Leaky faucets

This unit on ratio and proportional understanding will be taught over the course of three weeks. This unit is designed to provide students with a thorough understanding of ratios and proportions, because they are used so much in everyday life applications, and they are a natural extension after the student understands the basics of fractions taught in the 6th grade. Students will analyze proportional relationships and use them to create equations, compute unit rates, and sketch graphs of relationships on the coordinate plane. Ratio and proportional reasoning is taught at the beginning of the year. It is anticipated that students will come from 6th grade with a basic introduction and foundation of ratio and proportional reasoning. Students should have a basic understanding of fractions and equivalent fractions. The concept of ratio is taught thoroughly, including its connection with fractions. Learning about equivalent ratios will lead into the discussions of proportions. Proportions are solved by thinking about equivalent ratios and with the concept of cross-multiplication. While restoring an old house, it was noticed that there was a leaky faucet. At first it was the kitchen faucet, then extended to the bathroom. The Common Core-aligned task requires students to determine at what rate the faucet is leaking and create a table to display observations. The task continues by having students create an equation to represent the situation. Students are asked to compare the unit rates of both faucets and identify the constant of proportionality. On a coordinate plane, students are asked to sketch the graph of both faucets and use evidence from the graph to justify a proportional relationship.