Lesson
2
Common Core State Standards
5.NBT.B.5 Fluently multiply multi-digit
whole numbers using the standard algorithm.
Multiply Multidigit Numbers
Students can readily apply place value concepts to operations with whole
numbers and decimals. Standard algorithms for computing with numbers
employ place value concepts as useful steps. Algorithms summarize
conceptual understanding in an efficient strategy. They are important
tools of computation that students need to learn as they develop their
math fluency.
Vocabulary
Write a simple problem on the board, such as 25 + 37 = _____.
Have students describe how they would find the answer. Look for
common approaches.
■■ Ask: What if we write out the steps we used to solve the problem?
Elicit all of the steps from students. [Step 1 might be to add the ones,
5 and 7, or the tens 20 and 30.]
■■ Say: A step-by-step approach like we used here is called an algorithm.
Write algorithm on the board. Ask students what other computations they
can do using an algorithm. [subtraction, multiplication]
■■ An algorithm is a method, or procedure, for doing a
Objective
Multiply multidigit whole numbers using
area models and the standard algorithm.
Algorithms can
be used for
mental math, but
they are more
often associated
with paper and
pencil methods.
mathematical computation.
Operations with Whole Numbers and Decimals
Set
the Stage
Engage WHOLE CLASS
Present the problem 12 × 14 = __.
■■ Ask: How can you use place value as a strategy to find
the product?
Invite as many different responses as you can. Students might
suggest decomposing 12 into 10 + 2 and finding the product as
(10 × 14) + (2 × 14). Or they might instead suggest decomposing
14 into 10 + 4 and proceeding in similar fashion. If they suggest
decomposing both factors, let them see if they can carry out that
approach.
■■ Ask: How do these strategies help you?
Acknowledge with students that the strategies may help them find the
product mentally. At the minimum, they help students break down the
problem into well-defined steps that will work every time.
Warm-Up
Foundation Skill Practice
Use this short thinking exercise to jump-start
the instructional session.
Use this VersaTiles activity to help students activate
their prior knowledge.
®
Patterns and Products
Answer Key
Name
2
Find the missing number.
Suppose you know that 14 × 10 is 140.
You can use what you know about multiplication facts to find
the product of large numbers.
a. Tell how you can figure out what 14 × 11 is.
b. Tell how you can figure out what 14 × 9 is.
60 × 30 = ■
Think: 6 × 3 = 18
60 × 30 = 1,800
So, 60 × 30 = 1,800.
■ × 8,000 = 560,000
Think: 7 × 8 = 56
70 × 8,000 = 560,000
So, 70 × 8,000 = 560,000.
Find the missing number.
ANSWER: a. 154, or (14 × 10) + 14;
b. 126, or (14 × 10) – 14
COMMENTS & EXTENSIONS: It is important, especially when doing
higher level math and when estimating, to be able to find shortcuts.
1 7 × 6 = 42, so 70 × 60 = ■
2 8 × 6 = 48, so ■ × 60 = 48,000
3 4 × 2 = 8, so 40 × 200 = ■
4 3 × 3 = 9, so 3,000 × 30 = ■
5 5 × 4 = 20, so 50 × 4,000 = ■
6 7 × 6 = 42, so 70,000 × 60 = ■
7 9 × ■ = 72, so 90 × 800 = 72,000
8 5 × ■ = 45, so 50 × 900 = 45,000
9 3 × 8 = 24, so 30 × ■ = 2,400
10 2 × 7 = 14, so ■ × 70 = 14,000
11 4 × 9 = 36, so 4,000 × ■ = 360,000
12 9 × 2 = 18, so ■ × 200 = 180,000
Mental arithmetic:
a. 99 × 32 =
b. 9 × 14 =
c. 16 × 101 =
d. 15 × 102 =
© ETA hand2mind®
Tell how you got each answer.
Operations with Whole Numbers and Decimals
■
Lesson 2
Hands-On Standards® Number & Operations
Online resources available at hand2mind.com/hosnumbergr5
20
8
200
8,000
80
900
9
4,200
90,000
90
200,000
800
4,200,000
Objective: Use multiples of 10 to find a product or a factor.
