Unit Plan 15 (Grade 6 Math): Equations from Context—x + p = q and px = q
6th graders understand solving as finding values that make an equation true. They write and solve one-step equations (x + p = q and px = q) with rational numbers, check solutions by substitution, and explain results clearly with units and reasoning.
Focus: Understand solving as “which values make it true”; write and solve one-step equations with nonnegative rational numbers.
Grade Level: 6
Subject Area: Mathematics (Expressions & Equations – One-Step Equations from Context)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students deepen the idea that solving an equation means finding the value(s) that make the statement true. Using real-world contexts, they write and solve one-step equations of the forms x + p = q and px = q where p and q are nonnegative rational numbers (fractions/decimals). They use substitution to check solutions and explain results with units.
Essential Questions
- What does it mean to solve an equation, and how do I know when a value makes it true?
- How can I represent a situation with an equation and choose the operation that matches the context?
- How do tape diagrams, balance models, or unit reasoning help me solve and justify my steps?
- Why is substitution the most reliable way to check a solution?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Explain solving as truth-testing: determine whether a number makes an equation true; use substitution to check (for example, test x = 6 in x + 2 = 8).
- Write equations from verbal descriptions and diagrams using variables to represent unknowns or sets of possible values.
- Solve one-step equations of the forms x + p = q and px = q with nonnegative rational p and q; show steps and interpret the solution in context with units.
- Choose representations (tape/balance/number line) to justify why the solving step is valid.
- Identify and correct common errors (operation reversal, unit mismatch, checking with the wrong value).
Standards Alignment — CCSS Grade 6
- 6.EE.5: Understand solving an equation or inequality as a process of answering a question: which values, if any, make the equation true? Use substitution to check.
- 6.EE.6: Use variables to represent numbers and write expressions/equations to solve problems; understand a variable can represent an unknown or any number in a specified set.
- 6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for nonnegative rational numbers p and q.
Success Criteria — Student Language
- I can tell whether a number makes an equation true by substituting it.
- I can write an equation from a real situation and label units.
- I can solve equations like x + p = q (use the inverse operation) and px = q (use division) and explain why my step works.
- I can check my answer by substitution and explain what it means in the situation.