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 5
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
1-3
5-A: Round to the
Nearest Ten or Hundred
Round
4.NBT.3
Chapter 1,
Lesson 5
4-6
5-B: Add Two-Digit
Numbers
Addition
4.NBT.4
Chapter 2,
Lesson 3
7-8
5-C: Repeated Addition
Model
multiplication
4.NBT.5
Chapter 4,
Lesson 4
9-10
5-D: Multiplication Facts
Through 9
Multiplication
4.NBT.5
Chapter 4,
Lesson 3
Check My Progress 1
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
4-6
5-E: Multiples of 10
Multiply by tens
4.NBT.5
5-F: Estimate Products
Estimate products
4.NBT.3
7-9
Chapter 5,
Lesson 1
Chapter 5,
Lesson 2
Review
Where is this
concept in
My Math?
If
Students miss
Exercises…
Then
use this Strategic
Intervention Activity…
Concept
6-9
5-G: Multiplication Facts
Multiply by tens
4.NBT.5
Chapter 5,
Lesson 1
5-I: Compare Numbers
with Two- and
Three -Digits
Estimate products
4.NBT.3
Chapter 5,
Lesson 2
5-J: Multiplication with
Regrouping
Multiply two, twodigit numbers
4.NBT.5
Chapter 5,
Lesson 4
5-H: Round to the
Nearest Ten
10-13
14-17
Name
Round to the Nearest Ten
or Hundred
Lesson
5-A
You can round numbers by using place value.
thousands
3
What Can I Do?
I want to round to the
nearest ten or hundred.
hundreds tens ones
3
6
1
Round 3,361 to the nearest hundred.
• Find the hundreds place.
• Look at the digit to its right.
3,361
If the digit is 5 or greater,
round up.
If the digit is less than 5, round down. Since 6 > 5,
round up.
To the nearest hundred, 3,361 rounds up to 3,400.
Round 3,361 to the nearest ten.
• Find the tens place.
• Look at the digit to its right.
3,361
Copyright © The McGraw-Hill Companies, Inc.
If the digit is 5 or greater, round up.
If the digit is less than 5,
round down. Since 1 < 5, round down.
To the nearest ten, 3,361 rounds down to 3,360.
Round each number to the nearest ten.
1. 35
2. 83
3. 671
4. 982
5. 1,309
6. 3,357
Round each number to the nearest hundred.
7. 293
8. 646
9. 485
10. 8,128
11. 4,151
12. 1,207
Name
Round each number to the
underlined place.
13. 4,147
14. 281
15. 867
16. 54
17. 3,163
18. 5,247
19. 8,724
20. 3,955
21. 7,299
22. 2,709
23. 4,277
24. 5,529
Lesson
5-A
Round to the nearest ten.
25. 3,849
26. 4,323
27. 9,322
28. 8,234
29. 483
30. 5,801
31. 3,735
32. 969
33. 365
34. 492
35. 3,655
36. 9,118
37. 779
38. 789
39. 2,615
40. 583
41. 1,488
42. 883
43. 3,814
44. 698
45. 8,712
46. 6,479
47. 5,656
48. 3,344
Copyright © The McGraw-Hill Companies, Inc.
Round to the nearest hundred.
USING LESSON 5-A
Name
Round to the Nearest Ten
or Hundred
Lesson Goal
thousands
I want to round to the
nearest ten or hundred.
• Identify the tens place.
• Identify the hundreds place.
• Identify multiples of 10 and 100.
• Repeat the activity by marking
15 on the number line. Students
should find that 15 appears exactly
halfway between two tens. Tell
students that if a number is
halfway between two tens, it is
rounded to the greater ten.
6
1
Round 3,361 to the nearest hundred.
• Find the hundreds place.
• Look at the digit to its right.
3,361
Round 3,361 to the nearest ten.
• Find the tens place.
• Look at the digit to its right.
3,361
Copyright © The McGraw-Hill Companies, Inc.
If the digit is 5 or greater, round up.
If the digit is less than 5,
round down. Since 1 < 5, round down.
To the nearest ten, 3,361 rounds down to 3,360.
Round each number to the nearest ten.
1. 35
40
2. 83
4. 982
980
5. 1,309
80
1,310
3. 671
6. 3,357
670
3,360
Round each number to the nearest hundred.
7. 293
10. 8,128
300
8,100
8. 646
11. 4,151
600
4,200
9. 485
12. 1,207
500
1,200
141_142_S_G4_C05_SI_119816.indd 141
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WHAT IF THE STUDENT NEEDS HELP TO
Identify the Tens Place
10 11 12 13 14 15 16 17 18 19 20
3
If the digit is 5 or greater,
round up.
If the digit is less than 5, round down. Since 6 > 5,
round up.
To the nearest hundred, 3,361 rounds up to 3,400.
Getting Started
Read the question and the response.
Then read and discuss the examples.
• Ask students to mark 11 and 18 on
a number line and draw an arrow
connecting each number with the
number they round to. Point out
that each number is closer to the
multiple of ten that it rounds to on
the number line.
hundreds tens ones
3
What Can I Do?
What the Student Needs
to Know
What Can I Do?
5-A
You can round numbers by using place value.
• Round to the nearest ten or
hundred.
• Write 40, 50, and 60 on the board.
Remind students that these are
called multiples of 10.
• Ask: What are the two multiples of
10 nearest to 43? (40 and 50) To 57?
(50 and 60)
• Write 400, 500, and 600 on the
board. Remind students that these
are called multiples of 100.
• Ask: What are the two multiples of
100 nearest to 438? (400 and 500)
To 572? (500 and 600)
Lesson
• Use place-value charts for two-,
three-, and four-digit numbers.
• Use base-ten blocks to review
the meaning of the digits in
two- and three-digit numbers.
Identify the Hundreds
Place
• Use place-value charts and
base-ten blocks to model
three- and four-digit numbers.
• Use color-coded cards. Give
each pair of students 3 crayons
(red, yellow, and blue) and 3
index cards. Students should
write a number from 1 to 9 on
each card, using a different
color for each. Create three-digit
place-value charts. Have the
students shade the columns:
ones, red; tens, yellow;
hundreds, blue. Have pairs
match each number card by its
color to a column on the chart.
Identify Multiples of 10
and 100
• Count aloud by 10s from 10
to 100. Have the student write
these multiples of 10 on the
board. Point out that a multiple
of 10 has a zero in the ones
place. Repeat the activity with
multiples of 100.
Name
Lesson
Round each number to the
underlined place.
13. 4,147
16. 54
4,150
50
14. 281
300
15. 867
5-A
• Have students write 3,361 in a
place-value chart and round it to
the nearest ten, explaining the rule
used. (3,360; If the ones digit is less
than 5, round down.)
• Ask students to round 3,361 to
the nearest hundred. Explain that
instead of using the ones digit, they
will use the tens digit and the same
rules for rounding. Have students
identify the digit in the tens place
and determine whether to round to
the next greater hundred. (6 tens;
Round 3,361 up to 3,400.)
