Download Grade 4: Step Up to Grade 5

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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
Scott Foresman and enVisionMATH™
are trademarks, in the U.S. and/or other
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or its affiliates.
®
45096_SLPSHEET_FSD 1
6/6/08 3:57:49 PM
45096_SLPSHEET_FSD 2
F19
Adding Integers
H19
Comparing and Ordering Fractions
F33
Graphing Points in the
Coordinate Plane
H24
Place Value Through Thousandths
H31
Decimals to Fractions
H42
Estimating Sums and Differences of
Mixed Numbers
F34
Graphing Equations in the
Coordinate Plane
F40
Using the Distributive Property
H46
Multiplying Two Fractions
F43
More Variables and Expressions
I17
Measuring and Classifying Angles
G60
Divisibility by 2, 3, 5, 9, and 10
I20
Constructions
G63
Prime Factorization
I33
G65
Least Common Multiple
Converting Customary Units
of Length
G73
Dividing by Multiples of 10
I36
Converting Metric Units
G75
Dividing by Two-Digit Divisors
I49
Area of Parallelograms
6/6/08 3:57:55 PM
Math Diagnosis and
Intervention System
Intervention Lesson
Adding Integers
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F19
Teacher Notes
F19
Adding Integers
Materials scissors, tape
Ongoing Assessment
10 9 8 7 6 5 4 3 2 1 0
1
2
3
4
5
6
7
8
Ask: 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.
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
To add 4 7, move the figure backward
4 spaces to 4. Then move it forward
7 spaces to 3. So 4 7 3.
facing the positive
numbers.
• Move forward for
positive numbers.
• Move backward for
negative numbers.
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) ⴚ5
Error Intervention
• Always start at zero,
6
3. Use the figure to find 2 8.
If 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.
.
ⴚ4
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) =
ⴚ6
Have students find a pattern in sets of sums, like
the ones below.
ⴚ8
7. Use the figure to find 3 (5).
© Pearson Education, Inc.
If You Have More Time
.
8. How many units is 2 from 0 on the number line?
2
3 5
3 4
3 3
3 2
The magnitude of a number is its distance from zero.
8
9. What is the magnitude of 8?
10. What is the magnitude of 5?
5
Intervention Lesson F19
3 1
3 0
3 (1)
3 (2)
93
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F19
Adding Integers (continued)
Use the number line to find each sum. Look for a pattern.
11. 2 (3)
ⴚ5
12. 6 (1)
ⴚ7
13. 4 (2)
14. When you add two integers with the same sign, do
add
you add or subtract the magnitudes of the numbers?
15. When you add two negative integers, what is
ⴚ6
negative
the sign of the sum?
Use the number line to find each sum. Look for a pattern.
16. 6 3
19. 9 (4)
ⴚ3
5
17. 5 3
20. 8 (2)
ⴚ2
6
18. 1 (6)
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?
ⴚ5
6
subtract
ⴚ6
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?
negative
9
positive
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
positive
Add. Use rules for adding integers or a number line.
29. 6 (3)
30. 1 (5)
ⴚ9
33. 9 (4)
ⴚ6
34. 3 (6)
5
ⴚ9
31. 2 (5)
ⴚ3
35. 8 (4)
ⴚ12
32. 7 5
ⴚ2
© Pearson Education, Inc.
© Pearson Education, Inc. 4
and the one with the greater magnitude is
positive, what is the sign of the sum?
36. 2 7
5
94 Intervention Lesson F19
Intervention Lesson F19
Math Diagnosis and
Intervention System
Graphing Points in the
Coordinate Plane
Intervention Lesson
Teacher Notes
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F33
F33
Graphing Points in the Coordinate Plane
Materials red and blue crayons, markers, or colored pencils
Ongoing Assessment
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.
Make 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.
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.
Error Intervention
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
If students have trouble plotting points,
from the origin, along the x-axis, to the point directly below point B.
y
4. How many units
7
did you move left
from the origin?
5
4
5. So, what is the
x-coordinate
of point B?
If You Have More Time
3
B
ⴚ5
2
1
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.
© Pearson Education, Inc.
then use F30: Graphing Ordered Pairs.
6
y-axis
5
⫺7 ⫺6 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
⫺1
Origin
x-axis
⫺2
1
3
2
4
5
6
7
x
⫺3
⫺4
7. How many units did
A
⫺5
you move up from the
x-axis to point B?
⫺6
2
⫺7
8. So, what is the
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.
2
y-coordinate of point B?
9. What are the coordinates of point B?
(ⴚ5, 2)
Intervention Lesson F33
121
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F33
Graphing Points in the Coordinate Plane (continued)
Write the ordered pair for each point.
10. E
(ⴚ3, 2)
11. F
(ⴚ1, ⴚ4)
12. G
(3, 3)
13. H
(4, ⴚ3)
E
L
I
15. (1, ⫺2)
1
⫺5 ⫺4 ⫺3 ⫺2⫺1 0
⫺1
J
⫺2
⫺3
F
⫺4
Name the point for each ordered pair.
14. (4, 0)
y
5
K
4
3
2
G
L
1 2 3 4 5 x
I
H
⫺5
16. (1, 4)
K
J
17. (⫺4, ⫺2)
18. Reasoning What is the y-coordinate
for any point on the x-axis?
0
Write the ordered pair for each point.
21. P
(ⴚ2, ⴚ3)
20. N
(ⴚ2, 1)
22. Q
(2, ⴚ4)
Name the point for each ordered pair.
23. (1, 3)
T
V
25. (0, ⫺2)
24. (4, 4)
R
26. (⫺3, 4)
S
y
5
4
T
3
2
R
N
1
M
⫺5 ⫺4 ⫺3 ⫺2⫺1 0 1 2 3 4 5 x
⫺1
V
⫺2
P
⫺3
Q
⫺4
⫺5
S
for any point on the y-axis?
0
28. Is the point (⫺3, ⫺4) located above, below,
or on the x-axis?
29. Is the point (0, ⫺8) located above, below,
or on the x-axis?
122 Intervention Lesson F33
Intervention Lesson F33
below
below
© Pearson Education, Inc.
27. Reasoning What is the x-coordinate
© Pearson Education, Inc. 4
(3, 0)
19. M
Math Diagnosis and
Intervention System
Graphing Equations in the
Coordinate Plane
Intervention Lesson
F34
Teacher Notes
Math Diagnosis and
Intervention System
Name
Intervention Lesson
F34
Graphing Equations in the Coordinate Plane
Graph the equation y x 1 by doing the following.
Ongoing Assessment
1. Find y when x 2, x 0, and x 4. Complete.
When x 2:
When x 0:
When x 4:
yx1
yx1
yx1
y 2 1
y
1
y
y 2 (1)
y
(1)
y
y
0
0
y 1
3
x
y
3
0
4
1
y
2. Complete the table of ordered pairs.
2
4
3
Ask: 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.
4
Error Intervention
2
1
3
4
2
x
0
2
4
2
3. Plot each ordered pair.
4. Draw a line through the points.
then use F19: Adding Integers, F20: Subtracting
Integers, or F21: Multiplying and Dividing Integers.
4
If the points are not on a line,
check your work above.
Graph y 2x by doing the following.
If students plot points incorrectly,
y
5. Complete the table of ordered pairs
4
then use F33: Graphing Points in the Coordinate
Plane.
© Pearson Education, Inc.
for the equation y 2x.
2
x
y
2
4
0
4
0
2
If students add, subtract, or multiply integers
incorrectly
4
2
x
0
2
4
If You Have More Time
2
6. Plot each ordered pair.
4
7. Draw a line through the points.
If the points are not on a line,
check your work above.
Intervention Lesson F34
123
Have 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.
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F34
Graphing Equations in the Coordinate Plane (continued)
Complete each table of ordered pairs. Then graph the equation.
8. y x 2
x
y
4
2
2
4
0
2
x
4
1
0
1
2
2
4
2
0
x
0
2
4
2
x
0
4
11. y 2 x
x
4
2
2
2
2
4
4
y
4
4
0
4
4
2
y
3
0
3
2
y
y
2
10. y 3x
x
9. y 2x
y
0
x
0
2
4
3
2
4
2
4
y
y
4
2
1
4
2
4
2
x
0
2
2
4
4
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.
No, the point (2, 8) is not on the graph of y 4x
because y 4x is not true when x 2 and y 8.
© Pearson Education, Inc.
© Pearson Education, Inc. 4
The point (6, 1) is on the graph of y 5 x,
because y 5 x is true when x 6 and y 1.
124 Intervention Lesson F34
Intervention Lesson F34
Math Diagnosis and
Intervention System
Using the Distributive Property
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
F40
Teacher Notes
F40
Using the Distributive Property
Materials counters, 100 per pair or group
Ongoing Assessment
Discover the Distributive Property by following 1–8.
Ask: Does 3 ⴛ (4 ⴙ 7) ⴝ (3 ⴛ 4) ⴙ 7? No, the 3
must be distributed or passed out to each addend.
3 ⫻ (4 ⫹ 7) ⫽ (3 ⫻ 4) ⫹ (3 ⫻ 7)
1. Make an array with 4 rows and 5 counters in each row.
20
2. The array shows 4 ⫻ 5 ⫽
.
Error Intervention
3. Make another array with 4 rows and 3 counters in each row.
If students don’t know how to evaluate expressions
like 5 ⫻ (2 ⫹ 6) and (5 ⫻ 2) ⫹ (5 ⫻ 6),
then use F39: Order of Operations.
3
4. The second array shows 4 ⫻
12
⫽
.
5. Put the two arrays together.
If You Have More Time
Have students describe a real world situation for
4 ⫻ (5 ⫹ 3) and/or (4 ⫻ 5) ⫹ (4 ⫻ 3).
20
© Pearson Education, Inc.
How many counters in all?
12
⫹
⫽
32
6. Fill in the blanks, using your answers above.
(4 ⫻ 5) ⫹ (4 ⫻ 3) ⫽
20
12
⫹
⫽
32
7. After putting the two arrays together, how
8
5⫹3⫽
many counters are in each of the 4 rows?
8. Fill in the blanks.
(4 ⫻ 5) ⫹ (4 ⫻ 3) ⫽
4
4
⫻ (5 ⫹ 3) ⫽
⫻8⫽
32
Intervention Lesson F40
135
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F40
Using the Distributive Property (continued)
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.
10
5 ⫻ 19 ⫽ 5 ⫻ (
10
⫹ 9) ⫽ (5 ⫻
⫽
⫽
50
95
9
) ⫹ (5 ⫻
)
45
⫹
Fill in the blanks using the Distributive Property.
10
12. 3 ⫻ 14 ⫽ 3 ⫻ (
13. 2 ⫻ 27 ⫽
2
) ⫽ (6 ⫻ 4) ⫹ (6 ⫻
⫻ (20 ⫹
2
14. 12 ⫻ 8 ⫽ (10 ⫹
7
)⫽(
) ⫻ 8 ⫽ (10 ⫻
15. 9 ⫻ 47 ⫽ (9 ⫻ 40) ⫹ (9 ⫻
7
)⫽
16. 16 ⫻ 105 ⫽ (16 ⫻ 100) ⫹ (16 ⫻
17. 25 ⫻ 204 ⫽ (
25
10
⫹ 4) ⫽ (3 ⫻
5
⫻ 200) ⫹ (25 ⫻
8
⫻ (100 ⫺ 4) ⫽ (
19. 7 ⫻ 48 ⫽
7
⫻ (50 ⫺
2
2
8
⫻ 4)
2
)⫹(
⫻ (40 ⫹
)⫽
16
4
⫻
7
7
)
200
) ⫽ 25 ⫻ (
5
8
⫻ 50) ⫺ (
⫹
)
4
7
(4 ⴛ 40) ⴙ (4 ⴛ 9) and (4 ⴛ 50) ⴚ (4 ⴛ 1)
Intervention Lesson F40
)
⫻ 4)
⫻
2
20. Reasoning Describe two different ways to find 4 ⫻ 49 with mental math.
136 Intervention Lesson F40
)
⫻ 8)
⫻ (100 ⫹
⫻ 100) ⫺ (
7
2
⫻ 20) ⫹ (
9
8
)⫽(
)
3
)
© Pearson Education, Inc.
