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

Lesson 2.62.6 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 156 ÷ 12 = 13, the dividend is 156 — it is the total being split up
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 156 ÷ 12 = 13, the divisor is 12 — it is the size of each group
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
Long divisionSpanish: División larga A method that repeats four steps — divide, multiply, subtract, bring down — until there are no digits left to bring down. 1,344 ÷ 12 → divide, multiply, subtract, bring down, repeat
Bring downSpanish: Bajar el dígito The fourth step of long division: move the next digit of the dividend down next to what is left, then start the cycle again. 13 − 12 = 1, then bring down the 4 to make 14

How it worksWorked example

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

1,350 students go on a trip. Each bus holds 48 students. How many buses are needed?

  1. Divide 135 by 48. Multiply and subtract: 135 ÷ 48 → 2; 2 × 48 = 96; 135 − 96 = 39
  2. Bring down the 0. Divide 390 by 48: 390 ÷ 48 → 8; 8 × 48 = 384; 390 − 384 = 6
  3. Write the quotient and the remainder: 1,350 ÷ 48 → 28 R 6
  4. Decide what the remainder means: 28 full buses + 6 students
  5. 29 buses are needed. 28 buses are full, and 1 more bus carries the last 6 students.

Now you trySame steps, your turn

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

Find 384 ÷ 8.

Answer:

Say it and write itSentence starters

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

  • 3,822 ÷ 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 DividendDivisorQuotientRemainderLong divisionBring downdividemultiplysubtractbring 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 2.62.6 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    What is 4,375 ÷ 25?

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    54R 101582075−7060−10
    15 does not fit into 8, so start with 82.

    820 fans ride to a game. Each van holds 15 fans. How many vans are needed?

    1. 1Divide 82 by 15. Multiply and subtract.
    2. 2Bring down the 0. Divide 70 by 15. What is the remainder?
    3. 3Write the quotient and the remainder.
    4. 454 vans are full. 10 fans are left. How many vans are needed?
    Final answer:
  2. 3Complete each step, then write the final answer.
    134R 616215016−5548−7064−6

    A factory has 2,150 batteries. Each pack holds 16 batteries. How many full packs can it make?

    1. 1Run the cycle: divide 21, then 55, then 70 by 16.
    2. 2What is the remainder?
    3. 3How many full packs can the factory make?
    4. 4Why do you drop the remainder here, but add a van for the fans?
    Final answer:
  3. 4Complete each step, then write the final answer.

    A number divided by 23 gives 46 R 5. What is the number?

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.

    A school collects 1,525 cans. Each box holds 36 cans. How many boxes are needed to hold all the cans?

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.

    Rosa has $1,000. Concert tickets cost $35 each. She says she can buy 29 tickets. How many tickets can she really buy?

    Show your work
    Final answer:

Explain your thinkingFor the fans, you added one more van. For the batteries, you dropped the remainder. How do you decide what to do with a remainder?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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