Using Scale factor and Volume

Scale factor and Volume

By YCIS CQ

If you double every edge of a 3D shape, why doesn’t the volume just double?

Poll

If every edge of a cube is doubled, the volume doubles.

• Agree

• Disagree

• Not sure

Word Cloud

Type 1-3 words you connect with the idea of volume.

Open Ended

A cube has side length 3 cm. A larger similar cube has side length 6 cm. Without fully calculating both volumes yet, predict: Will the volume be 2 times, 4 times, 6 times, or 8 times bigger? Explain your thinking.

Choose 1 of 3 AI as a math coach

Support Prompt: You are my Year 8 maths coach. We are learning about scale factor and volume. Rules: - Explain in simple language. - Ask me one question at a time. - Give hints before answers. - Use cubes, cuboids, and easy numbers. - If I make a mistake, help me spot it. Start by helping me answer: If every edge of a cube doubles, what happens to the volume, and why?

2- AI as a math coach

Stretch Prompt: You are my challenge maths coach. I want reverse and reasoning questions about scale factor and volume. Make me justify each answer using words, numbers, and if helpful a table. Do this: - Give me one challenge problem at a time. - Ask me to explain why the rule is k cubed. - Include reverse problems where I know the volume scale factor and need the linear scale factor. - Do not accept a one-line answer from me. Start with a challenge question.

3- AI as a math coach

Misconception checker Prompt: I think that if all side lengths double, the volume doubles. Please do not just tell me I am wrong. Instead: - test my idea with an example - show a small cube model or table - ask me what I notice - then help me rewrite the rule correctly

Multiple Choice

A cube is enlarged by a linear scale factor of 2. What is the volume scale factor?

• 2

• 4

• 6

• 8

Multiple Choice

A solid has a volume scale factor of 64. What is the linear scale factor?

• 2

• 3

• 4

• 8

Dropdown

When a cube is enlarged by a linear scale factor of 3, the volume is [9 times larger / 27 times larger / 81 times larger] because the scale factor affects [one dimension / two dimensions / three dimensions].

​

Select answer

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Select answer

Match

Match each linear scale factor to the correct volume scale factor.

• 2

• 3

• 4

• 5

• 10

8

27

64

125

1000

• 8

• 27

• 64

• 125

• 1000

Reorder

Put these steps in the correct order for solving a scale factor and volume problem.

• Read the dimensions or scale factor carefully

• Decide whether the question is asking for linear or volume scale factor

• Cube the linear scale factor

• Multiply or divide the volume as needed

• Check whether the answer makes sense

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Math Response

A cube has side length 4 cm.

It is enlarged by a linear scale factor of 3.

What is the volume of the enlarged cube?

Type answer here

Correct Answer: 1728

Deg^°

Rad

Math Response

A cuboid has a volume of 30 cm³.

It is enlarged by a linear scale factor of 2.

What is the new volume?

Type answer here

Correct Answer: 240

Deg^°

Rad

Math Response

A solid is enlarged and its volume becomes 27 times larger.

What is the linear scale factor?

Type answer here

Correct Answer: 3

Deg^°

Rad

Open Ended

A cinema company makes a “Mega Popcorn Tub” that is similar in shape to the regular tub.

If every length is multiplied by 3, will it hold 3 times as much popcorn?

Explain clearly using scale factor and volume.

Multiple Choice

Exit ticket 1: A solid is enlarged by a linear scale factor of 4. The volume scale factor is:

• 6

• 12

• 16

• 64

Math Response

A prism has volume 18 cm³. It is enlarged by a linear scale factor of 2.

What is the new volume?

Type answer here

Correct Answer: 144

Deg^°

Rad

Poll

How confident do you feel with scale factor and volume now?

• I can explain it to someone else

• I mostly get it

• I need a bit more practice

• I am still confused