Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.2

Lesson 2.6Divide Multi-Digit Numbers Using an Algorithm

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide multi-digit whole numbers and explain the meaning of the quotient and remainder.

Why This Matters 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?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
AlgorithmSpanish: Algoritmo A step-by-step set of rules or instructions to solve a math problem. Long Division Algorithm — D (Divide), M (Multiply), S (Subtract), B (Bring Down)
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 1,344 ÷ 12 = 112, the dividend is 1,344 — the total amount being divided
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 1,344 ÷ 12 = 112, the divisor is 12 — the number of equal groups
QuotientSpanish: Cociente The answer when you divide. In 156 ÷ 12 = 13, the quotient is 13 — there are 13 groups
RemainderSpanish: Residuo What is left over when a number does not divide evenly. 17 ÷ 5 = 3 R 2 means 3 groups of 5 with 2 left over
Divide Multi-Digit NumbersSpanish: Dividir números de varias cifras Separate a multi-digit number into equal groups to find a quotient. 1,344 ÷ 12 = 112

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

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.

  1. 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.
  2. MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.
  3. SUBTRACT: 13 − 12 = 1. That is what is left so far.
  4. BRING DOWN: I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
  5. REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I bring down the last 4 to make 24.
  6. 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.
  7. The digits I wrote are 1, 1, 2, so 1,344 ÷ 12 = 112. I check by multiplying: 12 × 112 = 1,344.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

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.)

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • 2,184 ÷ 14 = 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 .

Word bank AlgorithmDividendDivisorQuotientRemainderDivide Multi-Digit Numbersdividemultiplysubtractbring downrepeatquotient

Watch out!A common 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. For example, dividing 3,216 ÷ 3: 3 ÷ 3 = 1, but the next digit 2 doesn't divide by 3, so a 0 must be written before continuing

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.2

Lesson 2.6Divide Multi-Digit Numbers Using an Algorithm

Level 0Most support · every hint printed

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can divide multi-digit whole numbers and explain the meaning of the quotient and remainder.

Why This Matters 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?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

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.

  1. 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.
  2. MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.
  3. SUBTRACT: 13 − 12 = 1. That is what is left so far.
  4. BRING DOWN: I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
  5. REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I bring down the last 4 to make 24.
  6. 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.
  7. The digits I wrote are 1, 1, 2, so 1,344 ÷ 12 = 112. I check by multiplying: 12 × 112 = 1,344.
Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Run the long-division cycle. Fill in the quotient.

    ProblemDivideMultiply & SubtractBring DownQuotient
    384 ÷ 8
    672 ÷ 6
    Steps to try
    1. Read the row left to right — it is one trip around the cycle: divide, multiply, subtract, bring down.
    2. The Quotient column wants the WHOLE answer, not just the first digit. Keep repeating the cycle until no digits are left to bring down.
    3. Row 1: after you bring down the 4 you are looking at 64. Divide, multiply and subtract once more, then read the digits you wrote across the top.
    Show your work
Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 936 ÷ 12?

    1. A68
    2. B76
    3. C78
    4. D87
    Steps to try
    1. Estimate first: 12 × 70 = 840 and 12 × 80 = 960, so the quotient must land between 70 and 80.
    2. Set it up as long division and DIVIDE first — how many 12s fit into 93?
    3. DIVIDE: 93 ÷ 12 → 7. MULTIPLY: 7 × 12 = 84. SUBTRACT: 93 − 84 = 9. BRING DOWN the 6 to make 96, then repeat the cycle.
    12936
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.
  2. 3Circle the letter of the best answer. Show how you know.

    What is 2,485 ÷ 5?

    1. A487
    2. B496
    3. C497
    4. D507
    Steps to try
    1. Size it up: 5 × 500 = 2,500, just a bit more than 2,485 — so the quotient is a little under 500.
    2. Set it up as long division and DIVIDE first — how many 5s fit into 24?
    3. DIVIDE: 24 ÷ 5 → 4. MULTIPLY: 4 × 5 = 20. SUBTRACT: 24 − 20 = 4. BRING DOWN the 8 to make 48, then repeat until the last digit is used.
    52485
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.
  3. 4Circle the letter of the best answer. Show how you know.

    What is 756 ÷ 9?

    1. A83
    2. B84
    3. C86
    4. D94
    Steps to try
    1. Anchor on a fact you know: 9 × 80 = 720, which is close to 756 — so the quotient is just above 80.
    2. Set it up as long division and DIVIDE first — how many 9s fit into 75?
    3. DIVIDE: 75 ÷ 9 → 8. MULTIPLY: 8 × 9 = 72. SUBTRACT: 75 − 72 = 3. BRING DOWN the 6 to make 36, then repeat the cycle.
    9756
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.

Explain your thinkingYou ran the cycle three times. What is 2,184 ÷ 14, and how did you know when to stop repeating divide, multiply, subtract, bring down?

Sentence starter 2,184 ÷ 14 = ___ 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 ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help