870
17. 3,163
3,200
18. 5,247
5,250
19. 8,724
8,700
20. 3,955
4,000
21. 7,299
7,300
22. 2,709
2,710
23. 4,277
4,300
24. 5,529
5,500
Round to the nearest ten.
25. 3,849
3,850
26. 4,323
4,320
27. 9,322
9,320
28. 8,234
8,230
29. 483
480
30. 5,801
5,800
31. 3,735
3,740
32. 969
34. 492
490
35. 3,655
970
3,660
33. 365
36. 9,118
370
Try It
9,120
• Work through Exercises 1 and 2
with students. Have students
use the ones digit to round to
the nearest ten. Have students
demonstrate or explain how they
found their answers to each
exercise. For Exercises 3–6, have
students tell you the tens digit in
each number. For Exercises 7–12,
have them tell you the hundreds
digit.
37. 779
800
38. 789
40. 583
600
41. 1,488
43. 3,814
3,800
44. 698
46. 6,479
6,500
47. 5,656
800
1,500
700
5,700
39. 2,615
42. 883
2,600
900
45. 8,712
8,700
48. 3,344
3,300
Copyright © The McGraw-Hill Companies, Inc.
Round to the nearest hundred.
Power Practice
141_142_S_G4_C05_SI_119816.indd 142
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WHAT IF THE STUDENT NEEDS HELP TO
Complete the Power
Practice
• Have the student draw number
lines to show the exercises. When
rounding to the nearest ten, the
number line is numbered by 1s.
When rounding to the nearest
hundred, the number line is
numbered by 10s.
• Have the student underline
the number in the place they
are rounding to, then circle the
digit to the right.
• The student may have difficulty
finding the halfway point on a
number line. Distribute number
lines marked 0–100, 100–200,
300–400, and so on up to
900–1,000. Have the student
point and follow on their
number lines as you model how
he or she can count forward
to find the middle or halfway
point. Mark each halfway point
with a symbol such as a stop
sign. Repeat with different
marked number lines until the
student recognizes the pattern
that the halfway point always
includes the number 50.
• Before doing the exercises, check
that students fully grasp the
importance of ones when rounding
to the nearest ten. The digit in the
ones place determines how the
digit in the tens place is rounded.
• Have the students read the
directions and look over the
practice items.
Lesson 5-A
Name
Add Two-Digit Numbers
What Can I Do?
Lesson
5-B
Decide whether to regroup.
26
+ 47
26
+ 43
I want to
add two-digit
numbers.
Think: I can add 6
ones and 3 ones
without regrouping.
I can’t add 6 ones
and 7 ones without
regrouping.
No Regrouping
Regroup 13 ones
as 1 ten 3 ones.
1
26
+ 47
73
26
+ 43
69
Add the other way to check.
Copyright © The McGraw-Hill Companies, Inc.
Check addition by adding in the other
direction.
26
+ 43
69
43
+ 26
69
26
+ 47
73
1
47
+ 26
73
Circle Regroup or No Regrouping.
Then add.
1.
55
+ 34
Regroup
No Regrouping
2.
62
+ 19
Regroup
No Regrouping
Name
Lesson
Circle Regroup or No Regrouping.
Then add.
3.
28
+ 17
Regroup
5-B
4.
31
+ 27
No Regrouping
5.
24
+ 48
Regroup
No Regrouping
6.
Regroup
No Regrouping
16
+ 27
Regroup
No Regrouping
7.
32
+ 8
8.
40
+ 22
9.
57
+ 27
10.
33
+ 29
11.
64
+ 31
12.
65
+ 6
13.
42
+ 52
14.
35
+ 45
15.
86
+ 12
16.
14
+ 68
17.
21
+ 67
18.
47
+ 39
19.
13
+ 18
20.
53
+ 8
21.
46
+ 19
Copyright © The McGraw-Hill Companies, Inc.
Add. Check by adding in the other direction.
USING LESSON 5-B
Name
Add Two-Digit Numbers
Lesson
5-B
Lesson Goal
• Add two-digit numbers, with and
without regrouping.
What Can I Do?
Decide whether to regroup.
What the Student Needs
to Know
• Regroup ones as tens and ones.
• Check addition.
Think: I can add 6
ones and 3 ones
without regrouping.
I can’t add 6 ones
and 7 ones without
regrouping.
No Regrouping
Regroup 13 ones
as 1 ten 3 ones.
Getting Started
Add the other way to check.
Check addition by adding in the other
direction.
26
+ 43
69
43
+ 26
69
26
+ 47
73
1
47
+ 26
73
Circle Regroup or No Regrouping.
Then add.
1.
What Can I Do?
Read the question and the
response. Then read and discuss
the examples. Ask:
• Why can you add 6 ones and 3 ones
without regrouping? (They add up
to 9 ones, which is less than the 10
ones needed for regrouping.)
• Why do you need to regroup when
you add 6 ones and 7 ones? (They
add up to 13 ones, which is more
than 10 ones or 1 ten.)
1
26
+ 47
73
26
+ 43
69
Copyright © The McGraw-Hill Companies, Inc.
Use tens and ones base-ten blocks to
show the numbers 13 and 18. Ask:
• How many tens are in each number?
How many ones are in each number?
(1 ten, 3 ones; 1 ten, 8 ones)
Put the blocks together. Say:
• I’m adding 13 and 18. Now how
many tens do I have? How many
ones do I have? (2 tens, 11 ones)
• What can I do with 11 ones?
(Regroup as 1 ten and 1 one.)
• Now how many tens do I have? How
many ones do I have? (3 tens, 1 one)
26
+ 47
26
+ 43
I want to
add two-digit
numbers.
55
+ 34
89
Regroup
No Regrouping
2.
62
+ 19
81
Regroup
No Regrouping
145_146_S_G4_C05_SI_119816.indd 145
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WHAT IF THE STUDENT NEEDS HELP TO
Regroup Ones as Tens
and Ones
• Give the student 18 ones
base-ten blocks and 5 tens
blocks. Have the student show
addends like these: 32 + 18;
17 + 25; 29 + 17. After showing
the addends, have the student
put the base-ten blocks together
and regroup any groups of 10
ones for 1 ten before finding
the sum. Encourage the student
to talk about each step of the
process.
Check Addition
• Display addition fact cards to
18 and have the student use
counters to model the facts.
• Then ask the student to check
the addition by adding the
numbers in a different direction
and using counters to model
the new fact.
Name
Lesson
Circle Regroup or No Regrouping.
Then add.
3.
5.
28
+ 17
45
Regroup
24
+ 48
72
Regroup
5-B
4.
No Regrouping
6.
No Regrouping
31
+ 27
58
Regroup
16
+ 27
43
Regroup
Try It
• Remind students that they only
need to look at the ones digits to
know whether or not to regroup.
