 7? No, the 3 must be distributed or passed out to each addend. 3 � (4 � 7) � (3 � 4) � (3 � 7)

Error InterventionIf students don’t know how to evaluate expressions like 5 � (2 � 6) and (5 � 2) � (5 � 6),

then use F39: Order of Operations.

If You Have More TimeHave students describe a real world situation for 4 � (5 � 3) and/or (4 � 5) � (4 � 3).



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Materials counters, 100 per pair or group

Discover the Distributive Property by following 1–8.

1. Make an array with 4 rows and 5 counters in each row.

2. The array shows 4 � 5 � .

3. Make another array with 4 rows and 3 counters in each row.

4. The second array shows 4 � � .

5. Put the two arrays together.

How many counters in all? � �

6. Fill in the blanks, using your answers above.

(4 � 5) � (4 � 3) � � �

7. After putting the two arrays together, howmany counters are in each of the 4 rows? 5 � 3 �

8. Fill in the blanks.

(4 � 5) � (4 � 3) � � (5 � 3) � � 8 �

20

3 12

20 12 32

20 12 32

8

3244

9. Make an array with 5 rows and 19 in each row. Separate the array into one that is 5 by 10 and one that is 5 by 9.

10. Use the array above to fill in the blanks.

5 � 19 � 5 � ( � 9) � (5 � ) � (5 � )

� �

�

Fill in the blanks using the Distributive Property.

11. 6 � 9 � 6 � (4 � ) � (6 � 4) � (6 � )

12. 3 � 14 � 3 � ( � 4) � (3 � ) � ( � 4)

13. 2 � 27 � � (20 � ) � ( � 20) � ( � )

14. 12 � 8 � (10 � ) � 8 � (10 � ) � ( � 8)

15. 9 � 47 � (9 � 40) � (9 � ) � � (40 � )

16. 16 � 105 � (16 � 100) � (16 � ) � � (100 � )

17. 25 � 204 � ( � 200) � (25 � ) � 25 � ( � )

18. 8 � 96 � � (100 � 4) � ( � 100) � ( � 4)

19. 7 � 48 � � (50 � ) � ( � 50) � ( � )

20. Reasoning Describe two different ways to find 4 � 49 with mental math.


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Using the Distributive Property (continued)

Name


(4 � 40) � (4 � 9) and (4 � 50) � (4 � 1)

10 10 950 4595

5 5

10 10

7 2

2 8

7 7

5 16

25 4

8 8

2 7

3

722

2

9

5

2004

8

277



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More Variables and Expressions

Teacher Notes

Ongoing AssessmentAsk: For a � 6 and b � 2, does 2a � b equal (2 � 2) � 6? No, a must be replaced with 6 and b with 2 to get (2 � 6) � 2.

Error InterventionIf students have difficulty simplifying expressions after they substitute values for the variables,

then use F39: Order of Operations.

If You Have More TimeChallenge students to write an expression that simplifies to 14 when x � 5 and y � 4. Sample answers: 2x � 3


More Variables and Expressions

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To evaluate an expression, place the known value in place of the variable. Then use the order of operations to simplify.

1. Find 3n � 5, when n � 7.

3 � � 5 Put 7 in place of n.

� � 5 Use the order of operations, multiply first.

� Subtract.

2. Find 3k � k__4 , when k � 8.

3 � �8____4 Put 8 in place of k.

� � Multiply and divide first.

� Subtract.

3. Find 4y � 2z, when y � 5 and z � 7.

4 � � 2 � Put 5 in place of y and 7 in place of z.

� � Multiply first.

� Add.

4. Find (3a � b) � c, when a � 10, b � 6, and c � 2.

(3 � � ) � Put 10 in place of a, 6 in place of b, and 2 in place of c

� ( � ) � Use the order of operations, do parentheses first. Inside the parentheses, multiply first.

� � Subtract inside the parentheses.

� Divide.

7

21

16

8

24

22

5

20

34

10

30

24

6 2

6 2

2

2

7

14

12

Evaluate each expression for x � 3.

5. � x __ 3 � � 15 6. 24 � (2x) 7. (3x) � 5

16 18 14

8. (4x) � 12 9. (5x) � � 15 ___ x � 10. 35 � � 21 ___ x � 0 10 42

11. (19 � x) � 11 12. (6x) � x � 12 13. 5x � 3

2 9 5

Evaluate each expression for a � 9, b � 2, and c � 0.

14. (a � 7b) � c 15. 13c � a 16. (a � b) � 3

23 9 33

17. 12b � 14c 18. (a � b � c) � 2 19. (11 � a) � b

24 22 10

20. c � (b � c) 21. 4a � 5b 22. (a � b � c) � 4

0 26 28

23. 7b � 12c 24. (2a � b) � 5 25. a � (b � c)

14 4 18

Use the data at the right to answer Exercises 26–28.

26. The cost of x small pizzas with y small beverages is given by the expression 5x � y. How much do 3 small pizzas and 2 small beverages cost? $17

27. The cost of x large pizzas with y large beverages is given by the expression 8x � 2y. How much do2 large pizzas with 3 large beverages cost? $22

28. Reasoning Micka purchases 4 small veggie pizzas and 3 large beverages. Romano purchases 3 large pizzas and 4 small beverages. Who spent more money? Explain.


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More Variables and Expressions (continued)

Name


Veggie Pizza House

Size Pizza Beverages

small $5.00 $1

large $8.00 $2

Micka spent 4(5) � 3(2) � $26 and Romano spent 3(8) � 4(1) � $28; Romano spent more money.

Intervention Lesson G60

Math Diagnosis and Intervention SystemIntervention Lesson G60

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Divisibility by 2, 5, 9, and 10

Teacher Notes

Ongoing AssessmentAsk: What does it mean that 135 is divisible by 5? It means that if you divide 135 by 5 the quotient is a whole number with no remainder.

Error InterventionIf students have trouble remembering the divisibility rules,

then have the students use a calculator to generate multiples of each number and look for patterns.

If You Have More TimeHave students work with a partner. Each partner writes a three- or four-digit number. The partners switch numbers and determine if that number is divisible by 2, 5, 9, and/or 10.


Divisibility by 2, 3, 5, 9, and 10

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Intervention Lesson G60 197

Name

A number such as 256 is divisible by a number like 2 if 256 ÷ 2 has no remainder. If 256 is a multiple of 2, then 256 is divisible by 2.

Use the divisibility rules and answer 1 to 10 to determine if 256 is divisible by 2, 3, 5, 9, or 10.

Divisibility RulesNumber Rule

2 The last digit is even: 0, 2, 4, 6, 8.3 The sum of the digits is divisible by 3.5 The last digit ends in a 0 or 5.9 The sum of the digits is divisible by 9.

10 The ones digit is a 0.

1. Is the last digit in 256 an even number? yes

2. Is 256 divisible by 2? yes

3. Is the last digit in 256 a 0 or 5? no

4. Is 256 divisible by 5? no


6. What is the sum of the digits of 256? 2 + 5 + 6 = 13

7. Is the sum of the digits of 256 divisible by 3? no


9. Is the sum of the digits of 256 divisible by 9? no


Use the divisibility rules to determine if 720 is divisible by 2, 5, 9, or 10.

11. Is 720 divisible by 2? yes 12. Is 720 divisible by 5? yes

13. Is 720 divisible by 10? yes 14. Is 720 divisible by 9? yes

Test each number to see if it is divisible by 2, 3, 5, 9, or 10. List the numbers each is divisible by.

15. 56 16. 78 17. 182

2 2, 3 2

18. 380 19. 105 20. 126

2, 5, 10 3, 5 2, 3, 9

21. 4,311 22. 8,356 23. 2,580

3, 9 2 2, 3, 5, 10

24. 7,265 25. 4,815 26. 630

5 3, 5, 9 2, 3, 5, 9, 10

27. Feliz has 225 baseball trophies. He wants to display his trophies on some shelves with an equal number of trophies on each. He can buy shelves in packages of 5, 9, or 10. Which shelf package should he NOT buy? Explain.

Feliz should not buy the package with 10 shelves. 225 is divisible by 5 and 9, but not by 10.

28. Reasoning Are all numbers that are divisible by 5 also divisible by 10? Explain your reasoning.

Not all numbers that are divisible by 5 are also divisible by 10. For example, 25 is divisible by 5 but not by 10.

29. Reasoning Are all numbers that are divisible by 10 also divisible by 5? Explain your reasoning.

All numbers that are divisible by 10 are divisible by 5. If a number ends in a zero, and thus is divisible by 10, it must end in either a zero or 5 and thus be divisible by 5.

198 Intervention Lesson G60

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Divisibility by 2, 3, 5, 9, and 10 (continued)

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Prime Factorization

Teacher Notes

Ongoing AssessmentAsk: What number has a prime factorization of 2 � 32 � 4? 72 Is there only one number with this prime factorization? Yes, you multiply the numbers together to find the number so there is only one possible answer.

Error InterventionIf students have difficulty factoring composite numbers,

then use G59: Factoring Numbers.

If You Have More TimeHave students work in pairs to find the prime factorization of 5040 (24 � 32 � 5 � 7).


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Prime Factorization

1. Use the two factor trees shown to factor 240. For the first circle, think of what number times 6 is 24. For the next two circles, factor 10. Continue factoring each number. Do not use the number 1.

2 34 5 2

2 26

2 2 2 34

2. What are the numbers at the ends of the branches for each tree?

2, 3, 2, 2, 2, 5 2, 2, 2, 5, 2, 3

3. Reasoning What do all the numbers at the end of each branch have in common?

They are prime.

4. Reasoning What do you notice about the numbers in the two groups?

They are the same.

5. Arrange the numbers from least togreatest and include a multiplicationsign between each pair of numbers. 2 � 2 � 2 � 2 � 3 � 5

Your answer to 5 above shows the prime factorization of 240. If you multiply all the factors back together, you get 240.

6. Write the prime factorization of 240 using exponents.

24� 3 � 5


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Prime Factorization (continued)

Complete each factor tree. Write the prime factorization with exponents, if you can. Do not use the number 1 as a factor.

7. 8.

3 � 7

23 � 3

9. 10.

34

23 � 7

For Exercises 11 to 22, if the number is prime, write prime. If the number is composite, write the prime factorization of the number.

11. 11 12. 18 13. 41 14. 40

Prime 2 � 32 Prime 23 � 5

15. 16 16. 17 17. 80 18. 95

24 Prime 24 � 5 5 � 19

19. 35 20. 72 21. 48 22. 55

5 � 7 23 � 32 24 � 3 5 � 11

23. Reasoning Holly says that the prime factorization for 44 is 4 � 11. Is she right? Why or why not?

No; 4 is not prime.



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Least Common Multiple

Teacher Notes

Ongoing AssessmentAsk: Could 10 and another number have an LCM of 5? Sample answer: No, the smallest multiple of 10 is 10. So, the LCM must be greater than or equal to 10.

Error InterventionIf students are making mistakes in finding multiples of two-digit numbers,

then use G49: Multiplying Two-Digit Numbers.

If You Have More TimeHave students write the prime factorization of 15 and 6. Show students that the least common multiple can be found by multiplying the 5 from the prime factorization of 15, the 2 from the prime factorization of 6, and the 3 which is common to both. The prime factorization of 30, which is the least common multiple, should contain the prime factorization of both 15 and 6.


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Least Common Multiple

A student group is having a large cookout. They wish to buy the same number of hamburgers and hamburger buns. Hamburgers come in packages of 12 and buns come in packages of 8. What is the least amount of each they can buy in order to have the same amount?

Follow 1 to 4 below to answer the question.

1. Complete the table.

Packages 1 2 3 4 5 6

Hamburgers 12 24 36 48 60 72Buns 8 16 24 32 40 48

2. What are some common multiples from the table? 24, 48

3. What is the least of these common multiples? 24

So, the least common multiple (LCM) of 12 and 8 is 24.

4. What is the least amount of hamburgers and buns that the students can buy and have the same amount of each? 24

Find the least common multiple of 6 and 15 by following the steps below.