18. 8 ⫻ 96 ⫽
5
)⫹(
© Pearson Education, Inc. 4
5
11. 6 ⫻ 9 ⫽ 6 ⫻ (4 ⫹
Math Diagnosis and
Intervention System
Intervention Lesson
More Variables and Expressions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F43
Teacher Notes
F43
More Variables and Expressions
To evaluate an expression, place the known value in place of the
variable. Then use the order of operations to simplify.
Ongoing Assessment
1. Find 3n ⫺ 5, when n ⫽ 7.
7
3⫻
⫽
21
⫽
16
⫺5
Put 7 in place of n.
⫺5
Use the order of operations, multiply first.
Subtract.
k
2. Find 3k ⫺ __, when k ⫽ 8.
Error Intervention
4
8
8
3⫻
⫽
24
⫽
22
⫺ ____
4
Put 8 in place of k.
2
⫺
Ask: For a ⴝ 6 and b ⴝ 2, does 2a ⴙ b equal
(2 ⴛ 2) ⴙ 6? No, a must be replaced with 6 and b
with 2 to get (2 ⫻ 6) ⫹ 2.
If students have difficulty simplifying expressions
after they substitute values for the variables,
Multiply and divide first.
Subtract.
then use F39: Order of Operations.
3. Find 4y ⫹ 2z, when y ⫽ 5 and z ⫽ 7.
5
4⫻
⫽
20
⫽
34
7
⫹2⫻
Put 5 in place of y and 7 in place of z.
14
⫹
If You Have More Time
Multiply first.
Challenge students to write an expression that
simplifies to 14 when x ⫽ 5 and y ⫽ 4. Sample
answers: 2x ⫹ 3
Add.
© Pearson Education, Inc.
4. Find (3a ⫺ b) ⫼ c, when a ⫽ 10, b ⫽ 6, and c ⫽ 2.
10
(3 ⫻
30
⫽(
⫽
24
⫽
12
6
⫺
⫺
6
⫼
2
2
)⫼
)⫼
Put 10 in place of a, 6 in place of b, and 2
in place of c
2
Use the order of operations, do parentheses
first. Inside the parentheses, multiply first.
Subtract inside the parentheses.
Divide.
Intervention Lesson F43
141
Math Diagnosis and
Intervention System
Intervention Lesson
Name
F43
More Variables and Expressions (continued)
Evaluate each expression for x ⫽ 3.
5.
__3x ⫹ 15
6. 24 ⫺ (2x)
16
7. (3x) ⫹ 5
18
0
11. (19 ⫹ x) ⫼ 11
14
15
9. (5x) ⫺ ___
x
8. (4x) ⫺ 12
21
10. 35 ⫹ ___
x
10
12. (6x) ⫹ x ⫺ 12
2
42
13. 5x ⫼ 3
9
5
Evaluate each expression for a ⫽ 9, b ⫽ 2, and c ⫽ 0.
14. (a ⫹ 7b) ⫹ c
15. 13c ⫹ a
23
17. 12b ⫺ 14c
18. (a ⫹ b ⫹ c) ⫻ 2
24
20. c ⫻ (b ⫹ c)
33
19. (11 ⫹ a) ⫼ b
22
21. 4a ⫺ 5b
0
23. 7b ⫺ 12c
16. (a ⫹ b) ⫻ 3
9
10
22. (a ⫺ b ⫺ c) ⫻ 4
26
24. (2a ⫹ b) ⫼ 5
14
28
25. a ⫻ (b ⫺ c)
4
18
Veggie Pizza House
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 do
2 large pizzas with 3 large beverages cost?
Size
Pizza
Beverages
small
$5.00
$1
large
$8.00
$2
$22
© Pearson Education, Inc.
© Pearson Education, Inc. 4
Use the data at the right to answer Exercises 26–28.
28. Reasoning Micka purchases 4 small veggie pizzas and 3 large beverages.
Romano purchases 3 large pizzas and 4 small beverages. Who spent more
Micka spent 4(5) ⴙ 3(2) ⴝ $26 and Romano spent
money? Explain.
3(8) ⴙ 4(1) ⴝ $28; Romano spent more money.
142 Intervention Lesson F43
Intervention Lesson F43
Math Diagnosis and
Intervention System
Divisibility by 2, 5, 9, and 10
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
G60
Teacher Notes
G60
Divisibility by 2, 3, 5, 9, and 10
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.
Ongoing Assessment
Use the divisibility rules and answer 1 to 10 to determine if 256
is divisible by 2, 3, 5, 9, or 10.
Number
2
3
5
9
10
The
The
The
The
The
1. Is the last digit in 256 an even number?
2. Is 256 divisible by 2?
If students have trouble remembering the divisibility
rules,
yes
no
then have the students use a calculator to generate
multiples of each number and look for patterns.
no
no
5. Is 256 divisible by 10?
13
6. What is the sum of the digits of 256? 2 + 5 + 6 =
7. Is the sum of the digits of 256 divisible by 3?
8. Is 256 divisible by 3?
© Pearson Education, Inc.
If You Have More Time
no
Have 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.
no
9. Is the sum of the digits of 256 divisible by 9?
10. Is 256 divisible by 9?
Error Intervention
yes
3. Is the last digit in 256 a 0 or 5?
4. Is 256 divisible by 5?
Ask: 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.
Divisibility Rules
Rule
last digit is even: 0, 2, 4, 6, 8.
sum of the digits is divisible by 3.
last digit ends in a 0 or 5.
sum of the digits is divisible by 9.
ones digit is a 0.
no
no
Use the divisibility rules to determine if 720 is divisible by 2, 5,
9, or 10.
11. Is 720 divisible by 2?
yes
13. Is 720 divisible by 10?
yes
12. Is 720 divisible by 5?
yes
14. Is 720 divisible by 9?
yes
Intervention Lesson G60
197
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G60
Divisibility by 2, 3, 5, 9, and 10 (continued)
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
18. 380
2, 3
19. 105
2, 5, 10
21. 4,311
3, 5
22. 8,356
3, 9
24. 7,265
2, 3, 9
23. 2,580
2
25. 4,815
5
2
20. 126
2, 3, 5, 10
26. 630
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
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
Intervention Lesson G60
© Pearson Education, Inc.
Not all numbers that are divisible by 5 are also
divisible by 10. For example, 25 is divisible by 5 but
not by 10.
© Pearson Education, Inc. 4
divisible by 10? Explain your reasoning.
Math Diagnosis and
Intervention System
Intervention Lesson
Prime Factorization
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G63
Teacher Notes
G63
Prime Factorization
1. Use the two factor trees shown to factor 240. For the first circle,
Ongoing Assessment
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
4
3 2
Ask: What number has a prime factorization of
2 ⴛ 32 ⴛ 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.
')%
')%
&%
5
-
'
2
2
4
2
(%
* 6
2
2
3
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
Error Intervention
3. Reasoning What do all the numbers at the end of each branch
have in common?
If students have difficulty factoring composite
numbers,
They are prime.
then use G59: Factoring Numbers.
4. Reasoning What do you notice about the numbers in the two
groups?
They are the same.
If You Have More Time
5. Arrange the numbers from least to
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greatest and include a multiplication
sign between each pair of numbers.
2⫻
2
2
3
⫻5
Intervention Lesson G63
203
⫻
⫻
2
⫻
Have students work in pairs to find the prime
factorization of 5040 (24 ⫻ 32 ⫻ 5 ⫻ 7).
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.
4
2
⫻3⫻5
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G63
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.
+
3ⴛ7
23 ⴛ 3
-&
9.
.
*+
10.
,
'
34
23 ⴛ 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
Prime
15. 16
16. 17
24
5ⴛ7
13. 41
17. 80
Prime
20. 72
23 ⴛ 32
14. 40
Prime
21. 48
24 ⴛ 5
24 ⴛ 3
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.
23 ⴛ 5
18. 95
5 ⴛ 19
22. 55
5 ⴛ 11
© Pearson Education, Inc.
© Pearson Education, Inc. 4
19. 35
2 ⴛ 32
204 Intervention Lesson G63
Intervention Lesson G63
Math Diagnosis and
Intervention System
Intervention Lesson
Least Common Multiple
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G65
Teacher Notes
G65
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?
Ongoing Assessment
Ask: 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.
Follow 1 to 4 below to answer the question.
1. Complete the table.
Packages
Hamburgers
Buns
1
2
12
24
3
8
16
4
5
6
36 48 60 72
24 32 40 48
Error Intervention
24, 48
24
2. What are some common multiples from the table?
3. What is the least of these common multiples?
If students are making mistakes in finding multiples
of two-digit numbers,
So, the least common multiple (LCM) of 12 and 8 is 24.
4. What is the least amount of hamburgers and buns that
24
the students can buy and have the same amount of each?
then use G49: Multiplying Two-Digit Numbers.
Find the least common multiple of 6 and 15 by following the steps
below.
If You Have More Time
© Pearson Education, Inc.
5. Complete the table.
2ⴛ
3ⴛ
4ⴛ
5ⴛ
6ⴛ
7ⴛ
8ⴛ
9ⴛ
10 ⴛ
6
12
18
15
30
45
24
60
30
75
36 42 48 54 60
90 105 120 135 150
30, 60
6. What are the common multiples from the table?
7. What are the next three common multiples that are
90, 120, 150
not in the table?
30
8. What is the least common multiple of 6 and 15?
Intervention Lesson G65
Have 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.
207
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G65
Least Common Multiple (continued)
Find the least common multiple (LCM).
9. 30, 4
10. 18, 9
60
12. 6, 12
11. 12, 36
18
13. 8, 20
12
15. 6, 25
150
36
14. 3, 14
40
16. 8, 12, 15
42
17. 3, 4, 5
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.
15? Explain.
No, the common multiples will continue forever.
208 Intervention Lesson G65
Intervention Lesson G65
© Pearson Education, Inc.
20. Reasoning Can you find the greatest common multiple of 6 and
© Pearson Education, Inc. 4
Answers will vary. Sample answer: 6, 12
Math Diagnosis and
Intervention System
Intervention Lesson
Dividing by Multiples of 10
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G73
Teacher Notes
G73
Dividing by Multiples of 10
Use the multiplication sentences to find each quotient. Look
for a pattern.
80
40 ⫻ 20 ⫽ 800
400 ⫻ 20 ⫽ 8,000
Ongoing Assessment
4
800 ⫼ 20 ⫽ 40
8,000 ⫼ 20 ⫽ 400
1. 4 ⫻ 20 ⫽
80 ⫼ 20 ⫽
Ask: 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.
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
Error Intervention
In 24 ⫼ 8 ⫽ 3, 24 is the dividend, 8 is the divisor, and 3 is the
quotient.
4. Look for a pattern.
Zeros in the
Dividend
Zeros in the
Divisor
Zeros in the
Quotient
3
1
1
0
30
1
0
1
300
2
0
2
30
2
1
1
Number Sentence
240 ⫼ 80 ⫽
240 ⫼ 8 ⫽
2,400 ⫼ 8 ⫽
© Pearson Education, Inc.
2,400 ⫼ 80 ⫽
Complete.
Zeros in the dividend ⫺ Zeros in the divisor ⫽
zeros
then use some of the intervention lessons on
division facts, G38 to G41.
If You Have More Time
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 ⴚ 1 ⴝ 1, so the quotient has 1 zero.
Intervention Lesson G73
223
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G73
Dividing by Multiples of 10 (continued)
Divide. Use mental math.
6. 300 ⫼ 30 ⫽
10
7. 60 ⫼ 20 ⫽
9. 240 ⫼ 60 ⫽
4
10. 490 ⫼ 70 ⫽
12. 100 ⫼ 50 ⫽
2
13. 2,700 ⫼ 90 ⫽
30
14. 1,800 ⫼ 60 ⫽
16. 1,500 ⫼ 30 ⫽
50
17. 800 ⫼ 40 ⫽
20
19. 3,600 ⫼ 60 ⫽
60
20. 140 ⫼ 70 ⫽
2
22. 8,100 ⫼ 90 ⫽
90
23. 560 ⫼ 80 ⫽
7
50
15. 3,500 ⫼ 70 ⫽
8
18. 640 ⫼ 80 ⫽
60
21. 1,200 ⫼ 20 ⫽
24. 600 ⫼ 30 ⫽
20
25. 400 ⫼ 20 ⫽
27. 1,200 ⫼ 40 ⫽
30
28. 2,500 ⫼ 50 ⫽
30. 4,500 ⫼ 90 ⫽
50
31. 480 ⫼ 80 ⫽
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
7
20
50
6
8. 200 ⫼ 40 ⫽
5
11. 450 ⫼ 90 ⫽
5
30
26. 2,400 ⫼ 60 ⫽
40
29. 2,100 ⫼ 70 ⫽
30
32. 450 ⫼ 50 ⫽
Have 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.
