Download 5th Grade CH 8 Targeted Strategic Intervention

EACH CHAPT ER INCLUDES:
• Prescriptive targeted strategic
intervention charts.
• Student activity pages aligned to the Common Core State Standards.
• Complete lesson plan pages with lesson
objectives, getting started activities,
teaching suggestions, and questions to
check student understanding.
Grade 5
Targeted Strategic Intervention
Grade 5, Chapter 8
Based on student performance on Am I Ready?, Check My Progress, and Review, use these charts
to select the strategic intervention lessons found in this packet to provide remediation.
Am I Ready?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
1-6
8-A: Identify Missing
Factors
Factors
7-11
8-B: Multiplication Facts
Through 8
8-C: Division Facts
Through 9
12-13
8-D: Points on a Number
Line
Where is this
concept in
My Math?
Prep for
5.NF.2
Grade 4,
Chapter 3,
Lesson 7
Multiplication and
division
5.NBT.5
Chapter 2,
Lesson 9;
Chapter 3,
Lesson 3
Graph decimals on
a number line
5.NBT.3
Chapter 1,
Lesson 7
Check My Progress 1
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
4-5
8-E: Identify the Shaded
Part
Interpret fractions
as division
5.NF.3
Chapter 8,
Lesson 1
6-7
8-F: Multiples, Factors,
and Greatest Common
Factor
Find the GCF
Prep for
5.NF.2
Chapter 8,
Lesson 2
8-10
8-G: Simplifying
Fractions
Write fractions in
simplest form
5.NF.5b
Chapter 8,
Lesson 3
Review
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
9-10
8-H: Factors, Common
Factors, and Greatest
Common Factor
GCF
Prep for
5.NF.2
Chapter 8,
Lesson 2
11-12
8-I: Use a Multiplication
Table to Divide
Simplest form of
fractions
5.NF.5b
Chapter 8,
Lesson 3
13-14
8-J: Multiples of a
Number
LCM
Prep for
5.NF.2
Chapter 8,
Lesson 5
15-17
8-K: Shade and Compare
Fractions
Compare fractions
5.NF.5b
Chapter 8,
Lesson 6
18-23
8-L: Identify Fractions
and Decimals
Write fractions as
decimals
5.NF.5b
Chapter 8,
Lesson 8
Name
Identify Missing Factors
Lesson
8-A
Use basic multiplication facts.
What Can I Do?
I want to find a
missing factor.
Write the missing factor.
2×
?
= 10
Think: 2 times what number is equal to 10?
Find the multiplication fact for 2 with a
product of 10.
2×1=2
2×2=4
2×3=6
2×4=8
2 × 5 = 10
So, 5 is the missing factor.
Write each product. Then write each missing factor.
1. 3 × 4 =
= 12
4×
= 20
Write each missing factor.
3. 2 ×
= 14
4. 5 ×
= 15
5. 4 ×
= 16
6. 3 ×
= 24
7. 6 ×
= 24
8. 4 ×
= 36
9. 7 ×
= 63
10. 5 ×
= 20
Copyright © The McGraw-Hill Companies, Inc.
3×
2. 4 × 5 =
Name
Identify Missing Factors
Lesson
8-A
Lesson Goal
• Use basic multiplication facts to
find a missing factor.
What the Student Needs to
Know
Use basic multiplication facts.
What Can I Do?
I want to find a
missing factor.
2×
?
= 10
Think: 2 times what number is equal to 10?
Find the multiplication fact for 2 with a
product of 10.
• Recall basic multiplication facts
from 1 to 9.
2×1=2
2×2=4
2×3=6
2×4=8
2 × 5 = 10
Getting Started
Remind students that they usually
multiply two factors to get a product.
Here they will have the product and
one of the factors and have to find
the other factor. Say:
• Let’s see how we can find a missing
factor. When I see 2 × __ = 6, and
I immediately recognize a missing
factor, that’s all there is to the
problem. If I don’t recognize it
immediately, there is a simple
method to use.
• I can set up a list of facts for 2. I write
out 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6.
Since 2 × 3 = 6, 3 is the missing
factor.
Write the missing factor.
So, 5 is the missing factor.
Write each product. Then write each missing factor.
2. 4 × 5 = 20
1. 3 × 4 = 12
3×
4
= 12
4×
5
= 20
Write each missing factor.
3. 2 ×
7
= 14
4. 5 ×
3
= 15
5. 4 ×
4
= 16
6. 3 ×
8
= 24
7. 6 ×
4
= 24
8. 4 ×
9
= 36
9. 7 ×
9
= 63
10. 5 ×
4
= 20
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-A
What Can I Do?
Read the question and the response.
Then discuss the example. Ask:
• What do we do if we don’t recognize
the missing factor in 2 × __ = 10?
(Make a list of facts for 2.)
• How far do you have to go to find
the factor? (2 × 5)
Try It
• Have students read each of the
exercises and use a list of facts,
if necessary, to find each of the
missing factors.
Power Practice
• Have students complete the
practice items. Then review each
answer.
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WHAT IF THE STUDENT NEEDS HELP TO
Recall Basic Multiplication
Facts from 1 to 9
Complete the Power
Practice
• Have the student use physical
counters to make groups of
objects.
• Have the student write out lists
of multiplication facts and keep
them in his or her math journal/
notebook to use as a reference.
• Discuss each incorrect answer.
Review how the student can
check his or her answers by
using counters or a list of
multiplication facts.
Name
Multiplication Facts Through 8
Lesson
8-B
Use equal groups.
Use doubling.
Find 6 × 5.
Find 8 × 8.
Draw 6 groups of
5 circles.
You can double a 4s
fact to find an 8s fact.
What Can I Do?
I want to
practice multiplication
facts through 8.
4 × 8 = 32
Double the product.
32 + 32 = 64
So, 8 × 8 = 64.
There are 30 circles in all.
So, 6 × 5 = 30.
Use equal groups or doubling to multiply.
1. 8 × 5 =
Multiply.
3. 8 × 2 =
4. 7 × 5 =
5. 6 × 8 =
6. 7 × 3 =
7. 7 × 7 =
8. 6 × 9 =
Copyright © The McGraw-Hill Companies, Inc.
2. 7 × 6 =
Name
Multiplication Facts Through 8
Lesson
8-B
Lesson Goal
• Use equal groups or doubling
to practice multiplication facts
through 8.
Use doubling.
Use equal groups.
Find 6 × 5.
Find 8 × 8.
Draw 6 groups of
5 circles.
You can double a 4s
fact to find an 8s fact.
What the Student Needs to
Know
What Can I Do?
I want to
practice multiplication
facts through 8.
4 × 8 = 32
Double the product.
• Recall basic addition and
multiplication facts.
Getting Started
• Ask students to draw and count a
group of 3 objects. Then ask:
• How can you find out how many
are in 6 groups of 3 objects? (Draw
5 more groups of 3 objects, then
count the total number.)
32 + 32 = 64
So, 8 × 8 = 64.
There are 30 circles in all.
So, 6 × 5 = 30.
Use equal groups or doubling to multiply.
2. 7 × 6 = 42
1. 8 × 5 = 40
What Can I Do?
Read the question and the response.
Then discuss the first example. Ask:
• In the first example, what would
you draw to show equal groups?
(6 groups of 5 circles)
• How many circles are there in all?
