Multiplication

Math

of Multi-Digit Numbers

Created By: The Owl Teacher Grade 4

FREEBIE

Lesson 1What are factors

and how do we find them?

Lesson 2What are factors

and how do we find them?

Lesson 3What are multiples and how dowe find

them?

Lesson 4Whatare multiples

and how do we find them?

Lesson 5What are prime and composite

numbers? (Multiples &

Factors Review)

Lesson 6What isthe area

model and how do we use it? (2, 3, and

4 digit by 1 digit numbers)

Lesson 7What is the area

model and how can we use use it with the box method? (2, 3, 4

digit by 1 digit numbers)

Lesson 8What isthe partial products method and how can we use it? (2, 3, 4 digit by 1 digit numbers)

Lesson 9Howcan the distributive

property help us when multiplying?

Lesson 10How do we

multiply a 2 digit number by a2 digit number using the area

model?

Lesson 1 1How do we multiply a 2 digit by2 digit number using the

box method?

Lesson 12How do we multiplya 2 digit by 2 digit

number using partial products?

Lesson 13How do we multiplyusing the traditional algorithm? (2, 3, 4

digit by 1 digit numbers)

Lesson 14How do we

multiply a 2digit number by a 2 digit number using the

traditional algorithm?

Lesson 15How can I

demonstrate all that I have

learned? (Show what I know)

Area ModelFactorFactor PairMultipleArrayBox ModelPartial ProductsAlgorithm

Pretest pg. 12-15 Post-Test pg. 143-146

pg. 16

Unit Overview

Vocabulary Covered

pg. 24 pg. 42pg. 33pg. 27

pg. 110pg. 101pg. 95 pg. 125pg. 118

pg. 54 pg. 62 pg. 89pg. 81pg. 73

Prime NumberComposite NumberProductMultiplyEquationDecomposeDistributive Property

©T

he O

wl T

each

er,

20

18

Lesson 12: How do we multiply a 2 digit number by a 2 digit number using Partial Products?

I Can Statement I can use place value strategies to solve multiplication problems. I can multiply a 2 digit number by a 2 digit number.

CCSS4.NBT.5

VocabularyPartial Products; Strategy; Decompose; Distributive Property

MaterialsPartial Products Anchor Chart; Markers (red, yellow, green, blue); Brown Bag with Problems; Folding Sheet;

Mini-lessonSo far we have talked about the area model and the box model. Today, we are going to focus on the partial products method when solving double digits multiplication problems. There are three steps to solving the problems and when you are all finished, you will have created a bow tie! Let me show you what I mean. Let’s say I have the problem 32x29. The first thing I’m going to do is decompose my factors into expanded form. So I’m going to write them out parallel to my problem, 30+2 and 20+9. Now, I’m going to multiply using a bow tie method and record my products. To start and make it easier for you to see, I’m going to do this in different colors. To do the bow tie method, I’m going to first start with the 9 and multiply it by the 2 on the top. (Using a red marker draw an arrow from the 9 to the 2 and then record 18 below the problems. Also include in parenthesis the problem so students know where you got it from. Continue doing this similar to the Partial Products Anchor Chart as you work through the problem.) Next, I’m going to take the 2 and multiply it by the 20. (Draw a yellow arrow from the 2 to the 20. Using the same colored marker, write 40.) Now, I’m going to multiply 20 x 30. (Draw a green arrow from the 20 to the30 and write down 600.) Finally, I’m going to multiply my 30 x 9 and that will return me back to the beginning creating a bow tie. (Draw a blue arrow from the 30 to the 9 and write down 270.) Now that I have multiplied all my numbers and found the partial products for each factor, I’m going to add them up to get my final product. So if I add up 18+40+600+270 I get 928. (Model with another example using the same method and different colored markers so students can understand. The bow tie method helps them not miss any factors.)

Active Engagement Now I have an example I want you to try out. I’m going to pass around a brown bag and in it are some slips of paper with a multiplication problem on it. You are going to reach into the bag, draw out one piece of paper, and write it in your notebook. Then you are going to solve it just like I did here with several different colors – red, yellow, green, and blue. Then when you have the answer I want you to close your notebook, sit quietly, and wait for everyone else to be done. Then when everyone else is done, we will check it together. Are you ready? (Pass around the bag of pre-cut slips [provided] for students to complete. Circulate the room and take note of who needs additional assistance. If using the bow tie method, make sure students are including the arrows in their notebooks, along with the different colors. When finished, model the answers for students to see. These are also provided.)