If the ones add up to less than 10,
no regrouping is needed. If they
add up to 10 or more, you must
regroup.
• Make sure students realize that
they are to add as well as to
circle the correct choice.
No Regrouping
No Regrouping
Add. Check by adding in the other direction.
8.
10.
33
+ 29
62
13.
40
+ 22
62
9.
57
+ 27
84
11.
64
+ 31
95
12.
65
+ 6
71
42
+ 52
94
14.
35
+ 45
80
15.
86
+ 12
98
16.
14
+ 68
82
17.
21
+ 67
88
18.
47
+ 39
86
19.
13
+ 18
31
20.
53
+ 8
61
21.
46
+ 19
65
Power Practice
• If necessary, provide additional
paper for students to check their
answers.
• Have students complete the
practice items. Then review each
answer.
Copyright © The McGraw-Hill Companies, Inc.
32
+ 8
40
7.
145_146_S_G4_C05_SI_119816.indd 146
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WHAT IF THE STUDENT NEEDS HELP TO
Complete the Power
Practice
• Discuss each incorrect answer.
Have the student tell which
addition problems require
regrouping and which do not.
• Watch for students who
consistently forget to add the
regrouped ten. Remind them to
write the 1 above the tens after
they add the ones.
Lesson 5-B
Name
Repeated Addition
Lesson
5-C
Use skip counting.
What Can I Do?
I want to add the same
number more than
one time.
Find 4 + 4 + 4 + 4 + 4.
Look at the number of 4s. There are five 4s.
Skip count by 4s five times.
4 + 4 + 4 + 4 + 4
4,
8,
12,
16,
20
So, 4 + 4 + 4 + 4 + 4 = 20
Find each sum. Skip count to help.
1. 2 + 2 + 2 + 2 =
2. 5 + 5 + 5 =
Skip count by 2s
Copyright © The McGraw-Hill Companies, Inc.
,
,
Skip count by 5s.
,
,
,
Find each sum.
3. 3 + 3 + 3 + 3 + 3 =
4. 6 + 6 + 6 =
5. 4 + 4 + 4 + 4 =
6. 5 + 5 + 5 + 5 + 5 + 5 =
7. 7 + 7 + 7 + 7 =
8. 8 + 8 + 8 + 8 =
9. 2 + 2 + 2 + 2 + 2 + 2 =
10. 9 + 9 + 9 + 9 + 9 + 9 =
USING LESSON 5-C
Name
Repeated Addition
Lesson
5-C
Lesson Goal
Use skip counting.
• Use skip counting to add the same
number three or more times.
What Can I Do?
Find 4 + 4 + 4 + 4 + 4.
I want to add the same
number more than
one time.
What the Student Needs
to Know
Look at the number of 4s. There are five 4s.
Skip count by 4s five times.
4 + 4 + 4 + 4 + 4
• Use skip counting.
4,
Getting Started
Ask students to look at this
example: 2 + 2 + 2. Say:
• When you add these numbers, you
skip the numbers between them.
• The numbers you count are ? .
(2, 4, 6)
• The numbers you skip are ? .
(3, 5)
Read the question and the response.
Then look at the example. Ask:
• How many 4s are being added? (5)
• How many times do you skip
count 4? (5)
Skip count with students: 4, 8, 12, 16,
20. You may want to have students
count the in-between numbers with a
ruler: Say: 4; Use your finger to point to
5, 6, and 7 on the ruler.
Try It
• Have students read Exercise 1 and
count the number of 2s. Have
students write the correct numbers
on the lines by skip counting.
• Have students follow the same
procedure for Exercise 2.
Power Practice
• Have students complete the
practice items. Then review each
answer.
12,
16,
20
Find each sum. Skip count to help.
8
1. 2 + 2 + 2 + 2 =
2. 5 + 5 + 5 = 15
Skip count by 2s
2
Copyright © The McGraw-Hill Companies, Inc.
What Can I Do?
8,
So, 4 + 4 + 4 + 4 + 4 = 20
,
4
,
Skip count by 5s.
6
,
8
5 , 10 , 15
Find each sum.
3. 3 + 3 + 3 + 3 + 3 = 15
4. 6 + 6 + 6 = 18
5. 4 + 4 + 4 + 4 = 16
6. 5 + 5 + 5 + 5 + 5 + 5 = 30
7. 7 + 7 + 7 + 7 = 28
8. 8 + 8 + 8 + 8 = 32
9. 2 + 2 + 2 + 2 + 2 + 2 = 12
10. 9 + 9 + 9 + 9 + 9 + 9 = 54
149_S_G4_C05_SI_119816.indd 149
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WHAT IF THE STUDENT NEEDS HELP TO
Use Skip Counting
• Use counters to form groups for
skip counting. Show the student
that by gathering the counters
into groups of, say, 4, they can
count 1-2-3-4, then 5-6-7-8, and
so on. The last number in each
group of 4 becomes the next
number in the skip counting
pattern.
• Practice selected addition facts
daily for 5 or 10 minutes:
adding equal numbers, such as
4 + 4, then 4 to the sum of that
(8 + 4), and so on. Repeat until
the student can recall the
sums for these addition facts
automatically.
Complete the Power
Practice
• Discuss each incorrect answer.
• Perhaps the student will
understand the concept of skip
counting if presented in a
different modality; for example,
draw picture models (shade
every fourth frog he or she
draws) or playing a game (every
fourth student stands up).
Name
Multiplication Facts Through 9
Lesson
5-D
Use any multiplication strategy.
What Can I Do?
I want to multiply
two numbers.
Find 6 × 5.
Double a known fact. Use repeated addition.
Double 3 × 5 to find
6 × 5.
Add 5 six times.
3 × 5 = 15
15 + 15 = 30
5 + 5 + 5 + 5 + 5 + 5 = 30
So, 6 × 5 = 30.
So, 6 × 5 = 30.
Skip count on a number line.
Skip count by 5s six 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 25 26 27 28 29 30
Copyright © The McGraw-Hill Companies, Inc.
So, 6 × 5 = 30.
Double a known fact to find each product.
1. 4 × 9 =
Double 2 × 9
3. 6 × 5 =
Double 3 × 5.
2. 8 × 5 =
Double 4 × 5
4. 10 × 7 =
Double 5 × 7
Name
Lesson
Use repeated addition to find each product.
5. 3 × 7 =
5-D
6. 5 × 5 =
Add:
Skip count to find each product.
8. 4 × 6 =
7. 5 × 3 =
Count:
Count:
9. 2 × 6 =
10. 4 × 4 =
11. 5 × 7 =
12. 6 × 7 =
13. 3 × 8 =
14. 9 × 3 =
15. 7 × 4 =
16. 8 × 6 =
17. 5 × 8 =
18.
8
×2
19.
3
×6
20.
7
×7
21.
9
×3
22.
6
×6
23.
9
×8
24.
8
×4
25.
6
×9
26.
9
×4
27.
