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 4
Targeted Strategic Intervention
Grade 4, Chapter 3
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?
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
1-4
3-A: Skip Counting
Repeated addition
4.NBT.5
5-7
3-B: Equal Groups
Arrays
4.NBT.5
8-11
3-C: Repeated Addition
and Skip Counting
Number patterns
4.NBT.5
Grade 3,
Chapter 4,
Lesson 2
Grade 3,
Chapter 4,
Lessons 3 and 4
Grade 3,
Chapter 2,
Lesson 3
Check My Progress 1
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
2-3
3-D: Use a Number Line
to Divide
Repeated
subtraction
4.NBT.6
Chapter 3,
Lesson 2
4-6
3-E: Addition and
Subtraction Fact
Families
Fact families
4.NBT.6
Chapter 3,
Lesson 1
Review
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
14-15
3-F: Fact Families
Fact families
4.NBT.6
Chapter 3,
Lesson 1
16-18
3-G: Subtract with a
Number Line
Repeated
subtraction
4.NBT.6
Chapter 3,
Lesson 2
19
3-H: Write Multiplication
Sentences
Multiplication as
comparison
4.OA.1
Chapter 3,
Lesson 3
20-21
3-I: Add with the
Commutative Property
Properties
4.NBT.5
Chapter 3,
Lesson 5
22-24
3-J: Missing Factors
Factors
4.OA.4
Chapter 3,
Lesson 7
25-27
3-K: Multiples of a
Number
Multiples
4.OA.4
Chapter 3,
Lesson 7
Name
Skip Counting
Lesson
3-A
Use repeated addition and skip counting to find each sum.
1.
+
+
,
=
,
There are
scissors in all.
2.
+
+
,
,
There are
Copyright © The McGraw-Hill Companies, Inc.
3.
+
,
=
,
pencils in all.
blue
blue
blue
blue
blue
blue
blue
blue
blue
blue
blue
blue
+
blue
blue
blue
blue
+
,
There are
+
+
,
=
,
crayons in all.
4.
+
,
There are
+
,
paintbrushes in all.
=
USING LESSON 3-A
Name
Skip Counting
Lesson Goal
1.
4
What the Student Needs to
Know
Practice
• Have students complete Exercises
2 through 4.
• Check their work.
12
4
+
8
There are
=
12
=
15
=
16
=
30
12
,
scissors in all.
2.
Getting Started
Read and discuss Exercise 1 at the top
of the page.
• How many scissors are in each
group? (4)
• Let’s use repeated addition and skip
counting to find the sum.
• How many times should we add 4?
(3) Why? (There are 3 groups of 4
scissors.)
• What is 4 + 4 + 4? (4 + 4 = 8,
8 + 4 = 12)
• Ask a volunteer to skip count by 4s.
(4, 8, 12)
• Make sure students fill in the blanks
correctly on their worksheet.
4
+
,
• Use skip counting.
Teach
3-A
Use repeated addition and skip counting to find each sum.
• Use repeated addition and skip
counting to add the same number
three or more times.
3
+
,
There are
3.
Copyright © The McGraw-Hill Companies, Inc.
• Ask students, “What is repeated
addition?” (Adding the same
number more than one time.)
• What is an example of an addition
sentence that shows repeated
addition? (Sample example:
2 + 2 + 2 + 2)
• What does the skip in skip counting
mean? (You skip numbers as you
count.)
• How can you skip count by 2s from 0
to 8? (0, 2, 4, 6, 8)
• Let’s use a hundreds chart to practice
skip counting. Display a hundreds
chart for all students to see.
• Practice skip counting down each
vertical column on the hundreds
chart. Examples of numbers to skip
count by: 2s, 5s, and 10s.
• Continue to repeat the activity as
needed.
Lesson
3
6
15
,
+
12
,
3
15
,
blue
blue
blue
blue
4
8
,
16
3
+
9
pencils in all.
+
There are
3
blue
blue
blue
blue
blue
blue
blue
blue
4
+
blue
blue
blue
blue
4
+
,
4
+
12
16
,
crayons in all.
4.
10
+
There are
10
20
,
30
+
,
10
30
paintbrushes in all.
077_S_G4_C03_SI_119816.indd 77
7/9/12 11:08 AM
WHAT IF THE STUDENT NEEDS HELP TO
Use Skip Counting
• Provide the student with a set
of counters to be used to form
equal groups.
• Have the student make 4
groups of 2 counters.
• Have the student skip count
out loud by 2s while pointing
to each group of counters. Then
have the student skip count
again, writing the numbers as
he or she counts.
• Repeat the activity, with groups
of 3, 4, 5, 6, and 10 counters.
Each time, have the student
skip count out loud at least
three times. Provide number
lines as needed for skip
counting.
Name
Equal Groups
Lesson
3-B
Draw a picture.
What Can I Do?
I want to find the total
number of items in a
problem with groups
of items.
José has 4 groups of 6 pencils. How
many pencils does he have in all?
Think: There are 4 groups of 6 pencils.
Draw a picture to solve.
There are 24 pencils in all.
Finish drawing each picture.
Then write the total amount.
Copyright © The McGraw-Hill Companies, Inc.
1. Draw 3 groups of 2 triangles.
Total =
triangles
2. Draw 2 groups of 5 squares.
Total =
squares
Name
Draw each picture.
Then write the total amount.
