Teach the Cast
Some of RatioRealm’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
Teach Scale the Doubler
Teach the connections
Show how the ratio ideas connect
Pair (a simple ratio (a:b)) × Scale (equivalent ratios (scale both parts by the same factor))
How do you make a new ratio that means the SAME as 2:3?
Pair then says: “To keep 2:3 equal I'll ADD 2 to each part: 2:3 becomes 4:5.” — is that right?
Now they see it: an equivalent ratio isn't a new ratio — it's the same one wearing bigger clothes.
Scale (equivalent ratios) × Cross (proportions & cross-multiplication)
How can you CHECK whether 3:4 and 9:12 are really equivalent, without scaling step by step?
Scale then says: “3:4 and 9:12 are equivalent because 3+9 = 12 and it "looks right".” — is that right?
Now they see it: cross-multiplication isn't a random trick — it's the equivalence test in disguise.
Unit (unit rates (per ONE)) × Centa (percentages (per HUNDRED))
How is a percent like "45%" related to Unit's idea of a rate "per one"?
Unit then says: “45% means 45 per ONE, so 45% of 10 is 450.” — is that right?
Now they see it: "per cent" literally means "per hundred" — it's Unit's per-one idea, rescaled.
Capstone — run the lemonade stand
You're running a lemonade stand. Each part below needs ONE of the cast's ideas — bring in the right person for each.
Write the recipe as a ratio: 2 lemons to 3 cups of water.
Triple the recipe for a big batch, keeping the taste the same.
Find the cost of ONE cup so you can price it.
If 2 lemons make 3 cups, how many lemons for 18 cups? Solve the proportion.
You spent $8 and made $10 — express the profit as a percent.
The whole cast, working together — because you taught each one and saw how they fit.
Your concept map