Algebra I · 35 minutes
Suggested grades 9–10 · Unit 1: Expressions and equivalent equations · Lesson 1 of 2
Interpret a Cost Expression
Connect terms, coefficients and factors to a fictional event budget.
Mr. S Teaches · Original starter lesson · HS-ALG1-01 · Grade range is planning guidance.Watch, notice, discuss
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Interpreting linear expressions, 2 | Introduction to algebra | Algebra I | Khan Academy
By Khan Academy
Practice explaining what the parts of an expression mean before interpreting the lesson’s fixed and variable costs.
Open on YouTube: Interpreting linear expressions, 2 | Introduction to algebra | Algebra I | Khan Academy (opens a new tab) ↗Interpreting linear formulas example 1 | Algebra I | Khan Academy
By Khan Academy
Compare the meaning of a coefficient and constant with the cost expression; ask learners to attach units to each term.
Open on YouTube: Interpreting linear formulas example 1 | Algebra I | Khan Academy (opens a new tab) ↗Which part represents a fixed cost, which part varies, and how would you justify an equivalent expression?
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Learning objective
Interpret each part of an expression and justify an equivalent form.
Before you begin
- Distributive property
- Signed arithmetic
Gather your materials
- Paper and pencil
- Graph paper
- Calculator for checking results
Language to know
- term
- A part separated by addition at the top level of an expression.
- coefficient
- A numerical factor multiplying a variable.
- equivalent expressions
- Expressions with equal values for every input in their common domain.
Understand the concept
A community event rents n tables at $12 each and pays a $45 delivery charge. The expression 12n + 45 separates variable cost from fixed cost. Rewriting an expression can reveal a different grouping without changing the total. A numerical test can catch an error, but checking one input alone does not prove equivalence for all inputs.
Teach it step by step
- Write 12n + 45 and label the units represented by n, 12 and 45.
- Compare it with 3(4n + 15), distributing to justify equivalence for every allowed n.
- Evaluate both forms at n = 5 and connect the result to tables plus delivery.
- Contrast 12(n + 45), identify its extra multiplication of the fee and explain the contextual error.
Make the thinking visible
Worked example or model response
At n = 5, 12(5)+45 = $105. The form 3(4n+15) gives 3(20+15) = $105. Distributing 3 proves the equivalence; 12(n+45) instead adds a $540 fixed amount.
Guided practice
Interpret 8b + 24 for $8 bundles and one fixed charge. Factor it and explain what the factorization reveals.
Independent practice
1. Interpret 6(2x+5) and expand it. 2. A learner claims 4p+20 = 4(p+20). Explain and repair the error.
Quick assessment
Why can two different formulas agreeing at one input still fail to be equivalent?
Answer key & assessment criteria
Answers and teaching guidance
- Guided: 8(b+3); the fee equals the cost of three bundles, while b remains the actual bundle count.
- Independent 1: 12x+30; six groups each containing 2x+5 units. 2: 4(p+5) is correct; 4(p+20) has fixed term 80.
- Quick check: Different expressions can coincide at one input; general equivalence requires a valid identity or reasoning for all inputs.
Look for: Require the learner to explain the interpretation and check, not only state a result. Distinguish an exact value from a rounded approximation and attend to the stated domain.
Make it work for your learner
More support
Color-code variable and fixed terms and use a table of two input values.
Extension challenge
Construct two expressions that agree at x=1 but differ at x=2, then explain why testing is not proof.
Verified references · Selected contributions
Standards connections
Subject-content standards
These records identify the part of a subject standard practiced here. Course placement is instructional guidance; the source’s category or band remains authoritative.
Contributes to Common Core standard
HSA.SSE.A.1.a
Common Core · High school · Algebra
Regular high school mathematics standard
Interpret terms, factors and coefficients in a contextual expression.
Read the official standard ↗This lesson contributes selected skills; broader applications and full standard coverage require further instruction.
Verified 2026-11-04. Selected contribution, not full attainment.