Comparing Quantities
In course I, we developed a percentage model based on ten-by-ten grids. You can follow the link above to see that lesson. In this lesson, the meaning of percentage explored with area and linear models, and students develop procedures for performing computations with percentages. Comparing portions of quantities of unlike size is also a focus of this lesson. We do this with grids that are not ten-by-ten.
This example demonstrates the value of percentage as a way of comparng two quantities of different sizes. One key idea is that 1/100 of any quantity is 1%. Here are a couple of examples to demonstrate. We want to see what 1% of each grid is, what % each square is, and how many squares are 35%:
You can practice on these:
We can also use a linear model to represent percentage comparisons.
Exercises like this help students build intuitive and flexible thinking with respect to percentage calculations which they will apply in the next lesson, Picturing Percentage Problems. The idea is not to memorize rules for certain types of problems but to develop an understanding of percent models and computations which will allow students to see a variety of solution strategies to percentage problems.