(30)
• What multiplication sentence shows
this? (6 × 5 = 30)
Read and discuss the second
example. Ask:
• What method are you going to use
to solve this? (doubling a 4s
multiplication fact)
• What multiplication sentence will
you use first? (4 × 8 = 32)
• How do you double the product?
(by adding 32 + 32)
Try It
• Have students read Exercise 1:
8 × 5 = ____. Ask whether to use
equal groups or doubling a 4s fact
to multiply. (doubling)
• Now, have students read and go
through the steps on the second
exercise.
Power Practice
• Have students complete the
practice items. Then review each
answer and method.
Multiply.
3. 8 × 2 = 16
4. 7 × 5 = 35
5. 6 × 8 = 48
6. 7 × 3 = 21
7. 7 × 7 = 49
8. 6 × 9 = 54
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-B
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WHAT IF THE STUDENT NEEDS HELP TO
Recall Basic Addition and
Multiplication Facts
Complete the Power
Practice
• Practice addition and
multiplication facts 10 to 15
minutes daily until the student
can recall the sums for the
addition facts and the products
for the multiplication facts with
ease.
• Discuss each incorrect answer.
• Have the student model any
fact he or she missed.
Name
Division Facts Through 9
Lesson
8-C
Use any division strategy to find 24 ÷ 6.
What Can I Do?
Use a related
multiplication fact.
Think: How many 6s
make 24?
I want to divide one
number by another
number.
4 × 6 = 24, so 24 ÷ 6 = 4
Use an array.
Use repeated
subtraction.
Subtract 6 four times.
24 - 6 = 18
18 - 6 = 12
12 - 6 = 6
6-6=0
So, 24 ÷ 6 = 4.
Make 6 equal groups
of 4. So, 24 ÷ 6 = 4.
Skip count backward on a number line.
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
So, 24 ÷ 6 = 4.
Use a related multiplication fact to find the quotient.
1.
× 7 = 28, so 28 ÷ 7 =
2.
× 6 = 30, so 30 ÷ 6 =
Copyright © The McGraw-Hill Companies, Inc.
Skip count backward by 6 four times.
Name
Lesson
Use an array to find each quotient.
3. 27 ÷ 3 =
8-C
4. 15 ÷ 3 =
Use repeated subtraction to find each quotient.
5. 9 ÷ 3 =
6. 30 ÷ 5 =
Subtract:
Subtract:
Skip count backward to find each quotient.
8. 42 ÷ 6 =
7. 45 ÷ 5 =
Count backward:
Count backward:
Copyright © The McGraw-Hill Companies, Inc.
Find each quotient. Use any strategy.
9. 8 ÷ 4 =
10. 20 ÷ 4 =
11. 48 ÷ 8 =
12. 35 ÷ 5 =
13. 36 ÷ 6 =
14. 40 ÷ 5 =
15. 28 ÷ 4 =
16. 12 ÷ 6 =
17. 49 ÷ 7 =
18. 8 64
19. 9 81
20. 7 21
21. 4 16
22. 4 24
23. 7 42
24. 8 32
25. 4 36
USING LESSON 8-C
Name
Division Facts Through 9
Lesson Goal
• Use any division strategy to divide
using basic facts through 9.
What the Student Needs to
Know
Lesson
8-C
Use any division strategy to find 24 ÷ 6.
What Can I Do?
Use a related
multiplication fact.
Think: How many 6s
make 24?
I want to divide one
number by another
number.
4 × 6 = 24, so 24 ÷ 6 = 4
• Use related multiplication facts.
• Use repeated subtraction.
• Skip count backward.
Use an array.
Use repeated
subtraction.
Subtract 6 four times.
24 - 6 = 18
18 - 6 = 12
12 - 6 = 6
6-6=0
So, 24 ÷ 6 = 4.
Getting Started
What Can I Do?
Read the question and the response.
Then discuss each example. Ask:
• Can you use a related multiplication
fact to find the answer to 24 ÷ 6?
(Yes.)
• Which fact do you know that will
help you solve this division?
(6 × 4 = 24 and 4 × 6 = 24)
Make 6 equal groups
of 4. So, 24 ÷ 6 = 4.
Skip count backward on a number line.
Skip count backward by 6 four times.
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
So, 24 ÷ 6 = 4.
Use a related multiplication fact to find the quotient.
1.
4 × 7 = 28, so 28 ÷ 7 =
4
2.
5
× 6 = 30, so 30 ÷ 6 =
5
Copyright © The McGraw-Hill Companies, Inc.
Find out what students know about
division strategies. Write the division
fact 36 ÷ 9 on the board. Say:
• Of the four strategies, using a
related multiplication fact, an
array, repeated subtraction, or skip
counting backward on a number
line, which ones would be easiest
to use for this example? (related
multiplication fact and repeated
subtraction)
• What related multiplication fact
can you name to solve this division
fact? (9 × 4 = 36 or 4 × 9 = 36)
How can you use the related
multiplication fact to solve the
division fact 36 ÷ 9? (If 4 × 9 = 36,
then 36 ÷ 9 must be 4.) So, 36 ÷ 4
= ? . (9)
• How can you use repeated
subtraction to solve 36 ÷ 9? (Start
at 36 and subtract 9 to get 27.
Then subtract 9 again to get 18.
Subtract 9 from 18 to get 9, and
then subtract 9 from 9 to get 0.
Nine was subtracted 4 times to
reach zero.) So, what is the quotient
of 36 ÷ 9? (4)
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WHAT IF THE STUDENT NEEDS HELP TO
Use Related Multiplication
Facts
• Have the student use a
multiplication table to create
related multiplication and
division facts on index cards.
Have the student choose facts
that are troublesome for him or
her and write a related pair of
facts on each card.
• Have the student practice these
facts daily until he or she can
recall them with ease.
Use Repeated Subtraction
• Have the student use
counters to perform
repeated addition such as
3 + 3 + 3 + 3 + 3 = 15
• Then have the student “undo”
the repeated addition with
repeated subtraction. For the
example above,
subtract 15 - 3 = 12;
12 - 3 = 9; 9 - 3 = 6;
6 - 3 = 3; and 3 - 3 = 0.
Name
Lesson
Use an array to find each quotient.
9
3. 27 ÷ 3 =
8-C
5
4. 15 ÷ 3 =
Use repeated subtraction to find each quotient.
3
5. 9 ÷ 3 =
6. 30 ÷ 5 =
Subtract: 9 - 3 = 6, 6 - 3 = 3,
6
Subtract: 30 - 5 = 25, 25 - 5 = 20,
3-3=0
20 - 5 = 15, 15 - 5 = 10,
10 - 5 = 5, 5 - 5 = 0
Skip count backward to find each quotient.
8. 42 ÷ 6 =
9
7. 45 ÷ 5 =
Try It
7
Count backward:
Count backward: 45, 40, 35,
30, 25, 20, 15, 10, 5, 0
42, 36, 30,
24, 18, 12, 6, 0
Copyright © The McGraw-Hill Companies, Inc.
Find each quotient. Use any strategy.
