Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 0 - Positive and negative integers

Positive and negative integers

Compare, order, add and subtract integers and interpret signs in practical contexts.

Updated 2026-07-24 - 6 min read

Compare, order, add and subtract integers and interpret signs in practical contexts. This draft teaching resource is aligned to the cited Year 7 content descriptions and still requires named human curriculum approval.

Track the value represented at every step: an efficient method is valid only when it preserves the number, comparison or required accuracy.

1. Locate and compare signed numbers

Negative numbers lie left of zero. A number farther left is smaller, even when its numeral looks larger.

Decision check: Apply this lesson's rule to the worked example: Keep the sign attached to the number; compare positions, not just digits. Identify the exact value, label or property that satisfies the rule.

2. Add, subtract and interpret integers

Adding a positive moves right and adding a negative moves left. Subtracting a negative removes a leftward movement, so it moves right.

Decision check: Apply this lesson's rule to the worked example: Rewrite subtraction as addition of the opposite before calculating. Identify the exact value, label or property that satisfies the rule.

Worked examples with complete reasoning

Worked example 1

Question: Which list orders -8, -2 and 4 from least to greatest?

  1. On a number line, values farther left are smaller.
  2. The correct order is -8, -2, 4.

Answer: -8, -2, 4

Check: Picture the positions on a horizontal number line.

Worked example 2

Question: Calculate -7 + (12).

  1. Start at -7 on a number line.
  2. Move right 12 units.
  3. The endpoint is 5.

Answer: 5

Check: Use the sign of the second integer to choose the direction.

Worked example 3

Question: A temperature starts at -4 °C and changes by 9 °C. What is the new value?

  1. Represent the change by -4 + (9).
  2. Calculate to get 5 °C.

Answer: 5

Check: A decrease is a negative change and an increase is a positive change.

Method map for this topic

  1. Locate and compare signed numbers: Keep the sign attached to the number; compare positions, not just digits.
  2. Add, subtract and interpret integers: Rewrite subtraction as addition of the opposite before calculating.

Common mistakes and how to correct them

  • negative direction: Not yet. Use the sign of the second integer to choose the direction. Recheck the negative direction step, then try again.
  • subtract negative: Not yet. Change subtraction to addition of the opposite. Recheck the subtract negative step, then try again.
  • negative order: Not yet. Picture the positions on a horizontal number line. Recheck the negative order step, then try again.
  • context sign: Not yet. A decrease is a negative change and an increase is a positive change. Recheck the context sign step, then try again.
  • multi step sign: Not yet. Work from left to right and keep each sign attached to its number. Recheck the multi step sign step, then try again.
  • integer distance: Not yet. Subtract the lower value, including its negative sign. Recheck the integer distance step, then try again.

Practice

  1. Which list orders -8, -2 and 4 from least to greatest?
  2. Which list orders -3, 0 and 5 from least to greatest?
  3. Calculate -7 + (12).
  4. Calculate 9 + (-14).
  5. A temperature starts at -4 °C and changes by 9 °C. What is the new value?
  6. A lift position starts at 3 floors and changes by -11 floors. What is the new value?

<details> <summary>Answers and reasoning</summary>

  1. -8, -2, 4 — On a number line, values farther left are smaller. The correct order is -8, -2, 4.
  2. -3, 0, 5 — On a number line, values farther left are smaller. The correct order is -3, 0, 5.
  3. 5 — Start at -7 on a number line. Move right 12 units. The endpoint is 5.
  4. -5 — Start at 9 on a number line. Move left 14 units. The endpoint is -5.
  5. 5 — Represent the change by -4 + (9). Calculate to get 5 °C.
  6. -8 — Represent the change by 3 + (-11). Calculate to get -8 floors.

</details>

Checklist and vocabulary

| Skill | Observable evidence | | --- | --- | | compare order integers number line | Compare and order positive and negative integers using position on a number line. | | add subtract integers | Calculate additions and subtractions of integers and explain each movement. | | model integer change contexts | Model temperature, elevation, score or financial changes with signed integers. |

Retrieval prompts

  • State the defining relationship for each method above without looking.
  • Give one example where two visually similar representations mean different things.
  • Diagnose one misconception from the list and explain the first corrective step.
  • Name a check that is independent of simply repeating the same calculation.

Teach-back and self-check

Close the worked examples and explain positive and negative integers as if you were helping another Year 7 student. Begin by naming the clue that tells you which relationship, representation or operation is needed. Then show one complete example with labels and units where they matter. At each line, explain what stayed equivalent and why the next step is allowed.

Use this four-part check before calling the method secure:

  1. Identify: What information is given, and what must be found or justified?
  2. Represent: Which number line, diagram, table, expression, graph or organised list makes the relationship visible?
  3. Reason: Which rule connects the representation to the required answer?
  4. Verify: Can you check by estimation, substitution, an inverse operation, a second representation or the original context?

If the explanation depends on “I just knew”, return to the method map and name the missing decision. A durable method is one you can explain, check and use in a changed context after a delay.

Transfer task

Create a positive and negative integers decision from a shopping, recipe, travel or measurement context. State the quantities and required accuracy, solve it, then explain why your representation and rounding are suitable.

Sources