Total =
rectangles
5. 2 groups of 9 circles
Total =
circles
7. 7 groups of 8 squares
Total =
squares
3-B
4. 4 groups of 7 rectangles
Total =
rectangles
6. 6 groups of 3 triangles
Total =
triangles
8. 9 groups of 4 circles
Total =
circles
Copyright © The McGraw-Hill Companies, Inc.
3. 5 groups of 5 rectangles
Lesson
USING LESSON 3-B
Name
Equal Groups
Lesson
3-B
Lesson Goal
• Draw a picture to find the total
number of items in a problem with
groups of items.
Draw a picture.
What Can I Do?
José has 4 groups of 6 pencils. How
many pencils does he have in all?
I want to find the total
number of items in a
problem with groups
of items.
What the Student Needs
to Know
Think: There are 4 groups of 6 pencils.
Draw a picture to solve.
• Draw recognizable objects.
• Multiply to find the total number
of objects.
There are 24 pencils in all.
Getting Started
Finish drawing each picture.
Then write the total amount.
1. Draw 3 groups of 2 triangles. Check students’ drawings.
Copyright © The McGraw-Hill Companies, Inc.
• Present students with a picture
or a physical group of 20 objects
scattered about in no particular
order. Then present students with
the same 20 objects arranged in
groups of 4. Ask:
• Which way makes it easier to count
the objects? Why? (Answers may
vary.)
• Once you have grouped the objects,
how can you go about finding the
total number? (count by 1s, use
repeated addition, skip count,
multiply)
• If I’m going to use repeated
addition to find the total number in
these groups, what number should I
repeatedly add? (4)
• How many times should I add 4? (5)
• This is the same as multiplying what
two numbers? (5 × 4)
Total =
6
triangles
2. Draw 2 groups of 5 squares.
Total =
10
squares
079_080_S_G4_C03_SI_119816.indd 79
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WHAT IF THE STUDENT NEEDS HELP TO
What Can I Do?
Read the question and the response.
Then discuss the example. Ask:
• How many pencils are in a group?
(6)
• How many groups of pencils are
there? (4)
• How can I find how many pencils
I have all together? (count by 1s,
repeatedly add, multiply)
• How will you show multiplication?
(4 × 6)
• What is the total number of pencils?
(24)
Draw Recognizable
Objects
Multiply to Find the Total
Number of Objects
• Have the student make dots,
draw small circles, or use
counters.
• Have the student practice this
skill during “free time.”
• Practice basic multiplication
facts for 10 to 15 minutes daily
until the student can recall the
products for multiplication facts
automatically.
Name
Draw each picture.
Then write the total amount.
3-B
Students should draw
5 groups of 5 rectangles.
Students should draw
4 groups of 7 rectangles.
Total =
Total =
25
rectangles
5. 2 groups of 9 circles
28
6. 6 groups of 3 triangles
Students should draw
6 groups of 3 triangles.
Total =
Total =
circles
7. 7 groups of 8 squares
Students should draw
7 groups of 8 squares.
Total =
56
squares
• Have students make their drawings
as clear and organized as possible.
• Check students’ drawings for
Exercises 1 and 2.
• Have volunteers tell you how they
go from their drawings to totaling
the number of objects.
rectangles
Students should draw
2 groups of 9 circles.
18
Try It
4. 4 groups of 7 rectangles
18
Students should draw
9 groups of 4 circles.
36
• For each of the exercises, have
volunteers draw their answers on
the board. Have them tell what
method they used to find the total
number of objects.
triangles
8. 9 groups of 4 circles
Total =
Power Practice
circles
Copyright © The McGraw-Hill Companies, Inc.
3. 5 groups of 5 rectangles
Lesson
079_080_S_G4_C03_SI_119816.indd 80
7/9/12 11:21 AM
WHAT IF THE STUDENT NEEDS HELP TO
Complete the Power
Practice
• Discuss each incorrect answer.
Have the student model any
fact he or she missed, using
physical counters rather than
drawn ones.
Lesson 3-B
Name
Repeated Addition and Skip
Counting
repeated addition
2 + 2 + 2 + 2
Lesson
3-C
skip count
= 8
2,
4,
6,
8
Draw cubes to show repeated addition.
Copyright © The McGraw-Hill Companies, Inc.
1. 5 + 5 + 5 + 5 + 5 =
2. 2 + 2 + 2 =
Skip count.
4.
3.
,
,
,
,
,
USING LESSON 3-C
Name
Repeated Addition and Skip
Counting
Lesson Goal
• Use skip counting or repeated
addition to add the same number
three or more times.
repeated addition
What the Student Needs to
Know
Lesson
3-C
skip count
2 + 2 + 2 + 2
= 8
2,
4,
6,
8
• Use skip counting.
Draw cubes to show repeated addition.
Getting Started
1. 5 + 5 + 5 + 5 + 5 = 25
Practice
• Read the directions as students
complete Exercises 1 through 4.
• Check student work.
• If students have difficulty with
the activity, work with them to
model skip counting and repeated
addition with groups of cubes.
Encourage students to practice
skip counting each problem aloud
to find the sum.
6
Skip count.
Teach
Read and discuss the example at the
top of the page.
• How many groups of cubes are in
the example? (4)
• How many cubes are in each
group? (2)
• Let’s break down the repeated addition sentence to find the answer.
• If 2 + 2 = 4 and 2 + 2 = 4. What’s
4 + 4? (8)
• Skip counting can also be used to
find the total amount of cubes.
• Let’s skip count by 2s for each group
of cubes. (2, 4, 6, 8)
• How many cubes are there in all? (8)
2. 2 + 2 + 2 =
See students’ work.