7
×8
28.
7
×9
29.
9
×9
Copyright © The McGraw-Hill Companies, Inc.
Find each product. Use any method.
USING LESSON 5-D
Name
Multiplication Facts Through 9
Lesson Goal
5-D
Use any multiplication strategy.
• Use any multiplication strategy to
multiply two numbers through 9.
What Can I Do?
I want to multiply
two numbers.
What the Student Needs
to Know
• Double a basic multiplication fact.
• Use repeated addition.
• Skip count.
Find 6 × 5.
Double a known fact. Use repeated addition.
Double 3 × 5 to find
6 × 5.
Add 5 six times.
3 × 5 = 15
15 + 15 = 30
5 + 5 + 5 + 5 + 5 + 5 = 30
So, 6 × 5 = 30.
So, 6 × 5 = 30.
Skip count on a number line.
Getting Started
Skip count by 5s six 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 25 26 27 28 29 30
So, 6 × 5 = 30.
Copyright © The McGraw-Hill Companies, Inc.
• Write the multiplication fact
3 × 7 on the board. Say:
• Of the three strategies of doubling
a known fact, repeated addition,
and skip counting on a number
line, which ones can be used for this
example? (repeated addition, skip
counting on a number line)
• Explain that it is necessary to have
one of the factors be an even
number to be able to use the
doubling method, because you
don’t get a whole number when
you divide an odd number by 2.
Lesson
Double a known fact to find each product.
1. 4 × 9 = 36
Double 2 × 9
3. 6 × 5 = 30
Double 3 × 5.
2. 8 × 5 = 40
Double 4 × 5
4. 10 × 7 = 70
Double 5 × 7
What Can I Do?
Read the question and the response.
Then discuss the first example. Ask:
• Can you use the doubling
method to find the answer to
the example 6 × 5? (Yes)
• What would you double?
(3 × 5 = 15)
• How would you use repeated
addition to solve? (add 5 six
times: 5 + 5 + 5 + 5 + 5 + 5)
Use an existing number line from
1 to 30 or draw a new one.
Demonstrate skip counting 6 groups
of 5 by drawing arrows that show
“jumps” between 0 and 5, 5 and 10,
10 and 15, 15 and 20, 20 and 25, and
25 and 30.
• Ask: Which two methods are most
alike? (repeated addition and skip
counting)
151_152_S_G4_C05_SI_119816.indd 151
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WHAT IF THE STUDENT NEEDS HELP TO
Double a Basic
Multiplication Fact
• Have the student keep handy
a chart of numbers and their
doubles (2 × 2 = 4, 3 × 3 = 9,
and so on) to refer to.
• Have the student practice these
doubling facts daily until he or
she knows them.
Use Repeated Addition
• Practice selected addition facts
daily for 5 or 10 minutes:
adding equal numbers, such as
4 + 4, then 4 to the sum of that
(8 + 4), and so on. Repeat until
the student can recall the sums
for these addition facts
automatically.
• If this is still difficult, have the
student use counters to form
groups for repeated addition.
Name
Lesson
Use repeated addition to find each product.
5. 3 × 7 = 21
5-D
Try It
6. 5 × 5 = 25
• Have students do Exercises 1–4
using the doubling method. Check
that students understand that they
must use the even number as their
“double.” Ask what would happen
if both numbers were even.
(They would have a choice of
which factor to use as the double.)
• Have students do Exercises 5 and
6 using repeated addition. Check
to make sure students are clear on
which is the number to add and
which tells the number of times it
gets added.
• Have students do Exercises 7
and 8 by skip counting. Check to
make sure students are clear on
which is the number to skip count
and which tells the number of
times it gets counted.
Add: 5 + 5 + 5 + 5 + 5 = 25
Add: 7 + 7 + 7 = 21
Skip count to find each product.
7. 5 × 3 = 15
8. 4 × 6 = 24
Count: 3, 6, 9, 12, 15
Count:
6, 12, 18, 24
Find each product. Use any method.
9. 2 × 6 = 12
10. 4 × 4 =
16
11. 5 × 7 = 35
12. 6 × 7 = 42
13. 3 × 8 =
24
14. 9 × 3 = 27
15. 7 × 4 = 28
16. 8 × 6 = 48
40
18.
8
×2
16
19.
3
×6
18
20.
7
×7
49
21.
9
×3
27
22.
6
×6
36
23.
9
×8
72
24.
8
×4
32
25.
6
×9
54
9
×4
36
27.
7
×8
56
28.
7
×9
63
29.
26.
9
×9
81
Copyright © The McGraw-Hill Companies, Inc.
17. 5 × 8 =
151_152_S_G4_C05_SI_119816.indd 152
Power Practice
• Have students complete the
practice items. Then review each
answer.
7/9/12 2:42 PM
WHAT IF THE STUDENT NEEDS HELP TO
Skip Count
• Show the student that by
gathering counters into groups
of, say, 4, he or she can count
1-2-3-4, then 5-6-7-8, and so on.
The last number in each group
of 4 becomes the next number
in skip counting.
Complete the Power
Practice
• Discuss each incorrect answer
and review the previous skills, if
necessary.
Lesson 5-D
Name
Multiples of 10
Lesson
5-E
Find 4 × 20.
Use a basic fact.
What Can I Do?
I want to use basic facts
and patterns to find a
multiple of 10.
Use multiples of 10.
20 is a multiple of
10 because
2 × 10 = 20
Think: 4 × 2 = 8
Think: 4 × 2 = 8
Apply the pattern:
4 × 20 = 80
Use basic facts to multiply.
1. 2 × 30 =
2. 2 × 70 =
3. 3 × 50 =
4. 3 × 40 =
5. 8 × 10=
6. 4 × 50 =
7. 5 × 70 =
8. 6 × 30 =
Copyright © The McGraw-Hill Companies, Inc.
Multiply.
9.
30
× 7
10.
50
× 5
11.
40
× 8
12.
30
× 9
13.
90
× 5
14.
60
× 6
15.
90
× 4
16.
80
× 3
17. 2 × 60 =
18. 3 × 70 =
19. 5 × 40 =
20. 9 × 20 =
21. 6 × 80 =
22. 4 × 70 =
USING LESSON 5-E
Name
Multiples of 10
Lesson
5-E
Lesson Goal
• Use basic facts and patterns to find
multiples of 10.
I want to use basic facts
and patterns to find a
multiple of 10.
What the Student Needs to
Know
20 is a multiple of
10 because
2 × 10 = 20
Think: 4 × 2 = 8
Apply the pattern:
4 × 20 = 80
Use basic facts to multiply.
Getting Started
• Conduct a brief review of the
multiplication facts, emphasizing
the more difficult facts. If
necessary, post a multiplication
facts table for student reference.
1. 2 × 30 = 60
2. 2 × 70 = 140 3. 3 × 50 = 150
4. 3 × 40 = 120
5. 8 × 10= 80
6. 4 × 50 = 200 7. 5 × 70 = 350
8. 6 × 30 = 180
Multiply.
