The mathematical purpose of this lesson is to explore the concept that the same relationship can be expressed in multiple equivalent equations. Students approach this concept primarily through contexts, and focus on identifying whether different equivalent and non-equivalent equations make sense with the context. During the first activity following the warm-up, students practice representing one situation with multiple equivalent expressions. They also identify errors made by others in an attempt to create an equation that is equivalent to the original. It is fine if students use the context of the situation to help them evaluate equivalence. This lesson prepares students for work in the associated Algebra 1 lesson by supporting them to reason about when and how different equations can express the same relationship.
Students reason absractly and quantitatively (MP2) as they connect symbolic expressions to contextual situations and using their understanding of what makes sense in context to evaluate the validity of symbolic manipulations.
- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- Let’s think about the how and why of solving equations, and use those ideas to make problems easier.