Copyright © The McGraw-Hill Companies, Inc.
• Ask eight students to come to the
front of the class. Have them make
four groups with two students in
each group.
• As you point to each group, say:
“2 + 2 + 2 + 2 = 8. I used repeated
addition to find the total.”
• Point to each group again and say:
“2, 4, 6, 8. I used skip counting to find
the total.”
• Repeat using ten students with
five groups of two. Have a volunteer say the repeated addition and
skip counting aloud.
4.
3.
3 ,
6 ,
9
4 ,
8 ,
12 ,
083_S_G4_C03_SI_119816.indd 83
16
7/17/12 3:00 PM
WHAT IF THE STUDENT NEEDS HELP TO
Use Skip Counting
• Give the student a hundred
chart. Ask him or her to skip
count by 2s beginning with the
number 2 and continuing to
the end of the chart.
• What was the last number you
counted? (100)
• Next, have the student model
skip counting by drawing equal
groups of two. The student can
draw equal groups on paper
to show the groups and then
use the hundreds chart to help
count.
• Example: “Draw 5 equal groups
of 2.” The student should draw
5 groups of 2 and then skip
count: 2, 4, 6, 8, 10.
• Continue to model equal
groups and use the hundreds
chart to practice skip counting.
Name
Use a Number Line to Divide
8
7
6
5
4
Lesson
3-D
3
2
1
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 25
You can subtract to help divide.
24 - 3 - 3 - 3 - 3 - 3 - 3 - 3 - 3 = 0
1
2
3
4
5
6
7
8
24 ÷ 3 = 8
Subtract to divide.
6
1.
5
4
3
2
1
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 25
24 - 4 - 4 - 4 - 4 - 4 - 4 = 0
24 ÷ 4 =
12
Copyright © The McGraw-Hill Companies, Inc.
2.
11
10
9
8
7
6
5
4
3
2
1
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 25
24 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 = 0
24 ÷ 2 =
3. Divide. Use the number line.
20 ÷ 4 =
0
1
2
3
4
5
6
7
8
9 10
11
12 13 14 15 16 17 18 19 20
USING LESSON 3-D
Name
Use a Number Line to Divide
Lesson
3-D
Lesson Goal
8
• Model division with repeated
subtraction and skip counting
backward.
7
6
5
Practice
• Have students complete Exercises
1 through 3. Check student work.
1
24 - 3 - 3 - 3 - 3 - 3 - 3 - 3 - 3 = 0
1
2
3
4
5
6
7
8
24 ÷ 3 = 8
Getting Started
Read and discuss the example at the
top of the page. Ask:
• What number is bold on the number
line? (24) What number is circled on
the number line? (0)
• In order to find the quotient to the
number sentence 24 ÷ 3, we need to
skip count backward.
• What number should we start at? (24)
• What should we skip count
backward by? (3)
• What number should we end on? (0)
• Use the number line to show students how to skip count backward.
• Let’s count the number of hops
backward. How many did you
count? (8)
• If we use repeated subtraction to
check our work, how many times
should we subtract 3? (8 times)
Show students the repeated
subtraction on the board.
• What is 24 ÷ 3? (8)
2
You can subtract to help divide.
• Skip count backward.
Subtract to divide.
6
1.
5
4
3
2
1
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 25
24 - 4 - 4 - 4 - 4 - 4 - 4 = 0
6
24 ÷ 4 =
12
2.
Copyright © The McGraw-Hill Companies, Inc.
Teach
3
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 25
What the Student Needs to
Know
• Use a number line to skip
count forward by 2s to 20.
• Then, show how to skip count
backward by 2s from 20.
• Skip count aloud as you draw
jumps backward on the number
line.
• Then write the repeated
subtraction: 20 - 2 - 2 - 2 - 2 2 - 2 - 2 - 2 - 2 - 2 = 0.
• Count the number of 2s aloud and
write the answer. (10)
• Related this to the division sentence 20 ÷ 2 = 10.
4
11
10
9
8
7
6
5
4
3
2
1
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 25
24 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 - 2 = 0
24 ÷ 2 = 12
3. Divide. Use the number line.
20 ÷ 4 =
5
5
0
1
2
4
3
4
5
6
3
7
8
9 10
2
11
1
12 13 14 15 16 17 18 19 20
085_S_G4_C03_SI_119816.indd 85
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WHAT IF THE STUDENT NEEDS HELP TO
Skip Count Backward
• Use counters to form groups for
skip counting backward.
• The student should start with
20 counters and gather them
into groups of 4.
• The student can remove one
group of four counters by
counting back one counter
at a time. (20-19-18-17)
• They have 16 left. Then remove
four more counters: 16-15-1413. There are 12 left.
• Have the student continue until
they have only four counters
left.
• Ask, “What is the skip counting
pattern?” (20, 16, 12, 8, 4)
• Repeat the activity with a
different number of counters
until the student can count
backward with ease.
Name
Addition and Subtraction
Fact Families
What Can I Do?
I want to complete
a family of facts.
Lesson
3-E
Use the sum.
If the addition facts are
3 + 5 = 8 and 5 + 3 = 8,
then start each subtraction fact
with the sum which is 8.
Subtract each addend.
8-3=5
8-5=3
Each fact uses the same
three numbers 3, 5, and 8.
Copyright © The McGraw-Hill Companies, Inc.
Complete each family of facts.
