Lesson 6

Distinguishing between Two Types of Situations

Lesson Narrative

The purpose of this lesson is to distinguish equations of the form \(px+q = r\) and \(p(x+q) = r\). Corresponding tape diagrams are used as tools in this work, along with situations that these equations can represent. First, students sort equations into categories of their choosing. The main categories to highlight distinguish between the two main types of equations being studied. Then, students consider two stories and corresponding diagrams and write equations to represent them. They use these representations to find an unknown value in the story.

Learning Goals

Teacher Facing

  • Categorize equations of the forms $px+q=r$ and $p(x+q)=r$, and describe (orally) the categories.
  • Interpret a verbal description of a situation (in written language), and write an equation of the form $px+q=r$ or $p(x+q)=r$ to represent it.

Student Facing

Let’s think about equations with and without parentheses and the kinds of situations they describe.

Required Preparation

Print and cut up copies of the blackline master ahead of time. You will need 1 set for every 2 students. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Learning Targets

Student Facing

  • I understand the similarities and differences between the two main types of equations we are studying in this unit.
  • When I have a situation or a tape diagram, I can represent it with an equation.

CCSS Standards


Building Towards

Glossary Entries

  • equivalent expressions

    Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.

    For example, \(3x+4x\) is equivalent to \(5x+2x\). No matter what value we use for \(x\), these expressions are always equal. When \(x\) is 3, both expressions equal 21. When \(x\) is 10, both expressions equal 70.