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Grade 6 · Mathematics · 30 minutes

Unit 2 · Expressions, equations and shape · Lesson 1 of 2

Expressions and Equations for a Garden

Translate a cost rule into an expression and solve a one-step equation.

Mr. S Teaches · Original starter mini-lesson · MS6-MATH-04

Learning objective

Write and evaluate an expression, then solve and check an equation for an unknown number of plants.

Before you begin

  • Order of operations
  • Whole-number division

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

variable
A letter representing a number.
expression
A mathematical phrase with values and operations.
equation
A statement that two expressions have equal value.

Understand the concept

An expression names a quantity; an equation states a relationship of equality. If a tray holds n plants and each costs $3, 3n represents the plant cost. A separate $4 pot gives 3n + 4. Substituting a number for n evaluates the expression. Solving an equation finds a value that makes the equality true.

Teach it step by step

  1. Translate “three dollars for each of n plants plus four dollars for a pot” into 3n + 4.
  2. Identify 3 as a coefficient and 4 as a fixed amount. Evaluate at n = 5 using multiplication before addition.
  3. For plants alone, set up 3n = 18. Divide both equal amounts by 3 and interpret the answer.
  4. Substitute the solution into the original equation and compare with an arithmetic solution.
  5. Contrast the roles of the expression 3n + 4 and the equation n + 4 = 11.

Make the thinking visible

Worked example or model response

At n = 5, 3n + 4 = 3(5) + 4 = 19 dollars. For a separate purchase of plants alone, 3n = 18 gives n = 6; 3 × 6 = 18 checks. In n + 4 = 11, subtracting 4 from both sides gives n = 7.

Guided practice

Write “twice a length l plus 7.” Evaluate it when l = 4. Then solve 5p = 35 and check.

Independent practice

1. Evaluate 4x + 2 when x = 3. 2. Solve a + 8 = 23. 3. Explain why 4x + 2 has no single value until x is specified.

Quick assessment

Write and solve an equation: an unknown number of equal $6 tickets costs $30 in total.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: 2l + 7; at l = 4 it equals 15. For 5p = 35, p = 7 and 5(7) = 35.
  2. Independent 1: 14. 2: a = 15; 15 + 8 = 23. 3: Different values of x produce different totals.
  3. Quick check: 6t = 30, t = 5 tickets.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use boxes for unknowns before letters and represent both sides with equal groups.

Extension challenge

Explain why 2(l + 7) differs from 2l + 7 using a context and a numerical check.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

6.EE.A.2.c

Common Core · Grade 6

Evaluate an expression at a specified variable value.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

6.EE.B.7

Common Core · Grade 6

Solve one-step addition and multiplication equations in context.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.