1. 8 + 4 = 12
2. 6 + 7 = 13
3. 4 + 3 = 7
4 + 8 = 12
7 + 6 = 13
3+4=7
-8=4
13 -
7-4=
-4=8
13 - 7 =
=7
7-
=4
4. 6 + 3 = 9
5. 3 + 9 = 12
6. 3 + 8 = 11
3+6=9
9 + 3 = 12
8 + 3 = 11
-6=3
12 -
11 - 3 =
-3=6
12 - 9 =
=9
11 -
=3
Name
Write the pair of related
subtraction facts for each
pair of addition facts.
7. 9 + 7 = 16
8. 9 + 1 = 10
9. 6 + 8 = 14
7 + 9 = 16
1 + 9 = 10
8 + 6 = 14
10. 4 + 6 = 10
11. 7 + 4 = 11
12. 9 + 4 = 13
6 + 4 = 10
4 + 7 = 11
4 + 9 = 13
14. 8 + 9 = 17
2+6=8
9 + 8 = 17
3-E
Fact Family Roll
You will need two 1– 6
number cubes.
15. 7 + 5 = 12
16. 8 + 5 = 13
5 + 7 = 12
5 + 8 = 13
• Toss the cubes to get two
numbers to add. If the
numbers are the same,
toss again.
• The first player to write
two addition and two
subtraction facts gets one
point.
• Play the game until one
player has 7 points.
Copyright © The McGraw-Hill Companies, Inc.
13. 6 + 2 = 8
Lesson
USING LESSON 3-E
Name
Addition and Subtraction
Fact Families
Lesson Goal
• Complete addition/subtraction fact
families.
I want to complete
a family of facts.
If the addition facts are
3 + 5 = 8 and 5 + 3 = 8,
then start each subtraction fact
with the sum which is 8.
• Complete addition and subtraction
facts.
• Understand the relationship
between addition and subtraction.
Subtract each addend.
8-3=5
8-5=3
Each fact uses the same
three numbers 3, 5, and 8.
Getting Started
Complete each family of facts.
Copyright © The McGraw-Hill Companies, Inc.
Find out what students know about
the relationship between addition
and subtraction. Write the following
addition facts on the board:
5 + 7 = 12
Ask:
• What is a subtraction fact you can
write using the same numbers?
(12 - 7 = 5; 12 - 5 = 7)
Have students write another addition
and subtraction fact to complete the
fact family.
1. 8 + 4 = 12
2. 6 + 7 = 13
3. 4 + 3 = 7
4 + 8 = 12
7 + 6 = 13
3+4=7
12 - 8 = 4
13 - 6 = 7
7-4= 3
12 - 4 = 8
13 - 7 = 6
7- 3 =4
4. 6 + 3 = 9
5. 3 + 9 = 12
6. 3 + 8 = 11
3+6=9
9 + 3 = 12
8 + 3 = 11
9 -6=3
12 - 3 = 9
11 - 3 = 8
9 -3=6
12 - 9 = 3
11 - 8 = 3
What Can I Do?
Read the question and the response.
Then read and discuss the examples.
Ask:
• What three numbers appear in each
addition and subtraction fact?
(3, 5, 8)
• Where does 8 appear in the
addition facts? (as the sum or after
the equals sign) Where does 8
appear in the subtraction facts?
(as the first number)
• How many number sentences are
in the fact family for 3, 5, and 8?
(4) How many numbers are in each
number sentence? (3)
• Do the numbers in a family of facts
change from fact to fact, or do they
remain the same? (remain the
same)
• Do any of the facts in a fact family
repeat themselves, or are they all
different? (all different)
3-E
Use the sum.
What Can I Do?
What the Student Needs to
Know
Lesson
087_088_S_G4_C03_SI_119816.indd 87
7/9/12 2:30 PM
WHAT IF THE STUDENT NEEDS HELP TO
Complete Addition and
Subtraction Facts
• Use counters to demonstrate
the principle of addition. Start
with smaller numbers, and work
up to showing that 9 + 9 = 18.
• Use counters to demonstrate
the principle of subtraction.
Start with simple subtraction
facts such as 3 - 1 = 2, and
work up to show that 18 - 9 = 9.
• Have the student write basic
addition and subtraction facts
on flash cards. Then have the
student practice with flash cards
until the facts can be recalled
with ease.
Understand the
Relationship between
Addition and Subtraction
• Use counters to illustrate addition facts, such as 3 + 9 = 12.
Then demonstrate with counters how the same numbers are
in the related subtraction fact
12 - 9 = 3.
• Have the student practice by
using addition facts to write
subtraction facts until the
student can do so with ease. For
example: 8 + 7 = 15;
15 - 7 = 8.
Name
Write the pair of related
subtraction facts for each
pair of addition facts.
7. 9 + 7 = 16
8. 9 + 1 = 10
9. 6 + 8 = 14
7 + 9 = 16
1 + 9 = 10
8 + 6 = 14
16 - 9 = 7
10 - 9 = 1
14 - 6 = 8
16 - 7 = 9
10 - 1 = 9
14 - 8 = 6
10. 4 + 6 = 10
11. 7 + 4 = 11
12. 9 + 4 = 13
6 + 4 = 10
4 + 7 = 11
4 + 9 = 13
10 - 4 = 6
11 - 7 = 4
13 - 9 = 4
10 - 6 = 4
11 - 4 = 7
13 - 4 = 9
Lesson
3-E
13. 6 + 2 = 8
14. 8 + 9 = 17
2+6=8
9 + 8 = 17
8-6=2
17 - 8 = 9
You will need two 1– 6
number cubes.