5. Complete the table.

2 � 3 � 4 � 5 � 6 � 7 � 8 � 9 � 10 �

6 12 18 24 30 36 42 48 54 6015 30 45 60 75 90 105 120 135 150

6. What are the common multiples from the table? 30, 60

7. What are the next three common multiples that are not in the table? 90, 120, 150

8. What is the least common multiple of 6 and 15? 30


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Least Common Multiple (continued)

Find the least common multiple (LCM).

9. 30, 4 10. 18, 9 11. 12, 36

60 18 36

12. 6, 12 13. 8, 20 14. 3, 14

12 40 42

15. 6, 25 16. 8, 12, 15 17. 3, 4, 5

150 120 60

18. Maria and her brother Carlos both got to be hall monitors today. Maria is hall monitor every 16 school days. Carlos is hall monitor every 20 school days. What is the least number of school days before they will both be hall monitors again?

80 days

19. Reasoning Find two numbers whose least common multiple is 12.

Answers will vary. Sample answer: 6, 12

20. Reasoning Can you find the greatest common multiple of 6 and 15? Explain.

No, the common multiples will continue forever.



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Dividing by Multiples of 10



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Use the multiplication sentences to find each quotient. Look for a pattern.

1. 4 � 20 � 80 80 � 20 � 4

40 � 20 � 800 800 � 20 � 40

400 � 20 � 8,000 8,000 � 20 � 400

2. What basic division fact is used in each quotient above?

8 � 2 � 4

Use basic facts and a pattern to find 2,400 � 80. Answer 3 to 5.

3. What basic division fact can be used to find 2,400 � 80?

24 � 8 � 3

In 24 � 8 � 3, 24 is the dividend, 8 is the divisor, and 3 is the quotient.

4. Look for a pattern.

Number SentenceZeros in the

DividendZeros in the

DivisorZeros in the

Quotient

240 � 80 � 3 1 1 0

240 � 8 � 30 1 0 1

2,400 � 8 � 300 2 0 2

2,400 � 80 � 30 2 1 1

Complete. Zeros in the dividend � Zeros in the divisor � zeros in the quotient

5. Reasoning Use the pattern to explain why 2,400 � 80 has one zero.

2,400 has 2 zeros and 80 has one zero. 2 � 1 � 1, so the quotient has 1 zero.

Divide. Use mental math.

6. 300 � 30 � 10 7. 60 � 20 � 3 8. 200 � 40 � 5

9. 240 � 60 � 4 10. 490 � 70 � 7 11. 450 � 90 � 5

12. 100 � 50 � 2 13. 2,700 � 90 � 30 14. 1,800 � 60 � 30

15. 3,500 � 70 � 50 16. 1,500 � 30 � 50 17. 800 � 40 � 20

18. 640 � 80 � 8 19. 3,600 � 60 � 60 20. 140 � 70 � 2

21. 1,200 � 20 � 60 22. 8,100 � 90 � 90 23. 560 � 80 � 7

24. 600 � 30 � 20 25. 400 � 20 � 20 26. 2,400 � 60 � 40

27. 1,200 � 40 � 30 28. 2,500 � 50 � 50 29. 2,100 � 70 � 30

30. 4,500 � 90 � 50 31. 480 � 80 � 6 32. 450 � 50 � 9


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Dividing by Multiples of 10 (continued)

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33. Dan has a coin collection. His sister Michaela has just started collecting. Michaela has 20 coins, and Dan has 400 coins. About how many times larger is Dan’s collection?

20 times larger

34. Hector must store computer CDs in cartons that hold 40 CDs each. How many cartons will he need to store 2,000 CDs?

50 cartons

35. Reasoning Write another division problem with the same answer as 2,700 � 90.

Sample answer: 270 � 9

Teacher Notes

Ongoing AssessmentAsk: How is dividing by 20 similar to dividing by 2? How is it different? When you divide by 20, if there is no remainder, the answer is the same as dividing by 2 except the answer will have one less zero.

Error InterventionIf students have trouble with the basic division facts,

then use some of the intervention lessons on division facts, G38 to G41.

If You Have More TimeHave student play a memory game in pairs. Each student makes 3 pairs of cards. Each pair of cards should have two different division problems that have the same whole number answer. Students should only use divisors that are multiples of 10 and write only the division expression on the card, not the quotient. For example, one pair of cards might have 2,400 � 30 and 1,600 � 20. The cards are shuffled and placed face down in a 3 by 4 array. Students take turns turning over 2 cards. If the cards have the same solution, the student keeps them. If not, the cards are turned back over and the next student takes a turn. The students continue until all cards are matched.



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Dividing by Two-Digit Divisors


Dividing by Two-Digit Divisors

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A carpenter cut a board that is 144 inches long. He cut pieces 32 inches long. How many pieces did he get and how much of the board was left?

Find 144 � 32 by answering 1 to 11.

1. First, estimate to find the approximate number of pieces.

150 � 30 � 5

2. Write the estimate in the ones place of the quotient, 5

32 � � 1 4 4

1 6 0on the right.

3. Multiply. 32 � 5 � 160

4. Compare the product to the dividend. Write � or �.

160 � 144

Since 160 is too large, 5 was too large. Try 4.

5. Multiply. 32 � 4 � 128

6. Compare the product to the dividend. Write � or �.

128 � 144

Since 128 is less than 144, 4 is not too large. Write 4 in 4

32 ��1 4 4

1 2 8

1 6

the ones place of the quotient on the right. Write 128 below 144.

7. Subtract. 144 � 128 � 16

8. Compare the remainder to the divisor. Write � or �.

16 � 32

Since the remainder is less than the divisor, the division is finished.

9. What is 144 � 32? 4 R 16

10. How many 32-inch pieces did the carpenter cut? 4 pieces

11. How much of the board was left? 16 inches

Divide.

6 R10 2 R72 7 R30 12. 32 ��202 13. 94 ��260 14. 45 ��345

2 R13 7 R16 9 R30 15. 62 ��137 16. 28 ��212 17. 58 ��552

8 R1 4 R3 8 R80 18. 82 ��657 19. 32 ��131 20. 93 ��824

5 R20 2 R56 8 R13 21. 89 ��465 22. 74 ��204 23. 78 ��637

7 R22 2 R59 5 R54 24. 77 ��561 25. 61 ��181 26. 73 ��419

8 R60 8 R62 5 R33 27. 63 ��564 28. 82 ��718 29. 57 ��318

30. A vegetable stand sells 192 cucumbers and 224 squash during the month of July. About how many cucumbers did they sell each day? Between 6 and 7

31. Reasoning To start dividing 126 by 23, Miranda used the estimate 120 � 20 � 6. How could she tell 6 is too high?

6 � 23 � 138 and 138 � 120.


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Dividing by Two-Digit Divisors (continued)

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Teacher Notes

Ongoing AssessmentAsk: How do you know if your estimate is too low? After you multiply and subtract, the estimate is too low if the remainder is more than the divisor. How do you know if your estimate is too high? After you multiply, the estimate is too high if the product is more than the dividend.

Error InterventionIf students have trouble finding an estimate,

then use G74: Estimating Quotients with Two-Digit Divisors.

If You Have More TimeHave students measure their heights in centimeters. Then have them measure the width of their hands in centimeters. Each student should divide their height by their hand width.

Intervention Lesson H19

Math Diagnosis and Intervention SystemIntervention Lesson H19

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Comparing and Ordering Fractions

Teacher Notes

Ongoing AssessmentAsk: Which is larger 1 __

4 or 1 __

3 ? How can you tell?

1 __ 3 is larger than 1 __

4 because when the numerators are

the same, you just compare the denominators. The

fraction with the smaller denominator is the larger

of the two fractions.

Error InterventionIf students can not find the LCD,

then use G65: Least Common Multiple.

If students are having problems writing equivalent fractions,

then use H7: Using Models to Find Equivalent Fractions or H14: Equivalent Fractions.

If You Have More TimeWrite a fraction, such as 5 __

6 , on the board. Ask

students to write 5 fractions that are greater than

the fraction and 5 fractions that are less. Encourage

students to use different denominators and

numerators as they create different fractions. Share

findings as a class.


Comparing and Ordering Fractions

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Intervention Lesson H19 121

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Jen ate 7__9 of a salad. Jack ate 5__

9 of a salad. Find out who ate the greater

part of a salad by answering 1–3.

Compare 7__9 and 5__

9 .

1. Are the denominators the same? yesIf the denominators are the same, then compare the numerators. The fraction with the greater numerator is greater than the other fraction.

2. Compare. Write �, �, or �. 7 � 5

7__9 � 5__

9

3. Who ate the greater part of a salad, Jen or Jack? Jen


4 by answering 4 to 6

4. Are the denominators the same? no

5. Are the numerators the same? yesIf the numerators are the same, compare the denominators. The fraction with the greater denominator is less than the other fraction.

6. Compare. Write �, �, or �. 5 � 4

3__5 � 3__

4


3 by answering 7 to 11.

7. Are the denominators the same? no

8. Are the numerators the same? noIf neither the numerators or the denominators are the same, change to equivalent fractions with the same denominator.

9. What is the LCM of 3 and 4? 12

10. Rewrite 2 __ 3 and 3 __ 4 as equivalent fractions with a denominator of 12.

3 9�

4 12

2 8�

3 12

11. Compare. Write �, �, or �. 9 ___ 12 � 8 ___ 12

3 __ 4 � 2 __ 3

Write 5 __ 6 , 5 __ 9 , and 1 __ 3 in order from least to greatest by answering 12 to 15.

12. Use the denominators to compare. Write �, �, or �. 5 __ 6 � 5 __ 9

13. Rewrite 1 __ 3 so that it has a denominator common with 5 __ 9 . 1 3�

3 9

14. Compare the numerators. Write �, �, or �. 5 __ 9 � 3 __ 9

5 __ 9 � 1 __ 3

15. Use the comparisons to write 5 __ 9 , 5 __ 6 , and 1 __ 3 in order from least to greatest.

1__3 �

5__9 �

5__6

Compare. Write �, �, or �.

16. 3 __ 7 � 1 __ 7 17. 5 __ 8 � 10 ___ 16 18. 3 ___ 11 � 4 ___ 10 19. 3 __ 4 � 2 __ 3

20. 3 __ 5 � 9 ___ 15 21. 5 __ 6 � 5 __ 8 22. 5 __

8 � 7 ___ 12 23. 7 __

9 � 4 __ 9

24. 1 __ 4 , 6 __ 7 , 3 __ 5 25. 5 __ 8 , 8 ___ 10 , 2 __ 7 26. 5 __

9 , 10 ___ 12 , 5 __ 7 27. 3 __

9 , 12 ___ 15 , 5 __ 6

1__4, 3__

5, 6__

7 2__7, 5__

8, 8__

10 5__9, 5__

7, 10__

12 3__9, 12__

15, 5__

6

28. Reasoning Mario has two pizzas the same size. He cuts one into 4 equal pieces and the other into 5 equal pieces. Which pizza has larger pieces? Explain.

If there are fewer pieces, then each piece is larger. The pizza with 4 pieces has larger pieces.

122 Intervention Lesson H19

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Place Value Through Thousandths

Teacher Notes

Ongoing AssessmentAsk: What is one and one thousandth written in standard form? 1.001

Error InterventionIf students are having problems writing the value of a digit such as 1 in 0.381,

then have them put blanks below each digit in 0.381, fill in the 1, and then fill in the rest of the places with zeros.

If You Have More TimeHave students work in pairs. Have them write a decimal in the thousandths in standard form on one index card and the same decimal in a different form on another index card. Students should make 10 pairs like this so no decimal is used twice. Have students shuffle the cards and arrange them in a face-down array. One student turns over two cards and keeps them if they match. If the cards do not match, the cards are turned back over and the other student takes a turn. Continue until all cards are matched.


