Level 3: Rates and graphs that tell stories

Change and motion · level 3 of 8 · rough age 9-10 (a guide for parents; anyone can start anywhere)

In level 2 you measured how much things changed. In this level you measure how fast they change, using one small word: per. You learn to read graphs as stories (where someone stopped, when the bath was emptied), to spot steady change in a table of numbers, and to see the curve of something that changes fast at first and then slower. The level ends with a famous trap: why the average of two speeds is usually not the average speed.

Lesson	You will be able to
"Per": what a rate tells you	Find a rate by dividing, use it to predict by multiplying, and compare rates fairly
Distance-time graphs	Read a journey from a graph: where it stopped, which part was fastest, and when it came back
Telling the story of a graph	Turn a graph into a story and a story into a graph, including sudden jumps and curves
Change in tables	Use differences to tell steady change from speeding up or slowing down, even when the time steps are uneven
Fast at first, then slower	Recognise change that slows itself down, like a cooling drink, and explain why it levels off
Average speed for a trip	Find the average speed of a trip with several parts and stops, and explain why it is not the average of the speeds

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