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: The quotient tells how many equal groups, and the remainder tells what is left. The question decides if you drop the remainder or add one more group.

Model to copy — Example · What does the remainder mean?

1,350 students go on a trip. Each bus holds 48 students. How many buses are needed?
Divide 135 by 48. Multiply and subtract: 135 ÷ 48 → 2; 2 × 48 = 96; 135 − 96 = 39
Bring down the 0. Divide 390 by 48: 390 ÷ 48 → 8; 8 × 48 = 384; 390 − 384 = 6
Write the quotient and the remainder: 1,350 ÷ 48 → 28 R 6
Decide what the remainder means: 28 full buses + 6 students
29 buses are needed. 28 buses are full, and 1 more bus carries the last 6 students.

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: Find 384 ÷ 8. Divide 38 by 8. Then multiply and subtract. (4 on top. 4 × 8 = 32, and 38 − 32 = 6) Bring down the 4. Divide, multiply and subtract again. (8 on top. 8 × 8 = 64, and 64 − 64 = 0) After you subtract, why must the result be less than 8? (If it were 8 or more, another 8 would still fit. Then the digit on top would be too small.)
Show your work
2
Warm restartWhat is 7 × 40?
1. A28
2. B47
3. C280
4. D2,800
How do you know?
3
Warm restartWhat is 96 ÷ 8?
1. A8
2. B11
3. C12
4. D14
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. C72
4. D80
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. AFewer, because 20 is less than 24
2. BThe same, because the total did not change
3. CMore, because the pencils are split among fewer rooms
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

Dividend (Dividendo)Divisor (Divisor)Quotient (Cociente)Remainder (Residuo)Long division (División larga)Bring down (Bajar el dígito)Algorithm (Algoritmo)

Use the words

Fill each blank with a word from the bank.

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 ___.
When a number does not divide evenly, the amount left over is 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. A137
2. B146
3. C147
4. D157
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 = 28; 28 is halfway between the quartiles
3. CIQR = 40; the data spans 40 units from end to end
4. DIQR = 56; the quartiles add to 56
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 best score was higher
2. BClass B had fewer students
3. CClass B's median is actually larger
4. DClass B's scores are less spread out, so more students scored near the median
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: The quotient tells how many equal groups, and the remainder tells what is left…
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