1. Math Module 3 Multi-Digit Multiplication and Division
Topic E: Division of Tens and Ones with Successive Remainders
Lesson 17: Represent and solve division problems requiring decomposing a remainder in the tens
4.OA NBT.6
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2. Lesson 17 Target
You will represent and solve division problems requiring decomposing a remainder in the tens

3. Fluency Count forward and backward by twos to 20. 10 12 8 14 6 16 4 18
Group Count
Lesson 17 10 12 8 14 6 16 4 18 2 20

4. Fluency Count forward and backward by threes to 30. 15 18 12 21 9 24 6
Group Count
Lesson 17 15 18 12 21 9 24 6 27 3 30

5. Fluency Count forward and backward by fours to 40. 20 24 16 28 12 32 8
Group Count
Lesson 17 20 24 16 28 12 32 8 36 4 40

6. Fluency Count forward and backward by fives to 50. 25 30 20 35 15 40
Group Count
Lesson 17 25 30 20 35 15 40 10 45 5 50

7. 4 tens 8 ones divided by 2 equals 2 tens 4 ones.
Fluency
Divide Mentally
48 ÷ 2
48 divided by 2 equals 24.
Lesson 17
40 ÷ 2
Say the completed division equation in unit form.
Say the completed division equation in regular form.
8 ÷ 2
Say the completed division equation in unit form.
4 tens divided by 2 equals 2 tens.
Say the completed division equation in unit form.
8 ones divided by 2 equals 4 ones.

8. 9 tens 3 ones divided by 3 equals 3 tens 1 one.
Fluency
Divide Mentally
93 ÷ 3
93 divided by 3 equals 31.
Lesson 17
90 ÷ 3
Say the completed division equation in unit form.
Say the completed division equation in regular form.
3 ÷ 3
Say the completed division equation in unit form.
9 tens divided by 3 equals 3 tens.
Say the completed division equation in unit form.
3 ones divided by 3 equals 1 one.

9. 8 tens 8 ones divided by 4 equals 2 tens 2 ones.
Fluency
Divide Mentally
88 ÷ 4
88 divided by 4 equals 22.
Lesson 17
80 ÷ 4
Say the completed division equation in unit form.
Say the completed division equation in regular form.
8 ÷ 4
Say the completed division equation in unit form.
8 tens divided by 4 equals 2 tens.
Say the completed division equation in unit form.
8 ones divided by 4 equals 2 ones.

10. Divide Using the Standard Algorithm
Fluency
Divide Using the Standard Algorithm
Lesson 17
On your boards, solve the division problem using the vertical method.
24÷2
36÷3
37÷3
55÷5
57÷5
88÷4
87÷4
96÷3
95÷3

11. Lesson 17
Application Problem
5 Minutes
Audrey and her sister found 9 dimes and 8 pennies. If they share the money equally, how much money will each sister get?

12. 3 ÷ 2 === = Concept Development / / Tens Ones
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
3 ÷ 2
Tens
Ones
=== =
Model this problem on your place value chart. / /
3 ones divided by 2 is?
One with a remainder of 1.
Record 3 ÷ 2 as long division.
1 one

13. 30 ÷ 2 === ===== = Concept Development / / Tens Ones
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2
Tens
Ones
===
===== =
Using mental math, tell your partner the answer to 30 ÷ 2.
Thirty divided by 2 is 15.
Let’s confirm your quotient. Represent 30 on the place value chart. / /
R10
Tell your partner how many groups below are needed.
3 tens divided by 2 is? Distribute your disks and cross off what’s been distributed. The answer is?
1 ten

14. 30 ÷ 2 === ===== = Concept Development / /
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2
Tens
Ones
===
===== = / /
Can we rename the left over ten?
Yes! Change 1 ten for 10 ones.
Let’s rename 1 ten.

