1. Math Module 3 Multi-Digit Multiplication and Division
Topic E: Division of Tens and Ones with Successive Remainders
Lesson 21: Solve division problems with remainders using the area model.
4.OA NBT.6
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2. You will solve division problems with remainders using the area model.
Lesson 21 Target
You will solve division problems with remainders using the area model.

3. Fluency Practice – Sprint A
Get set!
Fluency Practice – Sprint A
Take your mark!
Think!

4. Fluency Practice – Sprint B
Get set!
Take your mark!
Think!

5. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
18 ÷ 3 = 6
6 x ___ = 18

6. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
20 ÷ 4 = 5
4 x ___ = 20

7. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
25 ÷ 5 = 5
5 x ___ = 25

8. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
42 ÷ 6 = 7
6 x ___ = 42

9. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
56 ÷ 7 = 8
7 x ___ = 56

10. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
72 ÷ 9 = 8
9 x ___ = 72

11. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
54 ÷ 6 = 9
6 x ___ = 54

12. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
63 ÷ 7 = 9
7 x ___ = 63

13. Find the Unknown Factor.
Lesson 21
Fluency Development
Find the Unknown Factor.
Say the unknown factor.
Write the division problem. .
63 ÷ 9 = 7
9 x ___ = 63

14. 8 6 12 18 24 30 36 42 48 48 ÷𝟔= _____ Fluency Group Count to divide
Lesson 21 8
48 ÷𝟔= _____ 6 12 18 24 30 36 42 48

15. 8 7 14 21 28 35 42 49 56 56 ÷𝟕= _____ Fluency Group Count to divide
Lesson 21 8
56 ÷𝟕= _____ 7 14 21 28 35 42 49 56

16. 8 8 16 24 32 40 48 56 64 64 ÷𝟖= _____ Fluency Group Count to divide
Lesson 21 8
64 ÷𝟖= _____ 8 16 24 32 40 48 56 64

17. 8 9 18 27 36 45 54 63 72 72 ÷𝟗= _____ Fluency Group Count to divide
Lesson 21 8
72 ÷𝟗= _____ 9 18 27 36 45 54 63 72

18. Lesson 21
Application Problem
8 Minutes
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
Method 1:

19. Lesson 21
Application Problem
8 Minutes
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
Method 2:

20. Problem Set will be used for this lesson.
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 21
Concept Development
Problem Set will be used for this lesson.
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
This rectangle has a side length of 18. What would be the area of a rectangle with a width of 2 units and a length of 19 units?
38 square units.
So we cannot represent a rectangle with an area of 37 square units with whole number side lengths. Let’s build a rectangle part to whole as we did yesterday. 2

21. Problem Set will be used for this lesson.
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 21
Concept Development
Problem Set will be used for this lesson.
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
Draw a rectangle. Label the width as 2 units. 2 times how many tens gets us as close as possible to an area of 3 tens?
1 ten.

22. Problem Set will be used for this lesson.
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 21
Concept Development
Problem Set will be used for this lesson.
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
Label this rectangle with a length of 1 ten. Record 1 ten in the tens place.
What is 1 ten times 2?
2 tens.
How many square units of area is that?
20 square units.
How many tens remain?
1 ten.

23. Problem Set will be used for this lesson.
Concept Development
Problem Set will be used for this lesson.
A rectangle has an area of 36 square units and a width of 2 units. What is the unknown side length?
17 ones remain. 2 times how many ones gives us an area close to 17 square units?
8 ones.
Extend the rectangle and label its length as 8 ones.
8 ones times 2 is?
16 ones.
16 ones represents the area of this rectangle.
How many ones remain?
1 one.

24. Problem Set will be used for this lesson.
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 21
Concept Development
Problem Set will be used for this lesson.
One square unit remains. It doesn’t make another whole side length.