Place Value Through Thousandths

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1. Write 5.739 in the place-value chart below.

ones tenths hundredths thousandths

5 . 7 3 9 2. What is the value of the 5 in 5.739? 5

3. What is the value of the 7 in 5.739? 0.7



6. Write 5.739 in expanded form. 5 � 0.7 � 0.03 � 0.009

7. Write 5.739 in words.

five and seven hundred thirty-nine thousandths

Write seven and two hundred four thousandths in standard from by answering 8 to 14.

8. How many ones are in seven and two hundred four thousandths? 7

Write 7 in the ones place of the place-value chart below.

ones tenths hundredths thousandths

7 . 2 0 4

9. Write two hundred, thousandths as a fraction.

200_____1,000

10. Write an equivalent fraction. 200 2 � 1,000 10

11. How many tenths are in seven and two hundred four thousandths? 2

Write 2 in the tenths place of the place-value chart above.

12. How many hundredths are in seven and two hundred four thousandths? 0

Write 0 in the hundredths place of the place-value chart above.

13. How many thousandths are in seven and two hundred four thousandths? 4

Write 4 in the thousandths place of the place-value chart.

14. Write 7.204 in expanded form. 7 � 0.2 � 0.004

15. Reasoning What is 1 thousandth less than 7.204? 7.203

Write each value in standard form.

16. 507 thousandths 17. 5 and 6 thousandths 18. 9 and 62 thousandths

0.507 5.006 9.062

Write the value of the underlined digit.

19. 2.5 _5 3 20. 0.38 _1 21. 6. _6 47 22. 9.0 _9 7

0.05 0.001 0.6 0.09

Write each decimal in expanded form.

23. 4.685 24. 3.056

4 � 0.6 � 0.08 � 0.005 3 � 0.05 � 0.006

25. 0.735 26. 4.004

0.7 � 0.03 � 0.005 4 � 0.004

Write each decimal in word form.

27. 2.598

two and five hundred ninety-eight thousandths

28. 0.008

eight thousandths

29. 0.250

two hundred and fifty thousandths


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Place Value Through Thousandths (continued)

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Decimals to Fractions

Teacher Notes

Ongoing AssessmentAsk: What is 0.10 written as a fraction? 1 ___

10

Error InterventionIf students have trouble representing decimals with grids,

then use H22: Place Value through Hundredths.

If You Have More TimeHave students work in pairs. Each student writes a decimal on a piece of notebook paper. The students exchange papers and rewrite the decimal as a fraction. Have students check their partners’ work for accuracy.

Materials crayons, markers, or colored pencils

Write 0.45 as a fraction by answering 1 to 5.

1. Color the grid to show 0.45.

2. How small squares did you color? 45

3. How many squares are in the grid? 100

4. What fraction represents the part of the grid that you colored?

45___100

5. Write a fraction equal to 0.45. 0.45 �

45___100

You can also use place value to change a decimal to a fraction.

Write 0.3 as a fraction by answering 6 to 9

6. Write 0.3 in words. three tenths

7. What is the place value of the 3 in 0.3? tenths

8. What fraction represents three tenths?

3__10

Since the 3 is in the tenths place, you write 3 over 10.

9. Write a fraction equal to 0.3. 0.3 �

3__10

Write 3.07 as a mixed number by answering 10 to 13.

10. What is the whole number part of the decimal 3.07? 3

11. What is the place value of the last digit in 3.07? hundredths

12. Write the place value as the denominator 3.07 � 3 7______

100and write 7 as the numerator.

13. Write a mixed number equal to 3.07. 3.07 �3 7___

100



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Decimals to Fractions

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Write each decimal as a fraction or mixed number.

14. 0.4 15. 3.7 16. 5.274__10

3 7__10

5 27___100

17. 0.8 18. 1.2 19. 4.038__10

1 2__10

4 3___100

20. 0.12 21. 10.5 22. 0.1912___100

10 5__10

19___100

23. 0.42 24. 5.75 25. 8.642___100

5 75___100

8 6__10

26. 19.09 27. 0.01 28. 28.37

19 9___100

1___100

28 37___100

29. Jaime put 13.9 gallons of gas in the car. What is 13.9 written as a mixed number?

13 9__10

30. Candice ran 2.75 miles.What is 2.75 written as a mixed number?

2 75___100

31. Justin’s mom bought a 12.57 pound turkey. What is 12.57 written as a mixed number?

12 57___100

32. Reasoning Marco says 0.08 � 8___10 . Is he correct? Explain why.

No; 0.08 � 8___100

not 8__10

.

33. Reasoning 2.37 � 2 37____100 and 2.3 � 2 3___

10 . Explain why the 3 in

2.37 represents 3___10 .

Sample answer: In 2.37 � 2 � 0.3 � 0.07,

so the 3 represents 0.3 � 3__10

.


Decimals to Fractions (continued)

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Estimating Sums and Differences of Mixed Numbers

Teacher Notes

Ongoing Assessment

Ask: How does knowing that 2 __ 3 is greater than 1 __

2

help you to know that 1 2 __ 3 is closer to 2 on a

number line than to 1? Sample answer: On a

number line, 1 1 __ 2 is the halfway point between 1 and

2. Since 2 __ 3 � 1 __

2 , 1 2 __

3 � 1 1 __

2 and 1 2 __

3 is between 1 1 __

2 and

2 on the number line. Thus, 1 2 __ 3 is closer to 2 than to

1.

Error InterventionIf students have trouble understanding the location of mixed numbers on the number line,

then use H5: Fractions on the Number Line or H21: Fractions and Mixed Numbers on the Number Line.

If You Have More TimeHave students work in pairs. Ask students to create a list of activities they participate in after school. Next to each activity, have students write the time spent on each activity, as a mixed number. Have students trade lists with their partners. Then have the partners estimate how much time was spent on two of the activities together and how much more time was spent on one activity than another.


Estimating Sums and Differences of Mixed Numbers

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Last week, Dwayne spent 4 1__3 hours playing basketball and 1 2__

3 hours

playing soccer. Answer 1 to 9 to estimate how much time Dwayne

spent in all playing these two sports.

Estimate 4 1__3 � 1 2__

3 .

1. What two whole numbers is 4 1__3 between? 4 and 5

2. Use the number line.

4 4 1 __ 6 4 2 __ 6 4 3 __ 6 4 4 __ 6 4 5 __ 6 5

4 1 __ 3

Is 4 1__3 closer to 4 or 5? 4

3. What is the number halfway between 4 and 5?41__

2

4. Compare. Write �, �, or �. 1__3 � 1__

2

By comparing 1__3 and 1__

2 , you can tell that 4 1__3 is closer to 4 than 5,

without using a number line. So, 4 1__3 rounded to the nearest whole

number is 4.

5. What two whole numbers is 1 2__3 between? 1 and 2

6. Compare. Write �, �, or �. 2__3 � 1__

2

7. What is 1 2__3 rounded to the nearest whole number? 2

8. Use the rounded numbers to estimate 4 1__3 � 1 2__

3 .

9. About how much time did Dwayne spend playing basketball and soccer? 6 hours

4 1 __ 3 4

� 1 2 __ 3 � 2

6

About how much more time did Dwayne spend playing basketball than soccer?

10. Estimate 4 1__3 � 1 2__

3 at the right.

11. About how much more time did Dwayne spend playing basketball than soccer? 2 hours

4 1 __ 3 4

� 1 2 __ 3 � 2

2

Estimate each sum or difference.

12. 2 2 __ 3

� 1 1 __ 3

13. 2 9 ___ 10

� 1 5 ___ 10

14. 5

� 4 2 __ 4

15. 6 4 __ 6

� 1 5 __ 6

3 � 1 � 2 3 � 2 � 1 5 � 5 � 10 7 � 2 � 9

16. 6 7 __ 8

� 5 3 __ 8

17. 6

� 3 3 __ 9

18. 4 9 ___ 14

� 2 11 ___ 14

19. 6

� 4 2 ___ 16

7 � 5 � 2 6 � 3 � 3 5 � 3 � 8 6 � 4 � 10

20. 2 3__4 � 1 21. 7 2__

6 � 6 5__6 22. 3 2__

5 � 1 2__5

3 � 1 � 2 7 � 7 � 14 3 � 1 � 4

23. 6 1__8 � 1 5__

8 24. 7 � 2 3__7 25. 3 4__

8 � 1 7__8

6 � 2 � 4 7 � 2 � 5 4 � 2 � 6

26. Yolanda walked 2 3__5 miles on Monday, 1 1__

5 miles on

Tuesday, and 3 4__5 miles on Wednesday. Estimate

her total distance walked. 8 miles

27. Chris was going to add 2 1__4 cups of a chemical to the

swimming pool until he found out that Richard

already added 1 1__8 cups of the chemical. Estimate how

much more Chris should add so that the total is his

original amount. 1 cup

28. Reasoning Is 3 1__2 closer to 3 or 4? Explain.

31__2 is halfway between 3 and 4, so it isn’t closer

to either.


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Estimating Sums and Differences of Mixed Numbers (continued)

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Multiplying Two Fractions

Teacher Notes

Ongoing AssessmentMake sure students understand that they need to multiply both the numerators and denominators to multiply fractions. Make sure students are not getting this procedure confused with the procedure used for adding and subtracting fractions: find a common denominator and add or subtract only the numerators.

Error InterventionIf students multiply the numerators and denominators together and then make mistakes simplifying,

then encourage students to remove common factors before they multiply. This way, they can work with smaller numbers and are less likely to make computation errors.

If You Have More TimeHave students find more products using paper folding and show their product to a partner or to the class.

Materials crayons, markers, or colored pencils, paper to fold

Pablo’s yard is 3__4 of an acre. One-half of the yard is woods. What part of

an acre is wooded?

Find 1__2 of 3__

4 or 1__2 � 3__

4 by answering 1 to 5.

1. Fold a sheet of paper into 4 equal parts, as shown at

the right. Color 3 parts with slanted lines to show 3__4 .

Color the rectangle at the right to show what you did.

2. Now fold the paper in half the other way. Shade one half with lines slanted the opposite direction of the first set.Color the rectangle at the right to show what you did.

3. What fraction of the paper is shaded with crisscrossed lines?

3__8

4. The part shaded with crisscrossed lines

shows 1__2 of 3__

4 or 1__2 � 3__

4 .

So, what is 1__2 � 3__

4 ?

3__8

5. In Pablo’s yard, what part of his 3__4 acre is wooded?

3__8 acre

6. To find 1__2 � 3__

4 , how many sections did you divide the paper into? 8

7. What is the product of the denominators in 1__2 � 3__

4 ? 2 � 4 � 8

8. To find 1__2 � 3__

4 , how many sections did you crisscross? 3

9. What is the product of the numerators in 1__2 � 3__

4 ? 1 � 3 � 3

10. Write the product of the numerators over the product of the denominators. 1 � 3_____

2 � 4 � 3

_____

8 11. Is your answer to item 9 the same as item 4? yes

12. Use paper folding to find 2__3 � 3__

4 .Color the rectangle at the right to

show what you did. So, 2__3 � 3__

4 �6__12 .

13. To find 2__3 � 3__

4, how many sections

did you divide the paper into? 12



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Multiplying Two Fractions

14. What is the product of the denominators in 2 __ 3 � 3 __ 4 ? 3 � 4 � 12

15. To find 2 __ 3 � 3 __ 4 how many sections did you crisscross? 6

16. What is the product of the numerators in 2 __ 3 � 3 __ 4 ? 2 � 3 � 6

17. Complete: 2 __ 3 � 3 __ 4 � 2 � 3 _____ 3 � 4 � 6 ____

12

To multiply two fractions, you can multiply the numerators and then the denominators. Then simplify, if possible.

2 __ 3 � 3 __ 4 � 2 � 3 _____ 3 � 4 � 6 ___ 12 � 1 __ 2

18. Reasoning Shari found 3 ___ 10 � 5 __ 9 as shown

3 ___ 10 � 5 __ 9 � � 3 1

� � 51

_______ � 10 2 � � 9

3 � 1 __ 6

at the right. Why does Shari’s method work?