9
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
© Pearson Education, Inc.
© Pearson Education, Inc. 4
33. Dan has a coin collection. His sister
3
If students have trouble with the basic division
facts,
as 2,700 ⫼ 90.
Sample answer: 270 ⴜ 9
224 Intervention Lesson G73
Intervention Lesson G73
Math Diagnosis and
Intervention System
Dividing by Two-Digit Divisors
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
G75
Teacher Notes
G75
Dividing by Two-Digit Divisors
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?
Ongoing Assessment
Find 144 32 by answering 1 to 11.
1. First, estimate to find the approximate number of pieces.
150 30 5
5
4 4
32 1
2. Write the estimate in the ones place of the quotient,
on the right.
3. Multiply. 32 5 1 6 0
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 Error Intervention
128
If students have trouble finding an estimate,
6. Compare the product to the dividend. Write or .
128 144
4
4 4
32 1
Since 128 is less than 144, 4 is not too large. Write 4 in
the ones place of the quotient on the right. Write 128
below 144.
7. Subtract. 144 128 1 2 8
1 6
16
8. Compare the remainder to the divisor. Write or .
© Pearson Education, Inc.
16
⬍
Ask: 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.
If You Have More Time
32
Have 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.
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?
11. How much of the board was left?
then use G74: Estimating Quotients with Two-Digit
Divisors.
4
16
pieces
inches
Intervention Lesson G75
227
Math Diagnosis and
Intervention System
Intervention Lesson
Name
G75
Dividing by Two-Digit Divisors (continued)
Divide.
2 R13
15. 62 137
8 R1
18. 82 657
5 R20
21. 89 465
7 R22
24. 77 561
8 R60
27. 63 564
2 R72
13. 94 260
7 R16
16. 28 212
4 R3
19. 32 131
2 R56
22. 74 204
2 R59
25. 61 181
8 R62
28. 82 718
7 R30
14. 45 345
9 R30
17. 58 552
8 R80
20. 93 824
8 R13
23. 78 637
5 R54
26. 73 419
5 R33
29. 57 318
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 ⴛ 23 ⴝ 138 and 138 ⬎ 120.
228 Intervention Lesson G75
Intervention Lesson G75
© Pearson Education, Inc.
30. A vegetable stand sells 192 cucumbers and
© Pearson Education, Inc. 4
6 R10
12. 32 202
Math Diagnosis and
Intervention System
Intervention Lesson
Comparing and Ordering Fractions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H19
Teacher Notes
H19
Comparing and Ordering Fractions
_ of a salad. Jack ate _5_ of a salad. Find out who ate the greater
Jen ate _7
9
9
Ongoing Assessment
part of a salad by answering 1–3.
_ and _5_.
Compare _7
9
9
1. Are the denominators the same?
__ __
Ask: Which is larger 1 or 1 ? How can you tell?
4
3
1 because when the numerators are
1 is larger than __
__
4
3
the same, you just compare the denominators. The
fraction with the smaller denominator is the larger
of the two fractions.
yes
If 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_
⬎
_5_
9
9
Jen
3. Who ate the greater part of a salad, Jen or Jack?
_ and _3_ by answering 4 to 6
Compare _3
5
4
no
yes
4. Are the denominators the same?
5. Are the numerators the same?
Error Intervention
If 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_
⬍
_3_
5
If students can not find the LCD,
then use G65: Least Common Multiple.
4
If students are having problems writing equivalent
fractions,
_ and _2_ by answering 7 to 11.
Compare _3
4
3
© Pearson Education, Inc.
7.
8.
Are the denominators the same? no
Are the numerators the same? no
then use H7: Using Models to Find Equivalent
Fractions or H14: Equivalent Fractions.
If neither the numerators or the denominators are the same, change to
equivalent fractions with the same denominator.
12
9. What is the LCM of 3 and 4?
If You Have More Time
Intervention Lesson H19
121
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H19
Comparing and Ordering Fractions (continued)
3
2
10. Rewrite __ and __ as equivalent fractions with a denominator of 12.
4
3
3
4
9
2
12
3
11. Compare. Write , , or .
8
12
9
___
⬎
8
___
3
__
⬎
2
__
12
4
5 , on the board. Ask
Write a fraction, such as __
6
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.
12
3
5 __
1
Write __
, 5, and __
in order from least to greatest by answering 12 to 15.
6 9
3
⬎
12. Use the denominators to compare. Write , , or .
5
__
5
1
13. Rewrite __ so that it has a denominator common with __.
3
9
3
1
3
9
14. Compare the numerators. Write , , or .
5
__
⬎
3
__
5
__
⬎
1
__
6
9
9
5
__
9
9
3
5 5
1
15. Use the comparisons to write __, __, and __ in order from least to greatest.
9 6
3
_1_
_5_
3
9
_5_
6
Compare. Write , , or .
3
16. __
7
⬎
1
__
7
5
17. __
8
ⴝ
10
___
16
3
18. ___
11
3
20. __
ⴝ
9
___
5
21. __
⬎
5
__
5
22. __
15
6 __
1 , __
24. __
,3
4 7 5
_1_, _3_, _6_
6
8
5 8 2
25. __, ___, __
8 10 7
4 5 7
_2_, _5_, __8
7 8 10
8
⬎
4
___
10
7
___
12
5 10 5
26. __, ___, __
9 12 7
10
_5_, _5_, __
3
19. __
4
⬎
2
__
7
23. __
⬎
4
__
9
3
9
3 12 5
27. __, ___, __
9 15 6
9 7 12
_3_, __
12 _5_
,
9 15 6
28. Reasoning Mario has two pizzas the same size. He cuts one into
© Pearson Education, Inc.
© Pearson Education, Inc. 4
5
⬍
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
Intervention Lesson H19
Math Diagnosis and
Intervention System
Place Value Through Thousandths
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
H24
Teacher Notes
H24
Place Value Through Thousandths
1. Write 5.739 in the place-value chart below.
ones
5
tenths
hundredths
thousandths
7
3
9
.
5
0.7
What is the value of the 7 in 5.739?
What is the value of the 3 in 5.739? 0.03
What is the value of the 9 in 5.739? 0.009
5
Write 5.739 in expanded form.
0.7 0.03
Ongoing Assessment
Ask: What is one and one thousandth written in
standard form? 1.001
2. What is the value of the 5 in 5.739?
3.
4.
5.
6.
Error Intervention
If students are having problems writing the value of
a digit such as 1 in 0.381,
0.009
7. Write 5.739 in words.
five
thirty-nine
and seven hundred
thousandths
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.
Write seven and two hundred four thousandths in standard from by
answering 8 to 14.
7
8. How many ones are in seven and two hundred four thousandths?
Write 7 in the ones place of the place-value chart below.
ones
7
tenths
hundredths
thousandths
2
0
4
.
200
_____
© Pearson Education, Inc.
9. Write two hundred, thousandths as a fraction.
10. Write an equivalent fraction. 200
1,000
If You Have More Time
1,000
2
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.
Intervention Lesson H24
131
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Have 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.
H24
Place Value Through Thousandths (continued)
13. How many thousandths are in seven and
4
two hundred four thousandths?
Write 4 in the thousandths place of the place-value chart.
14. Write 7.204 in expanded form.
7
0.2
15. Reasoning What is 1 thousandth less than 7.204?
0.004
7.203
Write each value in standard form.
16. 507 thousandths
17. 5 and 6 thousandths
0.507
18. 9 and 62 thousandths
5.006
9.062
Write the value of the underlined digit.
19. 2.55
_3
20. 0.381
_
0.05
21. 6.6
_47
0.001
22. 9.09
_7
0.6
0.09
Write each decimal in expanded form.
23. 4.685
24. 3.056
25. 0.735
26. 4.004
4 ⴙ 0.6 ⴙ 0.08 ⴙ 0.005
0.7 ⴙ 0.03 ⴙ 0.005
3 ⴙ 0.05 ⴙ 0.006
4 ⴙ 0.004
two and five hundred ninety-eight thousandths
28. 0.008
eight thousandths
29. 0.250
two hundred and fifty thousandths
132 Intervention Lesson H24
Intervention Lesson H24
© Pearson Education, Inc.
27. 2.598
© Pearson Education, Inc. 4
Write each decimal in word form.
Math Diagnosis and
Intervention System
Intervention Lesson
Decimals to Fractions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H31
Teacher Notes
H31
Decimals to Fractions
Materials crayons, markers, or colored pencils
Ongoing Assessment
Write 0.45 as a fraction by answering 1 to 5.
1
Ask: What is 0.10 written as a fraction? ___
10
1. Color the grid to show 0.45.
45
100
2. How small squares did you color?
3. How many squares are in the grid?
45
___
100
45
___
4. What fraction represents the
part of the grid that you colored?
0.45 ⫽
5. Write a fraction equal to 0.45.
Error Intervention
If students have trouble representing decimals with
grids,
100
You can also use place value to change a decimal to a fraction.
then use H22: Place Value through Hundredths.
Write 0.3 as a fraction by answering 6 to 9
6. Write 0.3 in words.
7. What is the place value of the 3 in 0.3?
three tenths
tenths
Since the 3 is in the tenths place, you write 3 over 10.
Have 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.
10
0.3 ⫽
9. Write a fraction equal to 0.3.
If You Have More Time
__3
10
__3
8. What fraction represents three tenths?
Write 3.07 as a mixed number by answering 10 to 13.
3
hundredths
© Pearson Education, Inc.
10. What is the whole number part of the decimal 3.07?
11. What is the place value of the last digit in 3.07?
12. Write the place value as the denominator
7
3.07 ⫽ 3______
100
3 7
and write 7 as the numerator.
___
13. Write a mixed number equal to 3.07.
100
3.07 ⫽
Intervention Lesson H31
145
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H31
Decimals to Fractions (continued)
Write each decimal as a fraction or mixed number.
14. 0.4
__4
15. 3.7
17. 0.8
__8
18. 1.2
100
___
4 3
10
___
12
21. 10.5
___
42
24. 5.75
__
10 5
100
19
___
22. 0.19
10
100
26. 19.09
__
19. 4.03
___
5 27
12
100
23. 0.42
16. 5.27
10
10
20. 0.12
__
37
10
___
5 75
100
__
25. 8.6
86
100
___
27. 0.01
19 9
100
___
1
100
10
28. 28.37
___
28 37
__
10
75
___
2
100
57
12___
100
13 9
29. Jaime put 13.9 gallons of gas in the car.
What is 13.9 written as a mixed number?
30. Candice ran 2.75 miles.
What is 2.75 written as a mixed number?
31. Justin’s mom bought a 12.57 pound turkey.
What is 12.57 written as a mixed number?
100
___
__
No; 0.08 ⴝ 8 not 8 .
100
10
37
3
33. Reasoning 2.37 ⫽ 2____ and 2.3 ⫽ 2___. Explain why the 3 in
100
10
3
2.37 represents ___
.
10
Sample answer: In 2.37 ⴝ 2 ⴙ 0.3 ⴙ 0.07,
© Pearson Education, Inc.
© Pearson Education, Inc. 4
8
32. Reasoning Marco says 0.08 ⫽ ___. Is he correct? Explain why.
10
__
so the 3 represents 0.3 ⴝ 3 .
10
146 Intervention Lesson H31
Intervention Lesson H31
Math Diagnosis and
Intervention System
Estimating Sums and Differences
of Mixed Numbers
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
H42
Teacher Notes
H42
Estimating Sums and Differences
of Mixed Numbers
Ongoing Assessment
_ hours playing basketball and 1_2_ hours
Last week, Dwayne spent 4_1
3
3
playing soccer. Answer 1 to 9 to estimate how much time Dwayne
spent in all playing these two sports.
4
1
1. What two whole numbers is 4__ between?
3
2. Use the number line.
_ closer to 4 or 5?
Is 4_1
3
__
1
4__
6
4
4_1_
⬍
_1_
3
5
4__
6
4
4__
6
5
2
2 ⬎ __
1 , 1__
2 ⬎ 1__
1 and 1__
2 is between 1__
1 and
2. Since __
_1_
3
2
1
⬎
_2_
3
2
2
1
2
8. Use the rounded numbers to estimate 4__ ⫹ 1__ .
© Pearson Education, Inc.
