Numbers, space and change
What is your reference for comparison?
Distinguish how many more from how many times, then name parts and wholes. Explore equivalent ratios, per-one rates and percentages before checking direct proportion in tables and points.
Begin with differences and multipliers →Connect reference quantities one step at a time
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How many more, or how many times?
Compare the same quantities by difference and multiplier, naming the reference.
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Red to blue, red to the whole
Name ratio order and reference, distinguishing part-to-part from part-to-whole.
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Scaling an equivalent ratio
Check why scaling both quantities by the same factor preserves a ratio.
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How much per one?
Keep quantity names and units while making the reference one.
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Make the whole one hundred
Read percentages as ratios to a whole and examine changing reference wholes.
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Is every increasing relationship proportional?
Compare a constant-rate rule with a fixed-fee rule using tables and points.
Next: relationships between inputs and outputs
Both direct proportion and a fixed-fee rule can assign one output to each input. The function introduction connects these relationships through words, tables, expressions and graphs. Continue using the link below.
Revisit input-output rules →Represent a table row as a point →No quiz score locks the next story. Close the explanation and represent a new example in words or a drawing.