5th Grade Module 2 – Lesson 6

Lesson 6: I can connect area diagrams and the distributive

property to partial products of the standard algorithm without

renaming.

5th Grade Module 2 – Lesson 6

Get Ready toMultiply Mentally!

You will need the Pattern Sheet (2.B.49)

You will have 2 minutes to do as many problems as you can!

Remember to use mental math strategies!

5th Grade Module 2 – Lesson 6

Get Your White Board Ready!Multiply by Multiples of 100

21 x 100 = ____ Say the multiplication sentence.

2,100

2,100 x 4 = ____ Say the multiplication sentence.

8,400

21 x 400 = ____Say 21 x 400 as a three-

step multiplication sentence, taking out the

hundred.21 x 100 x 4 = 8,400

21 x 400 = 8,400

5th Grade Module 2 – Lesson 6

Get Your White Board Ready!Multiply by Multiples of 100

312 x 100 = _____ Say the multiplication sentence.

31,200

31,200 x 3 = ____ Say the multiplication sentence.

93,600

312 x 300 = ____Say 312 x 300 as a

three-step multiplication sentence, taking out the

hundred.312 x 100 x 3 =93,600

312 x 300 = 93,600

5th Grade Module 2 – Lesson 6

Get Your White Board Ready!Multiply by Multiples of 100

2,314 x 100 = _____ Say the multiplication sentence.

231,400

2,314 x 2 = ____ Say the multiplication sentence.

4,628

2,314 x 200 = ____

Say 2,314 x 200 as a three-step multiplication sentence, taking out the

hundred.2,314 x 100 x 2 = 462,800

2,314 x 200 = 462,800

5th Grade Module 2 – Lesson 6

Let’s Review MultiplyingUsing the Area Model & Algorithm

(solve in your notebook)

43 x 12 = _____

243 x 12 = _____

312 x 23= _____

1. Solve each using an area model

2. Solve each using the standard algorithm

Solutions on next slide.

5th Grade Module 2 – Lesson 6

43

2

10

86

430

4 3 x 1 2 8 6+ 4 3 0 5 1 6

243

2

10

486

2,430

2 4 3 x 1 2 4 8 6+ 2 4 3 0 2 9 1 6

312

3

20

936

6,240

3 1 2 x 2 3 9 3 6+ 6 2 4 0 7 1 7 6

5th Grade Module 2 – Lesson 6

Application Problem

Scientists are creating a material that may replace damaged cartilage in human joints. This hydrogel can stretch to 21 times its original length. If a strip of hydrogel measures 3.2 cm, what would its length be when stretched to capacity?

To watch a video of a hydrogel in action click here

5th Grade Module 2 – Lesson 6

Use ink to share solution orClick to Reveal Answer to Application Problem

5th Grade Module 2 – Lesson 6

Concept Development

Divide your white board into two sections. On one side we’ll solve with an area model, and on the other side, we will connect it to the standard algorithm.

Area Model Standard Algorithm64 x 73

Let’s represent 64 groups of 73.

734

60

However, how can we

decompose 73 to make

finding these partial

products easier to solve?

Yes! We can split it into 70 + 3. Let’s re-

create our area model.

70 + 34

60

Let’s fill in each partial product. Then add them

up!

280

4200

12

180

4200 + 180 + 280 + 12 = 4,672

Solve using the standard algorithm. Check with your partner that you solved

it correctly!

73 x 64 2 9 2+4 3 8 0 4 6 7 2

Let’s compare the two models. What do you notice?

5th Grade Module 2 – Lesson 6

Let’s Just Practice Creating an Area Model

Draw an area model for 56 x 34

Draw an area model for 326 x 27

*Draw using ink tools.

5th Grade Module 2 – Lesson 6

814 x 39

Partner A Solve using the

Standard Algorithm

Partner B Solve using the

Area Model

Compare your Solutions

7200 90 36

24000 300 120

800 10 4

9

30

7326

+24420 31,746

5th Grade Module 2 – Lesson 6

624 x 82

Partner B Solve using the

Standard Algorithm

Partner ASolve using the

Area Model

Compare your Solutions

1200 40 8

48000 1600 320

600 20 4

2

80

1248

+49920 51,168

5th Grade Module 2 – Lesson 6

Get Ready to Complete theProblem Set on Your Own!

Complete Pages 2.B.50 & 2.B.51You will have 10-15 minutes to work.

Try your Best!

5th Grade Module 2 – Lesson 6

LET’S DEBRIEF• What pattern did you notice between Parts (a) and (b) of Problem 1?

How did this slight difference in factors impact your final product?

• Explain to your partner how you recorded the regrouping in Problem 2(a). What were you thinking and what did you write as you multiplied 9 tens times 5 tens?

• Let’s think about a problem like 23 × 45 and solving it with the algorithm. What is the first partial product that we would find? (3 × 45) The second? (20 × 45) Would this be the only order in which we could find the partial products? What else could we do?

• What information did you need before you could find the cost of the

carpet in Problem 3? How did you find that information? Why is area measured in square units?

5th Grade Module 2 – Lesson 6

EXITTICKET

Page 2.B.52