She simplified before multiplying, instead of after.

Multiply. Simplify, if possible.

19. 1 __ 8 � 2 __ 3 �

1__12 20. 5 __

6 � 1 __ 2 �

5__12 21. 1 __ 4 � 3 __ 5 �

3__20

22. 6 __ 7 � 1 __ 3 �

2__7 23. 3 __ 4 � 3 __ 8 �

9__32 24. 1 __ 5 � 4 __ 5 �

4__25

25. 2 __ 3 � 4 __ 7 �

8__21 26. 3 __ 7 � 3 ___ 10 �

9__70 27. 4 __

9 � 3 __ 4 �

1__3

28. 5 __ 8 � 4 __ 5 �

1__2 29. 7 __

9 � 3 __ 5 �

7__15 30. 1 ___

10 � 5 __ 7 �

1__14

31. 7 __ 8 � 5 ___ 14 �

5__16 32. 3 ___ 11 � 1 __ 9 �

1__33 33. 1 ___

12 � 4 __ 5 �

1__15

34. There are 45 tents at the summer camp. Girls will use

2 __ 3 of the tents. How many tents will the girls use? 30 tents


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Multiplying Two Fractions (continued)

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Intervention Lesson I17

Math Diagnosis and Intervention SystemIntervention Lesson I17

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Measuring and Classifying Angles

Teacher Notes

Ongoing AssessmentAsk: Why is there no classification category for angles with measures greater than 180 degrees? Angles with measures greater than 180 degrees are really angles with measurements that are less than 180 degrees. For example, a 190 degree angle is the same as 170 degree angle.

Error InterventionIf students need more practice identifying angles,

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

If You Have More TimeHave student pairs take turns drawing and measuring angles. One student uses a protractor to draw an angle. Then he or she labels the angle with the correct measurement. The other student uses a protractor to measure the angle to see if the angle is drawn and labeled correctly.


Measuring and Classifying Angles

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Intervention Lesson I17 123

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Materials protractor, straightedge, and crayons, markers, or colored pencils

A protractor can be used to measure and draw angles. Angles are measured in degrees.

Use a protractor to measure the angle shown by answering 1 to 2.

1. Place the protractor’s center on the angle’s vertex and place the 0� mark on one side of the angle.

2. Read the measure where the other side of the angle crosses the protractor.What is the measure of the angle? 100�

Use a protractor to draw an angle with a measure of 60�by answering 3 to 5.

3. Draw __›AB by connecting the points shown

with the endpoint of the ray at point A.

4. Place the protractor’s center on point A. Place the protractor so the the 0� mark is lined up with

__›AB .

5. Place a point at 60�. Label it C and draw ___›AC .

Use a protractor to measure the angles shown, if necessary, to answer 6 to 9.

6. Acute angles have a measure between 0� and 90�. Trace over the acute angles with blue.

7. Right angles have a measure of 90�. Trace over the right angles with red.

8. Obtuse angles have a measure between 90�and 180�. Trace over the obtuse angles withgreen.

9. Straight angles have a measure of 180�. Trace over the straight angles with orange.

orange

green blue

red

green

blue

red

orange

Classify each angle as acute, right, obtuse, or straight. Then measure the angle.

10. 11. 12.

acute; acute; obtuse;

30� 75� 115�

13. 14. 15.

obtuse; acute; acute;

160� 15� 45�

Use a protractor to draw an angle with each measure.

16. 120� 17. 35� 18. 70�

19. Reasoning If two acute angles are placed next to each other to form one angle, will the result always be an obtuse angle? Explain. Provide a drawing in your explanation.

No; both acute angles could be small enough so that the sum of their measures is less than 90� or equal to 90�. Check student’s drawings.

124 Intervention Lesson I17

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Measuring and Classifying Angles (continued)

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Constructions

Teacher Notes

Ongoing AssessmentAsk: Can any compass opening be used to draw the first arc on an angle when constructing an angle congruent to it? Yes, the first arc can be any size as long as the same opening is used to draw the first arc on the construction of the angle.

Error InterventionIf students are not convinced that their constructions are accurate,

then have them measure angles using a protractor, and side lengths using a ruler, after they complete their constructions.

If You Have More TimeChallenge student pairs to find a way to construct an isosceles right triangle using the construction techniques they have learned. Students should begin by constructing two perpendicular lines and then constructing two congruent legs on the lines.


Constructions

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Materials compass and straightedge

Construct a segment congruent to _XY by answering 1 to 3.

1. Use a compass to measure the length of _XY , X Y

W

by placing one point on X and the other on Y.

2. Draw a horizontal ray with endpoint W. Place the compass point on point W. Use the compass measure of

_XY to draw an arc intersecting the ray

drawn. Label this intersection J.

3. Are _XY and

_WJ congruent? yes

Construct an angle congruent to �A by answering 4 to 6.

4. Place the compass point on A, and draw an arc intersecting both sides of �A. Draw a ray with endpoint S. With the compass point on S, use the same compass setting from �A to draw an arc intersecting the ray at point T.

5. Use a compass to measure the length of the arc intersecting both sides of �A. Place the compass point on T. Use the same measure from �A to draw an arc that intersects the first arc. Label the point of intersection R and draw the

__›SR .

6. Are �A and �RST congruent? yes

Construct a line perpendicular to ‹__›AB by answering 7 to 9.

7. Open the compass to more than half the distance between A and B. Place the compass point at Aand draw arcs above and below the line.

8. Without changing the compass setting, place the point at B. Draw arcs that intersect the arcs made from point A. Label the point of intersection above the line as C and below the line as D. Draw line CD.

9. Are ‹__›AB and

‹__›CD perpendicular? yes

Construct a line that is parallel to ‹__›AB on the previous page, by

answering 10 to 12.

10. Draw point E on ‹__›CD above point C.

11. Use points E and D to construct a line perpendicular to ‹__›CD .

(Hint: See 7 and 8.) Label this line FG.

12. Are ‹__›AB and

‹__›FG parallel? yes

Construct a triangle congruent to triangle LMN by answering 13 to 16.

13. Construct �R congruent to �L.

14. On one side of �R, construct _RS so that it is

congruent to _LM . On the other side of �R,

construct _RT so that it is congruent to

_LN .

15. Draw segment ST.

16. Are �LMN and �RST congruent? yes

Construct a rectangle by answering 17 to 21.

17. Construct a line that is perpendicular to ‹__›PQ .

P Q

KJ

GH

Label the point of intersection G.

18. Use points P and G to construct another line perpendicular to

‹__›PG . Label the point of

intersection H.

19. Choose a point on the first line and label it K. Construct segment HJ on the second line so that it is congruent to

_GK .

20. Draw segment JK.

21. Reasoning How do you know that GHJK is a rectangle?

The opposite sides are parallel and congruent and all four angles are right angles.


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Constructions (continued)

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Converting Customary Units of Length

Teacher Notes

Ongoing AssessmentAsk: Would you multiply or divide to change miles to inches? Multiply

Error InterventionIf students have trouble remembering the size of each unit,

then use I22: Using Customary Units of Length to familiarize students with relative sizes. This will help them decide whether they are changing from a smaller unit to a larger unit or a larger unit to a smaller unit.

If You Have More TimeWrite the following in one column on the board: feet to inches, yards to inches, yards to feet, miles to feet, and miles to yards. Have students make up fun word problems that involve the conversions on the board. Exchange stories with a partner and solve. For example: Yazmine’s dog’s tail is 2 yards long. How many inches long is the dog’s tail?



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Mayla bought 6 yards of ribbon. How Customary Units of Length

1 foot (ft) � 12 inches (in.)

1 yard (yd) � 36 (in.)

1 yard (yd) � 3 feet (ft)

1 mile (mi) � 5,280 feet (ft)

1 mile (mi) � 1,760 yards (yd)

many feet of ribbon did she buy?

Answer 1 to 4 to change 6 yards to feet.

To change larger units to smaller units, multiply. To change smaller units to larger units, divide.

1. 1 yard � 3 feet

2. Do you need to multiply or divide to change from yards to feet? multiply

3. What is 6 � 3 feet? 18 feet

4. How many feet of ribbon did Mayla buy? 18 ft

Deidra bought 60 inches of ribbon. How many feet of ribbon did she buy? Change 60 inches to feet by answering 5 to 8.

5. 1 foot � 12 inches

6. Do you need to multiply or divide to change from feet to inches? divide

7. What is 60 � 12? 5

8. How many feet of ribbon did Deidra buy? 5 ft

Troy ran 4 miles. How many yards did he run? Change 4 miles to yards by answering 9 to 11.

9. 1 mile � 1,760 yards

10. Do you need to multiply or divide to change from miles to yards? multiply

11. 4 miles � 7,040 yards

12. How many yards did Troy run? 7,040 yd

Find each missing number.

13. 1 yd � 3 ft 14. 72 in. � 6 ft 15. 3 mi � 15,840 ft

16. 5,280 ft � 1 mi 17. 5 mi � 8,800 yd 18. 4 yd � 12 ft

19. 48 in. � 4 ft 20. 1 yd � 36 in. 21. 6 mi � 31,680 ft

22. 5 yd � 15 ft 23. 3 mi � 5,280 yd 24. 2 ft � 24 in.

25. 21 ft � 7 yd 26. 3 yd � 108 in. 27. 4 yd � 144 in.

For Exercises 28 to 32 use the information in the table.

28. How many inches did Speedy crawl? Turtle Crawl Results

Turtle Distance

Snapper 38 inches

Speedy 3 feet

Pokey 2 yards

Pickles 4 feet

36 inches

29. How many inches did Pokey crawl?

72 inches

30. How many inches did Pickles crawl?

48 inches

31. Reasoning Which turtle crawled the greatest distance? Pokey

32. Reasoning Which turtle crawled the least distance? Speedy

33. Reasoning Explain how you could use addition to find how many yards are in 72 inches.

Sample answer: I know 36 in. � 1 yd. If I add 36 � 36, I get 72. Since I added 36 two times, 72 in. � 2 yd.


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Converting Customary Units of Length (continued)

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Converting Metric Units

Teacher Notes

Ongoing AssessmentAsk: When changing from smaller units to larger units, do you multiply or divide? Divide

Error InterventionIf students do not understand the relationship between moving the decimal and multiplying or dividing a number by 10,

then use H59: Multiplying Decimals by 10, 100, or 1,000 and H64: Dividing Decimals by 10, 100, or 1,000.

If You Have More TimeHave student pairs measure their heights in centimeters and convert the measurements into meters and into millimeters.


Converting Metric Units

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The table shows how metric units are related. Every unit is 10 times greater than the next smaller unit. Abbreviations are shown for the most commonly used units.

� 10 � 10 � 10 � 10 � 10 � 10

kilometer(km) hectometer dekameter meter

(m) decimeter centimeter(cm)

millimeter(mm)

kiloliter hectoliter dekaliter liter(L) deciliter centiliter milliliter

(mL)

kilogram(kg) hectogram dekagram gram

(g) decigram centigram milligram(mg)

� 10 � 10 � 10 � 10 � 10 � 10

To change from one metric unit to another, move the decimal point to the right or to the left to multiply or divide by 10, 100, or 1,000.

The length of a sheet of paper is 27.9 centimeters. Convert 27.9 cm to millimeters by answering 1 to 3.

1. To move from centimeters to millimeters in the table, do you move right or left? right

2. How many jumps are there between centimeters andmillimeters in the table? 1

Move the decimal one place to the right to convert from centimeters to millimeters. This is the same as multiplying by 10.

3. What is the length of the paper in millimeters? 279 mm

Convert 27.9 cm to meters by answering 4 to 6.

4. To move from centimeters to meters in the table, do you move right or left? left

5. How many jumps are there between centimeters andmeters in the table? 2

Move the decimal two places to the left to convert from centimeters to meters. This is the same as dividing by 100.

6. What is the length of the paper in meters? 0.279 m

Tell the direction and number of jumps in the table for each conversion. Then convert.

