Unit 1 · Standard 6.NS.2
Divide Multi-Digit Numbers
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
In 156 ÷ 12 = 13, the dividend is 156 — it is the total being split up
Dividend
The number you are splitting up in a division problem.
In 156 ÷ 12 = 13, the divisor is 12 — it is the size of each group
Divisor
The number you split by in a division problem.
In 156 ÷ 12 = 13, the quotient is 13 — there are 13 groups
Quotient
The answer when you divide.
17 ÷ 5 = 3 R 2 means 3 groups of 5 with 2 left over
Remainder
What is left over when a number does not divide evenly.
1,344 ÷ 12: first 12 × 100 = 1,200, then 12 × 12 = 144. Quotient = 100 + 12 = 112
Partial quotients
A way to divide by breaking the problem into smaller, easier steps.
Key Ideas & Notes
- The space station has 1,344 nutrition bars that must be divided equally among 12 crew sections for a 4-week rotation.
- How many bars does each section receive?
- Break apart the division 1,344 ÷ 12 using partial quotients. Sort each partial product — does it help build toward the answer, or is it NOT a step in this division?
Think About It
- What total amount needs to be divided?
- How many groups are the supplies being split into?
- Will each section get the same amount with none left over?
My Notes
Guided Examples
Example 1
What is 936 ÷ 12?
Solution: 12 × 78 = 936. You can verify: 12 × 70 = 840, 12 × 8 = 96, 840 + 96 = 936.
Answer: A. 78
Example 2
What is 2,485 ÷ 5?
Solution: 5 × 497 = 2,485. Check: 5 × 400 = 2,000, 5 × 90 = 450, 5 × 7 = 35. 2,000 + 450 + 35 = 2,485.
Answer: A. 497
Example 3
What is 756 ÷ 9?
Solution: 9 × 84 = 756. Check: 9 × 80 = 720, 9 × 4 = 36, 720 + 36 = 756.
Answer: A. 84
Write About the Math The Writing Revolution
I can explain my division using the words dividend, divisor, quotient, and remainder.
1. Kernel Sentence subject + verb
Model: Partial quotients is a way to divide by breaking the problem into smaller, easier steps.Cocientes parciales es una manera de dividir separando el problema en pasos más fáciles.
Write a kernel sentence about partial quotients. Use a subject and a verb.Escribe una oración base sobre cocientes parciales. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Partial quotients matters in mathCocientes parciales importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Partial quotients matters in math because ___.Cocientes parciales importa en matemáticas porque ___.
Partial quotients matters in math, but ___.Cocientes parciales importa en matemáticas, pero ___.
Partial quotients matters in math, so ___.Cocientes parciales importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about partial quotients.Di un hecho verdadero sobre partial quotients.
Partial quotients ___.
Ask a question about partial quotients.Haz una pregunta sobre partial quotients.
How does ___ ?¿Cómo ___ ?
Show excitement about partial quotients.Muestra entusiasmo sobre partial quotients.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with partial quotients.Dile a un compañero qué hacer con partial quotients.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
First I ___, then I ___.Primero ___, luego ___.
The quotient is ___ because ___.El cociente es ___ porque ___.
I would divide to ___.Dividiría para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is 1,125 ÷ 9?
- 125
- 115
- 135
- 124
2. A warehouse has 2,184 items to pack into boxes of 14. How many boxes are needed?
- 156 boxes
- 146 boxes
- 166 boxes
- 155 boxes
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A school has 1,680 pencils to distribute equally to 24 classrooms. Show how to solve this using partial quotients. Explain each step and check your answer by multiplying.
Sentence starter: 1,680 ÷ 24 = ___. First I used 24 × ___ = ___, then 24 × ___ = ___. The partial quotients add to ___. I checked by multiplying: 24 × ___ = 1,680.
Reflect — Exit Ticket
What is 2,352 ÷ 16?
- 147
- 137
- 157
- 146
Answer Key & Teacher Guide
- Try It 1: A. 125 — 9 × 125 = 1,125. Check: 9 × 100 = 900, 9 × 25 = 225, 900 + 225 = 1,125.
- Try It 2: A. 156 boxes — 2,184 ÷ 14 = 156. Check: 14 × 156 = 14 × 150 + 14 × 6 = 2,100 + 84 = 2,184.
- Exit Ticket: A. 147 — 16 × 147 = 2,352. Check: 16 × 100 = 1,600, 16 × 40 = 640, 16 × 7 = 112. 1,600 + 640 + 112 = 2,352.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Partial quotients is a way to divide by breaking the problem into smaller, easier steps.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).