8-2=6
17 - 9 = 8
• Toss the cubes to get two
numbers to add. If the
numbers are the same,
toss again.
• The first player to write
two addition and two
subtraction facts gets one
point.
• Play the game until one
player has 7 points.
16. 8 + 5 = 13
5 + 7 = 12
5 + 8 = 13
12 - 7 = 5
13 - 8 = 5
12 - 5 = 7
13 - 5 = 8
Have students look at Exercises 1
and 2. Ask:
• How do you know which number to
start with in the subtraction facts?
(You start with the number that is
the sum of the addition facts.)
• How do you know which of the
lesser numbers is missing from the
subtraction facts? (by comparing
the subtraction facts with the
addition facts; by solving one of
the equations)
• Have students complete
Exercises 1–6. Check to be sure
that students understand that
the numbers in a fact family
remain consistent.
Fact Family Roll
Copyright © The McGraw-Hill Companies, Inc.
15. 7 + 5 = 12
Try It
087_088_S_G4_C03_SI_119816.indd 88
WHAT IF THE STUDENT NEEDS HELP TO
Power Practice
• Select one of the exercises and
have students complete it. Be sure
students understand how to convert an addition fact into 2 related
subtraction facts.
• Have students complete the
remaining practice items. Then
review each answer.
7/9/12 12:09 PM
Learn with Partners &
Parents
• Remind the players they are to
write the addition and subtraction fact families in this game.
Complete the Power
Practice
• Discuss each incorrect answer.
Have the student compare each
incorrect subtraction fact with
a corresponding addition fact.
Then have the student use
counters to demonstrate the
correctness of the revised
subtraction fact or facts.
Lesson 3-E
Name
Lesson
3-F
Fact Families
Write the fact family.
Copyright © The McGraw-Hill Companies, Inc.
4
6
10
1.
+
=
2.
+
=
3.
-
=
4.
-
=
Complete each fact family.
5. 5 + 8 = 13
6. 2 + 7 = 9
+
=
+
=
-
=
-
=
-
=
-
=
USING LESSON 3-F
Name
Lesson
3-F
Fact Families
Lesson Goal
Write the fact family.
• Relate addition and subtraction
facts using fact families.
What the Student Needs to
Know
4
• Relate addition and subtraction.
• Identify fact families.
6
10
Getting Started
Teach
Read and discuss Exercise 1 at the top
of the page. The numbers on the roof
will be used to write addition and
subtraction number sentences for the
fact family in each window.
• Out of the numbers 4, 6 and 10,
what number is the greatest? (10)
• Where will the 10 appear in an
addition number sentence? (as the
sum or after the equals sign)
• Where will the 10 appear in a
subtraction number sentence? (as
the first number)
• In Exercise 1, what type of number
sentence will we write? (addition)
• Where should we place the 10 in the
number sentence? (as the sum or
after the equals sign)
• Does it matter what order the 4 and
6 are in? (No; 4 + 6 and 6 + 4 both
equal 10.)
• Make sure students understand
the addition and subtraction
sentences should be different.
Example: The addition sentences
should be 4 + 6 and 6 + 4.
Practice
• Have students complete Exercises
2 through 6. Check their work.
4
6
=
10
2.
10 - 6
=
4
4.
1.
3.
Copyright © The McGraw-Hill Companies, Inc.
• Explain to students that a fact family
is a set of two addition and two subtraction sentences that are related.
• Use connecting cubes of two
different colors and a bucket
balance to compare related
addition sentences.
• Place 3 blue cubes and 2 red cubes
on one side of the balance. On the
other side of the balance, place 2
blue cubes and 3 red cubes.
• Discuss how 3 + 2 = 2 + 3 and
both equal 7.
+
6
4
=
10
10 - 4
=
6
+
Complete each fact family.
5. 5 + 8 = 13
6. 2 + 7 = 9
8
+
5
=
13
7
+
2
=
9
13
-
5
=
8
9
-
2
=
7
13
-
8
=
5
9
-
7
=
2
091_S_G4_C03_SI_119816.indd 91
09/07/12 6:45 PM
WHAT IF THE STUDENT NEEDS HELP TO
Relate Addition and
Subtraction
• Give the student two number
cubes.
• Have the student roll the
number cubes and instruct him
or her to use the two numbers
to write a fact family.
• For example, if the student
rolled a 3 and 4, the student
would write: 3 + 4 = 7; 4 + 3 =
7; 7 - 3 = 4; 7 - 4 = 3.
Identify Fact Families
• Give the student 3 sets of fact
families, with each fact written
on an individual card.
• Have the student mix the cards
up and sort them into piles of
related facts.
• Then have the student read
aloud the four facts in each
family.
Name
Subtract with a Number Line
Divide. Use the number line.
Lesson
3-G
1. 16 ÷ 2 =
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2. 20 ÷ 5 =
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
3. 18 ÷ 3 =
Copyright © The McGraw-Hill Companies, Inc.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Use the number line to divide.
4.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10
÷
2
=
5.
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
24
÷
4
=
USING LESSON 3-G
Name
Lesson Goal
3-G
Divide. Use the number line.
• Model dividing with repeated
subtraction and skip counting
backward.
1. 16 ÷ 2 =
8
What the Student Needs to
Know
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2. 20 ÷ 5 =
• Use a number line to skip count
backward.
4
4
Getting Started
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
3. 18 ÷ 3 =
6
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Copyright © The McGraw-Hill Companies, Inc.
• On the board, write the equation
4 + 5 + 4 + 5.
• Ask, “Is this equation an example or
non-example of repeated addition?
