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

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

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

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

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

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? 60 + 4 (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, 70 + 3 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.

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

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

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

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 64 292 +4280 4672 1 1

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

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

Concept Development – Problem 2-3 Complete the problems using the standard algorithm and using the area model. 814 x 39 = 624 x 82 = 24,000 + 7,200 + 300 + 120 + 90 + 36 = 31,746 48,000 + 1,600 + 1,200 + 320 + 40 + 8= 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

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 82 1248 Step 1 multiply 624 by 2 814 X 39 7326 3 1 Step 1 multiply 814 by 9 624 X 82 1248 + 49920 51,168 3 Step 2 multiply 624 by 80 1 814 X 39 7326 + 24420 31,746 1 Step 2 multiply 814 by 30

Concept Development – Problem 4-5 Complete the problems using the standard algorithm or using the area model. 391 x 59 874 x 63 15,000 + 2,700 + 4,500 + 810 + 50 + 9 = 23,069 874 X 63 2622 2 1 300 90 1 50 9 + 15,000 4500 2,700 810 874 X 63 2622 +52440 55,062 2 4

Problem Set Draw an area model, and then solve using the standard algorithm. 48 x 35 648 x 35 Solve using the standard algorithm. 758 x 92 958 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.

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

Homework Draw an area model and solve using the standard algorithm. 27 x 36 527 x 36 Solve using the standard algorithm. 649 x 53 758 x 46 Solve using an area model. 496 x 53 529 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?