Solving One-Step Equations

Overview

Today students practise solving simple one-step equations using addition and subtraction. This builds on earlier work with number sentences and unknowns, and prepares students for multi-step solving later in the unit.

Learning intentions

• Students will identify what the unknown represents in an equation.
• Students will use inverse operations to solve one-step equations with addition and subtraction.
• Students will check their solutions by substituting back into the original equation.
• Students will connect equations to everyday situations (e.g., money, snacks, packing items).

Success criteria

• I can rewrite an equation so the unknown is alone.
• I can use the opposite operation to find the value of the pronumeral.
• I can explain my steps using words (e.g., “I add 3 because…”).
• I can check my answer by substitution.

Curriculum links

• Mathematics K–10 Stage 4 Equations: solve linear equations up to 2 steps and verify by substitution (MA4-EQU-C-01).
• Mathematics Stage 5 Equations: solve linear equations of up to 3 steps (context support for later lessons) (MA5-EQU-C-01).
• Students use strategies for addition and subtraction, applying them to find missing values.
• Solving unknowns in number sentences involving addition and subtraction as a foundations recap.

Lesson structure (45 minutes)

1. 0–5 min · Warm-up (number sentences). Teacher shows 3 quick boards: __ + 5 = 9, 12 - __ = 7, __ - 3 = 4. Students respond on mini-whiteboards with the missing number and a thumbs check for accuracy.

2. 5–12 min · Model (inverse operation). Teacher models one equation on the board: x + 6 = 10. Says: “I need x to be alone. The opposite of +6 is −6. So I subtract 6 from both sides.” Students echo the process aloud with teacher prompts, then copy the steps using sentence frames:

• “Start with: x + 6 = 10”
• “Opposite of +6 is −6”
• “Subtract 6 from both sides”
• “x = 4”

3. 12–22 min · Guided practice (teacher-led set). Students solve 4 equations in sequence, with gradual release. Teacher assigns a “step cue” card per equation (e.g., “Opposite of + is −”).

• x + 7 = 15
• x − 5 = 9
• x + 3 = 6
• x − 2 = 8 Students work in pairs for 2 items, then independently for the last 2. Teacher circulates using a checklist: unknown identified, opposite operation chosen, equation balanced, answer recorded.

4. 22–32 min · Real-life task (money/snacks). Teacher presents 2 short scenarios; students choose one to complete on a worksheet or on cards. Scenario A: “You have $x. You receive $9. Now you have $17.” Write and solve the equation. Scenario B: “You had $x. You spend $6. Now you have $11.” Write and solve the equation. Students must include: an equation, the solving steps, and a final sentence: “So x is ___.”

5. 32–40 min · Check solutions (substitution ritual). Teacher demonstrates checking with x = 4 for x + 6 = 10: “Replace x with 4.” Students follow with one equation from earlier (teacher assigns). Students complete a simple check table:

• Original equation
• Substitute value
• Left side equals right side? (Yes/No)

6. 40–45 min · Exit ticket (quick assessment). Individually, students solve 2 one-step equations and answer one “explain” prompt with a single sentence:

• x + 8 = 13
• x − 4 = 6
• “I chose the opposite operation because ____.”

Resources

• Mini-whiteboards, markers, erasers
• “Step cue” cards: Opposite of +, Opposite of −, Substitution check
• Worksheet with equation templates and sentence frames
• Scenario cards (money/snacks)
• Teacher checklist for guided practice
• Dyslexia-friendly option: text on coloured paper, larger font worksheet versions, audio read-aloud or teacher reading prompts

Assessment

• Formative: observation during guided practice (does the student choose the correct opposite operation and balance the equation?).
• Formative: accuracy of answers on mini-whiteboards during warm-up.
• Exit ticket: correct solution values and a brief explanation that shows inverse operation reasoning.
• Substitution check: whether students can confirm equality (not just compute).

Differentiation

• Support (missing fundamentals): provide equation blanks with prompts (e.g., “x + __ = __”), and use a three-step routine: 1) Circle the unknown, 2) Choose opposite operation, 3) Do it to both sides.
• Support for autism/behaviour: clear visual steps on the board, limited choices in scenarios (A or B), predictable timer for each section, and brief movement breaks if needed.
• Sentence starters for communication:
• “I want x alone, so I ____ from both sides.”
• “I checked by substituting ____.”
• Dyslexia-friendly reading: teacher reads instructions aloud; use large-print worksheets; allow coloured overlays or spacing; highlight symbols (x, +, −, =) with consistent colours.
• Extension for advanced learners: include one equation with a negative or a word equation leading to subtraction where the unknown is on the right, and ask for two different checks (one substitution, one “reverse operation” statement).