VersaTiles student book, page 20
®
55
Introduce the Concept
Explore WHOLE CLASS
Distribute Base Ten Blocks and Factor Tracks. Have
students build a model for 12 × 14, identify the four
partial-product regions, and sketch the area model.
rectangle
built with
1 flat,
6 rods,
8 units
Materials
• Base Ten Blocks
• Factor Track
™
The area model depicts the four main regions of the
Factor Track model.
Explore & Explain
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2
Name
Multiply Multidigit Numbers
Try This
Model problem 1 using Base Ten Blocks and a Factor Track. Sketch
your model. Label the area model, and complete the equation.
■
In problems 2–3, sketch an area model and find the product.
■
In problems 4–7, find the product.
10
1
10
5
100
50
10
5
10
10
1
10
10
5
1
5
= (____
× ____)
+ (____
× ____)
+ (____
× ____)
+ (____
× ____)
100
10
50
5
165
= ____
+ ____
+ ____
+ ____
= ____
15
60
50
200
325
10
3
4.
6.
26
× 33
225
× 32
20
5
200
50
60
15
10
40
400
150
600
6000
7200
7.
■
Lesson 2
125
× 23
15
60
300
100
400
2000
2875
5.
18
60
180
600
858
Operations With Whole Numbers and Decimals
3.
134
× 24
316
× 22
20
3
100
20
5
2000
400
100
300
60
15
16
120
400
80
600
2000
3216
12
20
600
120
200
6000
6952
Hands-On Standards® Number & Operations
Online resources available at hand2mind.com/hosnumbergr5
56
100
40
2
20
8
sketch of area model
10
1,000
2
200
10
4
114
× 12
2 × 4 ➞
8
100 40
2 × 10 ➞
20
2 × 100 ➞ 200
10 × 4 ➞
40
20 8
10 × 10 ➞100
10 × 100 ➞ 1,000
1,368
Explore & Explain SMALL GROUPS
Prepare ahead Each group of students will need a set of
Base Ten Blocks and a Factor Track.
© ETA hand2mind®
25
× 13
10
100
1. 11 × 15 = (10 + 1) × (10 + 5)
2.
4
Change the problem to 12 × 114. This product is too big
to model on the Factor Track, but you can have students
apply the reasoning by sketching the area model. Write
the problem in vertical format. Have students walk you
through the computation using an algorithm.
Answer Key
■
10
The activity helps students internalize the basic ideas of
multiplication with multidigit numbers. Students will build
and sketch a manipulative model, sketch area models,
and develop their fluency with the standard algorithm.
They should reason that as long as the steps in their
computations make sense, it doesn’t matter whether they
start from the right or the left.
Operations with Whole Numbers and Decimals
Reinforce the Concept
Explain & Elaborate WHOLE CLASS
Re-Engage
Have students describe their approach to Problem 7.
Evaluate Use this page to give students additional
concrete-to-representational-to-abstract practice.
esso
2
3X
n
computation generates three pairs of partial products in
which, for each pair, one product is 10 times the other.
Have students explain the reason for this pattern.
L
■■ Ask: Did you notice a pattern? Elicit that the
Name
Multiply Multidigit Numbers
Answer Key
Use a Factor Track and Base Ten Blocks to build the model.
Complete the number sentence.
WHOLE CLASS
2
2
2. 12 × 22 = (10 + _____)
× (20 + _____)
1. 11 × 13 = (10 + 1) × (10 + 3)
Present the area model—
2000
600 80
= (10 × 10) + (1 × 10) + (10 × 3) + (1 × 3)
= (10 × 20) + (2 × 20)
100 + _____
10 + _____
30 + _____
3
143
= _____
= _____
10
2
+ (_____
× 2) + (_____
× 2)
200 + _____
40 + _____
20 + _____
4
264
= _____
= _____
60
200
8
Complete the area model for the problem. Find the product.
3.
■■ Say: This is the area model for a multiplication problem.
26
× 13
18
60
60
200
338
Figure out what the problem is and determine the
product. [22 × 134 = 2,948]
10
3
20
6
200
60
60
18
4.
100
40
4
20
2000
800
80
4
400
160
16
144
× 24
16
160
400
80
800
2000
3456
Find the product.
Use this VersaTiles activity to give students more
practice with the skills they learned in the lesson.
5.