7. 742 cm to meters 8. 12.4 kg to g 9. 0.62 L to mL

2 jumps left 3 jumps right 3 jumps left7.42 m 12,400 g 620 mL

Write the missing numbers.

10. 150 mg = 0.15 g 11. 2,600 m = 2.6 km 12. 0.4 L = 400 mL

13. 300 mL = 0.3 L 14. 4 kg = 4,000,000 mg 15. 2.6 m = 2,600 mm

16. 2,670 mg = 2.67 g 17. 34 cm = 340 mm 18. 16 L = 16,000 mL

For Exercises 19 to 21 use the table at the right.

19. What is the height of the Building Height

John Hancock Center 344 m

Petronas Towers 452 m

Sears Tower 44,200 cm

CN Tower 553,000 mm

Petronas Towers in centimeters?

45,200 cm

20. What is the height of the CN Tower in meters?

553 m

21. What is the height of the John Hancock Center in km?

0.344 km

22. Reasoning Which is shorter, 15 centimeters or 140 millimeters? Explain.

15 centimeters is equal to 150 millimeters and 140 � 150, so 140 millimeters is shorter.


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Area of Parallelograms

Teacher Notes

Ongoing AssessmentAsk: How is the formula for the area of a parallelogram similar to the formula for the area of a rectangle? How is it different? Sample answer: To find the area of a rectangle or a parallelogram you multiply two dimensions. In a rectangle you multiply the length by the width, but in a parallelogram you multiply the base by the height.

Error InterventionIf students do not know the properties of parallelograms,

then use I7: Quadrilaterals.

If students are having trouble remembering the formula for the area of a parallelogram,

then have students create formula cards on note cards including examples of how to use the formula correctly. Add these note cards to cards made for the formulas for perimeter and area of rectangles and squares

If You Have More TimeGive each student three index cards. Have them label card 1 Base, card 2 Height, and card 3 Area. Have students write a value for the base of a parallelogram on card 1, the height of a parallelogram on card 2, and area of that parallelogram on card 3. Collect all the cards and shuffle them. Have students draw 3 cards from the pile. They need to actively trade their cards in order to have a base, height, and area card with values that make the formula for the area of a parallelogram true. As soon as they have a matching set of cards, they need to sit down.


Area of Parallelograms

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Materials grid paper, colored pencils or markers, scissors

Find the area of the parallelogram on the grid by answering 1 to 10.

1. Trace the parallelogram below on a piece of grid paper. Then cut out the parallelogram.

2. Cut out the right triangle created by the dashed line.

3. Take the right triangle and move it to the right of the parallelogram.

4. What shape did you create? a rectangle

5. Is the area of the parallelogram the same as the area of the rectangle? yes

6. What is the area of the rectangle? A � � � w � 10 � 4 � 40 sq meters

7. What is the base b of the parallelogram? 10 meters

8. What is the height h of the parallelogram? 4 meters

9. What is the base times the height of the parallelogram? 40

10. Is this the same as the area of the rectangle? yes

The formula for the area of a parallelogram is A � bh.

11. Use the formula to find the area of a parallelogram with a base of 9 ft and a height of 6 feet.

A � b � h

A � ( 9 ) � ( 6 ) � 54 square feet

Find the area of each figure.

12. 13. 14.

300 m2 80 hm2

50 ft2

15. 16. 17.

7.5 in.2 77 in.2 27.9 m2

18. 19. 20.

90 mm2 84 ft2

45 m2

21. Reasoning The area of a parallelogram is 100 square millimeters. The base is 4 millimeters. Find the height. 25 mm


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Area of Parallelograms (continued)

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F19

Practice F19

Adding IntegersAdd. Use a number line.

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 10

1. 1 � 3 � 2. 4 � (�7) � 3. �4 � (�2) �

4. �3 � 1 � 5. 6 � (�6) � 6. �1 � (�4) �

7. 9 � (�7) � 8. �6 � 12 � 9. �3 � (�8) �

10. In a game, you have 18 tiles but you cannot use 3 of them. What will your score be for that round if each tile is worth 1 point? Explain how you found the answer.

11. Which is the sum of �8 � 5?

A �13 B �3 C 3 D 13

Add.

12. �6 � (�2) 13. �1 � (�4) 14. 3 � (�4) 15. �8 � 8

16. 9 � (�5) 17. �2 � (�5) 18. �9 � (3) 19. �1 � 6

20. 5 � (�5) 21. 8 � (�9) 22. �8 � (�2) 23. 10 � (�3)

24. 3 � (�2) 25. �6 � 7 26. 1 � (�1) 27. �7 � 2

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Practice

F33

Practice F33

Graphing Points in the Coordinate PlaneWrite the ordered pair for each point.

1. A

2. B

3. C

4. D

5. E

6. F


7. (�5, 0) 8. (�1, �1) 9. (0, �7)

10. (�6, �5) 11. (�4, �8) 12. (�5, �5)

13. If a taxicab were to start at the point (0, 0) and drive 6 units left, 3 units down, 1 unit right, and 9 units up, what ordered pair would name the point the cab would finish at?

14. Use the coordinate graph above. Which is the y-coordinate for point X?

A �6 B �3 C �3 D 6

15. Explain how to graph the ordered pair (�2, �3).

y

x0 +2-4-10

+10

+4 +6 +8 +10-6-8 -2

+2

+4

+6

+8

-2

-4

-6

-8

-10

AB

CD

E

F

H

I

J

K

L

X

G

Y

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F34

Practice F34

Graphing Equations in the Coordinate PlaneComplete each table of ordered pairs. Then graph the equation.

8. y � x � 1 9. y � 3x

x y

�3

0

1

0

2

�2

4

�4

�2 �4 2 4 x

y

x y

�1

0

1

0

2

�2

4

�4

�2 �4 2 4 x

y

10. y � �2x 11. y � 3 � x

x y

�1

0

1

0

2

�2

4

�4

�2 �4 2 4 x

y

x y

�1

0

2

0

2

�2

4

�4

�2 �4 2 4 x

y

12. Is the point (3, 1) on the graph of y � 4 � x? Explain.

13. Is the point (3, �9) on the graph of y � 3x? Explain.

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Practice

F40

Practice F40


4 � 16 � 4 � ( � 6) � (4 � ) � (4 � )

� �

�


2. 3 � 8 � 3 � (4 � ) � (3 � 4) � (3 � )

3. 2 � 16 � 2 � ( � 6) � (2 � ) � ( � 6)

4. 2 � 25 � � (20 � ) � ( � 20) � ( � )

5. 15 � 8 � (10 � ) � 8 � (10 � ) � ( � 8)

6. 10 � 57 � (10 � 50) � (10 � ) � � (50 � )

7. 13 � 107 � (13 � 100) � (13 � ) � � (100 � )

8. 25 � 205 � ( � 200) � (25 � ) � 25 � ( � )

9. 9 � 96 � � (100 � 4) � ( � 100) � ( � 4)

10. 8 � 48 � � (50 � ) � ( � 50) � ( � )

11. Describe two different ways to find 6 � 38 with mental math.


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F43

Practice F43

More Variables and ExpressionsFor questions 1–4, evaluate each expression for x � 8.

1. x � 3 2. 5 � x 3. x � (�7) 4. 8 � x

For questions 5–12, evaluate each expression for x � 5.

5. ( x __ 5 ) � 15 6. 25 � (2x) 7. (4x) � 2 8. (4x) � 16

9. (5x) � ( 15 __ x ) 10. 25 � ( 25

__ x ) 11. (10 � x) � 3 12. (5x) � x � 10

For questions 13–20, evaluate each expression for a � �2, b � �1, and c � �8.

13. a � (�20) 14. c � 12 15. b � 1 16. �25 � a

17. c � a 18. a � b 19. a � c � b 20. a � b � c

21. The temperature at the pool was 65˚F at 6:00 A.M. Write an expression to name the temperature at 5:00 P.M. after it rose 7 degrees.

22. Which expression names the location of a turtle that started 3 feet under water and climbed up 4 feet onto a log?

A 3 � 4 B �3 � 4 C �3 � (�4) D �3 � 4

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G60

Practice G60


1. 81 2. 63 3. 102

4. 270 5. 99 6. 550

7. 2,105 8. 9,332 9. 3,660

10. 8,265 11. 5,162 12. 516

13. Mark has 225 trading cards. He wants to display his trading cards on some shelves with an equal number of cards on each. He can buy shelves in packages of 3, 5, or 10. Which shelf package should he NOT buy? Explain.

14. Are all numbers that are divisible by 2 also divisible by 4? Explain your reasoning.



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G63

Practice G63

Prime FactorizationFind the prime factorization of each number. If a number is prime, circle it.

1. 30 2. 16 3. 43 4. 35

5. 42 6. 9 7. 50 8. 61

9. 37 10. 125 11. 29 12. 49

13. In the space to the right, create a factor tree for the number 64.

14. Field Day is in March on a day that is a prime number. Which date could it be?

A March 4 B March 11 C March 18 D March 24

15. What is a factor tree, and how do you know when a factor tree is completed?

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Practice

G65

Practice G65

Least Common MultipleFind the LCM of each pair of numbers.

1. 3 and 6 2. 7 and 10

3. 8 and 12 4. 2 and 5

5. 4 and 6 6. 3 and 4

7. 5 and 8 8. 2 and 9

9. 6 and 7 10. 4 and 7

11. 5 and 20 12. 6 and 12

13. Rosario is buying pens for school. Blue pens are sold in packages of 6. Black pens are sold in packages of 3, and green pens are sold in packages of 2. What is the least number of pens she can buy to have equal numbers of pens in each color?

14. Jason’s birthday party punch calls for equal amounts of pineapple juice and orange juice. Pineapple juice comes in 6-oz cans and orange juice comes in 10-oz cans. What is the least amount he can mix of each kind of juice without having any left over?

15. Dawn ordered 4 pizzas each costing between 8 and 12 dollars. What is a reasonable total cost of all 4 pizzas?

A less than $24

B between $12 and $24

C between $32 and $48

D about $70

16. Why is 35 the LCM of 7 and 5?

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G73

Practice G73


1. 400 � 40 � 2. 60 � 30 � 3. 200 � 50 �

4. 240 � 40 � 5. 630 � 70 � 6. 540 � 90 �

7. 100 � 25 � 8. 2,800 � 70 � 9. 1,800 � 30 �

10. 3,600 � 90 � 11. 1,500 � 50 � 12. 800 � 20 �

13. 320 � 80 � 14. 3,600 � 40 � 15. 140 � 20 �

16. 1,200 � 60 � 17. 7,200 � 90 � 18. 540 � 60 �

19. 600 � 20 � 20. 400 � 25 � 21. 2,400 � 30 �

22. 1,500 � 30 � 23. 5,000 � 25 � 24. 2,400 � 80 �

25. 5,400 � 90 � 26. 480 � 60 � 27. 450 � 90 �


28. Jon has a marble collection. His sister Beth has just started collecting. Beth has 40 marbles, and Jon has 400 marbles. About how many times larger is Jon’s collection?

29. Carlos must put toys into cartons that hold 40 each. How many cartons will he need to store 4,000 toys?


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Practice

G75

Practice G75

Dividing by Two-Digit DivisorsComplete.

9. Robert and his sister Esther are going to make pancakes for their family reunion. They need 28 eggs. The store only sells eggs by the dozen, or 12 per box. They buy 3 dozen. How many more eggs will they have than the 28 they need?

A 12 extra B 8 extra C 3 extra D 0 extra

10. Explain why 0.5 and 0.05 are NOT equivalent.

R7 1. 98 �� 565 – 4 7

R 4. 37 �� 229 – 2

R3 2. 60 �� 577 – 5 3

R 5. 47 �� 381 – 3

R 3. 28 �� 198 – 1

R 6. 52 �� 474 – 4

7. 89 student runners are warming up on the morning of Track and Field Day. The track has six lanes. The coach wants each lane to have as equal a number of runners as possible. How many runners are in each lane?