Copyright © The McGraw-Hill Companies, Inc.
Read the question and the response.
Then read and discuss the examples.
Ask:
• What multiplication fact is
“hidden” in 4 × 30? (4 × 3 = 12)
• How does knowing the product of
4 × 3 help you solve 4 × 30?
(Possible answer: I can multiply
4 × 3 and then add a zero at the
end.)
Use multiples of 10.
Think: 4 × 2 = 8
• Identify ones and tens digits.
• Complete multiplication facts.
• Recognize multiples of 10.
What Can I Do?
Find 4 × 20.
Use a basic fact.
What Can I Do?
9.
30
× 7
210
10.
50
× 5
250
11.
40
× 8
320
12.
30
× 9
270
13.
90
× 5
450
14.
60
× 6
360
15.
90
× 4
360
16.
80
× 3
240
17. 2 × 60 = 120
18. 3 × 70 = 210
19. 5 × 40 = 200
20. 9 × 20 = 180
21. 6 × 80 = 480
22. 4 × 70 = 280
Try It
• Have students tell you the basic
fact that corresponds with each
exercise.
155_S_G4_C05_SI_119816.indd 155
7/9/12 2:45 PM
WHAT IF THE STUDENT NEEDS HELP TO
Power Practice
• Have students state the basic
fact that corresponds with each
exercise.
• Select a few of the exercises and
have volunteers demonstrate how
they solved it.
Identify Ones and Tens
Digits
• Write a two-digit number such
as 83 on the board. Ask: How
many tens are in this number?
How many ones? (8 tens, 3 ones)
Remind the student that the 8
is called the tens digit. It tells
the number of tens. The 3 is the
ones digit because it tells the
number of ones.
Complete Multiplication
Facts
• Have the student work in pairs
using flash cards to identify any
unknown facts. He or she can
use counters or base-ten blocks
to demonstrate the products
of multiplying 2 one-digit
numbers.
Recognize Multiples of 10
• Remind the student that any
number ending in zero is a
multiple of 10.
Name
Estimate Products
What Can I Do?
I want to estimate
the answer to a
multiplication problem.
Lesson
5-F
Round the
greater factor.
Multiply to
estimate.
Round the greater
number so that it
has only one digit
that is not zero.
6 × 3 = 18
60 × 3 = 180
So, 62 × 3 is about
180.
62 × 3 → 60 × 3
8 × 27 → 8 × 30
8 × 3 = 24
8 × 30 = 240
So, 8 × 27 is about
240.
8 × 6 = 48
80 × 6 = 480
So, 78 × 6 is about
480.
78 × 6 → 80 × 6
Copyright © The McGraw-Hill Companies, Inc.
Round the factor to the underlined digit.
1. 7 × 57 → 7 ×
2. 2 × 32 → 2 ×
3. 9 × 94 → 9 ×
4. 8 × 25 → 8 ×
5. 5 × 44 → 5 ×
6. 3 × 74 → 3 ×
Round the factor to the underlined
digit to estimate the product.
7. 3 × 67 → 3 ×
estimate:
9. 4 × 21 → 4 ×
8. 9 × 18 → 9 ×
estimate:
10. 7 × 89 → 7 ×
estimate:
estimate:
11. 6 × 78 → 6 ×
12. 5 × 35 → 5 ×
estimate:
estimate:
USING LESSON 5-F
Name
Estimate Products
Lesson
5-F
Lesson Goal
• Use rounding to estimate the
product of a one-digit number by
a two-digit number.
What Can I Do?
I want to estimate
the answer to a
multiplication problem.
What the Student Needs to
Know
Round the
greater factor.
Multiply to
estimate.
Round the greater
number so that it
has only one digit
that is not zero.
6 × 3 = 18
60 × 3 = 180
So, 62 × 3 is about
180.
62 × 3 → 60 × 3
• Round to the nearest ten.
• Complete multiplication facts.
8 × 27 → 8 × 30
Getting Started
78 × 6 → 80 × 6
What Can I Do?
Read the question and the response.
Then have students study the three
examples.
• How have the three problems been
changed? (The greater number has
been rounded.)
• Have students read the sentences
on the right to learn how to estimate.
Try It
• Have students identify the
underlined digit in the first
exercise. Ask: How will you round
the number 57? (Look at the digit
to the right of the underlined
digit. It is greater than 5, so 57
rounds up 60.)
Power Practice
• Have students complete the
practice items. Then review each
answer.
8 × 6 = 48
80 × 6 = 480
So, 78 × 6 is about
480.
Round the factor to the underlined digit.
Copyright © The McGraw-Hill Companies, Inc.
• Write 50, 60, and 70 on the board.
Remind students that these are
called multiples of 10.
• What are the two multiples of 10
nearest to 53? (50 and 60) To 67?
(60 and 70)
• Have students find the tens place
and identify the digit to its right.
(ones place)
• If the digit is 5 or greater, round up. If
the digit is less than 5, round down.
8 × 3 = 24
8 × 30 = 240
So, 8 × 27 is about
240.
1. 7 × 57 → 7 × 60
2. 2 × 32 → 2 × 30
3. 9 × 94 → 9 × 90
4. 8 × 25 → 8 × 30
5. 5 × 44 → 5 × 40
6. 3 × 74 → 3 × 70
Round the factor to the underlined
digit to estimate the product.
7. 3 × 67 → 3 × 70
8. 9 × 18 → 9 × 20
estimate: 210
estimate: 180
9. 4 × 21 → 4 × 20
10. 7 × 89 → 7 × 90
estimate: 80
estimate: 630
11. 6 × 78 → 6 × 80
12. 5 × 35 → 5 × 40
estimate: 480
estimate: 200
157_S_G4_C05_SI_119816.indd 157
7/9/12 2:53 PM
WHAT IF THE STUDENT NEEDS HELP TO
Round to the Nearest Ten
• Draw number lines using
two-digit numbers. Remind
the student of the rules for
rounding: If the ones digit
is equal to or greater than 5,
round up. If the ones digit is less
than 5, round down.
Complete Multiplication
Facts
• Have the student work in pairs
using flash cards to identify
those facts they do not know.
Then have students form small
groups to create and share fact
strategies for the unknown
facts.
Complete the Power
Practice
• If the student is not rounding
correctly, have him or her
identify two nearest multiples
first. For example, the two tens
closest to 21 are 20 and 30.
Name
Multiplication Facts
Lesson
5-G
Use an array.
Draw a picture or use counters.
What Can I Do?
I want to find the product
of two numbers.
6×7
6, the first factor, tells the
number of rows.
7, the second factor, tells
the number in each row.
Count to find the product.
6 × 7= 42
Use repeated addition.
6×7
6, the first factor, tells
6×7
how many times to add. = 7 + 7 + 7 + 7 + 7 + 7
= 42
7, the second factor, tells
which number to add.