Why?” (Non-example; The number
being added does not repeat the
same number.)
• What is an example of repeated
addition? (answers may vary;
example: 4 + 4 + 4)
• Write the equation: 15 - 5 - 4 - 3
- 2 - 1.
• Ask students, “Is this an example
or non-example of repeated subtraction? Why?” (Non-example; The
numbers being subtracted need to
be the same number.)
• What is an example of repeated
subtraction? (answers may vary;
example: 10 - 2 - 2 - 2)
Lesson
Subtract with a Number Line
Use the number line to divide.
5
4.
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10
÷
2
6
5.
=
5
5
4
3
2
1
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
24
÷
4
=
6
093_S_G4_C03_SI_119816.indd 93
Teach
Read and discuss Exercise 1 at the top
of the page.
• Let’s use a number line to divide.
• What number should we start at? (16)
• What are we going to count back
by? (2s)
• If we start at 16 and skip count back
by 2, what number will we reach
next? (14)
• What other numbers will we reach
when counting back by 2s? (12, 10,
8, 6, 4, 2, 0)
• Show students how to skip count
backward on the number line.
• How many times did we skip count
backward? (8) What is 16 ÷ 2? (8)
Practice
• Have students complete Exercises
2 through 5. Check their work.
7/9/12 12:30 PM
WHAT IF THE STUDENT NEEDS HELP TO
Use a Number Line to Skip
Count Backward
• Practice skip counting forward
by 2s prior to starting skip
counting backward.
• Use a number line to count by
2s. (2, 4, 6, 8, 10, etc.)
• When the student can skip
count forward independently,
move onto skip counting
backward.
• When dividing, the student
should skip count backward
by using a number line to find
equal groups.
• For example: How many
equal groups of 4 can be made
from 12?
• Start at 12 and count back by 4s
until you reach 0.
• Look at the number line. It is
divided into equal sections. How
many numbers are in each
section? (4)
• How many equal sections are
there? (3)
• What is 12 ÷ 4? (3)
• Continue to practice
counting back with a number
line until the student can do it
independently.
Name
Lesson
Write Multiplication Sentences
3-H
Write a multiplication sentence. Find each product.
2.
1.
×
=
=
×
=
×
=
4.
3.
×
Copyright © The McGraw-Hill Companies, Inc.
×
=
6.
5.
×
=
USING LESSON 3-H
Name
Lesson
Write Multiplication Sentences
Lesson Goal
3-H
Write a multiplication sentence. Find each product.
• Use arrays to represent
multiplication.
2.
1.
What the Student Needs to
Know
• Understand arrays.
• Use repeated addition to multiply.
2
Getting Started
3
=
6
3
×
4
=
12
3
×
5
=
15
5
×
5
=
25
4.
3.
4
Copyright © The McGraw-Hill Companies, Inc.
• Write the word array on the board.
Then draw four rows of circles with
two circles in each row.
• Say: “There are 4 rows with 2 circles
in each row.” Under the array, write
4 × 2 = 8.
• Point to the 4 and say: “This is the
number of rows.”
• Then point to the 2 and say: “This is
the number in each row.”
• Point to the multiplication sign.
Say: “This is a multiplication sign. It is
found in a multiplication sentence.”
• Point to the product. Say: “This is
the product, or answer.”
• Have students use cubes to model
arrays for other multiplication
sentences.
×
×
2
=
8
6.
5.
4
×
5
=
20
Teach
Read and discuss Exercise 1 at the top
of the page.
• Let’s use the array to write a multiplication sentence to find the product.
• How many rows of dragonflies are in
the array? (2) This will be our first
factor in our multiplication sentence.
• How many dragonflies are in each
row? (3) This will be our second
factor in our multiplication sentence.
• How many dragonflies are in the
array? (6) This will be our product.
• What will our multiplication
sentence look like? (2 × 3 = 6)
Practice
• Have students complete Exercises
2 through 6.
• Check student work.
• If students have difficulty with the
activity, work with them to use
connecting cubes to model each
equation.
095_S_G4_C03_SI_119816.indd 95
7/9/12 12:36 PM
WHAT IF THE STUDENT NEEDS HELP TO
Understand Arrays
• Help the student become
familiar with arrays.
• Write array on the board. Next
to it write arrange. Say both
words so the student can hear
the similarity. When you arrange
objects, you put them in a special
order. When we draw an array of
objects we put them in rows and
columns.
• Draw an array for 3 × 6 = 18
on the board. Point to the three
rows. The objects are arranged
in rows and columns. The array
shows 3 rows with 6 in each row.
• Draw other arrays on the board.
Have the student describe
each array in terms of how the
objects are arranged.
• Ask the student to say the
multiplication sentence represented by each array.
Use Repeated Addition to
Multiply
• Demonstrate the connection
between repeated addition and
a multiplication sentence. Point
out that the first number in a
multiplication sentence tells
you how many times to add the
second number.
• For example: 4 × 3 = 12 means
you should add 3 to itself 4
times: 3 + 3 + 3 + 3 = 12.
• Have the student practice
writing repeated addition
sentences for multiplication
sentences and vice versa.
Name
Add with the Commutative Property
Lesson
3-I
Commutative Property of Addition:
What Can I Do?
I want to write a different
addition sentence using
the same addends
and sum.
You can change the order of the addends
and the sum will be the same.
Use the Commutative Property of Addition
to write a different addition sentence for
1 + 2 = 3.
1+2=3
2+1=3
So, 1 + 2 = 2 + 1.