©T

he O

wl T

each

er,

20

18

Lesson 12: How do we multiply a 2 digit number by a 2 digit number using Partial Products?

Link and Independent Practice Now boys and girls, we are going to keep practicing the partial products method using different colors to help guide us. Today, I want you to partner up and with these folding sheets, complete these problems just like we did in class. Each of you will have your own sheet. Partner A will have Sheet A and Partner B will have Sheet B. You will fold the sheets on the dotted line so you only have a small portion of the sheet. Then you will complete your part of the sheet solving the problems using the partial products method just like we did here using the bow-tie method. I want you to draw the arrows and write each set in a different color. Then once you have finished your six problems on your sheet, you will trade papers with your partner and he or she will do their six problems. Make sure you don’t peak at your partner’s side as you work on it. When finished, you will unfold the sheet and see if your answers and colors match. Are there any questions? Alright, let’s get started. (Based on time, you may want students to work on 3 problems and then trade sheets or a number that works best for your time frame.)

InterventionContinue working on the expanded form of numbers and use a calculator if necessary. Consider smaller numbers and covering up other numbers so students can focus on one step at a time without being overwhelmed.

ExtensionHave students explain the relationship between the area model, the box model, and the partial products strategy. What is similar? What is different?

Closing Have students write on a sticky note what it means to have “partial products” and then either collect them or share.

©T

he O

wl T

each

er,

20

18

Multiplication

Multiplication Partial Products Two Digit by Two Digits– Anchor Chart

Partial Products

The problem: 32 x 29

3229x

18 (9 x 2)

270 (30 x 9)

40 (2 x 20)

600 (20 x 30)+

928

The Partial

Products

Solve using the Bow Tie Method

3229x

Step 1:Decompose your factors

30 + 220 + 9

Step 2:Multiply in the bow tie method and

record the products

30 + 2

20 + 9

18 (9 x 2)

40 (2 x 20)

600 (20 x 30)

270 (30 x 9)

Step 3:Add up the partial products

to get the final product.

18 + 40 + 600 + 270 =928

A model in multiplication where factors are split into an expanded form, multiplied, and then partial products are added to find the final product.

©T

he O

wl T

each

er,

20

18

Multiplication

Multiplication Partial Products Two Digit by Two Digits– Anchor Chart

Partial Products

The problem: 32 x 29

3229x

18 (9 x 2)

600 (20 x 30)

270 (9 x 30)

40 (20 x 2)

+

928

The Partial

Products

Solve using the Bow Tie Method

3229x

Step 1:Decompose your factors

30 + 220 + 9

Step 2:Multiply in the bow tie method and

record the products

30 + 2

20 + 9

18 (9 x 2)

40 (20 x 2)

600 (20 x 30)

270 (9 x 30)Step 3:

Add up the partial products to get the final product.

18 + 270 + 40 + 600 =928

A model in multiplication where factors are split into an expanded form, multiplied, and then partial products are added to find the final product.

Alternative – bow tie to match the algorithm bow tie (see algorithm chart)

©T

he O

wl T

each

er,

20

18

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Solve. 84 x 73 Solve. 45 x 96 Solve. 28 x 66

Brown Bag Strips & Key

8473x

12 (4 x 3)

240 (80 x 3)

280 (4 x 70)

5600 (70 x 80)+

6132

4596x

30 (6 x 5)

240 (40 x 6)

450 (5 x 90)

3600 (90 x 40)+

4320

2866x

48 (6 x 8)

120 (20 x 6)

480 (8 x 60)