Copyright © The McGraw-Hill Companies, Inc.
Use an array. Find each product.
1.
5
× 3
2.
4
× 6
3.
9
× 3
4.
7
× 5
5.
7
× 1
6.
3
× 6
7.
8
× 2
8.
6
× 9
9. 3 × 3 =
10. 9 × 2 =
11. 4 × 8 =
12. 1 × 6 =
Name
Use repeated addition. Find each product.
13.
7
× 2
14.
8
× 8
15.
3
× 7
Lesson
16.
17. 6 × 3 =
18. 2 × 1 =
19. 5 × 6 =
20. 7 × 9 =
5
× 9
5-G
21.
8
× 1
22.
4
× 0
23.
3
× 5
24.
7
× 7
25.
9
× 1
26.
8
× 5
27.
1
× 4
28.
5
× 2
29.
3
× 9
30.
7
× 4
31.
0
× 8
32.
6
× 8
33.
5
× 5
34.
7
× 9
35.
4
× 4
36.
5
× 1
37. 0 × 6 =
38. 5 × 5 =
39. 1 × 4 =
40. 7 × 8 =
41. 4 × 7 =
42. 8 × 9 =
43. 5 × 0 =
44. 6 × 7 =
Copyright © The McGraw-Hill Companies, Inc.
Find each product.
USING LESSON 5-G
Name
Multiplication Facts
Lesson
5-G
Lesson Goal
Use an array.
• Find products of basic
multiplication facts.
Draw a picture or use counters.
What Can I Do?
I want to find the product
of two numbers.
What the Student Needs to
Know
7, the second factor, tells
the number in each row.
• Add a 1- digit number to a 1- or
2- digit number.
• Skip-count by numbers 2
through 9.
• Recognize multiplication as
repeated addition.
Count to find the product.
What Can I Do?
Read the question and the response.
Then have students look over the first
example.
• How many rows of counters are in
the array? (6) How many counters
are in each row? (7)
• Skip count to find the number
of counters in all. 7, 14, . . .
(21, 28, 35, 42) What is the
product of 6 × 7? (42)
6 × 7= 42
Use repeated addition.
6×7
6, the first factor, tells
6×7
how many times to add. = 7 + 7 + 7 + 7 + 7 + 7
= 42
7, the second factor, tells
which number to add.
Getting Started
Use an array. Find each product.
Copyright © The McGraw-Hill Companies, Inc.
Have students skip count with you.
Say:
• I want to count by 5s. Count with
me. 5, 10, 15, 20, 25, 30. What
number comes next? (35) How did
you find that number? (I added 5 to
the last number.)
• To get to 35 starting from 0, how
many times did you add 5?
(7 times)
Demonstrate and array of 7 rows of
5 counters each. Say:
• How many counters are in each
row? (5) How many rows of counters? (7) How many counters
in all? (35) Can you write this as a
multiplication fact? (7 × 5 = 35)
Repeat the activity with other basic
multiplication facts, such as 8 × 3
and 2 × 9.
6×7
6, the first factor, tells the
number of rows.
1.
5
× 3
15
2.
4
× 6
24
3.
9
× 3
27
4.
7
× 5
35
5.
7
× 1
7
6.
3
× 6
18
7.
8
× 2
16
8.
6
× 9
54
9. 3 × 3 =
9
11. 4 × 8 = 32
10. 9 × 2 = 18
12. 1 × 6 =
6
159_160_S_G4_C05_SI_119816.indd 159
7/9/12 2:59 PM
WHAT IF THE STUDENT NEEDS HELP TO
Add a 1-Digit Number to a
1- or 2-Digit Number
Skip Count by Numbers 2
through 9
• Have the students use flash
cards or mental math to
practice addition facts on a
daily basis, until he or she
knows the sums of basic facts
by rote.
• Once the student has
demonstrated a mastery of
basic facts, have him or her
practice adding a 1-digit
number to a 2-digit number
every day for 5–10 minutes.
• Have the student use a
number line or counters to
practice skip counting by
numbers 2–9. After enough
practice, the student should
be able to use counting on to
find the next number in each
sequence.
Name
Use repeated addition. Find each product.
13.
14.
7
× 2
14
8
× 8
64
15.
Lesson
16.
3
× 7
21
5
× 9
45
17. 6 × 3 = 18
18. 2 × 1 =
19. 5 × 6 = 30
20. 7 × 9 = 63
5-G
Have the student look over the
second example.
• What number do you add? (the
second factor; 7) How many times do
you add that number? (the number
shown by the first factor; 6) Add the
numbers together two at a time. What
sums do you get? (7 + 7 = 14;
14 +7 =21; 21 + 7 = 28;
28 + 7 = 35; 35 + 7 = 42)
• How is this pattern like counting?
(It is the same as skip counting.)
What is the product of 6 × 7? (42)
2
Find each product.
8
× 1
8
22.
4
× 0
0
23.
3
× 5
15
24.
7
× 7
49
25.
9
× 1
9
26.
8
× 5
40
27.
1
× 4
4
28.
5
× 2
10
29.
3
× 9
27
30.
7
× 4
28
31.
0
× 8
0
32.
6
× 8
48
33.
5
× 5
25
34.
7
× 9
63
35.
4
× 4
16
36.
5
× 1
5
37. 0 × 6 =
0
38. 5 × 5 = 25
39. 1 × 4 =
4
40. 7 × 8 = 56
41. 4 × 7 = 28
42. 8 × 9 = 72
43. 5 × 0 =
44. 6 × 7 = 42
0
Try It
Copyright © The McGraw-Hill Companies, Inc.
21.
159_160_S_G4_C05_SI_119816.indd 160
7/9/12 3:00 PM
WHAT IF THE STUDENT NEEDS HELP TO
Recognize Multiplication
as Repeated Addition
Complete the Power
Practice
• Have the student practice
multiplying using arrays. First,
have the student model 4
groups of 6 counters each,
without putting them in rows.
Students can repeatedly add
6 four times to find the total.
Next, have the student arrange
the counters in an even array of
4 rows of 6 counters each and
find the total using skip
counting and counting by 1s.
Finally, have him or her write an
addition sentence and a
multiplication sentence for
the array.
• Discuss each incorrect answer
with the student. Have the
student make an array of each
exercise using counters. Be
sure the student correctly
identifies the factor that shows
the number of rows and the
number of counters in
each row.
Provide counters for students. Ask
• Look at the first exercise. How many
rows of counters will you make? (5)
How many counters in each row? (3)
What is the product of 5 × 3? (15)
Have the student complete
Exercises 2–12. Then ask:
• Look at Exercise 13. What
number will you repeatedly add? (2)
How many times will you add that
number? (7 times) What is the
product of 7 × 2? (14)
• Continue to check students’
understanding of the
multiplication process and how it
relates to building arrays, repeated
addition, and skip-counting.