Complete.
So, 1 + 8 = 8 +
2. 3 + 9 = 12 and 9 + 3 = 12
3. 4 + 9 = 13 and 9 + 4 = 13
So,
So, 3 + 9 =
.
4. 3 + 5 = 8 and 5 + 3 = 8
+ 9 = 9 + 4.
So, 3 +
Write a different addition sentence for each.
5.
6.
3+2=5
7.
1+2=3
8.
5+2=7
+ 3.
2+1=3
= 5 + 3.
Copyright © The McGraw-Hill Companies, Inc.
1. 1 + 8 = 9 and 8 + 1 = 9
Name
Complete.
Lesson
3-I
Write how many.
9. 2 + 7 = 7 +
10. 9 + 1 =
+9
11. 4 +
=3+4
12.
+4=4+9
13. 7 +
=1+7
14.
+9=9+6
15. 6 + 4 =
17.
+6
+5=5+2
16. 6 + 1 = 1 +
18. 8 +
=7+8
Copyright © The McGraw-Hill Companies, Inc.
Write a different addition sentence for each.
19. 4 + 6 = 10
20. 2 + 1 = 3
21. 6 + 7 = 13
22. 7 + 9 = 16
23. 3 + 6 = 9
24. 1 + 9 = 10
25. 4 + 5 = 9
26. 9 + 2 = 11
Write two different addition sentences for each model. Use the same
addends and sum for each.
27.
28.
Name
Add with the Commutative Property
Lesson
3-I
Lesson Goal
• Write a different addition sentence
using the same addends and sum.
What the Student Needs
to Know
Commutative Property of Addition:
What Can I Do?
• Identify the missing number as an
addend.
• Use the Commutative Property of
Addition.
• Use the same addends and sum to
write a different addition sentence.
Getting Started
Find out what students know about
writing different addition sentences
using the same addends and sum.
Display 6 red cubes and 4 blue
cubes. Say:
• Write a number sentence for the
cubes. (6 + 4) What is the sum? (10)
• Change the order of the cubes. Write
another addition sentence. (4 + 6)
What is the sum? (10)
• Does the order in which you add
the red cubes and the blue cubes
matter? (No) Why? (The sum is the
same.)
You can change the order of the addends
and the sum will be the same.
I want to write a different
addition sentence using
the same addends
and sum.
Use the Commutative Property of Addition
to write a different addition sentence for
1 + 2 = 3.
1+2=3
2+1=3
So, 1 + 2 = 2 + 1.
Complete.
1. 1 + 8 = 9 and 8 + 1 = 9
So, 1 + 8 = 8 +
l
2. 3 + 9 = 12 and 9 + 3 = 12
3. 4 + 9 = 13 and 9 + 4 = 13
So,
4
9
So, 3 + 9 =
.
+ 3.
4. 3 + 5 = 8 and 5 + 3 = 8
+ 9 = 9 + 4.
So, 3 +
5
= 5 + 3.
Write a different addition sentence for each.
6.
5.
3+2=5
2+3=5
7.
1+2=3
2+1=3
8.
5+2=7
2+5=7
Copyright © The McGraw-Hill Companies, Inc.
USING LESSON 3-I
2+1=3
1+2=3
What Can I Do?
Read the question and the response.
Then read and discuss the example.
Ask volunteers to model the example
with colored connecting cubes. Ask:
• Which numbers can you reorder
in an addition sentence? (the
addends)
• How can you tell which numbers
in an addition sentence are the
addends? (The addends are on
either side of the addition sign.)
• How can you tell which number in
an addition sentence is the sum?
(The sum is by itself after the
equals sign.)
• Can you reorder a sum and an
addend to make two addition sentences that are equal? (No)
097_098_S_G4_C03_SI_119816.indd 97
09/07/12 6:50 PM
WHAT IF THE STUDENT NEEDS HELP TO
Identify the Missing
Number as an Addend
Use the Commutative
Property of Addition
• For Exercises 1–4 and 9–18, the
student may incorrectly write
the sum in the blank instead of
the missing addend. Emphasize
that the student is combining
the same addends, just in a
different way. Have the student
use counters to demonstrate
each addition sentence missed.
• Direct the student’s attention
to Exercise 1. Explain that
the Commutative Property
of Addition can help him or
her find 1 + 8 if he or she
knows that 1 + 8 = 9. Have
the student use flashcards to
change the order of addends
in basic addition facts until this
can be done with ease.
Name
Complete.
Lesson
3-I
Write how many.
2
9. 2 + 7 = 7 +
1
10. 9 + 1 =
11. 4 +
3
=3+4
12.
9
+4=4+9
13. 7 +
1
=1+7
14.
6
+9=9+6
4
15. 6 + 4 =
17.
2
+6
+5=5+2
7
• Have students complete Exercises
1–8. Encourage them to use cubes
or counters to model the two
different sentences.
• Review their answers and have
students explain how their models
show that their answers are
correct.
6
16. 6 + 1 = 1 +
18. 8 +
Try It
+9
=7+8
Write a different addition sentence for each.
19. 4 + 6 = 10
20. 2 + 1 = 3
6 + 4 = 10
21. 6 + 7 = 13
9 + 7 = 16
24. 1 + 9 = 10
Copyright © The McGraw-Hill Companies, Inc.
6+3=9
25. 4 + 5 = 9
• Have students complete the
practice exercises. Then review
each answer.