25. Problem Set will be used for this lesson.
Concept Development
Problem Set will be used for this lesson.
To make a new length unit, we must have 2 square units. We only have 1. Let’s draw the remaining 1 square unit.
Let’s validate our drawing and algorithm using the distributive property.
20 square units divided by 2 is?
10.
10 length units.
16 square units divided by 2 is?
8 length units.
10 length units plus 8 length units is?
18 length units.

26. Problem Set will be used for this lesson.
Concept Development
Problem Set will be used for this lesson.
Let’s solve for the area.
18 length units times 2 length units equals?
36 square units.
We see that in our area model. Add 1 square unit, our remainder.
37 square units.

27. Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
I’m going to represent this with an area model moving from part to whole by place value just as we did with 37 ÷ 2. What should the total area be?
76 square units.
What is the width or the known side length?
3 length units.
3 times how many tens gets us as close as possible to an area of 7 tens?

28. 76 ÷ 3 Concept Development 2 tens. Let’s give 2 tens to the length.
Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
2 tens.
Let’s give 2 tens to the length.
Let’s record 2 tens in the tens place.
What is 2 tens times 3?
6 tens.
How many square units of area is that?
60 square units.
How many tens remain?
1 ten.

29. Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
Let’s add the remaining ten to the 6 ones. What is 1 ten + 6 ones?
16 ones.

30. Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
We have an area of 16 square units remaining with a width of 3.
3 times how many ones gets us as close as possible to an area of 16?
5 ones.
Let’s give 5 ones to the length.
This rectangle has an area of?
15 square units.
How many square units remaining?
1 square unit.
What is the unknown length and how many square units remain?

31. Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
We have an area of 16 square units remaining with a width of 3.
3 times how many ones gets us as close as possible to an area of 16?
5 ones.
Let’s give 5 ones to the length.
This rectangle has an area of?
15 square units.

32. 76 ÷ 3 Concept Development How many square units remaining?
Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
How many square units remaining?
1 square unit.
What is the unknown length and how many square units remain?
The unknown length is 25 with a remainder of 1 square unit.

33. Lesson 21
Concept Development
Problem Set 2
76 ÷ 3
60 square units divided by a side length of 3 gave us a side length of?
20.
Let’s say “length units.”
20 length units.
15 square units divided by a side length of 3 gave us a side length of?
5 length units.
The total length was?
25 length units.

34. Concept Development
Problem Set 2
Lesson 21
76 ÷ 3
With 1 square unit we did not add on to the length.
We built the area one rectangle at a time by place value. Each time after we divide, we have some area remaining. After dividing the tens, we had 16 square units remaining.

35. Concept Development
Problem Set 2
Lesson 21
76 ÷ 3
After dividing the ones, we had 1 square unit remaining.
Later when we study fractions more, we will be able to make a little more length from that area, but for now, we are just going to leave it as 1 square unit of area remaining.
Review with your partner how we solved this problem step by step.

36. Problem Set
10 Minutes

37. Problem Set
10 Minutes

38. Problem Set
10 Minutes

39. Problem Set
10 Minutes

40. Problem Set
10 Minutes

41. In Problem 3, explain to your partner the connection between the distributive property and the area model.
Because we often have remainders when we divide, we have to use the area model by building up from part to whole. What did the first rectangle you drew in Problem 1 represent? The next chunk of the rectangle?
Each time we divide, what happens to the amount of area we still have left to divide?
Why don’t we have this complication of leftovers or remainders with multiplication?
In Problem 4, we didn’t know if we were going to have a remainder in the ones place, so instead we built up to the area working with one place value unit at a time. How might the problems with remainders been challenging if you started with the whole area, like in Lesson 20?
(Optional.) Let’s look back at Problem 2, 76 ÷ 3. What if we cut this remaining square unit into 3 equal parts with vertical lines? What is the length of one of these units? What if we stack them to add more area? What is the total length of the new rectangle including this tiny piece?
Debrief
Lesson Objective: Solve division problems with remainders using the area model.

42. Exit Ticket
Lesson 1