8. Isaiah changes both his bike tires every 4 months. How many tires will he have changed after 2 years?

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H19

Practice H19

Comparing and Ordering Fractions and Mixed Numbers Write �, �, or � for each .

1. 3 __ 5 4 __ 5 2. 9 ___ 10 7 ___ 10 3. 2 __ 9 2 __ 9

4. 6 __ 7 6 __ 8 5. 4 __ 9 2 __ 3 6. 1 ___ 10 1 ___ 12

7. 4 __ 5 5 __ 6 8. 6 __ 9 2 __ 3 9. 2 __ 5 2 __ 8

Order the numbers from least to greatest.

10. 4 __ 6 , 4 __ 8 , 3 __ 4

11. 1 __ 4 , 1 __ 8 , 10 ___ 11

12. 3 __ 7 , 3 __ 4 , 2 __ 4

13. How do you know that 1 __ 5 is less than 4 ___ 10 ?

14. A mechanic uses four wrenches to fix Mrs. Aaron’s car. The wrenches are different sizes: 5 __ 16 in., 1 _ 2 in., 1 _ 4 in., and 7 __ 16 in. Order the sizes of the wrenches from greatest to least.

15. Which is greater than 1 _ 3 ?

A 1 __ 6 B 1 __ 5 C 1 __ 4 D 1 __ 2

16. Compare 3 __ 22 and 2 __ 33 . Which is greater? How do you know?

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Practice

H24

Practice H24

Place Value Through ThousandthsWrite the word form for each number and tell the value of the underlined digit.

1. 4.345

2. 7.880

3. 6.321

4. 3.004

Write each number in standard form.

5. 6 � 0.3 � 0.02 � 0.001 6. 3 � 0.0 � 0.00 � 0.004 7. 7 � 0.5 � 0.03 � 0.003

8. Two and five hundred fifty-five thousandths 9. Cheri’s bank account has $6.29. Write the word form of this

amount and the value of the 9 in Cheri’s bank account.

10. Which is the word form of the underlined digit in 46.504?

A 5 ones B 5 tenths C 5 hundredths D 5 thousandths

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H31

Practice H31

Decimals to FractionsWrite a decimal and fraction for the shaded portion of each model.

1. 2.

Write each decimal as either a fraction or a mixed number.

3. 0.6 4. 0.73

5. 6.9 6. 8.57

7. .7 8. 0.33

9. 7.2 10. 3.09

11. 0.62 12. 6.2

13. 0.9 14. 8.89

15. 0.748 16. 7.354

17. Think About the Process When you convert 0.63 to a fraction, which of the following could be the first step of the process?

A Since there are 63 hundredths, multiply 0.63 and 100.

B Since there are 63 tenths, divide 0.63 by 10.

C Since there are 63 tenths, place 63 over 10.

D Since there are 63 hundredths, place 63 over 100.

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Practice

H42

Practice H42

Estimating Sums and Differences of Mixed NumbersEstimate the sum first. Then add. Simplify if necessary.

1. 7 2 __ 3 � 8 5 __ 6 2. 4 3 __ 4 � 2 2 __ 5

3. 11 9 ___ 10 � 3 1 ___ 20 4. 7 6 __ 7 � 5 2 __ 7

5. 5 8 __ 9 � 3 1 __ 2 6. 21 11 ___ 12 � 17 2 __ 3

7. Which is a good comparison of the estimatedsum and the actual sum of 7 7 _ 8 � 2 11 __ 12 ?

A Estimated � actual B Actual � estimated

C Actual � estimated D Estimated � actual

Estimate the difference first. Then subtract. Simplify if necessary.

8. 10 3 __ 4 9. 7 3 __ 7

� 7 1 __ 4 � 2 8 ___ 21

10. 3 11. 17 7 __ 8

� 2 2 __ 3 � 12 3 ___ 12

12. 9 5 __ 9 � 6 5 __ 6 13. 4 3 __ 4 � 2 2 __ 3

14. 6 1 __ 4 � 3 1 __ 3 15. 5 1 __ 5 � 3 7 __ 8

16. 8 2 __ 7 � 7 1 __ 3 17. 2 9 ___ 10 � 2 1 __ 3

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H46

Practice H46

Multiplying Two FractionsWrite the multiplication problem that each model represents. Then solve. Put your answer in simplest form.

1. 2.

Find each product. Simplify if necessary.

3. 7 __ 8 � 4 __ 5 �

4. 3 __ 7 � 2 __ 3 �

5. 1 __ 6 � 2 __ 5 �

6. 2 __ 7 � 1 __ 4 �

7. 2 __ 9 � 1 __ 2 �

8. 3 __ 4 � 1 __ 3 �

9. 3 __ 8 � 4 __ 9 �

10. 1 __ 5 � 5 __ 6 �

11. 2 __ 3 � 5 __ 6 �

12. 1 __ 2 � 1 __ 3 � 1 __ 4 �

13. 4 __ 7 � 7 ___ 16 �

14. 5 __ 9 � 27 ___ 30 �

15. If 4 _ 5 � � � 2 _ 5 , what is �?

16. Ms. Shoemaker’s classroom has 35 desks arranged in 5 by 7 rows. How many students does Ms. Shoemaker have in her class if there are 6 _ 7 � 4 _ 5 desks occupied?

17. Which does the model represent?

A 3 _ 8 � 3 _ 5 B 3

_ 5 � 5 _ 8 C 7 _ 8 � 2 _ 5 D 4

_ 8 � 3 _ 5

18. Describe a model that represents 3 _ 3 � 4 _ 4

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Practice

I17

Practice I17

Measuring and Classifying AnglesClassify each angle as acute, right, obtuse, or straight. Then measure each angle. (Hint: Draw longer sides if necessary.)

1. 2.


3. 120° 4. 180°

5. Draw an acute angle. Label it with the letters A, B, and C. What is the measure of the angle?

6. Which kind of angle is shown in the figure below?

A Acute B Obtuse

C Right D Straight

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I20

Practice I20

Constructions

1. Construct a line segment that is congruent to line segment

___ XY .

3. Construct a line that is parallel to line

‹ ___

› RS .

2. Construct an angle that is congruent to angle Q.

4. Construct a line that is perpendicular to line

‹ ____

› MN .

R S M N

X Y

Q

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Practice

I33

Practice I33


1. 2 yd � ft 2. 72 in. � ft 3. 2 mi � ft

4. 31,680 ft � mi 5. 8 mi � yd 6. 5 yd � ft

7. 60 in. � ft 8. 6 yd � in. 9. 4 mi � ft

10. 10 yd � ft 11. 3 mi � yd 12. 3 ft � in.

13. 24 ft � yd 14. 5 yd � in. 15. 2 yd � in.


16. How many inches did Paul toss the bean bag? Bean Bag Toss Results

Boy Distance

Sam 18 inches

Paul 2 feet

Terence 3 yards

Carlos 6 feet

inches

17. How many inches did Terence toss the bean bag?

inches

18. How many inches did Carlos toss the bean bag?

inches

19. Which boy tossed the bean bag the greatest distance?

20. Which boy tossed the bean bag the least distance?


Customary Units of Length


1 yard (yd) � 36 (in.)




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I36

Practice I36

Converting Metric UnitsThe table shows how metric units are related. Every unit is 10 times greater than the next smaller unit. Abbreviations are shown for the most commonly used units.

� 10 � 10 � 10 � 10 � 10 � 10



millimeter(mm)


(mL)



� 10 � 10 � 10 � 10 � 10 � 10



jumps jumps jumps

m g mL

4. 202 kg to g 5. 55 km to m 6. 100 ml to L

jumps jumps jumps

g m L


7. 150 mg = g 8. 2,600 m = km 9. 0.4 L = mL

10. 300 mL = L 11. 4 kg = mg 12. 2.6 m = mm

13. 2,670 mg = g 14. 34 cm = mm 15. 16 L = mL

16. 5.75 kg = g 17. 8 mL = L 18. 300.6 m = km

19. 1,200 mm = km 20. 263 cm = km 21. 6 g = mg

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Practice

I49

Practice I49

2 mi

9 mi3 cm

5 cm

1 mm

2 mm

1.5 m

6 m

h � ?

A � 44 m2

b � 8 m

Area of ParallelogramsFind the area of each parallelogram. A � bh

1. 2.

3. 4.

Find the missing measurement for the parallelogram.

5. A � 34 in2, b � 17 in., h �

6. List three sets of base and height measurements for parallelograms with areas of 40 square units.

7. Which is the height of the parallelogram?

A 55 m

B 55.5 m

C 5 m

D 5.5 m

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F19 F33

F34 F40Answers: F19, F33, F34, F40

Answers for Practice

F19, F33, F34, F40

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Practice

F19

Practice F19

Adding IntegersAdd. Use a number line.

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 10

1. 1 � 3 � 2. 4 � (�7) � 3. �4 � (�2) �

4. �3 � 1 � 5. 6 � (�6) � 6. �1 � (�4) �

7. 9 � (�7) � 8. �6 � 12 � 9. �3 � (�8) �

10. In a game, you have 18 tiles but you cannot use 3 of them. What will your score be for that round if each tile is worth 1 point? Explain how you found the answer.

11. Which is the sum of �8 � 5?

A �13 B �3 C 3 D 13

Add.

12. �6 � (�2) 13. �1 � (�4) 14. 3 � (�4) 15. �8 � 8

16. 9 � (�5) 17. �2 � (�5) 18. �9 � (3) 19. �1 � 6

20. 5 � (�5) 21. 8 � (�9) 22. �8 � (�2) 23. 10 � (�3)

24. 3 � (�2) 25. �6 � 7 26. 1 � (�1) 27. �7 � 2

4 �3 �6�2 0 �5

2 6 �11

15 points 18 � (�3) � 15

�8 �5 �1 0

4 �7 �6 5

0 �1 �10 7

1 1 0 �5

45096_Practice_F19-I49.indd F19 6/30/08 12:02:48 PM

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Practice

F33

Practice F33

Graphing Points in the Coordinate PlaneWrite the ordered pair for each point.

1. A

2. B

3. C

4. D

5. E

6. F


7. (�5, 0) 8. (�1, �1) 9. (0, �7)

10. (�6, �5) 11. (�4, �8) 12. (�5, �5)

13. If a taxicab were to start at the point (0, 0) and drive 6 units left, 3 units down, 1 unit right, and 9 units up, what ordered pair would name the point the cab would finish at?

14. Use the coordinate graph above. Which is the y-coordinatefor point X?

A �6 B �3 C �3 D 6

15. Explain how to graph the ordered pair (�2, �3).

y

x0 +2-4-10

+10

+4 +6 +8 +10-6-8 -2

+2

+4

+6

+8

-2

-4

-6

-8

-10

AB

CD

E

F

H

I

J

K

L

X

G

Y

(3, 4)

Go left on the x-axis 2 units. Next, go up 3 units.

(�2, 3)(2, �3)(�5, �4)(�7, 1)(8, 6)

HI

JK

LG

(�5, 6)


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Practice

F34

Practice F34

Graphing Equations in the Coordinate PlaneComplete each table of ordered pairs. Then graph the equation.

8. y � x � 1 9. y � 3x

x y

�3

0

1 0

2

�2

4

�4

�2�4 2 4 x

y

x y

�1

0

1 0

2

�2

4

�4

�2�4 2 4 x

y

10. y � �2x 11. y � 3 � x

x y

�1

0

1 0

2

�2

4

�4

�2�4 2 4 x

y

x y

�1

0

2 0

2

�2

4

�4

�2�4 2 4 x

y

12. Is the point (3, 1) on the graph of y � 4 � x? Explain.

13. Is the point (3, �9) on the graph of y � 3x? Explain.

�212

�303

20

�2

431

Yes. Answers will vary.

No. Answers will vary.