3
3
1
4__
3
4
2
⫹ 1__
3
⫹2
6
6 hours
spend playing basketball and soccer?
About how much more time did Dwayne spend
playing basketball than soccer?
1
2
10. Estimate 4__ ⫺ 1__ at the right.
3
1
4__
3
4
2
⫺ 1__
⫺2
3
3
11. About how much more time did Dwayne
spend playing basketball than soccer?
2
2 hours
Intervention Lesson H42
167
Intervention Lesson
Name
H42
Estimating Sums and Differences of Mixed Numbers (continued)
Estimate each sum or difference.
2
2__
3
14.
5
⫺ 1___
10
3ⴚ1ⴝ2
16.
9
2___
10
13.
1
⫺ 1__
3
6
17.
5
5
⫹ 1__
6
5 ⴙ 5 ⴝ 10
18.
4
6__
6
15.
2
⫹ 4__
4
3ⴚ2ⴝ1
7
6__
8
9
4___
14
11
⫹ 2___
14
2
⫹ 4___
16
7ⴚ5ⴝ2
6ⴚ3ⴝ3
5ⴙ3ⴝ8
6 ⴙ 4 ⴝ 10
5
2
21. 7__ ⫹ 6__
6
6
7 ⴙ 7 ⴝ 14
5
1
23. 6__ ⫺ 1__
8
8
3
24. 7 ⫺ 2__
7
6ⴚ2ⴝ4
7ⴚ2ⴝ5
3
1
26. Yolanda walked 2__ miles on Monday, 1__ miles on
5
5
Tuesday, and 3_4_ miles on Wednesday. Estimate
5
her total distance walked.
If 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 Time
6
3
⫺ 3__
9
3ⴚ1ⴝ2
Error Intervention
7ⴙ2ⴝ9
19.
3
⫺ 5__
8
3
20. 2__ ⫺ 1
4
2
Have 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.
Math Diagnosis and
Intervention System
12.
3
_1_
2
7. What is 1__ rounded to the nearest whole number?
3
9. About how much time did Dwayne
2
1.
2
and
3
3
number is 4.
6. Compare. Write ⬎, ⬍, or ⫽.
2
2 is closer to 2 than to
2 on the number line. Thus, 1__
_ and _1_, you can tell that 4_1_ is closer to 4 than 5,
By comparing _1
2
3
3
_ rounded to the nearest whole
without using a number line. So, 4_1
3
2
5. What two whole numbers is 1__ between?
3
number line than to 1? Sample answer: On a
1 is the halfway point between 1 and
number line, 1__
2
3. What is the number halfway between 4 and 5?
4. Compare. Write ⬎, ⬍, or ⫽.
3
4__
6
2
4__
6
2
3
1
4__
3
4
__
3
help you to know that 12 is closer to 2 on a
5
and
__
Ask: How does knowing that 2 is greater than 1
_ ⫹ 1_2_.
Estimate 4_1
3
3
2
2
22. 3__ ⫹ 1__
5
5
3ⴙ1ⴝ4
4
7
25. 3__ ⫹ 1__
8
8
4ⴙ2ⴝ6
8 miles
1
27. Chris was going to add 2__ cups of a chemical to the
__
1 cup
31 is halfway between 3 and 4, so it isn’t closer
2
to either.
168 Intervention Lesson H42
Intervention Lesson H42
© Pearson Education, Inc.
1
28. Reasoning Is 3__ closer to 3 or 4? Explain.
2
© Pearson Education, Inc. 4
4
swimming pool until he found out that Richard
_ cups of the chemical. Estimate how
already added 1_1
8
much more Chris should add so that the total is his
original amount.
Math Diagnosis and
Intervention System
Intervention Lesson
Multiplying Two Fractions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
H46
Teacher Notes
H46
Multiplying Two Fractions
Materials crayons, markers, or colored pencils, paper to fold
Ongoing Assessment
_ of an acre. One-half of the yard is woods. What part of
Pablo’s yard is _3
4
an acre is wooded?
Make 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.
_ of _3_ or _1_ _3_ by answering 1 to 5.
Find _1
4
4
2
2
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_
3. What fraction of the paper is
8
shaded with crisscrossed lines?
4. The part shaded with crisscrossed lines
_ of _3_ or _1_ _3_.
shows _1
3
4
4
2
2
_ _3_?
8
So, what is _1
4
2
3
5. In Pablo’s yard, what part of his __ acre is wooded?
4
__
_3_ acre
3
1
7. What is the product of the denominators in __ __?
4
2
24
8
3
3
1
8. To find __ __, how many sections did you crisscross?
4
2
3
1
9. What is the product of the numerators in __ __?
4
2
13
10. Write the product of the numerators over the product
© Pearson Education, Inc.
If students multiply the numerators and
denominators together and then make mistakes
simplifying,
8
3
1
6. To find __ __, how many sections did you divide the paper into?
4
2
3
3
8
13
_____
_____
of the denominators.
11. Is your answer to item 9 the same as item 4?
Error Intervention
8
24
yes
3
2
12. Use paper folding to find __ __.
4
3
Color the rectangle at the right to
_ _3_ show what you did. So, _2
4
3
6
__
12
.
3
2
13. To find __ __, how many sections
3
4
If You Have More Time
12
did you divide the paper into?
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.
Intervention Lesson H46
175
Have students find more products using paper
folding and show their product to a partner or to
the class.
Math Diagnosis and
Intervention System
Name
Intervention Lesson
H46
34
12
Multiplying Two Fractions (continued)
3
2
14. What is the product of the denominators in __ __?
4
3
6
3
2
15. To find __ __ how many sections did you crisscross?
3
4
3
2
16. What is the product of the numerators in __ __?
23
4
3
6
6
12
3
23
2
17. Complete: __ __ _____ ____
4
3
34
To multiply two fractions, you can multiply the numerators and then the
denominators. Then simplify, if possible.
3
23
6
2
1
__
__
_____
___
__
3
4
34
12
2
3
5
18. Reasoning Shari found ___ __ as shown
10
9
at the right. Why does Shari’s method work?
She simplified before
multiplying, instead of after.
Multiply. Simplify, if possible.
2
1 __
19. __
3
8
1
6
22. __ __ 3
7
4
5
28. __ __ 5
8
5
7 ___
31. __
14
8
16
1
5
20. __ __ 2
6
3
3
23. __ __ 8
4
3
3
26. __ ___ 10
7
3
7 __
29. __
5
9
1
3
32. ___ __ 9
11
__5
12
__9
32
__9
70
__7
15
__1
33
34. There are 45 tents at the summer camp. Girls will use
2
__
of the tents. How many tents will the girls use?
3
10
9
1
10 9
2
3
1 __
21. __
5
4
4
1 __
24. __
5
5
3
4 __
27. __
4
9
5
1 __
30. ___
7
10
4
1 __
33. ___
5
12
3
6
__3
20
__4
25
_1_
3
__1
14
__1
15
© Pearson Education, Inc.
© Pearson Education, Inc. 4
4
2 __
25. __
7
3
__1
12
_2_
7
__8
21
_1_
2
__5
1
3 5
3
5 _______
1
___
__
__
30 tents
176 Intervention Lesson H46
Intervention Lesson H46
Math Diagnosis and
Intervention System
Measuring and Classifying Angles
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
I17
Teacher Notes
I17
Measuring and Classifying Angles
Materials protractor, straightedge, and crayons, markers, or
Ongoing Assessment
colored pencils
A protractor can be used to measure and draw angles. Angles are
measured in degrees.
Ask: 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.
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?
100ⴗ
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
Error Intervention
#
with the endpoint of the ray at point A.
If students need more practice identifying angles,
4. Place the protractor’s center on point A.
Place the protractor
so the the 0⬚ mark is
__›
"
!
lined up with AB.
then use I4: Acute, Right, and Obtuse Angles.
___›
5. Place a point at 60⬚. Label it C and draw AC.
orange
Use a protractor to measure the angles shown,
if necessary, to answer 6 to 9.
green
blue
red
blue
6. Acute angles have a measure between 0⬚ and
90⬚. Trace over the acute angles with blue.
© Pearson Education, Inc.
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 with
green.
green
9. Straight angles have a measure of 180⬚. Trace
red
over the straight angles with orange.
orange
Intervention Lesson I17
If You Have More Time
Have 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.
123
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I17
Measuring and Classifying Angles (continued)
Classify each angle as acute, right, obtuse, or straight. Then measure
the angle.
10.
11.
12.
acute;
acute;
obtuse;
30ⴗ
75ⴗ
115ⴗ
13.
14.
15.
obtuse;
acute;
acute;
160ⴗ
15ⴗ
45ⴗ
Use a protractor to draw an angle with each measure.
17. 35⬚
18. 70⬚
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
90ⴗ or equal to 90ⴗ. Check student’s drawings.
124 Intervention Lesson I17
Intervention Lesson I17
© Pearson Education, Inc.
19. Reasoning If two acute angles are placed next to each other to
© Pearson Education, Inc. 4
16. 120⬚
Math Diagnosis and
Intervention System
Intervention Lesson
Constructions
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I20
Teacher Notes
I20
Constructions
Materials compass and straightedge
Ongoing Assessment
_
Construct a segment congruent to XY by answering 1 to 3.
_
1. Use a compass to measure the length of XY,
X
Y
2. Draw a horizontal ray with endpoint W. Place the
W
%
Ask: 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.
by placing one point on X and the other on Y.
compass point
_ on point W. Use the compass
measure of XY to draw an arc intersecting the ray
drawn. Label this intersection J.
_
_
yes
3. Are XY and WJ congruent?
Construct an angle congruent to ⬔A by answering 4 to 6.
4. Place the compass point on A, and draw an arc
Error Intervention
!
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.
If students are not convinced that their
constructions are accurate,
2
3
5. Use a compass to measure the length of the arc
4
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.
then have them measure angles using a protractor,
and side lengths using a ruler, after they complete
their constructions.
yes
6. Are ⬔A and ⬔RST congruent?
‹__›
Construct a line perpendicular to AB by answering 7 to 9.
%
&
7. Open the compass to more than half the distance
© Pearson Education, Inc.
between A and B. Place the compass point at A
and draw arcs above and below the line.
#
!
8. Without changing the compass setting, place the
'
If You Have More Time
"
Challenge 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.
$
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
Intervention Lesson I20
129
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I20
Constructions (continued)
‹__›
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.
3
13. Construct ⬔R congruent to ⬔L.
_
14. On one side of
⬔R, construct RS so that it is
_
-
2
⬔R,
congruent_
to LM. On the other side of _
construct RT so that it is congruent to LN.
15. Draw segment ST.
.
,
16. Are 䉭LMN and 䉭RST congruent?
4
yes
Construct a rectangle by answering 17 to 21.
‹__›
17. Construct a line that is perpendicular to PQ.
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.
J
K
H
G
P
Q
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.
© Pearson Education, Inc.
© Pearson Education, Inc. 4
19. Choose a point on the first line and label it K.
130 Intervention Lesson I20
Intervention Lesson I20
Math Diagnosis and
Intervention System
Converting Customary
Units of Length
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Intervention Lesson
I33
Teacher Notes
I33
Converting Customary Units of Length
Mayla bought 6 yards of ribbon. How
many feet of ribbon did she buy?
Customary Units
of Length
Answer 1 to 4 to change 6 yards to feet.
1 yard (yd) 36 (in.)
To change larger units to smaller units,
multiply. To change smaller units to
larger units, divide.
3
1. 1 yard 1 yard (yd) 3 feet (ft)
1 mile (mi) 1,760 yards (yd)
2. Do you need to multiply or divide
to change from yards to feet?
18
multiply
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.
12
inches
6. Do you need to multiply or divide to change from feet
divide
to inches?
7. What is 60 12?
5
If You Have More Time
© Pearson Education, Inc.
Troy ran 4 miles. How many yards did he run? Change 4 miles
to yards by answering 9 to 11.
1,760 yards
10. Do you need to multiply or divide to change from miles
multiply
to yards?
11. 4 miles 7,040 yards
12. How many yards did Troy run?
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.
5 ft
8. How many feet of ribbon did Deidra buy?
9. 1 mile Error Intervention
If students have trouble remembering the size of
each unit,
feet
4. How many feet of ribbon did Mayla buy?
5. 1 foot Ask: Would you multiply or divide to change
miles to inches? Multiply
1 mile (mi) 5,280 feet (ft)
feet
3. What is 6 3 feet?
Ongoing Assessment
1 foot (ft) 12 inches (in.)
