First lesson
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Unit 01 · Whole Numbers and DecimalsLesson

Day 001Long Division and Place Value

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.B.2
LEARNING TARGET

I can divide multi-digit whole numbers and check the quotient.

01 · LEARN

Build the idea

Estimate the quotient first. Divide, multiply, subtract, and bring down one digit at a time. Keep each quotient digit in its place; write zero when needed. Check dividend = divisor × quotient + remainder.

WORKED EXAMPLE 1

Use long division: 138 ÷ 6. Show the algorithm and check.

23

13 ÷ 6: write 2, subtract 12, remainder 1; bring down the next digit: 18 ÷ 6: write 3, subtract 18, remainder 0. Check: 6 × 23 = 138.

WORKED EXAMPLE 2

Use long division: 12,183 ÷ 34. Show the algorithm and check.

358 R 11

121 ÷ 34: write 3, subtract 102, remainder 19; bring down the next digit: 198 ÷ 34: write 5, subtract 170, remainder 28; bring down the next digit: 283 ÷ 34: write 8, subtract 272, remainder 11. Check: 34 × 358 + 11 = 12183.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Use long division: 438 ÷ 6. Show the algorithm and check.

  2. Use long division: 175 ÷ 7. Show the algorithm and check.

  3. Use long division: 252 ÷ 6. Show the algorithm and check.

  4. Use long division: 14,174 ÷ 38. Show the algorithm and check.

  5. Use long division: 3,388 ÷ 14. Show the algorithm and check.

  6. Use long division: 12,408 ÷ 33. Show the algorithm and check.

  7. Use long division: 5,492 ÷ 29. Show the algorithm and check.

  8. Use long division: 5,575 ÷ 21. Show the algorithm and check.

  9. A club has 2351 cards. Each full packet holds 15. How many full packets can it make, and how many cards remain?

  10. A club has 3245 cards. Each full packet holds 12. How many full packets can it make, and how many cards remain?

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 73

    43 ÷ 6: write 7, subtract 42, remainder 1; bring down the next digit: 18 ÷ 6: write 3, subtract 18, remainder 0. Check: 6 × 73 = 438.

  2. 25

    17 ÷ 7: write 2, subtract 14, remainder 3; bring down the next digit: 35 ÷ 7: write 5, subtract 35, remainder 0. Check: 7 × 25 = 175.

  3. 42

    25 ÷ 6: write 4, subtract 24, remainder 1; bring down the next digit: 12 ÷ 6: write 2, subtract 12, remainder 0. Check: 6 × 42 = 252.

  4. 373

    141 ÷ 38: write 3, subtract 114, remainder 27; bring down the next digit: 277 ÷ 38: write 7, subtract 266, remainder 11; bring down the next digit: 114 ÷ 38: write 3, subtract 114, remainder 0. Check: 38 × 373 = 14174.

  5. 242

    33 ÷ 14: write 2, subtract 28, remainder 5; bring down the next digit: 58 ÷ 14: write 4, subtract 56, remainder 2; bring down the next digit: 28 ÷ 14: write 2, subtract 28, remainder 0. Check: 14 × 242 = 3388.

  6. 376

    124 ÷ 33: write 3, subtract 99, remainder 25; bring down the next digit: 250 ÷ 33: write 7, subtract 231, remainder 19; bring down the next digit: 198 ÷ 33: write 6, subtract 198, remainder 0. Check: 33 × 376 = 12408.

  7. 189 R 11

    54 ÷ 29: write 1, subtract 29, remainder 25; bring down the next digit: 259 ÷ 29: write 8, subtract 232, remainder 27; bring down the next digit: 272 ÷ 29: write 9, subtract 261, remainder 11. Check: 29 × 189 + 11 = 5492.

  8. 265 R 10

    55 ÷ 21: write 2, subtract 42, remainder 13; bring down the next digit: 137 ÷ 21: write 6, subtract 126, remainder 11; bring down the next digit: 115 ÷ 21: write 5, subtract 105, remainder 10. Check: 21 × 265 + 10 = 5575.

  9. 156 full packets; 11 cards remain

    2351 = 15 × 156 + 11.

  10. 270 full packets; 5 cards remain

    3245 = 12 × 270 + 5.

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