Percentage

Taking the base amount as 1 and expressing the compared amount as a multiple of it is the idea at the center. Conversions among decimals, percent, and wari, bu and rin come first, then the three question types, finding the ratio, finding the compared amount and finding the base amount, extended to increases, decreases and discount rates.

Mixing up which quantity comes before and after the word of, so the division runs the wrong way, is the most frequent error. If the answer sits on the opposite side of 1, suspect this. Handling of increases and decreases breaks down too, with a 20% increase taken as 0.2 times rather than 1.2 times, or a 2 wari discount worked out by multiplying the price by 0.2 and stopping there.

This unit supports the next one, Band Graphs and Pie Charts, where a proportion gets drawn as a picture. A simple ratio touched on briefly in Investigating Patterns of Change in grade 4 is expanded here into a full study, and a figure expressed as a percentage becomes, directly, the area or the angle in that picture.