lesson 6: i can connect area diagrams and the distributive property to partial products of the...
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5th Grade Module 2 – Lesson 5
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 5
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 5
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 5
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 5
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
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.
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
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
Use ink to share solution orClick to Reveal Answer to Application Problem
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?
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.
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
624 x 82
Partner B Solve using the
Standard Algorithm
Partner ASolve using the
Area Model
Compare your Solutions
1200 400 8
48000 1600 320
600 20 4
2
80
1248
+49920 51,168
5th Grade Module 1 – Lesson 5
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 1 – Lesson 5
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 1 – Lesson 5
EXITTICKET
Page 2.B.52