7,040 yd
Intervention Lesson I33
155
Write 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?
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I33
Converting Customary Units of Length (continued)
Find each missing number.
3
13. 1 yd 1
16. 5,280 ft 19. 48 in. 4
22. 5 yd 15
25. 21 ft 7
6
14. 72 in. ft
ft
mi
17. 5 mi 8,800 yd
ft
20. 1 yd 36
in.
ft
23. 3 mi 5,280 yd
yd
26. 3 yd 108
in.
15. 3 mi 18. 4 yd 21. 6 mi 15,840
12
ft
31,680
24. 2 ft 24
27. 4 yd 144
ft
ft
in.
in.
For Exercises 28 to 32 use the information in the table.
28. How many inches did Speedy crawl?
36
inches
29. How many inches did Pokey crawl?
72
inches
Turtle Crawl Results
Turtle
Distance
Snapper
38 inches
Speedy
3 feet
Pokey
2 yards
Pickles
4 feet
30. How many inches did Pickles crawl?
inches
31. Reasoning Which turtle crawled the greatest distance?
33. Reasoning Explain how you could use addition to find
how many yards are in 72 inches.
Sample answer: I know 36 in. ⴝ 1 yd.
If I add 36 ⴙ 36, I get 72.
Since I added 36 two times, 72 in. ⴝ 2 yd.
156 Intervention Lesson I33
Intervention Lesson I33
© Pearson Education, Inc.
32. Reasoning Which turtle crawled the least distance?
Pokey
Speedy
© Pearson Education, Inc. 4
48
Math Diagnosis and
Intervention System
Intervention Lesson
Converting Metric Units
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I36
Teacher Notes
I36
Converting Metric Units
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
kilometer
hectometer dekameter
(km)
kiloliter
kilogram
(kg)
hectoliter
⫼ 10
⫼ 10
decimeter
liter
(L)
deciliter
centiliter
milliliter
(mL)
gram
(g)
decigram
centigram
milligram
(mg)
dekaliter
⫻ 10
⫼ 10
meter
(m)
hectogram dekagram
⫻ 10
Ongoing Assessment
⫻ 10
⫻ 10
centimeter millimeter
(cm)
(mm)
⫻ 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.
right
do you move right or left?
2. How many jumps are there between centimeters and
© Pearson Education, Inc.
Move the decimal one place to the right to convert from
centimeters to millimeters. This is the same as
multiplying by 10.
279
3. What is the length of the paper in millimeters?
If students do not understand the relationship
between moving the decimal and multiplying or
dividing a number by 10,
If You Have More Time
1
millimeters in the table?
Error Intervention
then use H59: Multiplying Decimals by 10, 100, or
1,000 and H64: Dividing Decimals 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,
Ask: When changing from smaller units to larger
units, do you multiply or divide? Divide
mm
Have student pairs measure their heights in
centimeters and convert the measurements into
meters and into millimeters.
Convert 27.9 cm to meters by answering 4 to 6.
4. To move from centimeters to meters in the table,
left
do you move right or left?
Intervention Lesson I36
161
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I36
Converting Metric Units (continued)
5. How many jumps are there between centimeters and
2
meters in the table?
Move the decimal two places to the left to convert from
centimeters to meters. This is the same as dividing by 100.
0.279
6. What is the length of the paper in meters?
m
Tell the direction and number of jumps in the table for each conversion.
Then convert.
7. 742 cm to meters
2
jumps
7.42
8. 12.4 kg to g
left
9. 0.62 L to mL
3 jumps right
12,400 g
m
3
jumps
620
left
mL
Write the missing numbers.
0.15 g
0.3 L
2,670 mg = 2.67 g
2.6
10. 150 mg =
11. 2,600 m =
13. 300 mL =
14. 4 kg = 4,000,000 mg
16.
17. 34 cm =
340
km 12. 0.4 L =
15. 2.6 m =
mm 18. 16 L =
400 mL
2,600 mm
16,000 mL
For Exercises 19 to 21 use the table at the right.
19. What is the height of the
Petronas Towers in centimeters?
45,200 cm
20. What is the height of the CN Tower
in meters?
Height
344 m
Petronas Towers
452 m
Sears Tower
44,200 cm
CN Tower
553,000 mm
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.
© Pearson Education, Inc.
© Pearson Education, Inc. 4
553 m
Building
John Hancock Center
15 centimeters is equal to 150 millimeters and
140 ⬍ 150, so 140 millimeters is shorter.
162 Intervention Lesson I36
Intervention Lesson I36
Math Diagnosis and
Intervention System
Intervention Lesson
Area of Parallelograms
Math Diagnosis and
Intervention System
Intervention Lesson
Name
I49
Teacher Notes
I49
Area of Parallelograms
Materials grid paper, colored pencils or markers, scissors
Ongoing Assessment
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
Ask: 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.
out the parallelogram.
HEIGHT
SCALE
BASE
METER
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.
Error Intervention
If students do not know the properties of
parallelograms,
SCALE
METER
then use I7: Quadrilaterals.
a rectangle
4. What shape did you create?
© Pearson Education, Inc.
5. Is the area of the parallelogram the same as the area of the rectangle?
10
6. What is the area of the rectangle? A ⫽ ᐉ ⫻ w ⫽
7. What is the base b of the parallelogram?
8. What is the height h of the parallelogram?
10
4
⫻4⫽
40
sq meters
meters
meters
40
9. What is the base times the height of the parallelogram?
10. Is this the same as the area of the rectangle?
yes
yes
Intervention Lesson I49
187
Math Diagnosis and
Intervention System
Intervention Lesson
Name
Give 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.
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.
b
⫻
h
A⫽ (
9
)⫻(
6
)⫽
54
square feet
Find the area of each figure.
12.
13.
14.
FT
HM
M
M
FT
HM
2
80 hm2
300 m
15.
IN
IN
16.
50 ft2
17.
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 Time
I49
Area of Parallelograms (continued)
A⫽
If students are having trouble remembering the
formula for the area of a parallelogram,
M
IN
IN
M
IN
7.5 in.2
18.
77 in.2
19.
27.9 m2
20.
M
HFT
MM
M
84 ft2
45 m2
21. Reasoning The area of a parallelogram is
100 square millimeters. The base is 4 millimeters.
Find the height.
188 Intervention Lesson I49
Intervention Lesson I49
25 mm
© Pearson Education, Inc.
BFT
90 mm2
© Pearson Education, Inc. 4
MM
Name
Practice
F19
Adding Integers
Add. 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.
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
© Pearson Education, Inc. 4
12. 6 (2)
Practice F19
Name
Practice
F33
Graphing Points in the
Coordinate Plane
y
Write the ordered pair for each point.
+10
1. A
+8
L
2. B
X
3. C
B
-8
4. D
H
-6
-4
-2
J
D
5. E
A
+4
+2
E
-10
F
+6
G
0
-2
+2
C
-4
+4
+6
+8 +10
x
Y
I
-6
K
6. F
-8
-10
Name the point for each ordered pair.
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
© Pearson Education, Inc. 4
15. Explain how to graph the ordered pair (2, 3).
Practice F33
Name
Practice
F34
Graphing Equations in the
Coordinate Plane
Complete each table of ordered pairs. Then graph the equation.
8. y ⫽ x ⫹ 1
9. y ⫽ 3x
y
y
x
y
⫺3
1
⫺4
⫺2
10. y ⫽ ⫺2x
4
⫺4
⫺2
1
⫺4
⫺2
x
0
⫺2
⫺4
⫺4
4
2
4
y
x
y
4
⫺1
x
0
2
11. y ⫽ 3 ⫺ x
2
0
2
⫺2
4
⫺1
1
2
y
y
4
0
x
0
y
⫺1
2
0
x
x
4
2
4
2
0
2
⫺4
⫺2
x
0
⫺2
⫺2
⫺4
⫺4
12. Is the point (3, 1) on the graph of y ⫽ 4 ⫺ x ? Explain.
© Pearson Education, Inc. 4
13. Is the point (3, ⫺9) on the graph of y ⫽ 3x? Explain.
Practice F34
Name
Practice
F40
Using the Distributive
Property
1. Use the array above to fill in the blanks.
4 ⫻ 16 ⫽ 4 ⫻ (
⫹ 6) ⫽ (4 ⫻
⫽
) ⫹ (4 ⫻
)
⫹
⫽
Fill in the blanks using the Distributive Property.
2. 3 ⫻ 8 ⫽ 3 ⫻ (4 ⫹
3. 2 ⫻ 16 ⫽ 2 ⫻ (
4. 2 ⫻ 25 ⫽
5. 15 ⫻ 8 ⫽ (10 ⫹
) ⫽ (3 ⫻ 4) ⫹ (3 ⫻
⫹ 6) ⫽ (2 ⫻
⫻ (20 ⫹
)⫹(
)⫽(
)⫹(
)⫽
7. 13 ⫻ 107 ⫽ (13 ⫻ 100) ⫹ (13 ⫻
8. 25 ⫻ 205 ⫽ (
9. 9 ⫻ 96 ⫽
10. 8 ⫻ 48 ⫽
⫻ (100 ⫺ 4) ⫽ (
⫻ 8)
)
⫻ (100 ⫹
) ⫽ 25 ⫻ (
⫻ 100) ⫺ (
)⫽(
)
⫻
⫻ (50 ⫹
)⫽
⫻ 200) ⫹ (25 ⫻
⫻ (50 ⫺
⫻ 6)
⫻ 20) ⫹ (
) ⫻ 8 ⫽ (10 ⫻
6. 10 ⫻ 57 ⫽ (10 ⫻ 50) ⫹ (10 ⫻
)
⫻ 50) ⫺ (
)
⫹
)
⫻ 4)
⫻
)
© Pearson Education, Inc. 4
11. Describe two different ways to find 6 ⫻ 38 with mental math.
Practice F40
Name
Practice
F43
More Variables and
Expressions
For 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 ) 15
5
15
9. (5x) (__
x)
6. 25 (2x)
25
10. 25 (__
x)
7. (4x) 2
8. (4x) 16
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?
B 3 4
C 3 (4)
D 3 4
© Pearson Education, Inc. 4
A 34
Practice F43
Name
Practice
Divisibility by 2, 3, 5, 9, and 10
G60
Test each number to see if it is divisible by 2, 3, 5, 9, or 10. List
the numbers each is divisible by.
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.
© Pearson Education, Inc. 4
15. Are all numbers that are divisible by 9 also divisible by 3?
Explain your reasoning.
Practice G60
Name
Practice
G63
Prime Factorization
Find 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
© Pearson Education, Inc. 4
15. What is a factor tree, and how do you know when a factor tree
is completed?
Practice G63
Name
Practice
Least Common Multiple
G65
Find 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
16. Why is 35 the LCM of 7 and 5?
Practice G65
© Pearson Education, Inc. 4
D about $70
Name
Practice
G73
Dividing by Multiples of 10
Divide. Use mental math.
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 ⫽
© Pearson Education, Inc. 4
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?
30. Reasoning Write another division problem with the same answer
as 3,600 ⫼ 90.
Practice G73
Name
Practice
G75
Dividing by Two-Digit Divisors
Complete.
R7
1. 98
565
–4
7
R3
2. 60 577
–5
3
R
4. 37
229
–2
R
3. 28
198
–1
R
5. 47
381
–3
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?
R
6. 52
474
–4
8. Isaiah changes both his bike tires
every 4 months. How many tires will
he have changed after 2 years?
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
© Pearson Education, Inc. 4
10. Explain why 0.5 and 0.05 are NOT equivalent.
Practice G75
Name
Practice
H19
Comparing and Ordering
Fractions and Mixed Numbers
Write ⬎, ⬍, or ⫽ for each
.
3
1. __
4
__
9
2. ___
6
4. __
6
__
4
5. __
2
__
1
6. ___
4
7. __
5
__
6
8. __
2
__
2
9. __
5
5
7
10
8
5
9
6
9
7
___
2
3. __
10
2
__
9
3
9
1
___
10
12
2
__
5
3
8
Order the numbers from least to greatest.
3
4 , __
4 , __
10. __
6 8 4
10
1 , __
1 , ___
11. __
4 8 11
3 , __
3 , __
2
12. __
7 4 4
1 is less than ___
4?