15. 30 ÷ 2 === ===== = Concept Development / / Tens Ones
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2
Tens
Ones
===
===== =
Now rename and distribute the 10 ones with your partner. / /
Our answer is 1 ten 5 ones, or 15.
Why didn’t we stop when we had a remainder of 1 ten?
Because 1 ten is just 10 ones, and you can keep dividing.
So why did we stop when we got a remainder of 1 one?
The ones are the smallest unit on our place value chart, so we stopped there and made a remainder.
1 ten
5 ones

16. 30 ÷ 2 1 2 30 2 Concept Development / /
2 u
Concept Development
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2 1
Let’s solve 30 ÷ 2 using long division.
3 tens divided by 2?
1 ten.
2 30 2
You recorded 1 ten, twice.
Say a multiplication equation that tells that.
1 ten times 2 equals 2 tens. / /
1 ten
Twice

17. 30 ÷ 2 1 2 30 -2 2 1 Concept Development / /
2 u
Concept Development
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2
We started with 3 tens, distributed 2 tens, and have 1 ten remaining. Tell me a subtraction equation for that.
3 tens minus 2 tens equals 1 ten. 1
2 30 2 -2 1 / /

18. 30 ÷ 2 1 2 30 -2 2 1 Concept Development
2 u
Concept Development
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2
How many ones remain to be divided?
10 ones.
Yes. We changed 1 ten for 10 ones. Say a division equation for how you distributed 1 ten or 10 ones.
10 ones divided by 2 equals 5 ones. 1
2 30 2 -2 1

19. 30 ÷ 2 1 15 2 30 -2 2 1 10 Concept Development
2 u
Concept Development
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2 1 15
2 30
You recorded 5 ones, twice. 2 -2 1
Say a multiplication equation that tells that.
5 ones times 2 equals 10 ones. 10
5 ones
Twice

20. 30 ÷ 2 1 15 2 30 2 -2 10 10 -10 Concept Development
2 u
Concept Development
Problem 1: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
30 ÷ 2 1 15
We renamed 10 ones, distributed 10 ones, and have no ones remaining. Say a subtraction equation for that.
10 ones minus 10 ones equals 0 ones.
2 30 2 -2 10 10
-10
Share with a partner how the model matches the algorithm. Note that both show equal groups and how both can be used to check your work using multiplication.

21. 2 u
Concept Development
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
4 ÷ 3
Represent 4 ones on the place value chart. With your partner, solve for 4 ÷ 3 using number disks and long division.
The quotient is 1 and the remainder is 1.

22. 42 ÷ 3 == ===== = Concept Development ====
2 u
Concept Development
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
42 ÷ 3
Represent 4 tens 2 ones on the place value chart and get ready to solve using long division.
Tens
Ones
==== ==
===== =
4 tens divided by 3 is? Distribute your disks and cross off what is used. The answer is?
1 ten with a remainder of 1 ten. Oh! I remember from last time, we need to change 1 ten for 10 ones.

23. 42 ÷ 3 == ===== = Concept Development ==== How many ones remain? 12.
2 u
Concept Development
Problem 2: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
42 ÷ 3
Tens
Ones
==== ==
===== =
How many ones remain?
12.
10 ones + 2 ones is 12 ones.
Show 12 ones divided by 3. Complete the remaining steps. What is the quotient?
Our quotient is 1 ten 4 ones, or 14.

24. 2 u
Concept Development
Problem 3: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
84 ÷ 3
Solve for 84 ÷ 3 by using number disks and long division.
The quotient is 28.
What was different about the place value chart with this problem?
There were a lot more disks! We had to decompose 2 tens this time.

25. 2 u
Concept Development
Problem 3: Divide two-digit numbers by one digit numbers using number disks, regrouping in the tens
Lesson 17
84 ÷ 3
How many ones did you have after decomposing your 2 tens?
24 ones.
Show your partner where to find 24 ones in the numerical representation.
Check your answer using multiplication.
28 times 3 is 84. Our answer is right!

26. Problem Set
10 Minutes

27. Problem Set
10 Minutes

28. Problem Set How did Problem 2 allow you to see only the
remaining 1 ten in the ones column?
Problem Set
10 Minutes

29. Explain why 1 ten remains in Problem 4?
Problem Set
10 Minutes

30. Problem Set
10 Minutes

31. How is the long division recording different in today’s lesson compared to yesterday’s lesson?
What different words are we using to describe what we do when we have a remaining ten or tens? (Break apart, unbundle, change, rename, decompose, regroup.) Which of these words are you most comfortable using yourself?
What other operation involves changing 1 ten for 10 ones at times? What operations involve the opposite, changing 10 ones for 1 ten at times?
What would happen if we divided the ones before the tens?
What connection can you find between the written division and the multiplication you used to check your work?
Why are we learning long division after addition, subtraction, and multiplication?
How did the Application Problem connect to today’s lesson?
Debrief
Lesson Objective:
You will represent and solve division problems requiring decomposing a remainder in the tens

32. Exit Ticket
Lesson 1