46
× 34
7.
225
× 31
®
Products on the Loose!
24
160
180
1200
1564
5
20
200
150
600
6000
6975
6.
127
× 14
8.
333
× 26
28
80
400
70
200
1000
1778
18
180
1800
60
600
6000
8658
© ETA hand2mind®
Independent Practice
Find the product.
1 18 × 538
2 41 × 743
3 26 × 256
4 35 × 936
5 53 × 819
6 70 × 432
7 13 × 3,795
8 34 × 1,306
9 28 × 4,752
10 51 × 2,371
11 25 × 3,413
12 62 × 1,268
44,404
30,240
43,407
133,056
120,921
32,760
30,463
78,616
6,656
85,325
9,684
49,335
Operations With Whole Numbers and Decimals
■
Lesson 2
Hands-On Standards® Number & Operations
Online resources available at hand2mind.com/hosnumbergr5
Daily Routine
Anchor Poster
Find the product.
1 15 × 424
2 398 × 23
3 167 × 60
4 925 × 32
5 71 × 576
6 43 × 729
7 25 × 1,315
8 38 × 3,120
9 17 × 2,550
10 46 × 1,678
11 235 × 45
12 112 × 12
1,344
9,154
32,875
77,188
40,896
43,350
31,347
118,560
6,360
29,600
10,020
10,575
Objective: Find the product of a 3- or 4-digit number multiplied by a
2-digit number.
Review with your class the concepts of area
models and the distributive property. Create
an anchor poster with students. Include
area models for single-digit and two-digit
multiplication, with examples. Place the poster
in the writing center.
Writing assignment: Create a third example to
add to the anchor poster about multiplying a
three-digit number by a two-digit number.
21
VersaTiles student book, page 21
®
57
sso
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2
Multiply Multidigit Numbers
Name Try This
■■
Model problem 1 using Base Ten Blocks and a Factor Track. Sketch
your model. Label the area model, and complete the equation.
■■
In problems 2–3, sketch an area model and find the product.
■■
In problems 4–7, find the product.
1. 11 × 15 = (10 + 1) × (10 + 5)
= (____ × ____) + (____ × ____) + (____ × ____) + (____ × ____)
= ____ + ____ + ____ + ____ = ____
2. 25
× 13
3. 125
× 23
4. 26
× 33
5. 134
× 24
6. 225
× 32
7. 316
× 22
Operations With Whole Numbers and Decimals ■ Lesson 2
© ETA hand2mind®
Hands-On Standards® Number & Operations
Products on the Loose!
Find the product.
118 × 538
241 × 743
326 × 256
435 × 936
553 × 819
670 × 432
713 × 3,795
834 × 1,306
928 × 4,752
••51 × 2,371
••25 × 3,413
••62 × 1,268
44,404
30,240
43,407
133,056
120,921
32,760
30,463
78,616
6,656
85,325
9,684
49,335
Find the product.
115 × 424
2398 × 23
3167 × 60
4925 × 32
571 × 576
643 × 729
725 × 1,315
838 × 3,120
917 × 2,550
••46 × 1,678
••235 × 45
••112 × 12
1,344
9,154
32,875
77,188
40,896
43,350
31,347
118,560
6,360
29,600
10,020
10,575
Objective: Find the product of a 3- or 4-digit number multiplied by a
2-digit number.
21
2
3X
Name Multiply Multidigit Numbers
Use a Factor Track and Base Ten Blocks to build the model.
Complete the number sentence.
1. 11 × 13 = (10 + 1) × (10 + 3)
2. 12 × 22 = (10 + _____) × (20 + _____)
= (10 × 10) + (1 × 10) + (10 × 3) + (1 × 3)
= (10 × 20) + (2 × 20)
= _____ + _____ + _____ + _____ = _____
+ (_____ × 2) + (_____ × 2)
= _____ + _____ + _____ + _____ = _____
Complete the area model for the problem. Find the product.
20
3. 26
× 13
6
4. 144
× 24
10
3
Find the product.
5. 46
× 34
6. 127
× 14
7. 225
× 31
8. 333
× 26
Operations With Whole Numbers and Decimals ■ Lesson 2
© ETA hand2mind®
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n
esso
Hands-On Standards® Number & Operations