13. How do you know that __
5
10
14. A mechanic uses four wrenches to fix Mrs. Aaron’s car.
5
7
in., _12 in., _14 in., and __
in.
The wrenches are different sizes: __
16
16
Order the sizes of the wrenches from greatest to least.
15. Which is greater than _13 ?
1
A __
6
1
B __
5
1
C __
4
1
D __
2
© Pearson Education, Inc. 4
3
2
16. Compare __
and __
. Which is greater?
22
33
How do you know?
Practice H19
Name
Practice
H24
Place Value Through
Thousandths
Write 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
10. Which is the word form of the underlined digit in 46.504?
A 5 ones
Practice H24
B 5 tenths
C 5 hundredths
D 5 thousandths
© Pearson Education, Inc. 4
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.
Name
Practice
Decimals to Fractions
H31
Write 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.
© Pearson Education, Inc. 4
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.
Practice H31
Name
Practice
Estimating Sums and
Differences of Mixed Numbers
H42
Estimate the sum first. Then add. Simplify if necessary.
5
2 8__
1. 7__
2.
3 2__
2
4__
9 3___
1
3. 11___
4.
6 5__
2
7__
8 3__
1
5. 5__
6.
11 17__
2
21___
3
6
10
9
20
2
5
4
7
7
12
3
7. Which is a good comparison of the estimated
11
?
sum and the actual sum of 7_78 2__
12
A Estimated actual
B Actual estimated
C Actual estimated
D Estimated actual
Estimate the difference first. Then subtract. Simplify if necessary.
3
10__
4
7
8
2___
1
7__
4
10.
3
7__
9.
21
3
7
17__
11.
8
3
12___
2
2__
3
12
5 6__
5
12. 9__
6
3 2__
2
13. 4__
1 3__
1
14. 6__
1 3__
7
15. 5__
2 7__
1
16. 8__
9 2__
1
17. 2___
9
4
7
3
3
Practice H42
4
5
10
3
8
3
© Pearson Education, Inc. 4
8.
Name
Practice
H46
Multiplying Two Fractions
Write the multiplication problem that each model represents.
Then solve. Put your answer in simplest form.
1.
2.
Find each product. Simplify if necessary.
4
7
__
3. __
5 8
3
2
__
4. __
7 3 1
2 5. __
__
6
5
2
1
__
6. __
7
4
2
1
__
7. __
9 2 3
1
__
8. __
4 3 4
3
__
9. __
9 8
1
5
__
10. __
5 6
5
2
__
11. __
3 6 1
1
1
__
__
12. __
3
4 2
4 ___
7 13. __
5 ___
27 14. __
7
16
9
30
15. If _45 _25 , 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 _67 _45 desks occupied?
17. Which does the model represent?
© Pearson Education, Inc. 4
A _38 _35
B _35 _58
C
_7 _2 D
5
8
_4 _3
8
5
18. Describe a model that represents _33 _44
Practice H46
Name
Practice
I17
Measuring and
Classifying Angles
Classify each angle as acute, right, obtuse, or straight. Then
measure each angle. (Hint: Draw longer sides if necessary.)
1.
2.
Use a protractor to draw an angle with each measure.
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?
A Acute
B Obtuse
C Right
D Straight
Practice I17
© Pearson Education, Inc. 4
6. Which kind of angle is shown in the figure below?
Name
Practice
I20
Constructions
1. Construct a line segment that
___ is
congruent to line segment XY.
X
2. Construct an angle that is
congruent to angle Q.
Y
Q
3. Construct
a line that is parallel to
‹___›
line RS .
S
M
N
© Pearson Education, Inc. 4
R
4. Construct a line that is
‹____›
perpendicular to line MN .
Practice I20
Name
Practice
I33
Converting Customary Units
of Length
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)
Find each missing number.
ft
1. 2 yd 4. 31,680 ft 2. 72 in. mi
ft
5. 8 mi 7. 60 in. ft
8. 6 yd 10. 10 yd ft
11. 3 mi 13. 24 ft yd
14. 5 yd 3. 2 mi yd
6. 5 yd in.
yd
in.
ft
ft
9. 4 mi ft
12. 3 ft in.
15. 2 yd in.
For Exercises 16 to 20 use the information in the table.
16. How many inches did Paul toss the bean bag?
Bean Bag Toss Results
inches
17. How many inches did Terence toss the bean bag?
inches
18. How many inches did Carlos toss the bean bag?
Boy
Distance
Sam
18 inches
Paul
2 feet
Terence
3 yards
Carlos
6 feet
19. Which boy tossed the bean bag the greatest distance?
20. Which boy tossed the bean bag the least distance?
Practice I33
© Pearson Education, Inc. 4
inches
Name
Practice
I36
Converting Metric Units
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
kilometer
hectometer dekameter
(km)
kiloliter
hectoliter
⫻ 10
⫼ 10
meter
(m)
decimeter
liter
(L)
deciliter
dekaliter
kilogram
hectogram dekagram
(kg)
⫻ 10
⫼ 10
gram
(g)
⫻ 10
⫼ 10
centimeter millimeter
(cm)
(mm)
decigram centigram
⫻ 10
milliliter
(mL)
centiliter
⫻ 10
milligram
(mg)
⫻ 10
Tell the direction and number of jumps in the table for each
conversion. Then convert.
1. 636 cm to meters
2. 24.8 kg to g
3. 10.55 L to mL
jumps
jumps
jumps
g
m
4. 202 kg to g
mL
5. 55 km to m
6. 100 ml to L
jumps
jumps
jumps
m
g
L
Write the missing numbers.
7. 150 mg =
10. 300 mL =
g
L 11. 4 kg =
13. 2,670 mg =
© Pearson Education, Inc. 4
8. 2,600 m =
g14. 34 cm =
16. 5.75 kg =
g
17. 8 mL =
19. 1,200 mm =
km 20. 263 cm =
km 9. 0.4 L =
mg
mL
12. 2.6 m =
mm
mm 15. 16 L =
L
mL
18. 300.6 m =
km 21. 6 g =
km
mg
Practice I36
Name
Practice
I49
Area of Parallelograms
Find the area of each parallelogram. A bh
1.
2.
3 cm
2 mi
9 mi
5 cm
3.
4.
1 mm
1.5 m
6m
2 mm
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
A 44 m2
B 55.5 m
h?
D 5.5 m
b8m
Practice I49
© Pearson Education, Inc. 4
C 5m
Answers for Practice
F19, F33, F34, F40
Name
Name
Practice
F19
Adding Integers
Practice
F33
Graphing Points in the
Coordinate Plane
Add. Use a number line.
y
Write the ordered pair for each point.
(3, 4)
B (ⴚ2, 3)
C (2, ⴚ3)
D (ⴚ5, ⴚ4)
E (ⴚ7, 1)
F (8, 6)
+10
1. A
10 9 8 7 6 5 4 3 2 1 0
4
ⴚ2
2
9 (7) 1
1. 1 3 2. 4 (7) 4. 3 1 5. 6 (6) 7.
8. 6 12 2
3
4
ⴚ3
0
6
5
6
7
8
9 10
2.
ⴚ6
ⴚ5
3 (8) ⴚ11
3. 4 (2) 3.
6. 1 (4) 9.
4.
5.
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.
6.
18 ⴙ (ⴚ3) ⴝ 15
15 points
7. (5, 0)
10. (6, 5)
B 3
C 3
D 13
12. 6 (2)
13. 1 (4)
14. 3 (4)
15. 8 8
16. 9 (5)
17. 2 (5)
18. 9 (3)
19. 1 6
ⴚ1
ⴚ7
ⴚ6
0
21. 8 (9)
22. 8 (2)
23. 10 (3)
24. 3 (2)
25. 6 7
26. 1 (1)
27. 7 2
0
© Pearson Education, Inc. 4
1
ⴚ1
ⴚ10
1
0
-4
0
-2
-2
J
D
+2
+4
+6
+8 +10
I
-6
-8
-10
J
K
8. (1, 1)
9. (0, 7)
12. (5, 5)
L
G
(ⴚ5, 6)
C 3
B 3
D 6
15. Explain how to graph the ordered pair (2, 3).
Go left on the x-axis 2 units. Next, go
up 3 units.
7
ⴚ5
F19
6/30/08 12:02:48 PM
Name
Practice F33
F33
45096_Practice_F19-I49.indd F33
6/30/08 12:02:50 PM
Name
Practice
F34
Graphing Equations in the
Coordinate Plane
x
Y
C
-4
K
11. (4, 8)
A 6
Practice F19
45096_Practice_F19-I49.indd F19
H
-6
14. Use the coordinate graph above. Which is the y-coordinate
for point X?
5
20. 5 (5)
H
I
+2
E
-8
A
+4
B
© Pearson Education, Inc. 4
4
ⴚ5
X
-10
F
+6
G
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?
Add.
ⴚ8
L
Name the point for each ordered pair.
11. Which is the sum of 8 5?
A 13
+8
Practice
F40
Using the Distributive
Property
Complete each table of ordered pairs. Then graph the equation.
8. y x 1
9. y 3x
y
y
x
3
0
1
y
ⴚ2
1
2
x
4
1
2
4
2
0
x
0
2
1
4
2
y
ⴚ3
0
3
4
1. Use the array above to fill in the blanks.
2
4
2
x
0
2
4 16 4 (
4
10
2
4
4
6) (4 40
64
10 ) (4 6
24
)
Fill in the blanks using the Distributive Property.
10. y 2x
x
1
0
1
2
0
ⴚ2
1
2
2
x
0
2. 3 8 3 (4 y
x
4
4
4 ) (3 4) (3 4 )
10 6) (2 10 ) ( 2 6)
4. 2 25 2 (20 5 ) ( 2 20) ( 2 5
5. 15 8 (10 5 ) 8 (10 8 ) ( 5 8)
7 ) 10 (50 7 )
6. 10 57 (10 50) (10 7. 13 107 (13 100) (13 7 ) 13 (100 7 )
5
8. 25 205 ( 25 200) (25 5 ) 25 ( 200 9. 9 96 9 (100 4) ( 9 100) ( 9 4)
10. 8 48 8
(50 2 ) ( 8
50) ( 8
2
11. y 3 x
y
y
2
4
2
0
2
3. 2 16 2 (
y
4
3
1
4
4
2
4
2
x
0
2
4
2
4
12. Is the point (3, 1) on the graph of y 4 x ? Explain.
Yes. Answers will vary.
)
)
)
11. Describe two different ways to find 6 38 with mental math.
No. Answers will vary.
© Pearson Education, Inc. 4
© Pearson Education, Inc. 4
© Pearson Education, Inc. 4
(6 ⴛ 30) ⴙ (6 ⴛ 8) and (6 ⴛ 40) ⴚ (6 ⴛ 2)
13. Is the point (3, 9) on the graph of y 3x? Explain.
Practice F34
45096_Practice_F19-I49.indd F34
F34
6/30/08 12:02:52 PM
Practice F40
45096_Practice_F19-I49.indd F40
F40
6/30/08 12:02:54 PM
Answers: F19, F33, F34, F40
Answers for Practice
F43, G60, G63, G65
Name
Name
Practice
F43
More Variables and
Expressions
5
2. 5 x
Test each number to see if it is divisible by 2, 3, 5, 9, or 10. List
the numbers each is divisible by.
1. 81
3. x (7)
13
16
1
5
16
15
9. (5x) (__
x)
22
6. 25 (2x)
15
8. (4x) 16
4
22
11. (10 x) 3
30
5
12. (5x) x 10
20
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
ⴚ6
ⴚ1
8. 9,332
3, 9
11. 5,162
2, 5, 10
9. 3,660
2
2, 3, 5, 10
12. 516
2
2, 3
10
Answers will vary.
225 is not divisible by 10.
5
ⴚ11
5
2, 3
6. 550
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.
ⴚ27
0
ⴚ20
7. 2,105
3, 5
For questions 13–20, evaluate each expression for a 2,
b 1, and c 8.
ⴚ22
5. 99
10. 8,265
3. 102
3, 9
4. 270
2, 3, 5, 9, 10
7. (4x) 2
25
10. 25 (__
x)
2. 63
3, 9
4. 8 x
For questions 5–12, evaluate each expression for x 5.
5. (__x ) 15
G60
Divisibility by 2, 3, 5, 9, and 10
For questions 1– 4, evaluate each expression for x 8.
1. x 3
Practice
14. Are all numbers that are divisible by 2 also divisible by 4?
Explain your reasoning.
