Integer Adding

Overview

In this lesson (Lesson 2 of 20), students learn to add and subtract integers using number lines and simple visual aids. They will build on their understanding of negative numbers from the unit opener, focusing on correct movement rules and interpreting answers as location changes.

Learning intentions

Students will:

• understand addition and subtraction of integers as moving left/right on a number line
• use a number line to solve integer addition and subtraction problems
• explain the effect of changing sign in their calculations
• check answers by using the inverse relationship between addition and subtraction

Success criteria

Students can:

• represent an integer addition or subtraction on a number line with correct direction and steps
• compute the final integer answer accurately for given problems
• describe (in words) what the number line movement means
• verify results by using subtraction as the inverse of addition (and vice versa)

Curriculum links

• Number — use the 4 operations with integers, choosing and using efficient strategies (including number line strategies)
• Number — apply efficient strategies to solve problems involving positive and negative integers
• Mathematics reasoning — communicate and justify solution methods using visual representations (number line)

Lesson structure (30 minutes)

1. 0–3 min · Welcome and recall. Teacher asks: “If you start at −2 and add +3, where do you land?” and records key student ideas on the board. Students answer orally, then mark the landing point on a mini number line.

2. 3–10 min · Direct teach: addition on a number line. Teacher models two examples with a large number line:

• Start at −4, add +3 (move right 3)
• Start at +2, add −5 (move left 5) Teacher emphasises: moving right means “add a positive”; moving left means “add a negative”. Students copy one model and then complete the second with teacher prompts (direction, then steps, then landing).

3. 10–16 min · Guided practice: connect subtraction to movement. Teacher explains subtraction as “add the opposite”:

• “Subtract +3” means move left 3
• “Subtract −2” means move right 2 Teacher demonstrates with one full example (e.g., 1 − 4, then 1 − (−2)). Students complete two similar items on their worksheet, using the number line; teacher circulates and checks directions before they compute.

4. 16–24 min · Independent practice (with visual aids). Teacher gives a set of 6 questions, mixed difficulty, all requiring number lines (no calculator). Students solve using a drawn number line and record a short sentence for two questions: “I moved ___ because I was ___”. Teacher provides immediate feedback on at least the first three student responses to ensure correct rule use.

5. 24–28 min · Verification routine (inverse check). Teacher models a quick check: if you computed −3 + 5 = 2, then 2 − 5 should return −3. Students choose one of their own answers and write the inverse check as two steps (original calculation → inverse calculation).

6. 28–30 min · Exit ticket. Teacher collects a brief exit ticket (2 problems). Students complete in silence and submit:

• Problem A: −2 + 7
• Problem B: 3 − (−4)

Resources

• Student worksheet with blank number lines (centred at 0, showing at least −10 to +10)
• Coloured pencils or markers (one colour for positive movement, one for negative movement)
• Teacher number line slides/board diagram or laminated number line
• Small whiteboards or paper for quick checks (optional for teacher use)
• Exit ticket slips

Assessment

• Teacher observation during guided practice: correct direction, correct number of steps, and correct landing point
• Marking/quick scan of independent work: accuracy of final integers and evidence of a number line method
• Exit ticket accuracy and whether the student used correct interpretation of “subtract” as movement/opposite

Differentiation

• Support: sentence frames for explanations, e.g., “Subtracting a positive means I move ___”; partially completed number lines (starting point already plotted)
• Support: provide a “worked example” strip on the desk (one addition and one subtraction example)
• Extension (if ready within time): add a third step requirement, “Write an inverse check for both questions.”
• For students needing additional scaffolding: fewer problems (4 instead of 6) but still require full number line working and one written explanation.