• Students who have difficulty
relating the vertical form of
multiplication to the horizontal
can be asked to read the
exercises aloud.
Power Practice
• Have students complete the
practice items. Then review each
answer.
• Ask volunteers to describe how
they solved selected exercises.
Discuss which method might work
better when the factors are greater
numbers and which is better when
the factors are lesser numbers.
Stress that both methods are
equally valid.
Lesson 5-G
Name
Round to the Nearest Ten
Lesson
5-H
Use a number line.
What Can I Do?
I want to round a number
to the nearest ten.
The number 18 is between 10 and 20. It is
closer to 20. So, 18 rounds up to 20.
10
11 12 13 14 15 16 17 18 19
20
The number 32 is between 30 and 40. It is
closer to 30. So, 32 rounds down to 30.
30 31
32 33 34 35 36 37 38 39 40
Use the ones digit.
If the ones digit is less than 5, round down.
If it is 5 or greater, round up.
Copyright © The McGraw-Hill Companies, Inc.
Round 64 down to 60. Round 65 up to 70.
Use the number line. Round to the nearest ten.
1. 51
2. 17
3. 34
50 51
10
52 53 54 55 56 57 58 59 60
11 12 13 14 15 16 17 18 19
30 31
32 33 34 35 36 37 38 39
20
40
Name
4. 81
5. 24
6. 38
7. 62
8. 33
9. 74
10. 45
11. 13
12. 9
13. 78
14. 65
15. 44
16. 26
17. 77
18. 88
Lesson
5-H
Copyright © The McGraw-Hill Companies, Inc.
Look at the ones digit. Round
each number to the nearest ten.
USING LESSON 5-H
Name
Round to the Nearest Ten
Lesson Goal
Lesson
5-H
Use a number line.
• Round numbers to the nearest ten.
What Can I Do?
I want to round a number
to the nearest ten.
What the Student Needs to
Know
The number 18 is between 10 and 20. It is
closer to 20. So, 18 rounds up to 20.
10
• Count by 10s.
• Read a number line.
• Identify the ones digit.
11 12 13 14 15 16 17 18 19
20
The number 32 is between 30 and 40. It is
closer to 30. So, 32 rounds down to 30.
Getting Started
30 31
• Have students count by 10s to 100.
• Display a hundred chart and have
students locate the 10s.
(10, 20, 30, . . . 100)
32 33 34 35 36 37 38 39 40
Use the ones digit.
If the ones digit is less than 5, round down.
If it is 5 or greater, round up.
Round 64 down to 60. Round 65 up to 70.
Read the question and the response.
Then read and discuss the examples.
Ask:
• What does it mean when you say “18
rounds up to 20”? (20 is the nearest
ten to 18, and it is greater, so you
have to round up.)
• What does it mean when you say “32
rounds down to 30”? (30 is the
nearest ten to 32, and it is less,
so you have to round down.)
• Would you round 55 up or down?
Why? (Up; you round up when the
ones digit is 5 or greater.)
Copyright © The McGraw-Hill Companies, Inc.
What Can I Do?
Use the number line. Round to the nearest ten.
1. 51
50
2. 17
20
3. 34
30
50 51
10
52 53 54 55 56 57 58 59 60
11 12 13 14 15 16 17 18 19
30 31
32 33 34 35 36 37 38 39
20
40
163_164_S_G4_C05_SI_119816.indd 163
7/9/12 3:07 PM
WHAT IF THE STUDENT NEEDS HELP TO
Count by 10s
Read a Number Line
• Give the student 10 play dimes
and have the student count by
tens to 1 dollar.
• Have the student use base-ten
blocks to show the tens from 10
to 100. Then have the student
count the blocks by tens.
• Draw a 0–10 number line on
the board. Have the student
locate a number you say, the
number that is 1 less, and the
number that is 1 greater.
Name
Look at the ones digit. Round
each number to the nearest ten.
4. 81
80
5. 24
20
6. 38
40
7. 62
60
8. 33
30
9. 74
70
10. 45
50
11. 13
10
12. 9
Lesson
5-H
Try It
Suggest that students use these
steps:
• Find the number on the number
line.
• Find the tens on either side of
that number.
• Decide which ten is closer to
the number.
• Write that ten.
10
Power Practice
80
14. 65
70
15. 44
40
16. 26
30
17. 77
80
18. 88
90
Copyright © The McGraw-Hill Companies, Inc.
13. 78
• Have students complete the
practice items. Then review each
answer.
• If students have trouble, they
might draw a number line to help
them.
163_164_S_G4_C05_SI_119816.indd 164
Learn with Partners &
Parents
7/9/12 3:08 PM
WHAT IF THE STUDENT NEEDS HELP TO
Identify the Ones Digit
• Have the student practice
identifying the ones digit
by writing the numbers in
Exercises 4–18 in place-value
charts.
Complete the Power
Practice
Have students use the ages of
people in their families to practice
rounding to the nearest ten.
• Give each student a hundred
chart to take home.
• Have students circle numbers on
the hundred chart that represent
family members‘ ages.
• Tell students to round each
family member‘s age to the nearest ten and write a sentence for
each person; for example, To the
nearest ten, Grandpa Dennis is 70.
To the nearest ten, I am 10.
• Review the rules for rounding:
round down if the ones digit
is 0–4; round up if the ones
digit is 5–9.
• Have the student circle the
ones digit before rounding the
number.
Lesson 5-H
Name
Compare Numbers with
Two- and Three-Digits
Lesson
5-I
Start at the left.
Compare the digits.
What Can I Do?
I want to compare two
whole numbers.
If one number has
more digits, it is
greater.
469
482
same
468 > 42
> means is greater
than.
Compare the
hundreds digit. Then
compare tens digits.
< means is less than.
6 < 8, so 469 < 482.
Circle the number that is greater.
1. 91 or 204
2. 63 or 36
3. 710 or 107
4. 454 or 544
7. 856 or 865
8. 505 or 55
Circle the number that is less.
Copyright © The McGraw-Hill Companies, Inc.
5. 24 or 214
6. 11 or 17
Compare. Use > or <.
9. 96
10. 415
405
11. 64
13. 113
130 14. 667
646
15. 961
17. 132
232 18. 73
21. 24
86
42
22. 329
37
332
42
12. 611
496
916
16. 312
231
19. 491
419
20. 18
23. 202
222
24. 323
183
328
USING LESSON 5-I
Name
Compare Numbers with
Two- and Three-Digits
Lesson Goal
• Compare two- and three-digit
whole numbers.
Compare the digits.
What Can I Do?
I want to compare two
whole numbers.
What the Student Needs to
Know
Try It
• Have students read the
directions for the two sets of
exercises.
• Then have students find those
exercises in which the two
numbers have a different number
of digits. Ask: Why are these
exercises easier than the others?
(The number with more digits is
always greater.)
Power Practice
• Remind students that the smaller,
pointed part of the > or < symbol
always points to the number that
is less.
469
482
> means is greater
than.
