6.NOS.3 Group 2 · Challenge

Practice Set · Part 1

Divide Decimals Using an Algorithm

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can divide with decimals by making the divisor a whole number first, explain why the method works, and use it on a problem I have not seen before.

The big idea: Moving both points the same number of places multiplies both numbers by the same power of 10, so the quotient never changes.

Model to copy — Example 1 · Write a zero

  1. A bottle holds 2.1 liters. Each cup holds 0.35 liter. How many cups can you fill?
  2. Move the divisor's point 2 places right: 0.35 → 35
  3. Move the dividend's point 2 places too: 2.1 → 2.10 → 210
  4. Divide 210 by 35: 210 ÷ 35 → 6; 6 × 35 = 210; 210 − 210 = 0
  5. Check by multiplying: 0.35 × 6 = 2.1
  6. You can fill 6 cups. 2.1 ÷ 0.35 = 6.
  7. Find 9.12 ÷ 2.4.
  8. Move both points 1 place right: 2.4 → 24; 9.12 → 91.2
  9. Write the quotient's point over the dividend's point.
  10. Divide 91 by 24. Multiply and subtract: 91 ÷ 24 → 3; 3 × 24 = 72; 91 − 72 = 19
  11. Bring down the 2. Divide 192 by 24: 192 ÷ 24 → 8; 8 × 24 = 192; 192 − 192 = 0
  12. Check by multiplying: 2.4 × 3.8 = 9.12
  13. 9.12 ÷ 2.4 = 3.8

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

  1. 1

    Same stepsFinish what the group started. Use the model above, step for step.

    Try it together — then prove it: Find 8.4 ÷ 2.1. Move both points to make the divisor whole. What is the new problem? (84 ÷ 21) Divide. What is the quotient? (4, because 4 × 21 = 84) Why does moving both points keep the answer the same? (Both numbers are multiplied by 10. 8.4 ÷ 2.1 and 84 ÷ 21 both make 4.)
    Show your work
  2. 2

    Warm restartWhat is 84 ÷ 4?

    1. A12
    2. B20
    3. C21
    4. D336

    How do you know?

  3. 3

    Warm restartWhat is 396 ÷ 3?

    1. A13.2
    2. B122
    3. C132
    4. D133

    How do you know?

  4. 4

    Warm restartWhat is 936 ÷ 8?

    1. A107
    2. B116
    3. C117
    4. D127

    How do you know?

2.7 Small Group · Group 2 · Practice SetPart 1 of 4
6.NOS.3 Group 2 · Challenge

Practice Set · Part 2

Divide Decimals Using an Algorithm

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

  1. 5

    Think it through16.8 ÷ 2.4 = ?

    1. A0.7
    2. B4.2
    3. C7
    4. D70

    Why is that the answer?

  2. 6

    Think it throughWhy can you rewrite 16.8 ÷ 2.4 as 168 ÷ 24?

    1. ABecause decimals are not allowed in division
    2. BBecause 168 and 16.8 are equal
    3. CBecause you always drop the decimal point
    4. DMultiplying both numbers by 10 keeps the quotient the same

    How do you know? Give a second reason as well.

  3. 7

    Think it throughIf each piece were 2.8 feet instead, how many whole pieces could you cut?

    1. A5
    2. B6
    3. C7
    4. D8

    Explain your thinking. What would have to change for a different choice to be right?

  4. 8

    Back to the modelWhy does moving the point the same number of places in both numbers give you the same quotient — and why is it worth doing before you start the divide, multiply, subtract, bring down cycle?

2.7 Small Group · Group 2 · Practice SetPart 2 of 4
6.NOS.3 Group 2 · Challenge

Practice Set · Part 3

Divide Decimals Using an Algorithm

Words and reasoning

Word bank · Banco de palabras

Dividend (Dividendo)Divisor (Divisor)Quotient (Cociente)Decimal Division Algorithm (Algoritmo de división decimal)Equivalent division (División equivalente)Annex a zero (Agregar un cero)Algorithm (Algoritmo)

Use the words

Fill each blank with a word from the bank.

Explain the thinking

  1. 9

    Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

    The mistake: A common mistake in Divide Decimals is moving the decimal point in the divisor but forgetting to move it the same number of places in the dividend.
  2. 10

    Say moreWhen you divided 18.9 by 6.3, how did you use equivalent division to make the divisor a whole number?

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A school paid for math workbooks with the money shown. There are three identical stacks, and each stack holds one $5 bill, one $1 bill, and a single quarter.

    Show your work
2.7 Small Group · Group 2 · Practice SetPart 3 of 4
6.NOS.3 Group 2 · Challenge

Practice Set · Part 4

Divide Decimals Using an Algorithm

Show what you know

Last check

These two come from Lesson 2.6. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — What is 19.2 ÷ 0.8?

    1. A0.24
    2. B2.4
    3. C24
    4. D240

    Explain your choice.

  2. 13

    From Lesson 2.6Explain your thinking — What is 2,352 ÷ 16?

    1. A137
    2. B146
    3. C147
    4. D157

    How do you know?

  3. 14

    From Lesson 2.6If the pencils were split among 20 classrooms instead of 24, would each room get more or fewer?

    1. AFewer, because 20 is less than 24
    2. BThe same, because the total did not change
    3. CMore, because the pencils are split among fewer rooms
    4. DYou cannot tell

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can divide with decimals by making the divisor a whole number first, explain why the method works, and use it on a problem I have not seen before.
I can explain why it works: Moving both points the same number of places multiplies both numbers by the same power of 10…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time