Practice Set · Part 1
Divide Decimals Using an Algorithm
Pick up where we left off
Where we left off
Our goal: With my small group, I can divide with decimals by making the divisor a whole number first — one step at a time, with support.
The big idea: Move the decimal point the same number of places in both numbers, so the divisor is whole and the answer does not change.
Model to copy — Example · Divide by a decimal
- Find 18.9 ÷ 6.3.
- Move the divisor's decimal point 1 place right: 6.3 → 63
- Move the dividend's point 1 place right too: 18.9 → 189
- Divide 189 by 63: 189 ÷ 63 → 3; 3 × 63 = 189; 189 − 189 = 0
- Check by multiplying: 6.3 × 3 = 18.9
- 18.9 ÷ 6.3 = 3
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.
Let's do one together: Find 8.4 ÷ 2.1. How many places make 2.1 a whole number? (1 place. 2.1 becomes 21.) Move the point in 8.4 one place too. What do you get? (84. The new problem is 84 ÷ 21.) How many 21s fit into 84? (4, because 4 × 21 = 84) Subtract. Is anything left? (84 − 84 = 0. Nothing is left.)My first step is ___ , because the problem asks for ___ .
Show your work - 2
Warm restartWhat is 84 ÷ 4?
- A12
- B20
- C21
- D336
- 3
Warm restartWhat is 396 ÷ 3?
- A13.2
- B122
- C132
- D133
- 4
Warm restartWhat is 936 ÷ 8?
- A107
- B116
- C117
- D127
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 = ?
- A0.7
- B4.2
- C7
- D70
Why is that the answer?
I chose ___ because ___ .
- 6
Think it throughWhy can you rewrite 16.8 ÷ 2.4 as 168 ÷ 24?
- ABecause decimals are not allowed in division
- BBecause 168 and 16.8 are equal
- CBecause you always drop the decimal point
- DMultiplying both numbers by 10 keeps the quotient the same
How do you know?
I chose ___ because ___ .
- 7
Think it throughIf each piece were 2.8 feet instead, how many whole pieces could you cut?
- A5
- B6
- C7
- D8
Explain your thinking.
I chose ___ because ___ .
- 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?
Multiplying both numbers by ___ doesn't change the quotient because ___.
Practice Set · Part 3
Divide Decimals Using an Algorithm
Words and reasoning
Word bank · Banco de palabras
Use the words
Fill each blank with a word from the bank.
- 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 ___.
- The steps that make the divisor whole before you divide are called 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?
I moved both decimal points ___ place, changing it to ___ ÷ ___.
- 11
Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.
If ___ changed to ___ , then ___ .
Show your work
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 knowQuick check — you've got this: What is 19.2 ÷ 0.8?
- A0.24
- B2.4
- C24
- D240
Explain your choice.
I know it is ___ because ___ .
- 13
From Lesson 2.6Quick check — you've got this: What is 2,352 ÷ 16?
- A137
- B146
- C147
- D157
- 14
From Lesson 2.6If the pencils were split among 20 classrooms instead of 24, would each room get more or fewer?
- AFewer, because 20 is less than 24
- BThe same, because the total did not change
- CMore, because the pencils are split among fewer rooms
- DYou cannot tell
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 — one step at a time, with support. | |||
| I can explain why it works: Move the decimal point the same number of places in both numbers… | |||
| I can talk through each step out loud using a sentence frame and the lesson's key words. |
One question I want to ask my group next time