Lesson 10

In this lesson students are introduced to contexts involving sales tax and tips. They can use tape diagrams and double number lines from their grade 6 work, but the lesson provides an opportunity to be more efficient by using an equation of the form \(y = kx\). For example, if the tax rate is 6.2% they can calculate the tax, \(T\), for any price, \(p\), using the equation \(T = 0.062p\). They do not necessarily write this equation out with variables, but rather repeatedly use it with specific values of \(p\). By repeatedly calculating the tax for different prices and then generalizing the process they are engaging in expressing regularity in repeated reasoning (MP8).

Questions about rounding naturally come up in this lesson. This lesson primarily involves dollar amounts, so it is sensible to round to the nearest cent (the nearest hundredth of a dollar). When students attend to precision and make decisions about what is the appropriate level of rounding, they engage in MP6.

It is recommended that students be provided access to four-function calculators so that they can focus on reasoning about how numbers are related to each other, representing those relationships, and deciding which operations are appropriate (rather than focusing on computation.)