Compare the
hundreds digit. Then
compare tens digits.
< means is less than.
6 < 8, so 469 < 482.
1. 91 or 204
2. 63 or 36
3. 710 or 107
4. 454 or 544
7. 856 or 865
8. 505 or 55
Circle the number that is less.
5. 24 or 214
Copyright © The McGraw-Hill Companies, Inc.
Read the question and the response.
Then read and discuss the examples.
Ask:
• What numbers are being compared
in the first example? (468 and 42)
Which number is greater and how
do you know? (468, because it has
the hundreds digit)
• In the second example, do you use
the hundreds digits? (Yes, the
hundreds digits are the same. So,
compare the tens digits.)
Start at the left.
Circle the number that is greater.
Getting Started
What Can I Do?
5-I
same
468 > 42
• Compare one-digit numbers.
• Use the > and < symbols.
• Identify ones, tens, and
hundreds digits.
• Write 40 on the board. Say: Name a
number less than 40. What number
sentence can you write to show your
number is less than 40? (If students
choose 20, for example, they
write 20 < 40.)
• Now write a number sentence that
shows 40 is greater than your
number. (For example, 40 > 20.)
If one number has
more digits, it is
greater.
Lesson
6. 11 or 17
Compare. Use > or <.
9. 96 > 86
10. 415 > 405
11. 64 > 42
12. 611 > 496
13. 113 < 130 14. 667 > 646
15. 961 > 916
16. 312 > 231
17. 132 < 232 18. 73 > 37
19. 491 > 419
20. 18 < 183
21. 24 < 42
23. 202 < 222
24. 323 < 328
22. 329 < 332
167_S_G4_C05_SI_119816.indd 167
09/07/12 7:23 PM
WHAT IF THE STUDENT NEEDS HELP TO
Compare One-Digit
Numbers
Identify Ones, Tens, and
Hundreds Digits
• Write 8 and 2 on the board.
Ask the student which number
is greater. Write the sentence
“Eight is greater than two.”
Have the student change this
to math symbols: 8 > 2. Repeat,
using the sentence “Two is less
than eight.”
• Provide worksheets with blank
place-value charts.
• Have the student use a set
of 0–9 digit cards. He or she
should choose cards and write
digits in a chart. When the
charts are complete, have the
student read the numbers and
tell the place names of the
digits.
Use the > and < Symbols
• Write the > and < symbols
on the board and review their
meanings.
• Provide number cards and
cards with the > and <
symbols. Have students work in
small groups to make and
read comparison sentences.
Complete the Power
Practice
• Provide base-ten blocks. Have
the students work in pairs to
show the numbers.
Name
Multiplication with Regrouping
Lesson
5-J
Use basic facts and regrouping.
What Can I Do?
48
× 7
I want to multiply by
a 1-digit number.
Multiply the ones digit in the first factor by
the second factor. Regroup if needed.
5
7 × 8 = 56
48
× 7
6
Then, multiply the tens digit in the
first factor by the second. Add any
regrouped tens.
5
7 × 4 = 28
28 + 5 = 33
48
× 7
336
Copyright © The McGraw-Hill Companies, Inc.
Use basic facts and regrouping. Find each product.
1.
32
× 3
Think:
3 × 2 ones
3 × 3 tens
2.
61
× 5
Think:
5 × 1 ones
5 × 6 tens
3.
48
× 4
Think:
4 × 8 ones
4 × 4 tens
16 tens + 3 tens
Find each product.
4.
93
× 7
8. 73 × 5 =
5.
22
× 4
9. 94 × 4 =
6.
25
× 6
7.
56
× 8
10. 83 × 9 =
USING LESSON 5-J
Name
Multiplication with Regrouping
Lesson
5-J
Lesson Goal
Use basic facts and regrouping.
• Multiply a 2-digit number by a
1-digit number.
What Can I Do?
48
× 7
I want to multiply by
a 1-digit number.
What the Student Needs to
Know
Multiply the ones digit in the first factor by
the second factor. Regroup if needed.
5
• Recall basic multiplication facts.
• Recognize 10 ones as 1 ten for
regrouping.
Then, multiply the tens digit in the
first factor by the second. Add any
regrouped tens.
Getting Started
What Can I Do?
Have students read the question and
the response. Then read and discuss
the example. Ask:
• What is the first step in finding the
product of 48 × 7? (Multiply the
7 times the 8 in the ones place of
the second factor.) What is that
product? (56)
• What is the next step? (Multiply the
7 times the 4 in the tens place of
the first factor.) What is that
product? (28) What else do you
have to do? (You have to add the
5 regrouped tens.) What is that
sum? (28 + 5 = 33) What is the next
step? (Regroup the 30 tens as
3 hundreds.) Where do you write
that in the answer? (Write the 3
tens under the tens, and the 3
hundreds to the left of the tens.)
• What is 7 × 48? (336)
Try It
Have students read the directions and
look at the first exercise. Ask:
• When do you have to regroup to find
the product? (You have to regroup
when the product of the 1-digit
factor and the ones or tens digit of
the other factor is greater than 9.)
Power Practice
• Have students complete the
practice items. Then review each
answer.
5
7 × 4 = 28
28 + 5 = 33
48
× 7
336
Use basic facts and regrouping. Find each product.
1.
Copyright © The McGraw-Hill Companies, Inc.
Help students review multiplying
multiples of 10. Ask:
• I want to multiply 5 × 1. What is that
product? (5) What is the product of
5 × 10? (50)
• What is 2 × 4? (8) What is 2 × 40?
(80)
7 × 8 = 56
48
× 7
6
32
× 3
96
Think:
3 × 2 ones
3 × 3 tens
2.
61
× 5
305
Think:
5 × 1 ones
5 × 6 tens
3.
48
× 4
192
Think:
4 × 8 ones
4 × 4 tens
16 tens + 3 tens
Find each product.
4.
93
× 7
651
5.
8. 73 × 5 = 365
22
× 4
88
6.
25
× 6
150
9. 94 × 4 = 376
7.
56
× 8
448
10. 83 × 9 = 747
169_S_G4_C05_SI_119816.indd 169
7/9/12 3:26 PM
WHAT IF THE STUDENT NEEDS HELP TO
Recall Basic Multiplication
Facts
• Have the student use arrays or
repeated addition to find the
products of multiplication facts.
The student should practice
finding the products of these
facts for about 10 minutes each
day.
Recognize 10 Ones as 1
Ten for Regrouping
• Have the student work with
base-ten blocks. Have him
or her model addition that
will result in regrouping, for
instance 7 + 8.
• Help the student see that the
sum 15 can be regrouped as 1
ten and 5 ones. Point out that
there are the same number of
units in 10 ones as in 1 ten.
Complete the Power
Practice
• Discuss each incorrect or
incomplete answer with the
student. Have the student
name the product of each fact
within the exercise.
• Have the student write each
partial product, then add to
find the final product.