1. Module 2 Lesson 6
Objective: Connect area diagrams and the distributive property to partial products of the standard algorithm without renaming.

2. Fluency – Multiply Mentally
5 x 100
500 – 5
5 x 99
2 x 100
200 – 2
2 x 99
4 x 100
400 – 4
4 x 99
6 x 100
6 x 99
11 x 100
1100 – 11
11 x 99
2100 – 21
21 x 99
71 x 100
71 x 99
42 x 100
4200 – 42
42 x 99
8 x 10
80 – 8
8 x 9
15 x 10
150 – 15
15 x 9
99 x 9

3. Fluency – Multiply by Multiples of 100
5 x 100
4 x 400
312 x 200
22 x 100
5 x 500
4 x 1200
8 x 800
123 x 300
312 x 300
2,314 x 100
2,314 x 200
5 x 900
87 x 300
79 x 200
10 x 100
650 x 200
65 x 200
20 x 100
20 x 200
20 x 300
55 x 200
55 x 300
45 x 100
39 x 400
13 x 300
101 x 200
201 x 300
1 x 900

4. Fluency – Multiply Using the Area Model10 + 2
43 x 12
243 x 12
312 x 23
243
2430
486
= 2,916 10 + 2 43 20 + 3
430 86
312
6240
936
= 516
= 7,176

5. 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? Give the final answer in a statement of solution. Check to make sure your answer is reasonable by rounding 3.2 to the nearest whole number. 32
X 21
+640
672
tenths
= 67.2

6. Concept Development – Problem 1
64 x 73
Method 1 Area Model
Please draw a rectangle in you math notebook.
Write 64 x 73 above rectangle. Let’s represent units of 73
How many seventy-threes are we counting? 64
How can we decompose (break apart)(distributive property) to make out multiplication easier? Show this on your area model?
(easiest way)
Can we do 73 x 4 and 73 x 60 easy mentally?
Yes for some people, but not for all students.
Can we decompose 73?
Yes,
When splitting 73 and 64 how many total boxes do we need in our rectangle and why?
4 because we both are decomposed we have 4 numbers to place.

7. Concept Development – Problem 1
Sample area model.
Now let’s fill in the numbers and
Now let’s add all the numbers. 70 3 + 4 60
280 12
180
4200
= 4,672

8. Concept Development – Problem 1
Now let’s look at a different method (Method 2 – Standard algorithm.)
How would we write the problem for the standard algorithm?
Up and down similar to addition and subtraction problem.
What is the first step?
Times 73 by 4.
Where will our answer go?
Right under the problem. 73
X 64 1 73
X 64
292

9. Concept Development – Problem 1
What is the next step?
The value of 60 x 73.
Why 60 x 73 and not 64 x 73?
Because we have already done 4 x 73.
Where will our answer start and why?
Decompose 60
6 tens
What is 6 tens times 3?
18 tens
What is 18 tens in standard form?
180
How many hundred(s) do I have and how many tens and how many ones do I have?
1 hundred, 8 tens, and 0 ones 73
X 64
292 1

10. Concept Development – Problem 1
1 hundred, 8 tens, and 0 ones
Where will I write the 0 ones?
Under the 2 in the ones place value.
Where will I write the 8 tens?
Under the 9
Where will I write the 1 and why?
Above the 7 because we have to carry or just under or above the 2 in the hundreds place value (small to show our carry.)
Now we will do 6 tens (60) times 7 tens (70)
What is 6 tens times 7 tens?
42 hundred
Where will our answer go?
The 2 will go in the hundreds and then we have to place the 4 in the thousands place because 42 hundred is 4200. 73
X 64
292 1 73 X
292
+4280
4672 1 1

11. Concept Development – Problem 1
Another way to look at the problem is a cross between the area model and standard algorithm is to write each answer on a separate line and then add them all up.
For example:
First do 3 x 4 and write down the answer
Next do 7 tens (70) x 4 ones (Remember to line up place values for adding later. 73
X 64 12 73
X 64 12
280

12. Concept Development – Problem 1
Next move to the second line.
We will start in the tens place value because we have already done the ones.
6 tens (60) x 3
Next do 6 tens (60) x 7 tens (70).
(Remember to line up place values for adding later. 73
X 64 12
280
180 73
X 64 12
280
180
+4200
4,672

13. Concept Development – Problem 2-3
Complete the problems using the standard algorithm and using the area model.
814 x 39 =
624 x 82 =
24, , = 31,746
48, , , = 51,168
800 10 4 30 9 +
24,000
300
120
7,200 36 90 80 2 + 4
320 8 + 20
1600 40 +
600
48,000
1200

14. Concept Development – Problem 2-3
Complete the problems using the standard algorithm and using the area model.
814 x 39 =
624 x 82 =
624 X
1248
Step 1 multiply 624 by 2
814 X
7326 3 1
Step 1 multiply 814 by 9
624 X
1248
51,168 3
Step 2 multiply 624 by 80 1
814 X
7326
31,746 1
Step 2 multiply 814 by 30

15. Concept Development – Problem 4-5
Complete the problems using the standard algorithm or using the area model.
391 x 59
874 x 63
15, , , = 23,069
874
X 63
2622 2 1
300 90 1 50 9 +
15,000
4500
2,700
810
874 X
2622
+52440
55,062 2 4

16. Problem Set
Draw an area model, and then solve using the standard algorithm.
48 x x 35
Solve using the standard algorithm.
758 x x 94
Carpet costs $16 a square foot. A rectangle is 14 feet long by 16 fee wide. How much would it cost to carpet the floor?
General admission to The American Museum of Natural History is $19.
If a group of 125 students visits the museum, how much will the group’s tickets cost?
If the group also purchases IMAX movie tickets for an additional $4 per student, what is the new total cost of all the tickets? Write an expression that shows how you calculated the new price.

17. Exit Ticket
Draw an area model, and then solve using the standard algorithm.
78 x 42
783 x 42

18. Homework Draw an area model and solve using the standard algorithm.
27 x x 36
Solve using the standard algorithm.
649 x x 46
Solve using an area model.
496 x x 48
Each of the 25 students in Mr. McDonald’s class sold 16 raffle tickets. If each ticket cost $15 how much money did Mr. McDonald's students raise?
Jayson buys a car and pays by installments. Each installment is %567 per month. After 48 months, Jayson owes$1,250. What was the total price of the vehicle?