M4.4.6 For the adult
Similar areas and volumes
A jar is made twice as high and twice as wide. Does it hold twice as much?
What this chapter teaches
When a shape is enlarged by a scale factor k, lengths are multiplied by k, areas by k × k and volumes by k × k × k. Doubling every length makes the area four times as big and the volume eight times as big.
Three questions to ask
There is no one right wording. Listen for the idea.
- If every length of a box is doubled, how many times as big is the volume, and why?
- Why is the area scale factor k × k and not k?
- How can you find k when you know the two areas?
After the chapter, the learner can
- Use k, k² and k³ for length, area and volume scale factors
- Find the volume of a larger jar of the same shape
What they copy into their notebook
Scale factor k: lengths × k, areas × k², volumes × k³. Doubling every length gives 4 times the area and 8 times the volume.