SkillrHubYear 6 Australian Curriculum Maths • skillrhub.com

AC9M6N01 • Homework & Homework

Integers, Number Lines & the Cartesian Plane

Use zero as a reference point. Show number-line or coordinate reasoning where it helps.

Part A • 20 × 2 marks

Core mastery

1. Mark −4, −1, 2 and 5 on a number line.

2. Order −6, 3, −2, 0 from least to greatest.

3. Which is greater: −7 or −3? Explain.

4. Which values are the same distance from zero: −5, 5, −3, 3?

5. Explain why −2 < 0.

6. A stall earns $80 and spends $95. Represent the result as an integer.

7. A student earns $12 and spends $7. Write the net integer.

8. What integer represents break-even?

9. Write an integer showing a loss of $18.

10. Write an integer showing a profit of $45.

11. An elevator is 4 floors below ground. Represent this as an integer.

12. A diver is 30 m below sea level. Write the integer.

13. Which quadrant contains (−3, 4)?

14. Does (0, −5) lie on the x-axis or y-axis?

15. Plot (4, −2) and name its quadrant.

16. If right is positive, what does −20 m mean?

17. On a vertical line, a robot moves +12 units. Which direction?

18. Write an integer showing 25 m left of a reference point.

19. Write an integer showing 9 units down.

20. A robot starts at 0, moves 6 left then 4 right. What is its final position?

Part B • 10 × 5 marks

Multi-step reasoning

21. Place −9, −3, 0, 4, 7 and −1 on a number line and explain the order.

22. A fete earns $450, spends $520, then earns another $100. Represent each change and find the final result.

23. A submarine is at −120 m and a drone is at +40 m. Draw a vertical number line and show both positions.

24. Classify (3,2), (−4,1), (−2,−5), (5,−3) into quadrants and justify using signs.

25. A robot starts at 0 and moves 15 left, 8 right, 4 left and 12 right. Show each position and the final position.

26. Order −12°C, 4°C, −3°C and −20°C from coldest to warmest. Explain.

27. Plot (−2,3), (4,−1), (0,5), (−3,−4). State the quadrant or axis for each.

28. Relative to a starting altitude of 0 m, a hiker climbs 300 m, descends 450 m, then climbs 200 m. Model the path and find the final altitude.

29. Draw a thermometer showing −7°C, 0°C, 12°C and −3°C. Identify warmest and coldest.

30. A club starts at $0, earns $150, spends $75, earns $40 and spends $20. Model each step and find the final balance.

Part C • Enriched

31. Coordinate drone challenge

A research drone starts at (0,0). It moves 15 units right, 8 up, 22 left, 5 down, 10 right and 12 up. Represent each movement using signed x/y changes, record the cumulative coordinate after every step, determine the final coordinate and quadrant, and explain how positive and negative integers model direction on both axes.