22. 7 + 9 = 16
7 + 6 = 13
23. 3 + 6 = 9
Power Practice
1+2=3
9 + 1 = 10
26. 9 + 2 = 11
5+4=9
2 + 9 = 11
Write two different addition sentences for each model. Use the same
addends and sum for each.
27.
28.
2+3=5
4+1=5
3+2=5
1+4=5
097_098_S_G4_C03_SI_119816.indd 98
7/9/12 12:49 PM
WHAT IF THE STUDENT NEEDS HELP TO
Use the Same Addends
and Sum to Write
a Different Addition
Sentence
• Have the student use red and
blue connecting cubes to
model the sentence. Have the
student write the number of
red cubes on one sticky note
and the number of blue cubes
on another sticky note.
• Have the student match the
order of the addends to the
order of the cubes and write
the addition sentence.
• Then have the student change
the order of the colors of the
cubes. The student can then
match the order of the sticky
notes to the new order of the
cubes and write the new
addition sentence.
Complete the Power
Practice
• Discuss each incorrect answer.
Have the student use counters
or connecting cubes to help
show the correct answer.
Lesson 3-I
Name
Missing Factors
Lesson
Use basic multiplication facts.
3-J
Write the missing factor.
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.
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 =
Copyright © The McGraw-Hill Companies, Inc.
3×
2. 4 × 5 =
= 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
USING LESSON 3-J
Name
Missing Factors
Lesson Goal
Use basic multiplication facts.
• Use basic multiplication facts to
find a missing factor.
What Can I Do?
I want to find a
missing factor.
?
= 10
Think: 2 times what number is equal to
10?
2×1=2
2×2=4
2×3=6
2×4=8
2 × 5 = 10
So, 5 is the missing factor.
Getting Started
Write each product. Then write each missing factor.
1. 3 × 4 = 12
3×
Copyright © The McGraw-Hill Companies, Inc.
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)
2×
Find the multiplication fact for 2 with a
product of 10.
• Recall basic multiplication facts
from 1 to 5.
What Can I Do?
3-J
Write the missing factor.
What the Student Needs
to Know
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,
I immediately recognize a missing
factor.
• I can set up a list of facts for 2. I write
out 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6.
So, 3 is the missing factor.
Lesson
4
= 12
2. 4 × 5 = 20
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
101_S_G4_C03_SI_119816.indd 101
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.
7/9/12 12:58 PM
WHAT IF THE STUDENT NEEDS HELP TO
Recall Basic Multiplication
Facts from 1 to 5
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 handy to use as a
reference.
• Discuss each incorrect answer.
Review how the student can
check his or her answers by
using counters or lists.
Name
Multiples of a Number
Lesson
3-K
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
.
and
.
3. There are 4 rows of 3 clocks.
12 is a multiple of
A multiple of a number is the product of that number and any whole number.
Circle the number that is not a multiple.
4. 7
5. 4
14, 21, 28, 36, 42
18, 24, 28, 36, 40
6. 6
7. 8
Copyright © The McGraw-Hill Companies, Inc.
12, 18, 22, 30, 42
16, 24, 40, 56, 62
8. Complete the graphic organizer. One line is done for you.
Multiples of a Number
Examples
Non-Example
7: 14, 21, 28, 35
5:
,
,
,
10
Multiples of a Number
Examples
Non-Example
3:
,
9:
,
,
,
,
,
USING LESSON 3-K
Name
Multiples of a Number
Lesson Goal
Lesson
3-K
Use models to answer.
• Find examples and non-examples
of multiples of a number.
1. There are 4 rows of 10 bees.
40 is a multiple of
What the Student Needs
to Know
and
4
10
.
and
7
.
and
3
.
2. There are 4 rows of 7 hammers.
28 is a multiple of
• Use multiplication to find the
multiple.
4
3. There are 4 rows of 3 clocks.
4
12 is a multiple of
Getting Started
A multiple of a number is the product of that number and any whole number.
Circle the number that 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
Copyright © The McGraw-Hill Companies, Inc.
• Write the word multiple on the
board and explain the definition.
A multiple of a number is the
product of that 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.
16, 24, 40, 56, 62
8. Complete the graphic organizer. One line is done for you.
Multiples of a Number
Examples
Non-Example
Sample
answers:
7: 14, 21, 28, 35
Sample
answers:
10
5: 10 , 15 , 20 , 25
12
Multiples of a Number
Examples
Non-Example
Sample
answers:
3: 6 , 9 , 12 , 15
9: 18 , 27 , 36 , 45
Sample
answers:
13
20
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) In the number
sentence 4 × 10 = 40, what number
is the multiple? (40)
• 40 is a multiple of 4 and 10.
Practice
• Have students complete Exercises
2 through 8. Check their work.
103_S_G4_C03_SI_119816.indd 103
7/9/12 1:03 PM
WHAT IF THE STUDENT NEEDS HELP TO
Use Multiplication to Find
the Multiple
• Have the student use an array
to model a multiplication
sentence.
• For example, have the student
model the array 5 × 1 with
connecting cubes to help
identify the multiple.
• What is the first factor? (5) There
will be 5 rows.
• What is the second factor? (1)
There will be 1 column.
• Have the student construct the
array with connecting cubes.
• Label the array 5 × 1. Count the
number of connecting cubes in
the array. How many connecting
cubes are in the array? (5)
• The total number of cubes, or the
product, is a multiple.
• What two numbers is 5 a product
of? (5 and 1)
• Continue to have the student
model arrays with 5 × 2,
5 × 3, 5 × 4, etc. until the student understands the product
is also the multiple of the two
factors.