Integer Adding Rules

Overview

In this second lesson of the unit “Mastering Integers Together,” students focus on the rules and reasoning for adding positive and negative integers. They practise with number lines, integer chips/tiles, and a short game to build fluency.

Learning intentions

• Students will be able to add integers using rules supported by models such as number lines and integer tiles.
• Students will be able to explain why the sign and size change when adding a positive and a negative integer.
• Students will practise solving addition-with-integers questions accurately and efficiently.

Success criteria

• I can add integers and determine the correct sign using a model or number line.
• I can justify my answer by describing movement (left/right) or combining chip sets.
• I can solve integer addition questions with fewer than two errors on a short practice set.

Curriculum links

• Apply operations with integers, including addition of positive and negative integers.
• Represent integer sums using visual models (number lines and concrete/diagram models) and connect representations to rules.
• Use mathematical reasoning to explain and verify results.

Lesson structure (40 minutes)

1. 0–5 min: Warm-up retrieval

• Display 4 quick problems from the previous lesson (e.g., “Add: -3 + 1” and “Add: 2 + -5”). Students solve silently, then share one strategy each.
• Teacher prompts: “What changed—were you moving left or right, and why?”

2. 5–12 min: Teach the addition rules with models

• Model three cases using integer chips/tiles and a number line:
• Positive + positive
• Negative + negative
• Positive + negative (and negative + positive shown as the same structure)
• Key idea to emphasize: when signs are the same, keep the sign and add the magnitudes; when signs are different, subtract magnitudes and keep the sign of the integer with the larger magnitude.
• Students record one “rule summary” sentence in their own words.

3. 12–20 min: Guided practice—number line moves

• In pairs, students complete a set of 6 “move and add” tasks on provided number lines.
• Examples: -2 + -6, 5 + -3, -4 + 7, 3 + 2, -7 + 1, 0 + -5.
• Teacher circulates with prompts:
• “How many steps did you move?”
• “Which integer had the greater magnitude?”
• “Does your answer match what your chips show?”

4. 20–28 min: Hands-on practice—integer chips/tiles

• Students choose either chips or tiles to solve 8 problems independently (same types, increasing variety).
• Include at least 3 “unbalanced magnitude” cases (e.g., 6 + -2, -9 + 4).
• Students must show at least one representation (chips OR number line) for the first two problems, then may use mental strategies for the rest if correct.

5. 28–35 min: Game—Integer Addition Duel

• Set up “duel” stations with a small set of cards for each pair:
• Each round, one student draws two integer cards and states the sum using a rule.
• Partner checks using a quick number line sketch (or chips if needed).
• Scoring: 1 point for correct answer with a correct justification; 1 bonus point for a clear explanation (e.g., “subtract magnitudes because signs differ”).

6. 35–40 min: Exit ticket and wrap-up

• Exit ticket (3 questions):
• A same-sign sum (e.g., 4 + 6)
• A different-sign sum where the positive has larger magnitude (e.g., 7 + -3)
• A different-sign sum where the negative has larger magnitude (e.g., -8 + 5)
• Students submit and write one sentence: “When adding integers with different signs, I…”.

Resources

• Integer chips/tiles (positive and negative counters in two colours), with 0 chips if available
• Large classroom number lines (from at least -20 to 20) and individual printed number lines
• Prepared problem cards for the Duel game
• Student worksheets with:
• Rule summary space
• Guided number line section
• Independent chips practice section
• Exit ticket slips
• Projector/board for teacher modelling and student sharing

Assessment

• Formative during guided practice: teacher uses observation and targeted questions to check understanding of sign and magnitude.
• Game checks accuracy and reasoning: students must justify using a model or number line.
• Exit ticket measures mastery of same-sign and different-sign integer addition with correct sign.

Differentiation

• Support:
• Provide number lines with more increments and a worked example template (e.g., “Signs differ → subtract magnitudes → keep sign of larger magnitude”).
• Offer sentence frames for explanations: “I moved ___ because… The larger magnitude is ___ so the sign is…”
• Use chips/tiles as the default representation for struggling students.
• Extension:
• Add challenge problems that require choosing the most efficient strategy (chips vs number line vs mental), and ask for a brief justification.
• Include problems with zero (e.g., -9 + 0, 0 + 6) and ask students to explain why answers stay the same.
• EAL/SEN:
• Keep instructions short and repeat key terms: “magnitude,” “sign,” “left/right.”
• Allow verbal justification or one diagram instead of full written explanations.
• Pair students strategically so language learners can participate through model-checking at first.