9. 8 ÷ 4 =
2
10. 20 ÷ 4 =
5
11. 48 ÷ 8 =
6
12. 35 ÷ 5 =
7
13. 36 ÷ 6 =
6
14. 40 ÷ 5 =
8
15. 28 ÷ 4 =
7
16. 12 ÷ 6 =
2
17. 49 ÷ 7 =
7
18. 8 64
8
19. 9 81
9
20. 7 21
3
21. 4 16
4
24
22. 4 6
23. 7 42
6
24. 8 32
4
25. 4 36
9
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WHAT IF THE STUDENT NEEDS HELP TO
Skip Count Backward
• Have the student put 3
counters into each of 8 groups.
Then have the student skip
count to find the total.
(3, 6, 9, 12, 15, 18, 21, 24)
• Then have the student start
with the total and skip count
backward by 3. (24, 21, 18, 15,
12, 9, 6, 3, 0)
• Repeat with other numbers of
counters and groups.
• How would you use repeated
subtraction to solve? (Start with
24 and subtract 6 four times:
24 - 6 = 18; 18 - 6 = 12;
12 - 6 = 6; 6 - 6 = 0)
Use an existing number line from
0 to 24 or draw a new one.
Demonstrate skip counting backward
4 groups of 6 by drawing arrows that
show the “jumps” between 24 and 18,
18 and 12, 12 and 6, and 6 and 0.
Complete the Power
Practice
• Discuss each incorrect answer.
Have the student model any
exercise he or she missed using
counters or a number line.
• Have students complete
Exercises 1 and 2 using related
multiplication and division facts.
Check that students understand
that the same three numbers are
used in each pair of related facts.
Once they know one fact, they can
write all four related facts. Ask:
• How much is 1 × 7? (7) How much
is 2 × 7? (14) How much is 3 × 7?
(21) How much is 4 × 7? (28) So,
what number times 4 is 28? (7) How
can I use the fact 4 × 7 = 28 to find
the quotient? (The numbers in the
related facts are the same, so 4 × 7
= 28 and 28 ÷ 7 = 4.)
• Have the students do Exercises 3
and 4 using the arrays. Check that
students understand that they
separate the elements of the array
into equal groups.
• Have the students do Exercises 5
and 6 using repeated subtraction.
Check to make sure that students
understand which number they
begin subtracting with and that
they continue subtracting the
same number from the difference
until they reach 0.
• Have students do Exercises 7 and
8 using skip counting backward.
Check that students understand
where they begin counting, the
number they skip count backward,
and how to count the number of
skips.
Power Practice
• Have students complete the
practice items using a strategy.
Then review each answer.
Lesson 8-C
Name
Points on a Number Line
Lesson
8-D
Make the number line.
What Can I Do?
Number the line starting at 70. The marks must
be the same distance apart.
I want to show the
location of a point
on a number line.
70
71
72
73
74
75
76
77
78
79
80
Mark and label the point.
Make a black circle on the point. Write a capital
letter to name the point. Point H is at 73. Point M
is at 79.
M
H
70
71
72
73
74
75
76
77
78
79
80
Write the missing numbers to complete each
number line.
0
1
2
4
8
5
9
10
2.
30
32
33
35
36
55
56
37
39
3.
51
52
58
60
Make a number line. Show the numbers 20 through 30.
4.
Copyright © The McGraw-Hill Companies, Inc.
1.
Name
Write the number that shows the
location of each point.
B
D
60 61
A
8-D
C
62 63 64 65 66 67 68 69 70
5. point A
6. point B
7. point C
8. point D
40
Lesson
G
E
H
F
41
42 43 44 45 46 47 48 49 50
9. point E
10. point F
11. point G
12. point H
Copyright © The McGraw-Hill Companies, Inc.
Mark a point at each location.
13. point S at the number 80
14. point T at the number 84
15. point U at the number 88
16. point V at the number 85
80 81
82 83 84 85 86 87 88 89 90
17. point W at the number 22
18. point X at the number 30
19. point Y at the number 26
20. point Z at the number 23
20 21
22 23 24 25 26 27 28 29 30
Name
Points on a Number Line
Lesson
8-D
Lesson Goal
• Identify or mark points on a
number line.
What the Student Needs to
Know
Make the number line.
What Can I Do?
Number the line starting at 70. The marks must
be the same distance apart.
I want to show the
location of a point
on a number line.
70
• Recognize equal intervals.
• Relate number lines to familiar
scales.
• Count to 10.
72
73
74
75
76
77
78
79
80
Mark and label the point.
Make a black circle on the point. Write a capital
letter to name the point. Point H is at 73. Point M
is at 79.
M
H
Getting Started
• Draw a large blank number line on
the board using a ruler to make
the marks 3 inches apart. Write a
zero under the left-hand mark. Ask:
• What is this diagram? What can you
use it for? (a number line; possible
uses are rounding numbers, skip
counting, making a line plot)
• Write the number 1 under the
second mark. Point out that you
have now established the meaning
of each section or interval. Each
interval stands for 1 unit. If you
had written 2, each interval would
stand for 2 units.
• Have volunteers come up to the
board and complete the number
line by writing the numbers 2
through 10 under the appropriate
marks.
• Draw students’ attention to the
arrowheads on the left and right
sides of the number line. Ask:
• What does the arrow on the right
side mean? (The counting numbers
continue on from 10. The next
number is 11.) What does the arrow
on the left side mean? (Some
students may know that the
negative numbers –1, –2, and so
on are to the left of zero. If you
wish to discuss this, a thermometer
is a good model for numbers less
than zero.)
• Have students draw a number
line from 0 to 10 on their paper.
Students can use the number line
on the board for help.
71
70
71
72
73
74
75
76
77
78
79
80
Write the missing numbers to complete each
number line.
1.
0
1
2
3
4
5
6
7
8
36
37
38 39 40
9
10
2.
30 31 32
33 34 35
3.
50
51
52 53 54 55
56 57 58 59 60
Make a number line. Show the numbers 20 through 30.
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-D
4.
20 21
22 23 24 25 26 27 28 29 30
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WHAT IF THE STUDENT NEEDS HELP TO
Recognize Equal Intervals
• Draw two number lines on
the board, one in which the
intervals are equally spaced and
one in which the intervals are
obviously not equally spaced.
Number the marks from 0
onward, counting by 1s. Have
the student discuss the two
lines, identifying how they are
alike and how they are different.
• Show the student a ruler and
ask what would happen if
the marks were not the same
distance apart. (Possible
response: The ruler would
not be very useful because
it wouldn’t give the same
measure every time.)
Relate Number Lines to
Familiar Scales
• Show the student a thermometer and ask how this
measuring tool is like a number
line. (The marks are an equal
distance apart; the numbers are
in order.)
• Have the student describe other
tools that use a scale similar to a
number line. (The student may
mention rulers, measuring cups,
bathroom scales, odometers on
cars, protractors for angles.) List
his or her ideas on the board.
Emphasize that the marks must
always be an equal distance
apart.
Name
Write the number that shows the
location of each point.
B
D
A
Lesson
8-D
What Can I Do?
C
Read the question and the response.
Then read and discuss the example.
Ask:
• What is meant by a point? How do
you show the location of a point on
a number line? (A point is a specific
location or spot; a black dot and
capital letter mark the location of a
point.)
• Use a number line from 0 to 10. Mark
the first letter of your first name at
8; mark the first letter of your last
name at 0. (Check that students
understand how to mark points on
the number line.)