1200 (60 x 20)+

1848

Answer Key

©T

he O

wl T

each

er,

20

18

Name ___________________________________________

fold

her

efold here

1.) A = ____________ 2.) A = ___________1.) A = ____________ 2.) A = ____________

Your Sidener’s Side Your Part

3.) A = ___________ 3.) A = ____________ 4.) A = ___________ 4.) A = ___________

5.) A = ___________ 5.) A = ____________ 6.) A = ____________ 6.) A = ____________

Student A

Partial Products

76

42x

76

42x

86

33x

86

33x

94

35x

94

35x

48

92x

48

92x

17

66x

17

66x

54

28x

54

28x

Multiplication Partial Products Two Digit by Two Digits– Folding Sheet

©T

he O

wl T

each

er,

20

18

Name ___________________________________________

fold

her

efold here

1.) A = ____________ 2.) A = ___________1.) A = ____________ 2.) A = ____________

Your Sidener’s Side Your Part

3.) A = ___________ 3.) A = ____________ 4.) A = ___________ 4.) A = ___________

5.) A = ___________ 5.) A = ____________ 6.) A = ____________ 6.) A = ____________

Student B

Partial Products

32

77x

32

77x

81

68x

81

68x

95

42x

95

42x

87

69x

87

69x

43

16x

43

16x

88

39x

88

39x

Multiplication Partial Products Two Digit by Two Digits– Folding Sheet

©T

he O

wl T

each

er,

20

18

Name ___________________________________________

fold

her

efold here

1.) A = ____________ 2.) A = ___________1.) A = ____________ 2.) A = ____________

Your Sidener’s Side Your Part

3.) A = ___________ 3.) A = ____________ 4.) A = ___________ 4.) A = ___________

5.) A = ___________ 5.) A = ____________ 6.) A = ____________ 6.) A = ____________

Student A

Partial Products

76

42x

76

42x

86

33x

86

33x

94

35x

94

35x

48

92x

48

92x

17

66x

17

66x

54

28x

54

28x

Multiplication Partial Products Two Digit by Two Digits– Folding Sheet

©T

he O

wl T

each

er,

20

18

KEY

12 (2 x 6)

140 (70 x 2)

240 (6 x 40)2800 (40 x 70)

+

3192

18 (3 x 6)

240 (80 x 3)

180 (6 x 30)2400 (30 x 80)

+

2838

20 (5 x 4)

450 (90 x 5)

120 (4 x 30)2700 (30 x 90)

+

3290

16 (2 x 8)

80 (40 x 2)

720 (8 x 90)3600 (90 x 40)

+

4416

42 (6 x 7)

60 (10 x 6)

420 (7 x 60)600 (60 x 10)

+

1122

32 (8 x 4)

400 (50 x 8)

80 (4 x 20)1000 (20 x 50)

+

1512

3192 2838

44163290

1122 1512

Name ___________________________________________

fold

her

efold here

1.) A = ____________ 2.) A = ___________1.) A = ____________ 2.) A = ____________

Your Sidener’s Side Your Part

3.) A = ___________ 3.) A = ____________ 4.) A = ___________ 4.) A = ___________

5.) A = ___________ 5.) A = ____________ 6.) A = ____________ 6.) A = ____________

Student B

Partial Products

32

77x

32

77x

81

68x

81

68x

95

42x

95

42x

87

69x

87

69x

43

16x

43

16x

88

39x

88

39x

Multiplication Partial Products Two Digit by Two Digits– Folding Sheet

©T

he O

wl T

each

er,

20

18

KEY

72 (9 x 8)

720 (80 x 9)

240 (8 x 30)2400 (30 x 80)

+

3432

3432

18 (6 x 3)

240 (40 x 6)

30 (3 x 10)400 (10 x 40)

+

688

688

63 (9 x 7)

720 (80 x 9)

420 (7 x 60)4800 (60 x 80)

+

6003

6003

10 (2 x 5)

180 (90 x 2)

200 (5 x 40)3600 (40 x 90)

+

3990

3990

14 (7 x 2)

210 (30 x 7)

140 (2 x 70)2100 (70 x 30)

+

3976

3976

8 (8 x 1)

640 (80 x 8)

60 (1 x 60)4800 (60 x 80)

+

5508

5508

Do you have a

A Special Thank You!Thank you for taking the time to download this resource! I know

as a teacher, you have so much to do and so little time, along with being limited on your resources. I am here to helpby creating products that help you take back your weekends,

without sacrificing quality teaching!Thank you for letting me help you!

TermsTerms of UseEach page of this document is © Copyright of Tammy DeShaw, The Owl Teacher. All rights reserved. (2014-current)*This product is to be used by the original downloader only for classroom and personal use ONLY. *Copying for teachers, classroom, department, school, or school system is prohibited.*Teachers may NOT upload the product to school / district servers or to any website, distribute via email, or share digital or print copies, including to file sharing sites such as Amazon Inspire or the like. *You do not have permission to claim any part of it as your own or to copy or modify it, and you may not share or sell anything based on this document.

A Special

Let’s Keep In Touch!

CreditsCredits

ProductsGreatGreatOther

Feedback helps me improve my

resources to better meet the needs of

you and your students. Thank you for taking the time to

do so.

request?

http://bit.ly/owlrequest

Do you have a

Math Workshop Adding and

Subtracting Large Numbers

Math Workshop Place Value of Large

Numbers