Level 5: Proportional reasoning

Ratio, rates and money · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you learned what a percent is and how to find one. In this level you reason with ratios like a mathematician: you solve proportions three ways and learn why cross multiplying works, tell direct proportion from inverse proportion (and from neither), and measure change as a percent. Then you put it to work on real money (tips, markups, commission, exchange rates and simple interest) and on gears, paint and recipes.

Lesson	You will be able to
Proportions	Solve a proportion by scaling, by unit rate and by cross multiplying, and explain why cross multiplying works
Direct and inverse proportion	Tell direct, inverse and neither apart from words, tables and graphs, and solve problems with each
Percent increase and decrease	Find a percent change from the original, explain why up 25% and down 20% can undo each other, and find a new amount
Commission, tips and markups	Work out tips in your head, markups and margins, and salary, straight and tiered commission
Exchange rates	Convert between currencies both ways, use the inverse rate, and explain what the buying and selling rates cost you
Simple interest	Use \(I = Prt\) for savings and short loans, for months and days, and solve for any of its letters
Gears, mixtures and recipes	Find how fast meshing gears turn, mix paint and juice to a ratio or a percent, and scale a recipe

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