60 61 62 63 64 65 66 67 68 69 70
5. point A
67
6. point B
60
7. point C
70
8. point D
66
40
G
E
H
F
41
42 43 44 45 46 47 48 49 50
9. point E
42
10. point F
49
11. point G
41
12. point H
45
Copyright © The McGraw-Hill Companies, Inc.
Mark a point at each location.
13. point S at the number 80
14. point T at the number 84
15. point U at the number 88
16. point V at the number 85
S
80 81
T
V
82 83 84 85 86 87 88 89 90
17. point W at the number 22
18. point X at the number 30
19. point Y at the number 26
W
20 21
Try It
U
Z
20. point Z at the number 23
Y
X
22 23 24 25 26 27 28 29 30
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WHAT IF THE STUDENT NEEDS HELP TO
Count to 10
• Count aloud with the student
from 0 through 10. Ask the
student to suggest ways to
show in writing what you have
just done. The student might
make a list of the numbers
separated by commas, or make
a number line.
Complete the Power
Practice
• Make sure the student
understands what is meant
by a point and can relate
the concept of point to the
black dots on the number lines.
Ask questions such as: Look at
the number line for Exercises 5–8,
how many points are marked
with letters? (four) What points
are marked? (B, D, A, and C)
Where are these points
located? (60, 66, 67, and 70)
These first exercises give students
practice in completing number lines.
Ask:
• How do you know what numbers to
write in the blank spaces on the lines
in Exercise 1? (When completed, the
numbers must go in order from 0
through 10.)
• For Exercise 4, how will you get the
marks to be an equal distance apart?
(Line them up with the marks on
the line in Exercise 3.) Have rulers
available for those students who
wish to use them.
Power Practice
• Review the directions with
students.
• When students have finished the
page, the completed number lines
can be used for practice in finding
the distance between two points
on a number line.
• Check to see if the student
understands the directions by
asking: What were you supposed
to do in this exercise? Once you
have clarified the directions,
the student can try again to do
the exercises.
Lesson 8-D
Name
Identify the Shaded Part
Lesson
8-E
Write each fraction that names each shaded part.
3.
2.
____
8
4.
____
____
6
9
5.
6.
____
____
____
4
5
6
7.
9.
8.
____
____
____
3
8
4
Copyright © The McGraw-Hill Companies, Inc.
1.
Name
Identify the Shaded Part
Lesson Goal
• Identify part of a whole by writing
a fraction.
What the Student Needs to
Know
8-E
Write each fraction that names each shaded part.
1.
3.
2.
• Identify fractions.
• Model part of a whole.
3
____
____
9
6
5.
4.
4
5
____
8
Getting Started
• On the board, draw a rectangle
divided into 4 equal parts. Shade
3 of the 4 parts.
• How many shaded parts are in the
rectangle? (3)
• How many equal parts are in the
rectangle? (4)
• What fraction names the
shaded part? __34
• Draw a hexagon with 6 different
parts. Shade 5 of the 6 parts.
• How many shaded parts are in the
hexagon? (5)
• How many equal parts are in the
hexagon? (6)
• What fraction names the shaded
part? __56
Lesson
2
6.
4
3
____
____
____
4
5
6
()
7.
9.
8.
3
____
3
7
8
____
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-E
3
____
4
()
Teach
Read and discuss Exercise 1 at the top
of the page.
• How many shaded parts are in the
rectangle? (3) This number will be
our top number, or numerator.
• How many equal parts are in the
rectangle? (8) This number will be
our bottom number, or denominator.
• What fraction of the rectangle is
shaded? __38
()
Practice
• Read the directions as students
complete Exercises 2 through 9.
• Check student work.
• If students have difficulty with the
activity, have them use fraction
tiles or fraction circles to model the
exercises.
256_S_G5_C08_SI_119817.indd 256
7/17/12 10:53 AM
WHAT IF THE STUDENT NEEDS HELP TO
Identify Fractions
• Place students in groups. Give
each group a set of recipes. Ask
students to circle the fractions
within the recipes.
• Provide fraction tiles and
fraction circles. Ask students to
model the fractions that they
identified in the recipes.
• Create a recipe box by having
students bring in recipes with
fractions. Students can find and
model the fractions from the
recipes until they can
identify fractions with ease.
Model Part of a Whole
• Place students in pairs. Student
1 should draw a picture of a
figure divided into equal parts,
and then shade some of the
parts. (Ex: The student could
draw a square divided into
4 equal parts with 3 parts
shaded.)
• Student 2 takes the drawing
and writes the fraction that
names the shaded part.
• Together the students should
count the number of shaded
parts and the total number of
equal parts to determine the
numerator and denominator
of the fraction.
• If the students agree the
answer is correct, they switch
roles and complete the activity
again as time allows.
Name
Multiples, Factors, and
Greatest Common Factor
Lesson
8-F
Activate Prior Knowledge
0
5
10
15
20
25
30
1. List the factors of 30 from least to greatest.
2. List the factors of 25 from least to greatest.
3. What numbers are factors of both 30 and 25?
A multiple of a number is the product of that number and any whole
number. For example, 10 is a multiple of 5 because 2 × 5 = 10.
A factor is a number that divides into a whole number evenly. For
example, 5 is a factor of 10 because 10 ÷ 5 = 2.
A greatest common factor (GCF) is the largest number that is a factor of
two or more numbers. For example, the greatest common factor (GCF)
of 30 and 25 is 5.
4. 5 is a
of 30.
5. 25 is a
of 5.
6. The
of 25 and 30 is 5.
List the factors of each multiple.
7. 24
8. 36
9. 9
10. 16
Find the common factors of each pair of multiples.
11. 9 and 36
12. 16 and 24
Copyright © The McGraw-Hill Companies, Inc.
Complete each sentence with the term “multiple,” “factor,” or
“greatest common factor.”
Lesson Goal
• Identify factors and multiples of
numbers.
Name
Multiples, Factors, and
Greatest Common Factor
Lesson
8-F
Activate Prior Knowledge
0
5
10
15
20
25
30
What the Student Needs to
Know
1. List the factors of 30 from least to greatest.
1, 2, 3, 5, 6, 10, 15, 30
2. List the factors of 25 from least to greatest.
1, 5, 25
• Identify factors.
3. What numbers are factors of both 30 and 25?
Getting Started
A multiple of a number is the product of that number and any whole
number. For example, 10 is a multiple of 5 because 2 × 5 = 10.
• Draw an array of circles with
3 rows and 4 columns on the
board.
• How many rows are in the array? (3)
How many circles are in each row?
(4) How many total circles are in the
array? (12)
• A factor is a number that can be
multiplied by another number and
can be divided into a whole number
evenly. The numbers 3 and 4 are
factors of 12.
• A multiple is the product of
multiplying two whole numbers.
Therefore, 12 is a multiple of 3 and 4.
1, 5
A factor is a number that divides into a whole number evenly. For
example, 5 is a factor of 10 because 10 ÷ 5 = 2.
A greatest common factor (GCF) is the largest number that is a factor of
two or more numbers. For example, the greatest common factor (GCF)
of 30 and 25 is 5.
Complete each sentence with the term “multiple,” “factor,” or
“greatest common factor.”
4. 5 is a
factor
5. 25 is a
multiple
of 30.
of 5.
6. The greatest common factor of 25 and 30 is 5.
List the factors of each multiple.