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Practice

F40

Practice F40


4 � 16 � 4 � ( � 6) � (4 � ) � (4 � )

� �

�


2. 3 � 8 � 3 � (4 � ) � (3 � 4) � (3 � )

3. 2 � 16 � 2 � ( � 6) � (2 � ) � ( � 6)

4. 2 � 25 � � (20 � ) � ( � 20) � ( � )

5. 15 � 8 � (10 � ) � 8 � (10 � ) � ( � 8)

6. 10 � 57 � (10 � 50) � (10 � ) � � (50 � )

7. 13 � 107 � (13 � 100) � (13 � ) � � (100 � )

8. 25 � 205 � ( � 200) � (25 � ) � 25 � ( � )

9. 9 � 96 � � (100 � 4) � ( � 100) � ( � 4)

10. 8 � 48 � � (50 � ) � ( � 50) � ( � )

11. Describe two different ways to find 6 � 38 with mental math.


(6 � 30) � (6 � 8) and (6 � 40) � (6 � 2)

10 10 640 2464

4 410 10

5 25 8

7 77 13

25 59 9

2 8

2522

510

720059

288


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F43 G60

G63 G65Answers: F43, G60, G63, G65


F43, G60, G63, G65

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Practice

F43

Practice F43

More Variables and ExpressionsFor questions 1–4, evaluate each expression for x � 8.

1. x � 3 2. 5 � x 3. x � (�7) 4. 8 � x

For questions 5–12, evaluate each expression for x � 5.

5. (x __5) � 15 6. 25 � (2x) 7. (4x) � 2 8. (4x) � 16

9. (5x) � ( 15__x ) 10. 25 � (25__

x ) 11. (10 � x) � 3 12. (5x) � x � 10

For questions 13–20, evaluate each expression for a � �2,b � �1, and c � �8.

13. a � (�20) 14. c � 12 15. b � 1 16. �25 � a

17. c � a 18. a � b 19. a � c � b 20. a � b � c

21. The temperature at the pool was 65˚F at 6:00 A.M.Write an expression to name the temperature at 5:00 P.M. after it rose 7 degrees.

22. Which expression names the location of a turtle that started 3 feet under water and climbed up 4 feet onto a log?

A 3 � 4 B �3 � 4 C �3 � (�4) D �3 � 4

5 13 1 16

16 15 22 4

22 30 5 20

�22 �20 0 �27

�6 �1 �11 5

65° � 7° � 72°


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Practice

G60

Practice G60


1. 81 2. 63 3. 102

4. 270 5. 99 6. 550

7. 2,105 8. 9,332 9. 3,660

10. 8,265 11. 5,162 12. 516

13. Mark has 225 trading cards. He wants to display his trading cards on some shelves with an equal number of cards on each. He can buy shelves in packages of 3, 5, or 10. Which shelf package should he NOT buy? Explain.




3, 9 3, 9 2, 3

2, 3, 5, 9, 10 3, 9 2, 5, 10

5 2 2, 3, 5, 10

3, 5 2 2, 3

Answers will vary. 225 is not divisible by 10.

10

No. Answers will vary.

Yes, because 9 is divisible by 3.

45096_Practice_F19-I49.indd G60 6/30/08 12:02:58 PM

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Practice

G63

Practice G63

Prime FactorizationFind the prime factorization of each number. If a number is prime, circle it.

1. 30 2. 16 3. 43 4. 35

5. 42 6. 9 7. 50 8. 61

9. 37 10. 125 11. 29 12. 49

13. In the space to the right, create a factor tree for the number 64.

14. Field Day is in March on a day that is a prime number. Which date could it be?

A March 4 B March 11 C March 18 D March 24

15. What is a factor tree, and how do you know when a factor tree is completed?

3 � 2 � 5 2 � 2 � 2� 2 43 � 1 7 � 5

7 � 3 � 2 3 � 3 2 � 5 � 5 61 � 1

37 � 1 5 � 5 � 5 29 � 1 7 � 7

Sample: A diagram that shows how to break a number into its prime factors. It is fi nished when all the factors shown are prime numbers.

64 8 8 2 � 4 � 2 � 42 � 2 � 2 � 2 � 2 � 2


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Practice

G65

Practice G65

Least Common MultipleFind the LCM of each pair of numbers.

1. 3 and 6 2. 7 and 10

3. 8 and 12 4. 2 and 5

5. 4 and 6 6. 3 and 4

7. 5 and 8 8. 2 and 9

9. 6 and 7 10. 4 and 7

11. 5 and 20 12. 6 and 12

13. Rosario is buying pens for school. Blue pens are sold in packages of 6. Black pens are sold in packages of 3, and green pens are sold in packages of 2. What is the least number of pens she can buy to have equal numbers of pens in each color?

14. Jason’s birthday party punch calls for equal amounts of pineapple juice and orange juice. Pineapple juice comes in 6-oz cans and orange juice comes in 10-oz cans. What is the least amount he can mix of each kind of juice without having any left over?

15. Dawn ordered 4 pizzas each costing between 8 and 12 dollars. What is a reasonable total cost of all 4 pizzas?

A less than $24

B between $12 and $24

C between $32 and $48

D about $70

16. Why is 35 the LCM of 7 and 5?

6

18 pens

7024 1012 1240 1842 2820 12

30 ounces

There exists no smaller number containing 7 and 5 both as factors


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G73, G75, H19, H24

G73 G75

H19 H24Answers: G73, G75, H19, H24

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G73

Practice G73


1. 400 � 40 � 2. 60 � 30 � 3. 200 � 50 �

4. 240 � 40 � 5. 630 � 70 � 6. 540 � 90 �

7. 100 � 25 � 8. 2,800 � 70 � 9. 1,800 � 30 �

10. 3,600 � 90 � 11. 1,500 � 50 � 12. 800 � 20 �

13. 320 � 80 � 14. 3,600 � 40 � 15. 140 � 20 �

16. 1,200 � 60 � 17. 7,200 � 90 � 18. 540 � 60 �

19. 600 � 20 � 20. 400 � 25 � 21. 2,400 � 30 �

22. 1,500 � 30 � 23. 5,000 � 25 � 24. 2,400 � 80 �

25. 5,400 � 90 � 26. 480 � 60 � 27. 450 � 90 �


28. Jon has a marble collection. His sister Beth has just started collecting. Beth has 40 marbles, and Jon has 400 marbles. About how many times larger is Jon’s collection?

29. Carlos must put toys into cartons that hold 40 each. How many cartons will he need to store 4,000 toys?


10 2 4

6 9 6

4 40 60

40 30 40

4 90 7

20 80 9

30 16 80

50 200 30

60 8 5

10 times 100 cartons

Answers will vary.


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G75

Practice G75

Dividing by Two-Digit DivisorsComplete.

9. Robert and his sister Esther are going to make pancakes for their family reunion. They need 28 eggs. The store only sells eggs by the dozen, or 12 per box. They buy 3 dozen. How many more eggs will they have than the 28 they need?

A 12 extra B 8 extra C 3 extra D 0 extra

10. Explain why 0.5 and 0.05 are NOT equivalent.

R7 1. 98 �� 565

– 4 7

R 4. 37 �� 229

– 2

R3 2. 60 �� 577

– 5 3

R 5. 47 �� 381

– 3

R 3. 28 �� 198

– 1

R 6. 52 �� 474

– 4

7. 89 student runners are warming up on the morning of Track and Field Day. The track has six lanes. The coach wants each lane to have as equal a number of runners as possible. How many runners are in each lane?

8. Isaiah changes both his bike tires every 4 months. How many tires will he have changed after 2 years?

5 5

90

5

6 7

22

7

9 7

40

7

8 5

76

5

7

96

2

9 6

68

6

There are 15 runners in 5 lanes and 14 runners in one lane.

0.5 � 5__10 � 1_

2 and 0.05 � 5___100 � 1__

201_2 > 1__

20

12 tires

2


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Practice

H19

Practice H19

Comparing and Ordering Fractions and Mixed Numbers Write �, �, or � for each .

1. 3__5 4__

5 2. 9___10 7___

10 3. 2__9 2__

9

4. 6__7 6__

8 5. 4__9 2__

3 6. 1___10 1___

12

7. 4__5 5__

6 8. 6__9 2__

3 9. 2__5 2__

8

Order the numbers from least to greatest.

10. 4__6, 4__

8, 3__4

11. 1__4, 1__

8, 10___11

12. 3__7, 3__

4, 2__4

13. How do you know that 1__5 is less than 4___

10?

14. A mechanic uses four wrenches to fix Mrs. Aaron’s car. The wrenches are different sizes: 5__

16 in., 1_2 in., 1_

4 in., and 7__16 in.

Order the sizes of the wrenches from greatest to least.

15. Which is greater than 1_3?

A 1__6 B 1__

5 C 1__4 D 1__

2

16. Compare 3__22 and 2__

33. Which is greater? How do you know?

<

>

<

>

<

�

�

>

>

4_8, 4_

6, 3_4

1_8, 1_

4, 10__11

3_7, 2_

4, 3_4

4__10 � 2_

5, and 1_5 < 2_

5. So, 1_5 < 4__

10

1_2 in., 7__

16 in., 5__16 in., 1_

4 in.

3__22. Sample answer: The denominator for 3__

22 is smaller than the denomina-tor for 2__

33, so each of the 3 parts of 3__22 is

larger than the 2 parts of 2__33.

45096_Practice_F19-I49.indd H19 6/30/08 12:03:07 PM

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Practice

H24

Practice H24

Place Value Through ThousandthsWrite the word form for each number and tell the value of the underlined digit.

1. 4.345

2. 7.880

3. 6.321

4. 3.004

Write each number in standard form.

5. 6 � 0.3 � 0.02 � 0.001

6. 3 � 0.0 � 0.00 � 0.004

7. 7 � 0.5 � 0.03 � 0.003

8. Two and five hundred fifty-five thousandths

9. Cheri’s bank account has $6.29. Write the word form of this amount and the value of the 9 in Cheri’s bank account.

10. Which is the word form of the underlined digit in 46.504?

A 5 ones B 5 tenths C 5 hundredths D 5 thousandths

0.005 (5 thousandths)four and three hundred forty-fi ve thousandths

0.8 (8 tenths)seven and eighty-eight hundredths (eight hundred eighty thousandths)

0.001 (1 thousandth)six and three hundred twenty-one thousandths

0.0 (zero tenths)three and four thousandths

6.321

7.533

six and twenty-nine hundredths, nine hundredths

3.004

2.555


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H31, H42, H46, I17

H31 H42

H46 I17Answers: H31, H42, H46, I17

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Practice

H31

Practice H31

Decimals to FractionsWrite a decimal and fraction for the shaded portion of each model.

1. 2.

Write each decimal as either a fraction or a mixed number.

3. 0.6 4. 0.73

5. 6.9 6. 8.57

7. .7 8. 0.33

9. 7.2 10. 3.09

11. 0.62 12. 6.2

13. 0.9 14. 8.89

15. 0.748 16. 7.354

17. Think About the Process When you convert 0.63 to a fraction, which of the following could be the first step of the process?

A Since there are 63 hundredths, multiply 0.63 and 100.

B Since there are 63 tenths, divide 0.63 by 10.

C Since there are 63 tenths, place 63 over 10.

D Since there are 63 hundredths, place 63 over 100.

.77__

10 .1616___

100

6__10

6 9__10 8 57___

100

73___100

7__10

7 2__10

33___100

3 9___100

62___100 6 2__

109__

10 8 89___100

748____1000 7 354____

1000


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Practice

H42

Practice H42

Estimating Sums and Differences of Mixed NumbersEstimate the sum first. Then add. Simplify if necessary.

1. 72__3 � 8 5__

6 2. 4 3__4 � 2 2__

5

3. 11 9___10 � 3 1___

20 4. 7 6__7 � 5 2__

7

5. 58__9 � 3 1__

2 6. 21 11___12 � 17 2__

3

7. Which is a good comparison of the estimatedsum and the actual sum of 7 7_8 � 2 11__

12 ?

A Estimated � actual B Actual � estimated

C Actual � estimated D Estimated � actual

Estimate the difference first. Then subtract. Simplify if necessary.

