1. Math Module 3 Multi-Digit Multiplication and Division
Topic E: Division of Tens and Ones with Successive Remainders
Lesson 20: Solve division problems without remainders using the area model.
4.OA NBT.6
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2. Lesson 20 Target
You will solve division problems without remainders using the area model.

3. Divide using the standard algorithm.
Fluency Development
Divide using the standard algorithm.
Lesson 20
67 ÷ 2
(2 x 33) + 1 = 67 67 33 1

4. Divide using the standard algorithm.
Fluency Development
Divide using the standard algorithm.
Lesson 20
60 ÷ 4
(15 x 4) + 0 = 60 60 60

5. Divide using the standard algorithm.
Fluency Development
Divide using the standard algorithm.
Lesson 20
29 ÷ 3
(3 x 9) + 2 = 29 29 27 2

6. Divide using the standard algorithm.
Fluency Development
Divide using the standard algorithm.
Lesson 19
77 ÷ 4
(19 x 4) + 1 = 77 77 76 1

7. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
15 ÷ 3 = 5
5 x ___ = 15

8. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
12 ÷ 4 = 3
4 x ___ = 12

9. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
35 ÷ 5 = 7
5 x ___ = 35

10. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
36 ÷ 6 = 6
6 x ___ = 36

11. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
49 ÷ 7 = 7
7 x ___ = 49

12. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
81 ÷ 9 = 9
9 x ___ = 81

13. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
48 ÷ 6 = 8
6 x ___ = 48

14. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
42 ÷ 7 = 6
7 x ___ = 42

15. Find the Unknown Factor.
Lesson 20
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
54 ÷ 9 = 6
9 x ___ = 54

16. Mental Multiplication
Fluency
Mental Multiplication
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
3 tens x 2 tens = 6 hundreds.
3 tens x 2 = 6 tens.
3 ones x 2 = 6 ones.
3 x 2 = ___
30 x 2 = ___
30 x 20 = ___

17. Mental Multiplication
Fluency
Mental Multiplication
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
4 tens x 2 = 8 tens.
4 tens x 2 tens = 8 hundreds.
4 ones x 2 = 8 ones.
4 x 2 = ___
40 x 2 = ___
40 x 20 = ___

18. Mental Multiplication
Fluency
Mental Multiplication
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
Say the multiplication sentence in unit form.
5 tens x 3 = 15 tens.
5 tens x 3 tens = 15 hundreds.
5 ones x 3 = 15 ones.
5 x 3 = ___
50 x 3 = ___
50 x 30 = ___

19. Lesson 20
Application Problem
5 Minutes
Write an equation to find the unknown length of each rectangle. Then find the sum of the two unknown lengths.

20. Lesson 20
Application Problem
5 Minutes
Write an equation to find the unknown length of each rectangle. Then find the sum of the two unknown lengths.

21. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.

22. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.

23. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a number bond to match the whole and parts of the rectangle.

24. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Let’s find the unknown side lengths of the smaller rectangles and add them.
What is 10 and 2?
Take a moment to record the number sentences, reviewing with your partner their connection to both the number bond and the area model.
What is 8 ÷ 4?
What is the length of the unknown side?
What is 48 divided by 4?

25. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Work with your partner to partition the same area of 48 as 2 twenties and 8.

26. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Try to find another way to partition the area of 48 so it’s easy to divide. You have 4 minutes – get to work!
I did it by using 4 rectangles, each with an area of 12 square units
30 and 18 don’t work well because 30 has a remainder when you divided it by 4.
I said divided by 4 is is 12.
Did anyone find another way to partition the area of 48 it’s easy to divide?

27. Problem 1: Decompose 48 ÷ 4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 1: Decompose 48 ÷ 4 from whole to part.
Explain to your partner why different ways of partitioning give us the same correct side length.
I use the same break apart and distribute strategy to find the answer to 56 ÷ 8.
40 ÷ 8 is 5.
16 ÷ 8 is 2.
5 and 2 makes 7.
The sum of the lengths is the same as the whole length
You can take a total, break it into two parts, and divide each of them separately.
You are starting with the same amount of area but just chopping it up differently.

28. Remember Part B of our Application Problem?
Repeat the process we just used to partition the area of 96. Find a different way to decompose the problem.
Lesson 20
Remember Part B of our Application Problem?
5 Minutes
Write an equation to find the unknown length of each rectangle. Then find the sum of the two unknown lengths.

29. Problem 2: Decompose 96 ÷4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 2: Decompose 96 ÷4 from whole to part.
How did you partition the area of 96?
Did anyone chop 96 into It was just like 48 ÷ 4.

30. Problem 2: Decompose 96 ÷4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 2: Decompose 96 ÷4 from whole to part.
Did anyone partition 96 into 4 twenties and 2 eights?
4 twenties
2 eights

31. Problem 2: Decompose 96 ÷4 from whole to part.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 2: Decompose 96 ÷4 from whole to part.
Who made 96 into 2 forty-eights and used our answer from 48 ÷ 4? All you had to do was double it.

32. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
Thinking about area, let’s try a new way to divide. The expression 96 ÷ 4 can describe a rectangle with an area of 96 square units. We are trying to find out the length of the unknown side.
What is the known side length? 4.

33. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
4 times how many tens gets us as close as possible to an area of 9 tens?
2 tens.
Let’s give 2 tens to the length.
Let’s record the 2 tens in the tens place.
What is 4 times 2 tens?

34. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
8 tens.
How many square units is that?
80 square units.
How many tens remain?
1 ten.

35. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
Let’s add the remaining ten to the 6 ones. What is 1 ten + 6 ones?
16.

36. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
We have 16 square units remaining with a width of 4.
4 times how many ones gets us as close as possible to an area of 16 ones?
4 ones.
Let’s give 4 ones to the length.
What is 4 times 4?
16. We have 16 square units.
We have no more area to divide.
Tell me the length of the unknown side.
24!
Our quotient tells us that length.

37. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
How can we express the length of the unknown side using the distributive property?
(80 ÷ 4) + (16 ÷ 4)
With your partner, draw arrows to connect the distributive property and the area model.

38. Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..

39. Problem 3: Compose 96 ÷4 from part to whole..
Lesson 20
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
Review our four drawings and our process with your partner. Try to reconstruct what we did step by step before we try another one.
We solved 96 divided by 4 in two very different ways using the area model. First, we started with the whole rectangle and partitioned it. The second way was to go one place value at a time and make the whole rectangle from parts.
We’re ready! Bring it on!

40. Problem Set
10 Minutes

41. Problem Set
10 Minutes

42. Problem Set
10 Minutes
In Problem 2, did you partition the rectangle the same way as your partner? Why were we able to go from whole to part?

43. Problem Set
10 Minutes
In Problems 2 and 3, explain the connection between the written method, the number bond, and the area model.

44. Problem Set
10 Minutes

45. Debrief
In the last problem, explain the connection between the algorithm and the area model.
Each time we divide, what happens to the amount of area we still have left to divide?
Even though division is messy, I think it is the most interesting operation of all because, imagine this, sometimes that little piece that is left to divide is always there, even though it gets infinitely small!
Talk to your partner about what you think I might mean by that.
Lesson Objective: Solve division problems without remainders using the area model.

46. Exit Ticket
Lesson 1