7. 24
1, 2, 3, 4, 6, 8, 12, 24
9. 9
1, 3, 9
8. 36 1, 2, 3, 4, 6, 9, 12, 18, 36
10. 16
1, 2, 4, 8, 16
Find the common factors of each pair of multiples.
Teach
Read and discuss Exercise 1 at the top
of the page.
• Use the number line to help identify
the factors of 30. Remember, factors
are two numbers that are multiplied
to equal the number 30.
• What number can be multiplied by 1
to equal 30? (30) What number can
be multiplied by 2 to equal 30? (15)
What number can be multiplied by 3
to equal 30? (10)
• What number can be multiplied by 4
to equal 30? (4 is not a factor of 30;
a number cannot be multiplied by
4 to equal 30)
• What number can be multiplied by 5
to equal 30? (6)
• Put the factors in order from least to
greatest. (1, 2, 3, 5, 6, 10, 15, 30)
• Have students check their work by
identifying factors on a
multiplication table.
Practice
• Read the directions and complete
Exercises 2 through 12. Check
student work.
11. 9 and 36
1, 3, 9
12. 16 and 24
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-F
1, 2, 4, 8
258_S_G5_C08_SI_119817.indd 258
7/12/12 6:20 PM
WHAT IF THE STUDENT NEEDS HELP TO
Identify Factors
• One effective way for the
student to learn how to find
factors is to use concrete
models, manipulatives, and
pictorial representations.
• For example: In order to find the
factors of 20, give the student
20 connecting cubes.
• Have the student create arrays
with the connecting cubes to
form equal rows and columns.
• The student will find they can
create an array 1 × 20, 2 × 10,
and 4 × 5.
• Show the student a nonexample by demonstrating
how 3 rows will NOT equal an
even amount of columns with
20 connecting cubes.
• Encourage the student to write
down the rows and columns
for each array and write the
numbers in order from least to
greatest.
Name
Simplifying Fractions
Lesson
8-G
Use division.
What Can I Do?
I want to simplify
a fraction.
Divide both the numerator and denominator
of the fraction by the same number. Divide until
the numerator and denominator have only 1 as
the common factor.
4
36 __
9
___
÷ = ___
36 and 72 can both be
divided by 4.
3 3
9
___
÷ __ = __
9 and 18 can both be
divided by 3.
3 1
3 __
__
÷ = __
3 and 6 can both be
divided by 3.
4
72
3
18
6
18
3
6
2
Since the numerator, 1, and the
denominator, 2, have no common factors
1
except 1, the fraction __
is in simplest form.
2
4
4 ÷ __
1. __
=
8 4
6 3
2. __ ÷ __ =
9 3
15 5
3. ___ ÷ __ =
25 5
3
9
4. ___ ÷ __ =
12 3
3
12 ÷ __
=
5. ___
15 3
32 4
6. ___ ÷ __ =
36 4
3
9
7. ___ ÷ __ =
21 3
2
6
8. ___ ÷ __ =
10 2
12
24 ÷ ___
9. ___
=
36 12
Copyright © The McGraw-Hill Companies, Inc.
Use division. Simplify each fraction.
Name
Simplifying Fractions
Lesson
8-G
Lesson Goal
• Simplify a fraction.
What the Student Needs to
Know
Use division.
What Can I Do?
I want to simplify
a fraction.
• Divide whole numbers.
• Find common factors of two
numbers.
Divide both the numerator and denominator
of the fraction by the same number. Divide until
the numerator and denominator have only 1 as
the common factor.
4
36 __
9
___
÷ = ___
36 and 72 can both be
divided by 4.
3 3
9
___
÷ __ = __
9 and 18 can both be
divided by 3.
3 1
3 __
__
÷ = __
3 and 6 can both be
divided by 3.
4
72
3
18
Getting Started
Ask students how to find the
common factor of the numbers 18
and 27. For example, ask:
• What are the factors of 18? (1, 2, 3,
6, 9, 18)
• What are the factors of 27? (1, 3, 9,
27)
• What are the common factors of 18
and 27? (1, 3, 9)
What Can I Do?
Read the question and the response.
Then read and discuss the example.
Ask:
• What are the factors of 36? (1, 2, 3,
4, 6, 9, 12, 18, 36)
• What are the factors of 72? (1, 2, 3,
4, 6, 8, 9, 12, 18, 24, 36, 72)
• What are the common factors of 36
and 72? (1, 2, 3, 4, 6, 9, 12, 18, 36)
• In the example, which common
factor are both 36 and 72 divided
9
by? (4) Is __
in simplest form? (No.)
18
• What common factor are both 9 and
18 divided by? (3) Is __36 in simplest
form? (No.)
• What common factor are both 3 and
6 divided by? (3)
• Is __12 in simplest form? Why?
(Yes. 1 and 2 have no common
factors except 1.)
• Would the simplest form still be __12 if
you used a different common factor
to divide by? (Yes.)
Try It
• Have students divide the
numerator and denominator by
the given common factor.
3
6
18
6
2
Since the numerator, 1, and the
denominator, 2, have no common factors
1
except 1, the fraction __
is in simplest form.
2
Use division. Simplify each fraction.
4
4 ÷ __
1. __
=
8 4
1
__
2
3
9
4. ___ ÷ __ =
12 3
3
__
3
9
7. ___ ÷ __ =
21 3
3
__
4
7
6 3
2. __ ÷ __ =
9 3
2
__
3
3
12 ÷ __
5. ___
=
15 3
4
__
2
6
8. ___ ÷ __ =
10 2
3
__
5
5
15 5
3. ___ ÷ __ =
25 5
3
__
32 4
6. ___ ÷ __ =
36 4
8
__
12
24 ÷ ___
9. ___
=
36 12
5
9
2
__
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-G
3
260_S_G5_C08_SI_119817.indd 260
7/12/12 6:33 PM
WHAT IF THE STUDENT NEEDS HELP TO
Divide Whole Numbers
• Practice division facts for 10
to 15 minutes daily until the
student can recall the quotients
automatically.
• Once the division facts are
mastered, have the student
practice dividing by 1-digit and
2-digit divisors.
Find Common Factors of
Two Numbers
• Have the student list all the
factors of a number by having
the student divide the number
by each whole number that is
less than the number until all
the factors have been found.
• Once the student has mastered
finding the factors of one
number, have the student find
the factors of two numbers and
then circle the common factors.
Name
Factors, Common Factors, and
Greatest Common Factor
What Can I Do?
I want to find the greatest
common factor of two
numbers.
Lesson
8-H
What is the greatest common
factor of 16 and 24?
Think: I will look for pairs of
numbers that can be multiplied
together to make the number.
16
24
16 × 1 24 × 1
8×2
12 × 2
4×4
8×3
6×4
List the factors.
The factors of 16 are 1, 2, 4, 8, 16.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Find the common factors.
1, 2, 4, and 8 are factors of both 16 and 24.
Find the greatest common factor (GCF).
8 is the greatest factor of both 16 and 24.
1. 12
2. 8
3. 18
4. 9
Find the common factors of each pair of numbers.
5. 8 and 12
6. 9 and 18
7. 12 and 18
Name the greatest common factor of each pair of numbers.
8. 8 and 12
9. 9 and 18
10. 12 and 18
Copyright © The McGraw-Hill Companies, Inc.
