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.

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 outA 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 — bring down the 1 to make 21 ÷ 3 = 7, then bring down 6 ÷ 3 = 2, giving the correct quotient 1,072. A student who skips writing that 0 and jumps straight to 21 ÷ 3 = 7 ends up with 172 instead of 1,072 — an answer off by a factor of ten. Always check: does a digit in your quotient go missing every time you 'can't divide'? If so, you dropped a placeholder zero.

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

Lesson 2.6Divide Multi-Digit Numbers Using an Algorithm

Version ASupported practice

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.

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

    Hint Read the row left to right — it is one trip around the cycle: divide, multiply, subtract, bring down.

    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

    Hint Estimate first: 12 × 70 = 840 and 12 × 80 = 960, so the quotient must land between 70 and 80.

    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

    Hint Size it up: 5 × 500 = 2,500, just a bit more than 2,485 — so the quotient is a little under 500.

    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

    Hint Anchor on a fact you know: 9 × 80 = 720, which is close to 756 — so the quotient is just above 80.

    9756
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.
  4. 5Circle the letter of the best answer. Show how you know.

    What is 1,125 ÷ 9?

    1. A115
    2. B124
    3. C125
    4. D135

    Hint Estimate first: 9 × 100 = 900 and 9 × 200 = 1,800, so the quotient lands between 100 and 200.

    91125
    1. 1DivideHow many fit?
    2. 2MultiplyMultiply back.
    3. 3SubtractWhat is left?
    4. 4Bring downNext digit.
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake in 1,134 ÷ 9

    1. 1ProblemDivide 1,134 ÷ 9 with long division. Dividend = 1,134, divisor = 9.
    2. 2Divide, Multiply, Subtract9 does not fit into 1, so start with 11. 11 ÷ 9 → 1. 1 × 9 = 9, and 11 − 9 = 2
    3. 3Bring down, repeatBring down the 3 to make 23. 23 ÷ 9 → 2. 2 × 9 = 18, and 23 − 18 = 5
    4. 4Final answerQuotient = 12, remainder = 5

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Count the digits of 1,134 that have been used so far. Is one of them still waiting to be brought down?

    Correct work
    Correct answer:

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 ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.2

Lesson 2.6Divide Multi-Digit Numbers Using an Algorithm

Version BCore practice

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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete each division problem.

    Division ProblemQuotient
    672 ÷ 8
    2,208 ÷ 16
    2,016 ÷ 14
    1,560 ÷ 15
    3,276 ÷ 12
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each division problem to its quotient.

    1. 450 ÷ 18
    2. 1,008 ÷ 16
    3. 1,440 ÷ 24
    4. 2,100 ÷ 15
    5. 864 ÷ 12
    6. 1,825 ÷ 25
    • A25
    • B63
    • C60
    • D140
    • E72
    • F73
  3. 3Complete the table. Show how you found each value.

    Divide each problem with the algorithm, then record the quotient and the remainder.

    DivisionQuotientRemainder
    144 ÷ 12
    480 ÷ 16
    1,000 ÷ 8
    100 ÷ 7
    500 ÷ 13
    250 ÷ 9
    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A warehouse has 2,184 items to pack into boxes of 14. How many boxes are needed?

    1. A146 boxes
    2. B155 boxes
    3. C156 boxes
    4. D166 boxes
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Mistake in 2,058 ÷ 14

    1. 1ProblemDivide 2,058 ÷ 14 with long division. Dividend = 2,058, divisor = 14.
    2. 2Divide, Multiply, Subtract14 does not fit into 2, so start with 20. 20 ÷ 14 → 1. 1 × 14 = 14, and 20 − 14 = 6
    3. 3Bring down, repeatBring down the 5 to make 65. 65 ÷ 14 → 4. 4 × 14 = 56, and 65 − 56 = 9
    4. 4Bring down, repeatBring down the 8 to make 98. 98 ÷ 14 → 8. 8 × 14 = 112, and 98 − 112 = −14
    5. 5Final answerQuotient = 148

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.2

Lesson 2.6Divide Multi-Digit Numbers Using an Algorithm

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Solve each problem using long division. Show the quotient and any remainder.

    Division ProblemQuotientRemainder
    2,578 ÷ 13
    3,456 ÷ 16
    1,987 ÷ 11
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Sonia's Mistake

    1. 1Problem1,536 ÷ 16
    2. 2Divide16 does not fit into 1 or 15, so start with 153. 153 ÷ 16 → 9, written above the 3
    3. 3Multiply9 × 16 = 144, written under the 153
    4. 4Subtract153 − 144 = 19
    5. 5Bring downBring down the 6 to make 196
    6. 6Final answerQuotient = 9 with 196 left over

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    The station must load 3,360 ration packs equally into 14 storage pods. Solve it with long division. Name each step — divide, multiply, subtract, bring down — and check your answer by multiplying.

    Write your answer

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?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help