Lesson 6: Writing Equations - Applications
Duration of Days: 2
Lesson Objective
Students will be able to read a narrative, find the relevant information to formulate a linear equation and then solve the resulting linear equation.
How do we use distribution and CLT to simplify and expression before solving.
How do we isolate a variable to find a solution to a one-step linear equation?
How can you check that your solution is correct?
Inverse operations; Equality
2G (CCS HSA.REI.A.1) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Lesson Description: This lesson focuses on the linguistic-to-mathematical pipeline. Students move away from solving pre-written equations and instead learn to identify the "equal sign" in a sentence (often the word "is," "was," or "results in").
The lesson covers: Defining unknowns using descriptive variables. Identifying operational keywords (e.g., "less than" implying subtraction, but with a reversed order).Setting up equations for consecutive integer problems (x, x+1, x+2). Formulating expressions for geometric relationships (e.g., "The length is 3 more than twice the width").Distinguishing between "expressions" (a phrase) and "equations" (a complete sentence).
Purpose: The purpose of this section is to eliminate the "blank page syndrome" many students face with word problems. By isolating the writing phase from the solving phase, students can focus on logic and reading comprehension without the cognitive load of arithmetic. This builds the precision required for higher-level courses where "setting up the problem" is 90% of the work. It reinforces the idea that algebra is a language used to describe relationships between quantities.
Depth of Knowledge (DOK) Level DOK
Level 2 & 3Level 2 (Skill/Concept): Converting standard mathematical phrases into algebraic symbols and organizing them into a standard equation format.
Level 3 (Strategic Thinking): Translating complex, non-linear sentences where the order of words does not match the order of operations (e.g., "subtract 5 from a number"). Students must interpret the relationship between multiple variables and decide how to represent them in terms of a single variable to create a solvable equation.
Class and online work
Use practice problems 12-15, pages 94-95 to assess students' understanding of the lesson concepts