List the factors of each number.
Name
List the factors of each number.
Lesson
8-H
11. 15
12. 6
13. 10
14. 20
15. 14
16. 27
Find the common factors for each pair of numbers.
17. 6 and 15
18. 10 and 20
19. 14 and 27
20. 15 and 27
21. 14 and 6
22. 15 and 14
23. 6 and 20
24. 6 and 27
25. 10 and 15
Copyright © The McGraw-Hill Companies, Inc.
Name the greatest common factor for each pair of numbers.
26. 6 and 15
27. 10 and 20
28. 14 and 27
29. 15 and 27
30. 14 and 6
31. 15 and 14
32. 6 and 20
33. 6 and 27
34. 10 and 15
Lesson Goal
• Find the greatest common factor
(GCF) of two numbers.
What the Student Needs to
Know
Name
Factors, Common Factors, and
Greatest Common Factor
What Can I Do?
I want to find the greatest
common factor of two
numbers.
• Find the factors of a number.
• Find the common factors of two
numbers.
• Find the greatest number in a set.
Lesson
8-H
What is the greatest common
factor of 16 and 24?
Think: I will look for pairs of
numbers that can be multiplied
together to make the number.
16
24
16 × 1 24 × 1
8×2
12 × 2
4×4
8×3
The factors of 16 are 1, 2, 4, 8, 16.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Find the common factors.
Getting Started
1, 2, 4, and 8 are factors of both 16 and 24.
Ask students to think of as many pairs
of numbers as they can that have the
following numbers as a product.
• 8 (1 × 8, 2 × 4)
• 12 (1 × 12, 2 × 6, 3 × 4)
• 18 (1 × 18, 2 × 9, 3 × 6)
• 19 (1 × 19)
• 20 (1 × 20, 2 × 10, 4 × 5)
• 25 (1 × 25, 5 × 5)
Find the greatest common factor (GCF).
What Can I Do?
Read the question and the response.
Then read and discuss the examples.
Ask:
• How can you find the factors of 16?
(Find pairs of numbers that have
16 as their product.)
• Why is it important to list the factors
of the two numbers in order? (When
the factors are listed in order it is
easier to compare the factors of
the two numbers and to locate
common factors.)
• How can you find the common
factors of 16 and 24? (Look for
numbers that are listed as factors
for both 16 and 24.)
• How can you tell that 4 is not the
greatest common factor of 16 and
24? (There is another number, 8,
that is greater than 4 and is a
factor of both 16 and 24.)
6×4
List the factors.
8 is the greatest factor of both 16 and 24.
List the factors of each number.
1. 12
1, 2, 3, 4, 6, 12
2. 8
1, 2, 4, 8
3. 18
1, 2, 3, 6, 9, 18
4. 9
1, 3, 9
Find the common factors of each pair of numbers.
5. 8 and 12
1, 2, 4
6. 9 and 18
1, 3, 9
7. 12 and 18
1, 2, 3, 6
Name the greatest common factor of each pair of numbers.
8. 8 and 12
4
9. 9 and 18
9
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-H
10. 12 and 18
6
262_263_S_G5_C08_SI_119817.indd 262
7/12/12 6:44 PM
WHAT IF THE STUDENT NEEDS HELP TO
Find the Factors of a
Number
Find the Common Factors
of Two Numbers
• Have the student think of pairs
of numbers that can be
multiplied together to make a
product. Explain that numbers
that are multiplied together are
called factors.
• Tell the student to start with
one and go through the
numbers in order, 1, 2, 3, 4, …
For each number, they should
decide if it can divide evenly
into the number for which they
are finding factors.
• Check that the student is
finding all of the factors of the
two numbers.
• Have the student compare the
factors of the two numbers
one-by-one. Have him or her
cross off any factors that are
not common to both numbers
and circle and draw lines
connecting the factors that are
common to both numbers.
Name
List the factors of each number.
Lesson
8-H
11. 15
1, 3, 5, 15
12. 6
13. 10
1, 2, 5, 10
14. 20
1, 2, 4, 5, 10, 20
15. 14
1, 2, 7, 14
16. 27
1, 3, 9, 27
Try It
1, 2, 3, 6
• Tell students that each number will
have at least two factors. Ask
students to name the two factors
that every number will have.
(1 and the number itself)
• Point out that 2 is listed as a
factor of 12. Ask students
what number times 2 equals
12. (6) Elicit from the students that
6 must also be a factor of 12.
• Encourage students to share their
methods for finding common
factors.
• Have students complete the
exercises. Then have volunteers
explain how they found the
greatest common factor for
Exercises 8–10.
Find the common factors for each pair of numbers.
17. 6 and 15
1, 3
18. 10 and 20
1, 2, 5, 10
19. 14 and 27
1
20. 15 and 27
1, 3
21. 14 and 6
1, 2
22. 15 and 14
1
23. 6 and 20
1, 2
24. 6 and 27
1, 3
25. 10 and 15
1, 5
Copyright © The McGraw-Hill Companies, Inc.
Name the greatest common factor for each pair of numbers.
26. 6 and 15
3
27. 10 and 20
10
28. 14 and 27
1
29. 15 and 27
3
30. 14 and 6
2
31. 15 and 14
1
32. 6 and 20
2
33. 6 and 27
3
34. 10 and 15
5
262_263_S_G5_C08_SI_119817.indd 263
Power Practice
7/12/12 6:44 PM
• Ask students if every pair of
numbers will have a common
factor. Then have them explain
their reasoning. (Each number has
at least two factors, one and itself.
So, each pair of numbers will have
at least one common factor, 1.)
• Have students complete the
exercises. Then review the answers
and ask volunteers to explain how
they found the greatest common
factors for Exercises 26–34.
WHAT IF THE STUDENT NEEDS HELP TO
Find the Greatest Number
in a Set
Complete the Power
Practice
• Have the student locate each
number in the set on a
number line. Explain that the
number farthest to the right
on the number line is the
greatest number. Ask the
student to use the number line
to name the greatest number in
the set.
• Review comparing pairs of
numbers. Name two
numbers such as 15 and 21.
Have the student compare the
numbers saying: 21 is greater
than 15 or 15 is less than 21.
• Work through finding factors,
common factors, and greatest
common factors with the
student to determine what help
the student needs. Then
provide reteaching and review
in those areas.
Lesson 8-H
Name
Use a Multiplication Table to Divide
Lesson
8-I
Use a multiplication table.
What Can I Do?
When you need to check a fact, use the
table to find it.
I want to practice
the division facts.
X 0
0
1
2
3
4
5
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
2
0
2
4
6
8
10
12
14
16
18
20
3
0
3
6
9
12
15
18
21
24
27
30
4
0
4
8
12
16
20
24
28
32
36
40
5
0
5
10
15
20
25
30
35
40
45
50
6
0
6
12
18
24
30
36
42
48
54
60
7
0
7
14
21
28
35
42
49
56
63
70
8
0
8
16
24
32
40
48
56
64
72
80
9
0
9
18
27
36
45
54
63
72
81
90
10
0
10
20
30
40
50
60
70
80
90
100
1. 25 ÷ 5 =
2. 35 ÷ 5 =
3. 27 ÷ 3 =
4. 24 ÷ 3 =
Divide.