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.
No. Answers will vary.
65° ⴙ 7° ⴝ 72°
15. Are all numbers that are divisible by 9 also divisible by 3?
Explain your reasoning.
22. Which expression names the location of a turtle that started
3 feet under water and climbed up 4 feet onto a log?
C 3 (4)
Yes, because 9 is divisible by 3.
D 3 4
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B 3 4
© Pearson Education, Inc. 4
A 34
Practice F43
F43
6/30/08 12:02:56 PM
Name
Name
Practice
G63
Prime Factorization
5. 42
7 ⴛ 3 ⴛ 2 6. 9
9. 37
37 ⴛ 1
3ⴛ3
43 ⴛ 1
7. 50 2 ⴛ 5 ⴛ 5
10. 125 5 ⴛ 5 ⴛ 5 11. 29
29 ⴛ 1
13. In the space to the right, create a
factor tree for the number 64.
Find the LCM of each pair of numbers.
4. 35
7ⴛ5
8. 61
61 ⴛ 1
12. 49
1. 3 and 6
3. 8 and 12
5. 4 and 6
7. 5 and 8
7ⴛ7
9. 6 and 7
11. 5 and 20
64
8
8
C March 18
4. 2 and 5
6. 3 and 4
8. 2 and 9
10. 4 and 7
12. 6 and 12
70
10
12
18
28
12
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?
D March 24
30 ounces
15. What is a factor tree, and how do you know when a factor tree
is completed?
Sample: A diagram that shows how to
break a number into its prime factors.
It is finished when all the factors
shown are prime numbers.
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
© Pearson Education, Inc. 4
16. Why is 35 the LCM of 7 and 5?
There exists no smaller number
containing 7 and 5 both as factors
Practice G63
45096_Practice_F19-I49.indd G63
2. 7 and 10
18 pens
14. Field Day is in March on a day that is a prime number.
Which date could it be?
B March 11
6
24
12
40
42
20
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?
2ⴛ4
ⴛ 2ⴛ4
2ⴛ2ⴛ2ⴛ2ⴛ2ⴛ2
A March 4
G65
G63
Answers: F43, G60, G63, G65
6/30/08 12:02:59 PM
Practice G65
45096_Practice_F19-I49.indd G65
G65
6/30/08 12:03:01 PM
© Pearson Education, Inc. 4
3 ⴛ 2 ⴛ 5 2. 16 2 ⴛ 2 ⴛ 2ⴛ 2 3. 43
6/30/08 12:02:58 PM
Practice
Least Common Multiple
Find the prime factorization of each number. If a number is prime,
circle it.
1. 30
G60
45096_Practice_F19-I49.indd G60
© Pearson Education, Inc. 4
45096_Practice_F19-I49.indd F43
Practice G60
Answers for Practice
G73, G75, H19, H24
Name
Name
Practice
G73
Dividing by Multiples of 10
Complete.
3. 200 ⫼ 50 ⫽
4
9
6. 540 ⫼ 90 ⫽
6
8. 2,800 ⫼ 70 ⫽
40
9. 1,800 ⫼ 30 ⫽
11. 1,500 ⫼ 50 ⫽
30
12. 800 ⫼ 20 ⫽
40
14. 3,600 ⫼ 40 ⫽
90
15. 140 ⫼ 20 ⫽
7
10
2. 60 ⫼ 30 ⫽
4. 240 ⫼ 40 ⫽
6
5. 630 ⫼ 70 ⫽
7. 100 ⫼ 25 ⫽
4
4
16. 1,200 ⫼ 60 ⫽
19. 600 ⫼ 20 ⫽
20
80
17. 7,200 ⫼ 90 ⫽
30
20. 400 ⫼ 25 ⫽
16
21. 2,400 ⫼ 30 ⫽
80
30
23. 5,000 ⫼ 25 ⫽
200
24. 2,400 ⫼ 80 ⫽
25. 5,400 ⫼ 90 ⫽
60
26. 480 ⫼ 60 ⫽
8
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?
6 R 7
100 cartons
A 12 extra
6/30/08 12:03:03 PM
Name
H19
Comparing and Ordering
Fractions and Mixed Numbers
5
4. _6_
7
>
_6_
5. _4_
<
_2_
1
6. ___
7. _4_
<
_5_
8. _6_
ⴝ
_2_
9. _2_
5
5
10
8
9
6
9
>
7
___
3. _2_
10
9
3
10
5
3
ⴝ
10
11. _1_, _1_, ___
12
_2_
12. _3_, _3_, _2_
7 4 4
4. 3.004
three and four thousandths
10
Write each number in standard form.
B _1_
C _1_
5
4
D _1_
8. Two and five hundred fifty-five thousandths
2
© Pearson Education, Inc. 4
How do you know?
3
__
. Sample answer: The denominator
22
3
for __
is smaller than the denomina-
six and twenty-nine hundredths, nine hundredths
10. Which is the word form of the underlined digit in 46.504?
22
3
2
tor for __
, so each of the 3 parts of __
is
33
22
2
__
larger than the 2 parts of 33.
A 5 ones
Practice H19
H19
2.555
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.
3
2
16. Compare __
and __
. Which is greater?
22
33
© Pearson Education, Inc. 4
3.004
7.533
6. 3 ⫹ 0.0 ⫹ 0.00 ⫹ 0.004
7. 7 ⫹ 0.5 ⫹ 0.03 ⫹ 0.003
15. Which is greater than _13?
0.0 (zero tenths)
6.321
5. 6 ⫹ 0.3 ⫹ 0.02 ⫹ 0.001
5
7
_1 in., __
in., __
in., _14 in.
2
16
16
45096_Practice_F19-I49.indd H19
H24
0.001 (1 thousandth)
six and three hundred twenty-one thousandths
14. A mechanic uses four wrenches to fix Mrs. Aaron’s car.
5
7
in., _12 in., _14 in., and __
in.
The wrenches are different sizes: __
16
16
Order the sizes of the wrenches from greatest to least.
6
Practice
3. 6.321
4
4
__
ⴝ _25, and _15 < _25. So, _15 < __
10
10
A _1_
6/30/08 12:03:05 PM
2. 7.880
4?
13. How do you know that _1_ is less than ___
5
G75
45096_Practice_F19-I49.indd G75
0.8 (8 tenths)
seven and eighty-eight hundredths
(eight hundred eighty thousandths)
8
8 4 11
_3 , _2 , _3
7 4 4
4 8 11
Practice G75
1. 4.345
1
___
_4 , _4 , _3
8 6 4
10
_1 , _1 , __
6 8 4
D 0 extra
0.005 (5 thousandths)
four and three hundred forty-five thousandths
9
Order the numbers from least to greatest.
10. _4_, _4_, _3_
C 3 extra
Write the word form for each number and tell the value of the
underlined digit.
_2_
>
>
B 8 extra
Place Value Through
Thousandths
.
9
2. ___
12 tires
Name
Practice
_4_
6
8. Isaiah changes both his bike tires
every 4 months. How many tires will
he have changed after 2 years?
5
5
1
0.5 ⴝ __
ⴝ _12 and 0.05 ⴝ ___
ⴝ __
10
100
20
1
_1 > __
2
20
G73
<
5
10. Explain why 0.5 and 0.05 are NOT equivalent.
Practice G73
1. _3_
7
9 R 6
6. 52
474
– 4 68
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?
Answers will vary.
Write ⬎, ⬍, or ⫽ for each
5. 47
381
– 3 76
There are 15 runners in
5 lanes and 14 runners
in one lane.
5
30. Reasoning Write another division problem with the same answer
as 3,600 ⫼ 90.
45096_Practice_F19-I49.indd G73
2
8 R 5
4. 37
229
– 2 22
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?
29. Carlos must put toys into cartons
that hold 40 each. How many
cartons will he need to store
4,000 toys?
10 times
© Pearson Education, Inc. 4
9
50
3. 28
198
– 1 96
60
18. 540 ⫼ 60 ⫽
22. 1,500 ⫼ 30 ⫽
7 R 2
2. 60 577
– 5 40
37
6/30/08 12:03:07 PM
B 5 tenths
C 5 hundredths
D 5 thousandths
© Pearson Education, Inc. 4
40
9 R3 7
5 R7 5
1. 98
565
– 4 90
75
© Pearson Education, Inc. 4
2
1. 400 ⫼ 40 ⫽
13. 320 ⫼ 80 ⫽
G75
Dividing by Two-Digit Divisors
Divide. Use mental math.
10. 3,600 ⫼ 90 ⫽
Practice
Practice H24
45096_Practice_F19-I49.indd H24
H24
6/30/08 12:03:08 PM
Answers: G73, G75, H19, H24
Answers for Practice
H31, H42, H46, I17
Name
Name
Practice
H31
Decimals to Fractions
Estimate the sum first. Then add. Simplify if necessary.
2.
1. 7_2_ 8_5_
3
16
___
.16
10
9 3___
1
3. 11___
10
100
6
__
9
7. .7
9. 7.2
11. 0.62
13. 0.9
15. 0.748
100
33
___
100
8. 0.33
9
3___
100
10. 3.09
16. 7.354
7
9; 9__
18
6.
11 17_2_
21___
10_3_
4; 3_12
9.
4
0; _13
11.
2_2_
4
3
9
6
4
3
16. 8_2_ 7_1_
7
Practice H31
H31
6/30/08 12:03:10 PM
Name
H46
Multiplying Two Fractions
3
9.
11.
13.
15.
7
9
7
__
4
3
2
4. _7_ _3_ 15. 5_1_ 3_7_
5
20
1; __
21
8
9 2_1_
17. 2___
10
3
1
2; 2__
12
13
1; 1__
40
17
1; __
30
H42
45096_Practice_F19-I49.indd H42
6/30/08 12:03:12 PM
Practice
I17
2.
2
_ 6. _7_ _1
4
3
1
8. _4_ _3_ 1
10. _5_ _5_ 6
_ _1_ _1_ 12. _1
3
4
2
27 14. _5_ ___
9
30
Right; 90°
_2
7
1
__
14
_1
4
_1
6
1
__
24
1
_
2
C
Acute; 22°
Use a protractor to draw an angle with each measure.
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?
Answers will vary.
C
A
_7 _2 D
5
8
B
6. Which kind of angle is shown in the figure below?
17. Which does the model represent?
_4 _3
8
5
18. Describe a model that represents _33 _44
A Acute
B Obtuse
C Right
D Straight
Sample answer: It would
equal one.
Practice H46
45096_Practice_F19-I49.indd H46
3
28
24
__
; 24 students
35
© Pearson Education, Inc. 4
4
11
3; 2__
12
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 _67 _45 desks occupied?
B _35 _58
13. 4_3_ 2_2_
5
_5 ⴛ _1 ⴝ __
10
1
__
_1_ _2_ 15
6
5
1
_
_2_
_1_
9
9 2 _1
_3_ _4_ 6
9
8
_5
_2_
_5_
9
3
6
1
_
7 _4_ ___
4
7
16
_1
If _45 _25 , what is ? 2
A _38 _35
6; 5_58
Practice H42
Find each product. Simplify if necessary.
7.
8
12
1.
5.
17_7_
3
12___
Classify each angle as acute, right, obtuse, or straight. Then
measure each angle. (Hint: Draw longer sides if necessary.)
2.
_ _4_ 3. _7
5
8
1
5; 5__
21
7
21
Measuring and
Classifying Angles
Write the multiplication problem that each model represents.
Then solve. Put your answer in simplest form.
10
7_3_
Name
Practice
6
7
40; 39__
12
3
8
2___
13
3; 2__
18
14. 6_1_ 3_1_
D Since there are 63 hundredths, place 63 over 100.
3
12
B Actual estimated
12. 9_5_ 6_5_
C Since there are 63 tenths, place 63 over 10.
2 ⴝ_
1
_2 ⴛ _1 ⴝ __
7
D Estimated actual
3
B Since there are 63 tenths, divide 0.63 by 10.
© Pearson Education, Inc. 4
13; 13_17
7
A Estimated actual
10.
A Since there are 63 hundredths, multiply 0.63 and 100.
1.
7_6_ 5_2_
2
7_1_
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?
45096_Practice_F19-I49.indd H31
4.
C Actual estimated
8.
89
8___
100
354
7____
1000
14. 8.89
19
15; 14__
20
Estimate the difference first. Then subtract. Simplify if necessary.
