This lesson is optional. The activities in this lesson can all be solved using grade-level mathematics, but are more sophisticated than earlier activities and are often left for future grades when students have access to a wider variety of algebraic tools.
Each of the situations described in the activities involve two or more unknown quantities and multiple relationships or actions. Initially students are walked through the steps of writing an expression to describe a situation, using properties to rewrite the expression with fewer terms, writing an equation to represent the situation, solving the equation, and considering the reasonableness of solutions. As they proceed through the lesson, the supports are slowly removed and students work on their own to reason through the problem (MP2).
As with all lessons in this unit, all related standards have been addressed in prior units. This lesson provides an optional opportunity to go more deeply into working with expressions and equations.
- Create expressions and equations to represent a linear relationship with two or more related quantities in context.
- Determine the solution to an equation of the form $px+q=r$ and explain (orally) the solution method.
- Interpret expressions, equations, and solutions that represent a linear relationship with two or more related quantities.
Let's solve harder problems by writing equivalent expressions.