Divide Multi-Digit Numbers Using an Algorithm

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can divide multi-digit whole numbers and explain the meaning of the quotient and remainder, explain why the method works, and use it on a problem I have not seen before.

The big idea: Repeat the cycle Divide → Multiply → Subtract → Bring Down until no digits are left to bring down; what is left at the end is the remainder — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me

I want 1,344 ÷ 12. The dividend is 1,344 and the divisor is 12, so 12 goes outside the bracket and 1,344 goes inside.
DIVIDE: 12 does not fit into 1, so I look at 13. How many 12s fit into 13? One. I write 1 above the 3.
MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.
SUBTRACT: 13 − 12 = 1. That is what is left so far.
BRING DOWN: I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I bring down the last 4 to make 24.
REPEAT: 24 ÷ 12 → 2 (written above the last 4), 2 × 12 = 24, 24 − 24 = 0. Nothing is left to bring down, so the remainder is 0.
The digits I wrote are 1, 1, 2, so 1,344 ÷ 12 = 112. I check by multiplying: 12 × 112 = 1,344.

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: Let's do 384 ÷ 8. DIVIDE: 8 does not fit into 3, so we look at 38. How many 8s fit into 38? (4 — write it above the 8.) MULTIPLY: 4 × 8 = ? (32 — write it under the 38.) SUBTRACT: 38 − 32 = ? (6.) BRING DOWN: bring the 4 down to make 64, then repeat. DIVIDE: 64 ÷ 8 = ? (8.) MULTIPLY: 8 × 8 = 64. SUBTRACT: 64 − 64 = 0. Nothing is left to bring down, so the remainder is 0 and 384 ÷ 8 = 48. Check: 8 × 48 = 384. Now prove it: say why that move had to work at all — not just that it did.
Show your work
2
Warm restartWhat is 7 × 40?
1. A280
2. B47
3. C2,800
4. D28
How do you know?
3
Warm restartWhat is 96 ÷ 8?
1. A11
2. B12
3. C14
4. D8
How do you know?
4
Warm restartWhich multiplication fact helps you divide 200 by 5?
1. A5 × 40 = 200
2. B5 × 20 = 100
3. C5 × 4 = 20
4. D5 × 50 = 250
How do you know?

6.NOS.2 Group 2 · Challenge

Practice Set · Part 2

Divide Multi-Digit Numbers Using an Algorithm

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

5
Think it through1,680 ÷ 24 = ?
1. A60
2. B70
3. C80
4. D72
Why is that the answer?
6
Think it throughEstimate first: rounding to 1,600 ÷ 20 gives about how many pencils per room?
1. A40
2. B60
3. C80
4. D100
How do you know? Give a second reason as well.
7
Think it throughIf the pencils were split among 20 classrooms instead of 24, would each room get more or fewer?
1. AMore, because the pencils are split among fewer rooms
2. BFewer, because 20 is less than 24
3. CThe same, because the total did not change
4. DYou cannot tell
Explain your thinking. What would have to change for a different choice to be right?
8
Back to the modelYou ran the cycle 3 times. What is 3,822 ÷ 14, and how did you know when to stop repeating divide, multiply, subtract, bring down?

6.NOS.2 Group 2 · Challenge

Practice Set · Part 3

Divide Multi-Digit Numbers Using an Algorithm

Words and reasoning

Word bank · Banco de palabras

Divide Multi-Digit Numbers (Dividir números de varias cifras)Dividend (Dividendo)Divisor (Divisor)Quotient (Cociente)Remainder (Residuo)Long division (División larga)Bring down (Bajar el dígito)

Use the words

Fill each blank with a word from the bank.

Long division repeats four steps: divide, multiply, subtract, ___ ___.
In 84 ÷ 7, the number 84 being divided is the ___.
In 84 ÷ 7, the number 7 that we divide by is the ___.
The answer to a division problem is called the ___.

Explain the thinking

9
Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.
The mistake: A common mistake in Divide Multi-Digit Numbers is skipping a placeholder zero in the quotient when a digit doesn't divide evenly, which shifts every digit after it out of place.
10
Say moreYou used long division for 1,344 ÷ 12. Walk through your divide, multiply, subtract, and bring down steps — what did each one tell you?
11
Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A school district has 13,275 elementary-age students. The district plans to redistrict and divide the students equally among its 15 elementary schools.
Show your work

6.NOS.2 Group 2 · Challenge

Practice Set · Part 4

Divide Multi-Digit Numbers Using an Algorithm

Show what you know

Last check

These two come from Lesson 2.5. If they are shaky, that is the lesson to revisit — not this one.

12
Show what you knowExplain your thinking — What is 2,352 ÷ 16?
1. A147
2. B137
3. C157
4. D146
Explain your choice.
13
From Lesson 2.5Explain your thinking — A box plot has Q1 = 20 and Q3 = 36, with a least value of 10 and a greatest value of 50. What is the IQR, and what does it tell you?
1. AIQR = 16; the middle half of the data spans 16 units
2. BIQR = 40; the data spans 40 units from end to end
3. CIQR = 56; the quartiles add to 56
4. DIQR = 28; 28 is halfway between the quartiles
How do you know?
14
From Lesson 2.5Both classes have a median of 81. What do the smaller range and smaller IQR tell you about Class B?
1. AClass B's scores are less spread out, so more students scored near the median
2. BClass B's best score was higher
3. CClass B had fewer students
4. DClass B's median is actually larger
How do you know?

Be honest — this tells your teacher what to do next

I can…	Not yet	Getting there	Got it
I can divide multi-digit whole numbers and explain the meaning of the quotient and remainder, explain why the method works, and use it on a problem I have not seen before.
I can explain why it works: Repeat the cycle Divide → Multiply → Subtract → Bring Down until no digits are left to bring down; what is…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time