Ratio and Proportion
Lessons in this chapter
About Ratio and Proportion
Ratio and Proportion builds a single connected skill set out of six related ideas: once two quantities are recognized as proportional, the same relationship can be written as a ratio, tested in a table, solved as an equation, plotted as a graph, or applied to resize a drawing.
It opens with compute ratios and ratio tables, comparing two quantities (like 3 cups of flour to 2 cups of sugar) and extending that comparison into a table of equivalent ratios, before find rates and unit rates, which reduces a rate like 120 miles in 2 hours down to a single-unit rate of 60 miles per hour.
Identify proportional relationships teaches kids to recognize when two quantities grow at a constant rate relative to each other — checking whether a ratio table or an equation stays consistent — before write and solve proportions has them set up and solve equations like 3/4 = x/20 using cross-multiplication or equivalent-ratio reasoning.
Graph proportional relationships plots those same quantities on the coordinate plane, where a proportional relationship always produces a straight line through the origin — a visual check that reinforces what ‘proportional’ means beyond just an equation.
The chapter closes with apply scale factors and scale drawings, using a single scale factor to resize a real drawing or map up or down, connecting the ratio and proportion skills from earlier lessons to a concrete, visual application.
Frequently asked questions
A ratio compares two quantities directly, like 3 cups of flour to 2 cups of sugar, written 3:2 or 3/2 — it can compare two different kinds of things. A fraction specifically compares a part to a whole of the same kind of thing, like 3 out of 5 total cups. Compute Ratios and Ratio Tables starts here before rates and proportions build on it.
A rate compares two quantities with different units, like 120 miles in 2 hours. A unit rate reduces that comparison down to a single unit — 60 miles per 1 hour — which is what makes rates easy to compare against each other, like which of two stores has the better price per ounce.
Check whether the ratio between the two quantities stays constant every time — in a ratio table, every row should reduce to the same simplified ratio; as an equation, y should always equal the same constant times x. Identify Proportional Relationships has kids test both a table and an equation this way before assuming a relationship is proportional.
Cross-multiply: for 3/4 = x/20, multiply 3 × 20 and set it equal to 4 × x, giving 60 = 4x, so x = 15. Write and Solve Proportions also covers solving the same problem by scaling the ratio directly — recognizing that 20 is 5 times 4, so x must be 5 times 3.
A proportional relationship means y is always the same constant multiplied by x, and when x is 0, y is also 0 — which is exactly the point where a line crosses the origin. Graph Proportional Relationships uses that straight-line-through-the-origin pattern as a visual test: if a graphed relationship doesn’t pass through (0, 0), it isn’t truly proportional.
A scale factor is the single number a real length is multiplied (or divided) by to get its size in a drawing or map, and back again. Apply Scale Factors and Scale Drawings has kids use one scale factor consistently across an entire drawing — a map where 1 inch represents 10 real miles, for instance — to resize every measurement by the same ratio.