32
5. 4 6. 6 24
7. 8 16
8. 9 18
9. 8 32
9
10. 3 50
11. 5 12
12. 3 10
13. 2 16
14. 2 21
15. 3 28
16. 7 14
17. 7 6
18. 6 12
19. 6 Copyright © The McGraw-Hill Companies, Inc.
Use the table to complete each fact.
Name
Use a Multiplication Table to Divide
Lesson Goal
• Complete division facts.
What the Student Needs to
Know
8-I
Use a multiplication table.
What Can I Do?
When you need to check a fact, use the
table to find it.
I want to practice
the division facts.
X 0
0
1
2
3
4
5
6
7
8
9
10
• Use counters to show the meaning
of division.
• Read a multiplication table.
• Use a multiplication fact to write
two related division facts.
Getting Started
• Write 20 ÷ 2 on the board. Ask:
What does this mean? (Divide 20
by 2; divide 20 into 2 equal groups;
divide 20 into groups of 2) What
is another way to write this division
20 )
problem? ( 2 • Explain your thinking when you do
a problem such as 36 ÷ 6. (Possible
strategies: How many times does 6
go into 36? What number times 6
equals 36? How many times can I
subtract 6 from 36?)
Lesson
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
2
0
2
4
6
8
10
12
14
16
18
20
3
0
3
6
9
12
15
18
21
24
27
30
4
0
4
8
12
16
20
24
28
32
36
40
5
0
5
10
15
20
25
30
35
40
45
50
6
0
6
12
18
24
30
36
42
48
54
60
7
0
7
14
21
28
35
42
49
56
63
70
8
0
8
16
24
32
40
48
56
64
72
80
9
0
9
18
27
36
45
54
63
72
81
90
10
0
10
20
30
40
50
60
70
80
90
100
Use the table to complete each fact.
1. 25 ÷ 5 = 5
2. 35 ÷ 5 = 7
3. 27 ÷ 3 = 9
4. 24 ÷ 3 = 8
Divide.
8
32
5. 4 4
24
6. 6 2
16
7. 8 2
18
8. 9 4
32
9. 8 3
10. 3 9
10
11. 5 50
4
12. 3 12
5
13. 2 10
8
14. 2 16
7
21
15. 3 4
28
16. 7 2
14
17. 7 1
6
18. 6 2
12
19. 6 Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-I
What Can I Do?
Read the question and the response.
• If you have not yet memorized the
division facts, what can you do?
(Practice using flash cards. Some
students may suggest computer
software.)
• Why can you use multiplication to
help you do division?
(Multiplication and division are
opposite or inverse operations.
One operation “un-does” the
other.)
Try It
• How can you use the table for
Exercise 1? (Find the row with
5 at the left. Go across this row
until you get to 25. Look at the top
of this column to find the
quotient, 5.)
Power Practice
• Have the students complete the
practice items. Then review each
answer.
266_S_G5_C08_SI_119817.indd 266
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WHAT IF THE STUDENT NEEDS HELP TO
Use Counters to Show the
Meaning of Division
• Provide pairs of students with
50 counters. One student takes
a handful of counters; the
partner divides them into 2
equal groups. Students record
their work using the ÷ symbol.
Repeat using groups of 3 and 4.
Read a Multiplication
Table
• Provide blank multiplication
tables. Direct the student to
model a fact such as 4 × 3.
He or she should shade the
4 row across to the 12; shade
the 3 column down to the 12.
Repeat with other facts.
Use a Multiplication Fact
to Write Two Related
Division Facts
• Write 5 × 6 on the board. Have
the student draw a model for
the fact. Use the model to write
and explain two division facts:
30 ÷ 5 = 6, 30 ÷ 6 = 5.
Complete the Power
Practice
• Have students work in pairs
using division flash cards to
identify which facts they still
need to memorize.
Name
Multiples of a Number
Lesson
8-J
Use models to answer.
1. There are 4 rows of 10 bees.
40 is a multiple of
and
.
2. There are 4 rows of 7 hammers.
28 is a multiple of
and
.
3. There are 4 rows of 3 clocks.
12 is a multiple of
and
.
A multiple of a number is the product of that number and any whole
number.
Circle the number which is not a multiple.
4. 7
5. 4
18, 24, 28, 36, 40
6. 6
7. 8
12, 18, 22, 30, 42
16, 24, 40, 56, 62
8. Complete the graphic organizer. One example is done for you.
Multiples of a Number
Multiples of a Number
Examples
Non-Examples
Examples
7: 14, 21, 28, 35
10
5:
,
,
,
3:
,
,
,
9:
,
,
,
Non-Examples
Copyright © The McGraw-Hill Companies, Inc.
14, 21, 28, 36, 42
Name
Multiples of a Number
Lesson Goal
1. There are 4 rows of 10 bees.
What the Student Needs to
Know
2. There are 4 rows of 7 hammers.
Getting Started
• Write the word multiple on the
board and explain the definition.
A multiple of a number is the product
of the number and any whole
number.
• Provide students with their own
multiplication table.
• Have students find the product of
4 × 1. What is 4 × 1? (4) The
product, 4, is a multiple of 4.
• What is 4 × 2? (8) The product, 8, is a
multiple of 4.
• What is 4 × 3? (12) The product, 12,
is a multiple of 4.
• What is another multiple of 4? (16,
20, 24, 28, 32, 36, 40, 44, 48…)
• Practice finding the multiples of
another number if needed.
8-J
Use models to answer.
• Find examples and non-examples
of multiples of a number.
• Use multiplication to find the
multiple.
Lesson
40 is a multiple of
28 is a multiple of
4
4
and
and
10
.
7
.
3
.
3. There are 4 rows of 3 clocks.
12 is a multiple of
4
and
A multiple of a number is the product of that number and any whole
number.
Circle the number which is not a multiple.
4. 7
5. 4
14, 21, 28, 36, 42
18, 24, 28, 36, 40
6. 6
7. 8
12, 18, 22, 30, 42
16, 24, 40, 56, 62
8. Complete the graphic organizer. One example is done for you.
Multiples of a Number
Multiples of a Number
Examples
Examples
Non-Examples
Non-Examples
Sample answers: Sample answers: Sample answers: Sample answers:
13
7: 14, 21, 28, 35
10
3: 6 , 9 , 12 , 15
10
15
20
25
12
18
27
36
45
20
5:
,
,
,
9:
,
,
,
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 8-J
Teach
Read and discuss Exercise 1 at the top
of the page.
• Let’s use the array to find the
multiple.
• How many rows does the array have?
(4)
• How many are in each row? (10)
• How many squares are in the array in
all? (40)
• What multiplication sentence can we
use to label the array? (4 × 10 = 40)
• What are the two factors? (4 and 10)
• What number is the product or
multiple? (40)
• Write the following statement
on the board: 40 is a multiple of
______ and _______. (4 and 10)
Practice
• Read the directions as students
complete Exercises 2 through 8.
• Check student work.
268_S_G5_C08_SI_119817.indd 268
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WHAT IF THE STUDENT NEEDS HELP TO
Use Multiplication to Find
the Multiple
• Have the student use arrays if
they need to model multiplication number sentences.
• For example, have the student
model the array 5 × 2 with
connecting cubes to help
identify the multiple.
• What is the first factor? (5) There
will be 5 rows.
