Practice Set · Part 1
Divide Multi-Digit Numbers Using an Algorithm
Pick up where we left off
Where we left off
Our goal: With my small group, I can divide multi-digit whole numbers and explain the meaning of the quotient and remainder — one step at a time, with support.
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.
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.
Let's try together: 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.My first step is ___ , because the problem asks for ___ .
Show your work - 2
Warm restartWhat is 7 × 40?
- A280
- B47
- C2,800
- D28
- 3
Warm restartWhat is 96 ÷ 8?
- A11
- B12
- C14
- D8
- 4
Warm restartWhich multiplication fact helps you divide 200 by 5?
- A5 × 40 = 200
- B5 × 20 = 100
- C5 × 4 = 20
- D5 × 50 = 250
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 = ?
- A60
- B70
- C80
- D72
Why is that the answer?
I chose ___ because ___ .
- 6
Think it throughEstimate first: rounding to 1,600 ÷ 20 gives about how many pencils per room?
- A40
- B60
- C80
- D100
How do you know?
I chose ___ because ___ .
- 7
Think it throughIf the pencils were split among 20 classrooms instead of 24, would each room get more or fewer?
- AMore, because the pencils are split among fewer rooms
- BFewer, because 20 is less than 24
- CThe same, because the total did not change
- DYou cannot tell
Explain your thinking.
I chose ___ because ___ .
- 8
Back to the modelYou ran the cycle 3 times. What is 1,472 ÷ 8, and how did you know when to stop repeating divide, multiply, subtract, bring down?
1,472 ÷ 8 = ___ because I repeated divide, multiply, subtract, and bring down until there were no digits left to bring down, and what was left at the end was ___.
Practice Set · Part 3
Divide Multi-Digit Numbers Using an Algorithm
Words and reasoning
Word bank · Banco de palabras
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?
First I divided ___ by 12 and wrote ___ in the quotient.
- 11
Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.
If ___ changed to ___ , then ___ .
Show your work
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 knowQuick check — you've got this: What is 2,352 ÷ 16?
- A147
- B137
- C157
- D146
Explain your choice.
I know it is ___ because ___ .
- 13
From Lesson 2.5Quick check — you've got this: 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?
- AIQR = 16; the middle half of the data spans 16 units
- BIQR = 40; the data spans 40 units from end to end
- CIQR = 56; the quartiles add to 56
- DIQR = 28; 28 is halfway between the quartiles
- 14
From Lesson 2.5Both classes have a median of 81. What do the smaller range and smaller IQR tell you about Class B?
- AClass B's scores are less spread out, so more students scored near the median
- BClass B's best score was higher
- CClass B had fewer students
- DClass B's median is actually larger
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 — one step at a time, with support. | |||
| 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 talk through each step out loud using a sentence frame and the lesson's key words. |
One question I want to ask my group next time