2. Math Module 3 Multi-Digit Multiplication and Division Topic A: Multiplicative Comparison Word Problems Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas 4.OA.1 4.OA.2 4.MD.3 4.OA.3

3. Lesson 2 Target You will solve multiplicative comparison word problems by applying the area and perimeter formulas I love word problems !

4. Fluency Lesson 2 Rename Units 4 min. Rename the Unit 7 tens = _______ 9 tens = ________ 10 tens = ________ 11 tens = ________ 70 90 100 110

5. Fluency Lesson 2 Rename Units 4 min. Rename the Unit 12 tens = _______ 17 tens = ________ 17 hundreds = ________ 17 thousands = ________ 120 170 1,700 17,000

6. Fluency Lesson 2 Rename Units 4 min. Rename the Unit 13 tens = _______ 13 hundreds = ________ 13 thousands = ________ 31 thousands = ________ 130 1,300 13,000 31,000

7. Fluency Lesson 2 4 cm 3 cm On your boards, write a multiplication sentence to find the area. Did you write 4 cm x 3 cm = 12 square cm? Write the formula for perimeter and solve. Did you write 2 x (4 cm + 3 cm) = 14 cm?

8. Fluency Lesson 2 4 cm 6 cm On your boards, write a multiplication sentence to find the area. Did you write 4 cm x 6 cm = 24 square cm? Write the formula for perimeter and solve. Did you write 2 x (4 cm + 6 cm) = 20 cm?

9. Fluency Lesson 2 2 meters This is a square. Say the length of the two sides. Did you write 2 m x 2 m = 4 square m? Write the formula for perimeter and solve. Did you write 2 x (2 m + 2 m) = 8 m? Write a multiplication sentence to find the area.

10. Application Lesson 2 Tommy’s dad is teaching him how to make tables out of tiles. Tommy makes a small table that is 3 feet wide and 4 feet long. How many square foot tiles does he need to cover the top of the table? How many feet of decorative border material will his dad need to cover the edges of the table? Bonus: Tommy’s dad is making a table 6 feet wide and 8 feet long. When both tables are placed together, what will their combined area be?

11. Concept Development Problem 1a Lesson 2 Problem 1 Problem 1: A rectangle is 1 inch wide. It is 3 times as long as it is wide. Use square tiles to find its length. Place three square inch tiles on your board. Talk to your partner about what the width and length of this rectangle are. If the width is 1 inch, the length is 3 inches. Now make it 2 times as long. It’s now 6 inches long. Three times as long would be 9 inches. Tell your partner how to find the length. I multiply the length times 3. Three times as long is the same as 3 times 3 inches.

12. Concept Development Problem 1b Lesson 2 Problem 1 Problem 1: A rectangle is 1 inch wide. It is 3 times as long as it is wide. Use square tiles to find its length. Now try it again! Use tiles to find a rectangle that is 3 inches wide and 3 times as long as it is wide. Talk to your partner about what the length and width of this rectangle are. That’s a good start! Now make it 2 times as long. It’s now 6 inches long and 3 inches wide. Tell your partner how to find the length and then do it! You are a mathematical genius!

13. Lesson 2 Problem 2 A rectangle is 2 meters wide. It is 3 times as long as it is wide. Draw to find its length. The rectangle is 2 meters wide. 2m It is 3 times as long as it is wide. That means the length can be thought of as 3 segments, or short lines, each 2 meters long. 2m Here is the same length, 2 times as long and then 3 times as long. What is the length when there are 3 segments, each 2 meters long? With your partner, draw this rectangle and label the length and width. Find the perimeter. Use the chart of formulas for perimeters from Lesson 1 for reference. Then find the area. Concept Development Problem 1b

14. Lesson 2 Problem 2 A rectangle is 3 meters wide. It is 4 times as long as it is wide. Draw to find its length. Let’s try it again! The rectangle is 3 meters long and 4 times as wide as it is long. 3m Find the area and the perimeter. Concept Development Problem 2b

15. Lesson 2 Problem 3 Christine painted a mural with an area of 18 square meters and a length of 6 meters. What is the width of her mural? Her next mural will be the same length as the first but 4 times as wide. What is the perimeter of her next mural? With your partner, determine the width of the first mural. Tell me a multiplication sentence to find how wide her next mural will be. Using those dimensions, draw and label Christine’s next mural. Begin with the side length you know, 6 meters. How many copies of Christine’s first mural will we see in her next mural? Draw them. The area is 18 square meters. 18 square meters divided by 6 meters is 3 meters. The width is 3 meters. Concept Development Problem 1b

16. Concept Development Problem 4 Lesson 2 Problem 4 Sherrie’s rectangular garden is 8 square meters. The longer side of the garden is 4 meters. Nancy’s garden is twice as long and twice as wide as Sherrie’s rectangular garden. With your partner, draw and label a diagram of Sherrie’s garden. What is the width of Sherrie’s garden? Two meters because 8 square meters divided by 4 meters is 2 meters. Help me draw Nancy’s garden. Twice as long as 4 meters is how many meters? Twice as wide as 2 meters is how many meters? Draw Nancy’s garden and find the perimeters of both gardens. Tell your partner the relationship between the two perimeters. Sherrie’s garden has a perimeter of 12 meters. Nancy’s garden has a perimeter of 24 meters. The length doubled and the width doubled, so the perimeter doubled! 12 meters times 2 is 24 meters.

17. Concept Development Problem 4 Lesson 2 Problem 4 Sherrie’s rectangular garden is 8 square meters. The longer side of the garden is 4 meters. Nancy’s garden is twice as long and twice as wide as Sherrie’s rectangular garden. If Sherrie’s neighbor had a garden 3 times as long and 3 times as wide as her garden, what would be the relationship of the perimeter between those gardens? The perimeter would triple! Let’s solve for the area of Sherrie’s, Nancy’s, and the neighbor’s gardens.

18. Concept Development Problem 4 Lesson 2 Problem 4 Sherrie’s garden has an area of 8 square meters. Nancy’s garden has an area of 32 square meters. The neighbor’s garden has an area of 72 square meters.

19. Concept Development Problem 4 Lesson 2 Problem 4 The length and width of Nancy’s garden is double that of Sherrie’s garden, but the area did not double. The length is doubled and the width is doubled, 2 times 2 is 4, so the area will be 4 times as large. We can put the area of Sherrie’s garden inside Nancy’s garden 4 times. The length and width of the neighbor’s garden tripled, so 3 times 3 is 9. The area of the neighbor’s garden is 9 times that of Sherrie’s.

20. Create a table to show the relationship among the areas and perimeters of the three gardens. Lesson 2 Problem 4 Fill in this chart!

21. Problem Set 10 Minutes Lesson 2

22. Problem Set Number 1 Lesson 2

24. Problem Set Number 3

25. Lesson 2

26. Problem Set Number 3 Discuss the relationship between the perimeters of the sandboxes in Problem 4. For Problem 4(e), why isn’t the area twice as much if the length and width are twice as much?

27. Lesson 2 Problem Set Number 3

28. Debrief Lesson Objective: You will solve multiplicative comparison word problems by applying the area and perimeter formulas Discuss the relationship between the area of an original rectangle and the area of a different rectangle whose width is 3 times as long as it was to start with. What conclusion can you make about the area of two rectangles when the widths are the same but the length of one is twice as much? What conclusion can you make about the area of two rectangles when the length and width of one rectangle are each twice as much as the length and width of the other rectangle? What significant math vocabulary did we use today to communicate precisely? How did the Application Problem connect to today’s lesson?

29. Exit Ticket Lesson 2