• What is the second factor? (2)
There will be 2 columns.
• Have the student construct the
array with connecting cubes.
• Label the array 5 × 2. Count the
number of connecting cubes in
the array. How many connecting
cubes are in the array? (10)
• The total number of cubes, or the
product, is a multiple.
• 10 is the multiple of the number
sentence 5 × 2.
• What two numbers is 10 a
multiple of? (5 and 2)
• Continue to have the student
model arrays with 5 × 3, 5 ×
4, 5 × 5, etc. until the student
understands the product is also
the multiple of the two factors.
Name
Shade and Compare
Fractions
Lesson
8-K
Compare the fractions. Write >, <, or =.
1.
2.
3.
2
__
4
__
2
__
3
__
6
6
3
3
4.
3
__
1
__
4
4
3
__
3
__
4
4
Shade and compare the fractions. Write >, <, or =.
5.
3
__
4
__
5
5
7.
5
__
2
__
8
8
4
__
3
__
8
8
8.
3
__
1
__
3
3
Copyright © The McGraw-Hill Companies, Inc.
6.
USING LESSON 8-K
Lesson Goal
• Compare fractions with common
denominators.
Name
Shade and Compare
Fractions
8-K
Compare the fractions. Write >, <, or =.
1.
2.
What the Student Needs
to Know
• Compare whole numbers.
• Use comparison symbols.
Lesson
3
2 < __
__
4
2 < __
__
6
6
3.
3
3
4.
Getting Started
3 > __
1
__
4
Practice
• Have students read the directions
and complete Exercises 2 through
8. Check their work.
4
4
Shade and compare the fractions. Write >, <, or =.
5.
6.
3 < __
4
__
5
2
5 > __
__
5
7.
8
8
8.
3 > __
1
__
3
3
4 > __
3
__
8
Teach
Read and discuss Exercise 1 at the top
of the page.
• Take a look at the two fractions in
Exercise 1. What do you notice about
the numbers in the numerator and
denominator? (The numbers in the
numerator are different and the
numbers in the denominator are
the same.)
• Since the numbers in the denominator
are the same, we need to compare
the numbers in the numerator. Is 2
less than, greater than, or equal to
4? (less than)
• How do you use the models to check
your work? (Sample answer: The
models show 2 shaded parts of
the rectangle is less than 4 shaded
parts of the rectangle.)
2 < __
4.
• Therefore, __
6 6
3
3 = __
__
4
Copyright © The McGraw-Hill Companies, Inc.
• Ask students to compare whole
numbers. Show students a group
of 6 connecting cubes and a group
of 3 connecting cubes.
• Which group has more connecting
cubes? (the group of 6)
• Is 6 greater than, less than, or equal
to 3? (greater than)
• Ask for a volunteer to come to the
board to use the “greater than”
comparison symbol for the two
numbers. (6 > 3)
• Remind students to point the
opening of the comparison symbol
(> or <) towards the greater
number.
8
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WHAT IF THE STUDENT NEEDS HELP TO
Compare Whole Numbers
• Give the student a pair of onedigit numbers such as 8 and 6.
• Have the student make a number line and label the numbers
from 0 to 10.
• Be sure the student understands
that the numbers increase as
you move from left to right.
• The student should circle the
two numbers being compared
on the number line. Have
students circle 8 and 6.
• Now, have the student identify
the greater number (8) and the
number that is less (6).
• Have the student use comparison symbols to compare the
two numbers. (8 > 6 or 6 < 8)
Use Comparison Symbols
• Explain that the signs (< and >)
are used to compare two
numbers. In a comparison like
12 > 3, the > sign means that
12 is greater than 3.
• The comparison can also be
written 3 < 12, where the
< sign means that 3 is less
than 12.
• Have the student practice
comparing one-digit numbers
until the concept becomes
clear.
Name
Identify Fractions and Decimals
Lesson
8-L
Use counting.
What Can I Do?
I want to name the fraction
and decimal shown by
the model.
Each shaded part stands for a tenth of 1,
or 0.1. Each shaded part also stands for one
1
___
part of the whole. The fraction 10
represents
one part shaded out of ten total parts.
0.1
Count the shaded parts. Write that number
as a decimal and fraction.
6
6 parts shaded = 0.6 or ___
10
Use counting. Write the fraction and decimal for the
shaded portion.
1.
2.
parts shaded
3.
parts shaded
parts shaded
Decimal:
Decimal:
Decimal:
Fraction:
Fraction:
Fraction:
Copyright © The McGraw-Hill Companies, Inc.
4
4 parts shaded = 0.4 or ___
10
USING LESSON 8-L
Name
Identify Fractions and Decimals
Lesson
8-L
Lesson Goal
• Name the fraction and decimal
shown by a tenths model.
What the Student Needs
to Know
Use counting.
What Can I Do?
I want to name the fraction
and decimal shown by
the model.
Each shaded part stands for a tenth of 1,
or 0.1. Each shaded part also stands for one
1
___
represents
part of the whole. The fraction 10
one part shaded out of ten total parts.
• Use a decimal point.
• Write a fraction.
0.1
Getting Started
What Can I Do?
Have students read the question
and the response. Then look at the
example. Ask:
• How many equal parts are in the
square? (ten) What does each part
of the square represent? (one tenth
of one)
• Can one square ever have more than
ten tenths? (No.)
• Look at the first example. How many
parts of the square are shaded?
(six parts) How do you write that
as a decimal? (Write the number
of shaded parts after the decimal
point; 0.6) How do you write that as
6
a fraction? (___; six parts are shaded
10
out of a total of 10 parts.)
Try It
• Remind students that a zero is
included as a placeholder before
the decimal to show that there are
no wholes.
Count the shaded parts. Write that number
as a decimal and fraction.
6
6 parts shaded = 0.6 or ___
10
4
4 parts shaded = 0.4 or ___
10
Use counting. Write the fraction and decimal for the
shaded portion.
1.
2.
3.
3 parts shaded
5 parts shaded
7 parts shaded
Decimal: 0.3
Decimal: 0.5
3
___
10
5
___
10
Fraction:
Fraction:
Decimal: 0.7
Fraction:
Copyright © The McGraw-Hill Companies, Inc.
Review decimals, their notation, and
meaning with students. Ask:
• What does a decimal and fraction
represent? (It represents a part of
a whole.) How can you recognize a
decimal? (A decimal always has a
decimal point.)
• What place does the digit to the left
of the decimal point hold? (ones)
What place does the digit to the
right of the decimal point hold?
(tenths)
7
___
10
272_S_G5_C08_SI_119817.indd 272
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WHAT IF THE STUDENT NEEDS HELP TO
Use a Decimal Point
Write a Fraction
• Present a decimal model with
five parts shaded. Have the
student identify the number of
parts. Have the student write a
number to show each part.
• Discuss how the number could
be written as 0.5. Stress that the
decimal point is used to
separate the number of wholes
from the number of parts of a
whole.
• Present several more models
and have the student write a
number to show each.
• Provide manipulatives for the
student if he or she needs
visuals.
• Remind the student that the
top number in a fraction identifies the amount of shaded
parts. The bottom number
identifies the total amount of
parts in a whole.
• Have the student use fraction
circles or fraction tiles to
practice modeling fractions.
Encourage the student to write
the fraction.