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: Move the decimal point the same number of places in BOTH the divisor and the dividend, put the point in the quotient straight above it, then repeat Divide → Multiply → Subtract → Bring Down — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me

I want 18.9 ÷ 6.3. The divisor is 6.3, and long division needs a whole-number divisor.
STEP 0 — MOVE THE POINT: I move the decimal point 1 place right in the divisor, so 6.3 becomes 63.
I slide the decimal point 1 place to the right in the dividend too, so 18.9 becomes 189. Both points slid the same 1 place, so the answer does not change. The problem is now 189 ÷ 63.
Now I write it the tall way — 63 into 189 — with the answer going on top of the bar and the answer's decimal point in the column directly above the dividend's point. Then I repeat the same four steps I always use: DIVIDE, MULTIPLY, SUBTRACT, BRING DOWN.
DIVIDE: 63 does not fit into 1 or 18, so my first working number is 189. How many 63s fit into 189? Three. I write 3 above the 9.
MULTIPLY: 3 × 63 = 189. I write it underneath.
SUBTRACT: 189 − 189 = 0.
BRING DOWN: there are no digits left to bring down, so the cycle is finished and the remainder is 0. 18.9 ÷ 6.3 = 3.
I check by multiplying: 6.3 × 3 = 18.9. Correct — 3 pods can be filled.

Start here

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

1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: Let's do 8.4 ÷ 2.1. STEP 0 — MOVE THE POINT: how many places make 2.1 a whole number? (1 place, so 2.1 becomes 21.) Now slide the decimal point 1 place to the right in the dividend too. What does 8.4 become? (84, so the new problem is 84 ÷ 21.) DIVIDE: 84 ÷ 21 → 4. MULTIPLY: 4 × 21 = 84. SUBTRACT: 84 − 84 = 0. BRING DOWN: nothing is left, so 8.4 ÷ 2.1 = 4. Check: 2.1 × 4 = 8.4. Now prove it: say why that move had to work at all — not just that it did.
Show your work
2
Warm restartWhat is 84 ÷ 4?
1. A21
2. B20
3. C12
4. D336
How do you know?
3
Warm restartWhat is 396 ÷ 3?
1. A132
2. B122
3. C133
4. D13.2
How do you know?
4
Warm restartWhat is 936 ÷ 8?
1. A107
2. B117
3. C127
4. D116
How do you know?

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.

5
Think it through16.8 ÷ 2.4 = ?
1. A7
2. B0.7
3. C70
4. D4.2
Why is that the answer?
6
Think it throughWhy can you rewrite 16.8 ÷ 2.4 as 168 ÷ 24?
1. AMultiplying both numbers by 10 keeps the quotient the same
2. BBecause decimals are not allowed in division
3. CBecause 168 and 16.8 are equal
4. DBecause you always drop the decimal point
How do you know? Give a second reason as well.
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?
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?

6.NOS.3 Group 2 · Challenge

Practice Set · Part 3

Divide Decimals Using an Algorithm

Words and reasoning

Word bank · Banco de palabras

Divide Decimals (Dividir decimales)Dividend (Dividendo)Divisor (Divisor)Quotient (Cociente)Decimal Division Algorithm (Algoritmo de división decimal)Equivalent division (División equivalente)

Use the words

Fill each blank with a word from the bank.

Make the ___ a whole number first, then slide the dividend's point right the same number of places.
In a division problem, the number being divided is the ___.
In a division problem, the number we divide by is the ___.
The answer to a division problem is the ___.

Explain the thinking

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.
10
Say moreWhen you divided 18.9 by 6.3, how did you use equivalent division to make the divisor a whole number?
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

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.

12
Show what you knowExplain your thinking — What is 19.2 ÷ 0.8?
1. A24
2. B2.4
3. C240
4. D0.24
Explain your choice.
13
From Lesson 2.6Explain your thinking — What is 2,352 ÷ 16?
1. A147
2. B137
3. C157
4. D146
How do you know?
14
From Lesson 2.6If the pencils were split among 20 classrooms instead of 24, would each room get more or fewer?
1. AMore, because the pencils are split among fewer rooms
2. BFewer, because 20 is less than 24
3. CThe same, because the total did not change
4. DYou cannot tell
How do you know?

Be honest — this tells your teacher what to do next

I can…	Not yet	Getting there	Got 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: Move the decimal point the same number of places in BOTH the divisor and the dividend…
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