Year 7 Mathematics · AC9M7N07

Comparing, Adding and Subtracting Integers

We are learning to compare, order and solve problems involving addition and subtraction of integers

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Learning goalsSay it simply

We are learning to compare, order and solve problems involving addition and subtraction of integers.

Integers are whole numbers, their negatives and zero. Their order is represented on a number line, with greater values to the right and opposites equally distant from zero.

Addition represents a signed change. Subtraction can be rewritten as addition of the opposite, so 5 − (−4) = 5 + 4 rather than a leftward move.

Contexts such as temperature, elevation and account balance need a reference zero and stated direction. A negative result can be valid, while distance between two integers is always non-negative.

Success criteria

  • I can compare and order integers on a number line.
  • I can add and subtract integers using opposites and directed movement.
  • I can interpret an integer result and distinguish change from distance.
Key conceptTeach from the board

Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.

Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.

Example 1

Model integer subtraction

  1. Start with 5−(−4).
  2. Subtracting −4 means adding its opposite, +4.
  3. Move four units right from 5.
  4. Arrive at 9.

Final answer: 5−(−4)=9.

Check: Check that 9+(−4)=5.

Example 2

Compare a temperature change

  1. Morning temperature is −6°C.
  2. Afternoon temperature is 5°C.
  3. Calculate change: 5−(−6)=11.
  4. Interpret this as an 11°C rise.

Final answer: The temperature rises by 11°C.

Check: Starting at −6 and moving 11 right reaches 5.

Example 3

Application problem 1

Problem: At 6 am the temperature is −4°C. It rises 9°C, falls 6°C, then rises 3°C. Find the final temperature and represent the changes as one integer calculation.

  1. Plan: Represent the information first, then calculate, interpret and independently check the result.
  2. Work: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.
  3. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

Final answer: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.

Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

Example 4

Application problem 2

Problem: Create and solve an integer expression for the change from −15°C to 8°C and back to −4°C.

  1. Plan: Check that −15+11=−4.
  2. Work: The changes are +23 then −12; net change is +11°C, ending at −4°C.
  3. Interpret: Net change equals final minus initial.

Final answer: The changes are +23 then −12; net change is +11°C, ending at −4°C.

Check: Net change equals final minus initial.

Clean visual examplesOne-page board

Clean one-page examples

AC9M7N07 - Comparing, Adding and Subtracting Integers
Example 1

Example 1 Model integer subtraction Start with 5−(−4). Subtracting −4 means adding its opposite, +4. Move four units right from 5. Arrive at 9. Final answer: 5−(−4)=9. Check: Check that 9+(−4)=5.

Example 2

Example 2 Compare a temperature change Morning temperature is −6°C. Afternoon temperature is 5°C. Calculate change: 5−(−6)=11. Interpret this as an 11°C rise. Final answer: The temperature rises by 11°C. Check: Starting at −6 and moving 11 right reaches 5.

Example 3

Example 3 Application problem 1 Problem: At 6 am the temperature is −4°C. It rises 9°C, falls 6°C, then rises 3°C. Find the final temperature and represent the changes as one integer calculation. Plan: Represent the information first, then calculate, interpret and independently check the result. Work: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills. Final answer: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C. Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

Example 4

Example 4 Application problem 2 Problem: Create and solve an integer expression for the change from −15°C to 8°C and back to −4°C. Plan: Check that −15+11=−4. Work: The changes are +23 then −12; net change is +11°C, ending at −4°C. Interpret: Net change equals final minus initial. Final answer: The changes are +23 then −12; net change is +11°C, ending at −4°C. Check: Net change equals final minus initial.

Curriculum examplesCopied content

Content description: compare, order and solve problems involving addition and subtraction of integers.

Questions and answersWith answers

Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.

  1. 1. Order −7, 2, −3 and 0 from least to greatest.

    Check answer

    Answer: −7, −3, 0, 2.

    Hint: Place them on a number line.

    Why: Numbers farther left are smaller.

  2. 2. Calculate −8+13.

    Check answer

    Answer: 5.

    Hint: Count through zero.

    Why: A rightward move of 13 from −8 reaches 5.

  3. 3. Calculate 6−(−9).

    Check answer

    Answer: 15.

    Hint: Rewrite as 6+9.

    Why: Subtracting a negative adds the opposite.

  4. 4. Find the distance between −4 and 7.

    Check answer

    Answer: 11 units.

    Hint: Subtract the lower coordinate from the higher.

    Why: Distance is the positive difference 7−(−4).

  5. 5. A lift moves from level 3 to level −5. What is its change?

    Check answer

    Answer: −8 levels.

    Hint: Use final−initial.

    Why: Final minus initial gives −5−3=−8.

  6. 6. The temperature changes from −2°C to −9°C. Find the change.

    Check answer

    Answer: −7°C.

    Hint: Calculate −9−(−2).

    Why: The negative change represents a fall of 7°C.

  7. 7. An account balance is −$18 and a $25 deposit arrives. Find the balance.

    Check answer

    Answer: $7.

    Hint: Calculate −18+25.

    Why: The deposit adds 25 to the signed balance.

  8. 8. A diver is at −12 m, rises 7 m, descends 9 m and rises 5 m. Find the final position.

    Check answer

    Answer: Starting at −12 m gives −12+7−9+5=−9 m, so the diver finishes 9 m below sea level.

    Hint: Record rises positive and descents negative.

    Why: Signed movements combine in sequence.

  9. 9. Create and solve an integer expression for the change from −15°C to 8°C and back to −4°C.

    Check answer

    Answer: The changes are +23 then −12; net change is +11°C, ending at −4°C.

    Hint: Check that −15+11=−4.

    Why: Net change equals final minus initial.

  10. 10. At 6 am the temperature is −4°C. It rises 9°C, falls 6°C, then rises 3°C. Find the final temperature and represent the changes as one integer calculation.

    Check answer

    Answer: −4 + 9 − 6 + 3 = 2, so the final temperature is 2°C.

    Hint: Represent the information first, then calculate, interpret and independently check the result.

    Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

Practice and reviewReady for practice

Common mistake: Negative sign treated only as subtraction.

Correction: It can indicate a number or direction.

Common mistake: -3-5 made positive.

Correction: Moving 5 left from -3 gives -8.

Common mistake: Subtracting negative rule memorised without meaning.

Correction: Connect it to removing a negative change or adding the opposite.

Curriculum alignmentStart here

We are learning to compare, order and solve problems involving addition and subtraction of integers.

Integers are whole numbers, their negatives and zero. Their order is represented on a number line, with greater values to the right and opposites equally distant from zero.

Addition represents a signed change. Subtraction can be rewritten as addition of the opposite, so 5 − (−4) = 5 + 4 rather than a leftward move.

Contexts such as temperature, elevation and account balance need a reference zero and stated direction. A negative result can be valid, while distance between two integers is always non-negative.

Success criteria

  • I can compare and order integers on a number line.
  • I can add and subtract integers using opposites and directed movement.
  • I can interpret an integer result and distinguish change from distance.
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