8. 10 3__4 9. 73__

7� 7 1__

4 � 2 8___21

10. 3 11. 177__8

� 22__3 � 12 3___

12

12. 95__9 � 6 5__

6 13. 43__4 � 2 2__

3

14. 61__4 � 3 1__

3 15. 51__5 � 3 7__

8

16. 82__7 � 7 1__

3 17. 2 9___10 � 2 1__

3

17; 16 1_2

15; 14 19__20

9; 9 7__18 40; 39 7__

12

13; 13 1_7

7; 7 3__20

4; 3 1_2 5; 5 1__21

0; 1_3 6; 5 5_8

3; 2 13__18

3; 2 11__12

1; 20__21

2; 2 1__12

1; 1 13__40

1; 17__30


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Practice

H46

Practice H46

Multiplying Two FractionsWrite the multiplication problem that each model represents. Then solve. Put your answer in simplest form.

1. 2.

Find each product. Simplify if necessary.

3. 7__8 �

4__5 �

4. 3__

7 �2__3 �

5. 1__6 � 2__

5 �

6. 2__7 � 1__

4 �

7. 2__9 �

1__2 �

8. 3__

4 �1__3 �

9. 3__8 �

4__9 �

10. 1__

5 � 5__6 �

11. 2__3 �

5__6 �

12. 1__

2 �1__3 �

1__4 �

13. 4__7 � 7___

16 �

14. 5__9 � 27___

30 �

15. If 4_5 � � � 2_5, what is �?

16. Ms. Shoemaker’s classroom has 35 desks arranged in 5 by 7 rows. How many students does Ms. Shoemaker have in her class if there are 6_

7 � 4_5 desks occupied?

17. Which does the model represent?

A 3 _ 8 � 3_5 B 3_

5 � 5 _ 8 C 7 _ 8 � 2 _ 5 D 4

_ 8 � 3 _ 5

18. Describe a model that represents 3_3 � 4_

4

2_3

� 1_6

� 2__10

� 1_9

7__10

5_7

� 1_4

� 5__28

1__15

2_71__14

1_9

1_4

1_6

1_6

5_9

1__24

1_4

1_2

1_2

24__35; 24 students

Sample answer: It would equal one.


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Practice

I17

Practice I17

Measuring and Classifying AnglesClassify each angle as acute, right, obtuse, or straight. Then measure each angle. (Hint: Draw longer sides if necessary.)

1. 2.


3. 120° 4. 180°

5. Draw an acute angle. Label it with the letters A, B, and C. What is the measure of the angle?

6. Which kind of angle is shown in the figure below?

A Acute B Obtuse

C Right D Straight

Right; 90° Acute; 22°

Answers will vary.

A B

C

45096_Practice_F19-I49.indd I17 6/30/08 12:03:16 PM

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I20, I33, I36, I49

I20 I33

I36 I49Answers: I20, I33, I36, I49

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Practice

I20

Practice I20

Constructions

1. Construct a line segment that is congruent to line segment

___XY.

3. Construct a line that is parallel to line

‹___›RS .

2. Construct an angle that is congruent to angle Q.

4. Construct a line that is perpendicular to line

‹____›MN .

R S M N

X Y

Q

Check students’ work.

Check students’ work.


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Practice

I33

Practice I33


1. 2 yd � ft 2. 72 in. � ft 3. 2 mi � ft

4. 31,680 ft � mi 5. 8 mi � yd 6. 5 yd � ft

7. 60 in. � ft 8. 6 yd � in. 9. 4 mi � ft

10. 10 yd � ft 11. 3 mi � yd 12. 3 ft � in.

13. 24 ft � yd 14. 5 yd � in. 15. 2 yd � in.


16. How many inches did Paul toss the bean bag? Bean Bag Toss Results

Boy Distance

Sam 18 inches

Paul 2 feet

Terence 3 yards

Carlos 6 feet

inches

17. How many inches did Terence toss the bean bag?

inches

18. How many inches did Carlos toss the bean bag?

inches

19. Which boy tossed the bean bag the greatest distance?

20. Which boy tossed the bean bag the least distance?


Customary Units of Length


1 yard (yd) � 36 (in.)




6 6 10,560

6 14,080 15

5 216

30 5,280 36

8 180 72

24

108

72Terence

Sam

21,120


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Practice

I36

Practice I36

Converting Metric UnitsThe table shows how metric units are related. Every unit is 10 times greater than the next smaller unit. Abbreviations are shown for the most commonly used units.

� 10 � 10 � 10 � 10 � 10 � 10



millimeter(mm)


(mL)



� 10 � 10 � 10 � 10 � 10 � 10



jumps jumps jumps

m g mL

4. 202 kg to g 5. 55 km to m 6. 100 ml to L

jumps jumps jumps

g m L


7. 150 mg = g 8. 2,600 m = km 9. 0.4 L = mL

10. 300 mL = L 11. 4 kg = mg 12. 2.6 m = mm

13. 2,670 mg = g 14. 34 cm = mm 15. 16 L = mL

16. 5.75 kg = g 17. 8 mL = L 18. 300.6 m = km

19. 1,200 mm = km 20. 263 cm = km 21. 6 g = mg

2 Left 3 Right 3

3 R 3 R 3 L

6.36 24,800 10,550

202,000 55,000 0.1

Right

0.150 2.6 4000.3 4,000,000 2,6002.670 340 16,000

5,750 0.008 0.30066,0000.002630.0012


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Practice

I49

Practice I49

2 mi

9 mi3 cm

5 cm

1 mm

2 mm

1.5 m

6 m

h � ?

A � 44 m2

b � 8 m

Area of ParallelogramsFind the area of each parallelogram. A � bh

1. 2.

3. 4.

Find the missing measurement for the parallelogram.

5. A � 34 in2, b � 17 in., h �

6. List three sets of base and height measurements for parallelograms with areas of 40 square units.

7. Which is the height of the parallelogram?

A 55 m

B 55.5 m

C 5 m

D 5.5 m

A � 15 cm2 A � 18 mi2

A � 9 m2A � 2 mm2

2 in.

8, 5; 4,10; 2, 20


y

x0 +2-4-10

+10

+4 +6 +8 +10-6-8 -2

+2

+4

+6

+8

-2

-4

-6

-8

-10

AB

CD

E

F

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Name Grade 4

Step Up to Grade 5 Test

T1

1. Add. 8 � (–4)

A –12

B 8

C 4

D –4

2. What is the ordered pair for point C?

A (2, 2)

B (–2, 2)

C (–2, –2)

D (2, –3)

3. Using the Distributive Property,

15 � 99 �

A (10 � 90) � (10 � 9) �

(5 � 90) � (5 � 9)

B (10 � 90) � (5 � 90) � (5 � 9)

C (10 � 90) � (15 � 9) � (15� 90)

D (15 � 90) � (5 � 90) � (5 � 9)

4. Evaluate 4b � 6, when b � 8.

A 36

B 26

C 18

D 6

5. Which ordered pair is on the graph of

y � x � 3?

A (4, 1)

B (2, 5)

C (3, 0)

D (8, 5)

Name Grade 4


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T2

6. By what numbers is 2,480 divisible?

A 2, 5, 8,10

B 2, 3, 8,10

C 2, 3, 7,10

D 2, 5, 7,10

7. What is the prime factorization of 18?

A 2 � 9

B 2 � 8

C 2 � 3 � 3

D 2 � 2 � 2 � 2

8. What is the LCM of 6 and 12?

A 2

B 3

C 6

D 12

9. Divide. 560 ÷ 80

A 6

B 7

C 60

D 70

10. 28 �� 342

A 6 R 12

B 12 R 6

C 126

D 612

11. Which is the greatest fraction in this

group?

1 _ 4 , 1 _ 2 , 3 _ 8 , 2 _ 3

A 1 _ 4

B 1 _ 2

C 3 _ 8

D 2 _ 3

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Name Grade 4


T3

12. What is the value of 2 in 4.289?

A 20

B 2

C 0.2

D 0.02

13. Write 4.6 as a fraction.

A 46 __ 10

B 46 ___ 100

C 4.6 ___ 10

D 4.6 ___ 100

14. Estimate the diff erence.

4 5 _ 8 � 1 2 _ 8

A 2

B 3

C 4

D 5

15. Classify this angle.

A straight

B right

C acute

D obtuse

16. Multiply. Simplify if possible.

3 _ 5 � 6 _ 5

A 9 _ 5

B 18 __ 5

C 9 __ 25

D 18 __ 25

17. Describe ‹

__ › RS and

‹

___ › XY .

A perpendicular

B parallel

C congruent

D obtuse

8 m

5 m

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T4

18. Find the missing number.

48 in. � ft

A 3

B 4

C 5

D 6

19. 1 L � mL

A 10

B 100

C 1,000

D 10,000

20. Find the area of this fi gure.

A 40 m

B 40 sq m

C 20 m

D 20 sq m

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Answers for Test

T1, T2, T3, T4

T1 T2

T3 T4Answers: T1, T2, T3, T4

y

x0 +2-4-10

+10

+4 +6 +8 +10-6-8 -2

+2

+4

+6

+8

-2

-4

-6

-8

-10

AB

CD

E

F

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Name Grade 4


T1

1. Add. 8 � (–4)

A –12

B 8

C 4

D –4

2. What is the ordered pair for point C?

A (2, 2)

B (–2, 2)

C (–2, –2)

D (2, –3)

3. Using the Distributive Property,

15 � 99 �

A (10 � 90) � (10 � 9) �

(5 � 90) � (5 � 9)

B (10 � 90) � (5 � 90) � (5 � 9)

C (10 � 90) � (15 � 9) � (15� 90)

D (15 � 90) � (5 � 90) � (5 � 9)

4. Evaluate 4b � 6, when b � 8.

A 36

B 26

C 18

D 6

5. Which ordered pair is on the graph of

y � x � 3?

A (4, 1)

B (2, 5)

C (3, 0)

D (8, 5)

45096_T1-T4.indd T1 7/1/08 2:13:00 PM

Name Grade 4


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T2

6. By what numbers is 2,480 divisible?

A 2, 5, 8,10

B 2, 3, 8,10

C 2, 3, 7,10

D 2, 5, 7,10

7. What is the prime factorization of 18?

A 2 � 9

B 2 � 8

C 2 � 3 � 3

D 2 � 2 � 2 � 2

8. What is the LCM of 6 and 12?

A 2

B 3

C 6

D 12

9. Divide. 560 ÷ 80

A 6

B 7

C 60

D 70

10. 28 �� 342

A 6 R 12

B 12 R 6

C 126

D 612

11. Which is the greatest fraction in this

group?

1 _ 4 , 1 _ 2 , 3 _ 8 , 2 _ 3

A 1 _ 4

B 1 _ 2

C 3 _ 8

D 2 _ 3

45096_T1-T4.indd T2 7/1/08 2:13:01 PM

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Name Grade 4


T3

12. What is the value of 2 in 4.289?

A 20

B 2

C 0.2

D 0.02

13. Write 4.6 as a fraction.

A 46 __ 10

B 46 ___ 100

C 4.6 ___ 10

D 4.6 ___ 100

14. Estimate the diff erence.

4 5 _ 8 � 1 2 _ 8

A 2

B 3

C 4

D 5

15. Classify this angle.

A straight

B right

C acute

D obtuse

16. Multiply. Simplify if possible.

3 _ 5 � 6 _ 5

A 9 _ 5

B 18 __ 5

C 9 __ 25

D 18 __ 25

17. Describe ‹

__ › RS and

‹

___ › XY .

A perpendicular

B parallel

C congruent

D obtuse

45096_T1-T4.indd T3 7/2/08 2:53:46 PM

8 m

5 m

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T4

18. Find the missing number.

48 in. � ft

A 3

B 4

C 5

D 6

19. 1 L � mL

A 10

B 100

C 1,000

D 10,000

20. Find the area of this fi gure.

A 40 m

B 40 sq m

C 20 m

D 20 sq m

45096_T1-T4.indd T4 7/2/08 2:19:50 PM

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Grade 4: Step Up to Grade 5

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