2
6__
10
12. 6.2
3
7; 7__
20
5
4
7. Which is a good comparison of the estimated
11
?
sum and the actual sum of 7_78 2__
12
57
8___
100
6. 8.57
4_3_ 2_2_
H46
Answers: H31, H42, H46, I17
6/30/08 12:03:14 PM
Practice I17
45096_Practice_F19-I49.indd I17
I17
6/30/08 12:03:16 PM
© Pearson Education, Inc. 4
5. 6.9
73
___
4. 0.73
2.
© Pearson Education, Inc. 4
10
9
6__
10
7
__
10
2
7__
10
62
___
100
9
__
10
748
____
1000
20
17; 16_12
5. 5_8_ 3_1_
Write each decimal as either a fraction or a mixed number.
3. 0.6
6
© Pearson Education, Inc. 4
7
__
.7
H42
Estimating Sums and
Differences of Mixed Numbers
Write a decimal and fraction for the shaded portion of each model.
1.
Practice
Answers for Practice
I20, I33, I36, I49
Name
Name
Practice
I20
Constructions
I33
Converting Customary Units
of Length
2. Construct an angle that is
congruent to angle Q.
1. Construct a line segment that
___ is
congruent to line segment XY.
X
Practice
Customary Units
of Length
1 foot (ft) 12 inches (in.)
Y
1 yard (yd) 36 (in.)
Q
1 yard (yd) 3 feet (ft)
1 mile (mi) 5,280 feet (ft)
1 mile (mi) 1,760 yards (yd)
Find each missing number.
Check students’ work.
6
1. 2 yd 4. 31,680 ft 5
30
8
7. 60 in. 4. Construct a line that is
‹____›
perpendicular to line MN .
3. Construct
a line that is parallel to
‹___›
line RS .
ft
6
10. 10 yd 13. 24 ft 10,560 ft
6 ft
14,080
5. 8 mi yd
8. 6 yd 216 in.
2. 72 in. mi
ft
3. 2 mi 15 ft
9. 4 mi 21,120 ft
6. 5 yd ft
11. 3 mi 5,280 yd
12. 3 ft yd
14. 5 yd 180 in.
15. 2 yd 36
72
in.
in.
For Exercises 16 to 20 use the information in the table.
24
Bean Bag Toss Results
Boy
inches
17. How many inches did Terence toss the bean bag?
108
M
S
N
18. How many inches did Carlos toss the bean bag?
© Pearson Education, Inc. 4
72
2 feet
Terence
3 yards
Carlos
6 feet
inches
20. Which boy tossed the bean bag the least distance?
I20
45096_Practice_F19-I49.indd I20
7/2/08 1:30:31 PM
Name
I36
10
10
10
kiloliter
hectoliter
liter
(L)
dekaliter
kilogram
hectogram dekagram
(kg)
10
10
10
meter
(m)
gram
(g)
10
2
jumps
6.36
Left
m
4. 202 kg to g
3 jumps
202,000
3 jumps Right
24,800 g
5. 55 km to m
R
g
3 jumps
55,000
3.
1.5 m
6m
2 mm
milligram
(mg)
A ⴝ 2 mm2
A ⴝ 9 m2
10
Find the missing measurement for the parallelogram.
3. 10.55 L to mL
3
jumps
10,550
5. A 34 in2, b 17 in., h 3
6. List three sets of base and height measurements for
parallelograms with areas of 40 square units.
mL
8, 5; 4,10; 2, 20
L
jumps
0.1
m
2 in.
Right
L
7. Which is the height of the parallelogram?
Write the missing numbers.
0.150 g 8. 2,600 m = 2.6 km 9. 0.4 L = 400 mL
10. 300 mL = 0.3 L 11. 4 kg = 4,000,000 mg 12. 2.6 m = 2,600 mm
13. 2,670 mg = 2.670 g14. 34 cm = 340 mm 15. 16 L = 16,000 mL
A 55 m
7. 150 mg =
5,750 g 17. 8 mL = 0.008 L
19. 1,200 mm =0.0012 km 20. 263 cm = 0.00263 km
16. 5.75 kg =
C 5m
18. 300.6 m = 0.3006km
21. 6 g =
I36
A 44 m2
B 55.5 m
h?
D 5.5 m
b8m
6,000 mg
Practice I36
45096_Practice_F19-I49.indd I36
A ⴝ 18 mi2
4.
1 mm
6. 100 ml to L
R
2 mi
9 mi
5 cm
milliliter
(mL)
centiliter
decigram centigram
2. 24.8 kg to g
2.
A ⴝ 15 cm2
Tell the direction and number of jumps in the table for each
conversion. Then convert.
1. 636 cm to meters
I49
3 cm
10
10
6/30/08 12:03:20 PM
Practice
1.
centimeter millimeter
decimeter
(cm)
(mm)
10
I33
45096_Practice_F19-I49.indd I33
Find the area of each parallelogram. A bh
10
deciliter
Practice I33
Area of Parallelograms
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.
kilometer
hectometer dekameter
(km)
Terence
Sam
Name
Practice
Converting Metric Units
© Pearson Education, Inc. 4
Paul
19. Which boy tossed the bean bag the greatest distance?
Practice I20
© Pearson Education, Inc. 4
18 inches
6/30/08 12:03:22 PM
© Pearson Education, Inc. 4
R
inches
Distance
Sam
© Pearson Education, Inc. 4
16. How many inches did Paul toss the bean bag?
Check students’ work.
Practice I49
45096_Practice_F19-I49.indd I49
I49
6/30/08 12:03:24 PM
Answers: I20, I33, I36, I49
Grade 4
Name
1.
Step Up to Grade 5 Test
Add. 8 ⫹ (–4)
3.
A –12
Using the Distributive Property,
15 ⫻ 99 ⫽
A (10 ⫻ 90) ⫹ (10 ⫻ 9) ⫹
(5 ⫻ 90) ⫹ (5 ⫻ 9)
B 8
C 4
B (10 ⫻ 90) ⫹ (5 ⫻ 90) ⫹ (5 ⫻ 9)
D –4
C (10 ⫻ 90) ⫹ (15 ⫻ 9) ⫹ (15⫻ 90)
D (15 ⫻ 90) ⫹ (5 ⫻ 90) ⫹ (5 ⫻ 9)
2.
4.
What is the ordered pair for point C?
A 36
y
+10
B 26
+8
-8
A
+4
D 6
+2
E
-10
C 18
F
+6
B
Evaluate 4b ⫺ 6, when b ⫽ 8.
-6
D
-4
-2
0
-2
-4
-6
A (2, 2)
+2
C
+4
+6
+8 +10
x
5.
Which ordered pair is on the graph of
y ⫽ x ⫹ 3?
A (4, 1)
-8
B (2, 5)
-10
C (3, 0)
D (8, 5)
B (–2, 2)
C (–2, –2)
© Pearson Education, Inc. 4
D (2, –3)
T1
Grade 4
Name
6.
7.
8.
By what numbers is 2,480 divisible?
Step Up to Grade 5 Test
9.
Divide. 560 ÷ 80
A 2, 5, 8,10
A 6
B 2, 3, 8,10
B 7
C 2, 3, 7,10
C 60
D 2, 5, 7,10
D 70
What is the prime factorization of 18?
10. 28
342
A 2⫻9
A 6 R 12
B 2⫻8
B 12 R 6
C 2⫻3⫻3
C 126
D 2⫻2⫻2⫻2
D 612
What is the LCM of 6 and 12?
A 2
B 3
11. Which is the greatest fraction in this
group?
1 _
_
, 1, _3, _2
4 2 8 3
C 6
A _14
D 12
B _12
C _38
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D _23
T2
Grade 4
Name
12. What is the value of 2 in 4.289?
Step Up to Grade 5 Test
15. Classify this angle.
A 20
B 2
C 0.2
D 0.02
A straight
B right
C acute
D obtuse
13. Write 4.6 as a fraction.
46
A __
10
46
B ___
100
4.6
C ___
10
4.6
D ___
100
16. Multiply. Simplify if possible.
3
6
_
_
5 ⫻ 5
A _95
18
B __
5
9
C __
25
18
D __
25
14. Estimate the difference.
‹__›
4_58 ⴚ 1_28
A 2
‹___›
17. Describe RS and XY.
R
X
S
Y
B 3
C 4
D 5
A perpendicular
B parallel
C congruent
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D obtuse
T3
Grade 4
Name
Step Up to Grade 5 Test
18. Find the missing number.
48 in. ⫽
20. Find the area of this figure.
ft
5m
A 3
8m
B 4
A 40 m
C 5
B 40 sq m
D 6
C 20 m
D 20 sq m
19. 1 L ⫽
mL
A 10
B 100
C 1,000
© Pearson Education, Inc. 4
D 10,000
T4
Answers for Test
T1, T2, T3, T4
Grade 4
Name
1.
Add. 8 ⫹ (–4)
3.
A –12
6.
Using the Distributive Property,
15 ⫻ 99 ⫽
A (10 ⫻ 90) ⫹ (10 ⫻ 9) ⫹
(5 ⫻ 90) ⫹ (5 ⫻ 9)
B 8
C 4
B (10 ⫻ 90) ⫹ (5 ⫻ 90) ⫹ (5 ⫻ 9)
D –4
Grade 4
Name
Step Up to Grade 5 Test
C (10 ⫻ 90) ⫹ (15 ⫻ 9) ⫹ (15⫻ 90)
Step Up to Grade 5 Test
9.
By what numbers is 2,480 divisible?
Divide. 560 ÷ 80
A 2, 5, 8,10
A 6
B 2, 3, 8,10
B 7
C 2, 3, 7,10
C 60
D 2, 5, 7,10
D 70
D (15 ⫻ 90) ⫹ (5 ⫻ 90) ⫹ (5 ⫻ 9)
2.
4.
What is the ordered pair for point C?
y
+10
+8
F
+6
-8
What is the prime factorization of 18?
10. 28
342
A 2⫻9
A 6 R 12
B 26
B 2⫻8
B 12 R 6
C 18
C 2⫻3⫻3
C 126
D 6
D 2⫻2⫻2⫻2
D 612
+2
E
-10
A
+4
B
7.
Evaluate 4b ⫺ 6, when b ⫽ 8.
A 36
-6
D
-4
-2
0
-2
+2
+4
+6
+8 +10
x
5.
C
-4
Which ordered pair is on the graph of
y ⫽ x ⫹ 3?
8.
What is the LCM of 6 and 12?
A (4, 1)
A 2
-8
B (2, 5)
B 3
-10
C (3, 0)
C 6
D (8, 5)
D 12
-6
A (2, 2)
11. Which is the greatest fraction in this
group?
3 _
1 _
1 _
2
_
4, 2, 8, 3
A _14
B _12
B (–2, 2)
C _38
C (–2, –2)
D _23
© Pearson Education, Inc. 4
© Pearson Education, Inc. 4
D (2, –3)
T1
T1
45096_T1-T4.indd T1
7/1/08 2:13:00 PM
Grade 4
Name
12. What is the value of 2 in 4.289?
T2
T2
45096_T1-T4.indd T2
7/1/08 2:13:01 PM
Grade 4
Name
Step Up to Grade 5 Test
15. Classify this angle.
Step Up to Grade 5 Test
18. Find the missing number.
48 in. ⫽
A 20
B 2
20. Find the area of this figure.
ft
5m
A 3
C 0.2
8m
B 4
D 0.02
A 40 m
C 5
A straight
B 40 sq m
D 6
B right
C 20 m
C acute
D 20 sq m
19. 1 L ⫽
D obtuse
mL
A 10
13. Write 4.6 as a fraction.
16. Multiply. Simplify if possible.
46
A __
10
B 100
3
6
_
_
5 ⫻ 5
46
B ___
100
C 1,000
D 10,000
A _95
4.6
C ___
10
18
B __
5
4.6
D ___
100
9
C __
25
18
D __
25
14. Estimate the difference.
‹__›
‹___›
17. Describe RS and XY.
4_58 ⴚ 1_28
R
X
A 2
S
Y
B 3
A perpendicular
C 4
B parallel
D 5
C congruent
© Pearson Education, Inc. 4
© Pearson Education, Inc. 4
© Pearson Education, Inc. 4
D obtuse
T3
45096_T1-T4.indd T3
T3
T4
7/2/08 2:53:46 PM
45096_T1-T4.indd T4
T4
7/2/08 2:19:50 PM
Answers: T1, T2, T3, T4