Solving Linear Equations
This lesson unit is intended to help you assess how well students are able to:
- Form and solve linear equations involving factorizing and using the distributive law.
In particular, this unit aims to help you identify and assist students who have difficulties in:
- Using variables to represent quantities in a real-world or mathematical problem.
- Solving word problems leading to equations of the form px + q = r and p(x + q) = r.
The lesson unit is structured in the following way:
- Before the lesson, students attempt the assessment task individually. You then review students’ responses and formulate questions that will help them improve their work.
- During the lesson, students work collaboratively in pairs or threes, matching equations to stories and then ordering the steps used to solve these equations. Throughout their work, students explain their reasoning to their peers.
- Finally, students again work individually to review their work and attempt a second task, similar to the initial assessment task.
- Each student will need copies of the assessment tasks Express Yourself and Express Yourself (revisited) and Card Set: Stories (not cut up), a mini-whiteboard, a pen, and an eraser.
- For each small group of students provide cut-up copies of Card Set: Stories, Card Set: Equations, and Card Set: Steps to Solving, a large sheet of paper for making a poster, a marker, and a glue stick.
15 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Exact timings will depend on the needs of your students.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- 7.EE: Use properties of operations to generate equivalent expressions.
- 7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.