Year 5 Maths: Cube Numbers

What are Cube Numbers?

Hello, Year 5! Today, we are going to learn about cube numbers. A cube number is a special type of number that is made when you multiply a number by itself, and then multiply that result by the same number again.

How Do We Get Cube Numbers?

To understand cube numbers, let’s break it down step-by-step:

1. Choose a number (let’s say 2).
2. Multiply it by itself: $$2 \times 2 = 4$$
3. Now multiply that result by the same number again: $$4 \times 2 = 8$$

So, the cube of 2 (written as (2^3)) is 8.

Key Rules

• Cube numbers are written with an exponent of 3. For example:
  • (1^3 = 1)
  • (2^3 = 8)
  • (3^3 = 27)
  • (4^3 = 64)
• The first few cube numbers are:
  • 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

Tips and Tricks

1. Visualisation: Think of a cube! If you have a cube shape, like a dice, the number of small cubes inside it represents the cube number.
2. Patterns: Notice how the gap between cube numbers increases. For example:
   • From 1 to 8, the gap is 7.
   • From 8 to 27, the gap is 19.
   • From 27 to 64, the gap is 37.
3. Practice: The more you practice, the easier it gets! Try calculating the cubes of numbers from 1 to 10.

Questions on Cube Numbers

Easy Level Questions

1. What is (1^3)?
2. What is (2^3)?
3. What is (3^3)?
4. What is (4^3)?
5. What is (5^3)?
6. What is (6^3)?
7. What is (7^3)?
8. What is (8^3)?
9. What is (9^3)?
10. What is (10^3)?

Medium Level Questions

11. What is (2^3 + 3^3)?
12. What is (4^3 – 1^3)?
13. What is (3^3 \times 2)?
14. What is (5^3 \div 5)?
15. Find the difference between (6^3) and (5^3).
16. What is the sum of (1^3), (2^3), and (3^3)?
17. If (x = 4), what is (x^3)?
18. What is (7^3 + 1^3 – 3^3)?
19. What is (8^3 – 2^3)?
20. What is the next cube number after (3^3)?

Hard Level Questions

21. Calculate (3^3 + 4^3 + 5^3).
22. What is (2^3 \times 3^3)?
23. If (y = 6), what is (y^3 – 5^3)?
24. Find the product of (4^3) and (2^3).
25. What is (10^3 – (7^3 + 2^3))?
26. If (a = 3) and (b = 2), what is (a^3 + b^3)?
27. Calculate the average of the first five cube numbers.
28. What is (5^3 + 3^3 – 1^3)?
29. If (z = 2), what is (z^3 + 4^3 – 3^3)?
30. What is the sum of all cube numbers from (1^3) to (4^3)?

Answers and Explanations

Easy Level Answers

1. (1^3 = 1)
2. (2^3 = 8)
3. (3^3 = 27)
4. (4^3 = 64)
5. (5^3 = 125)
6. (6^3 = 216)
7. (7^3 = 343)
8. (8^3 = 512)
9. (9^3 = 729)
10. (10^3 = 1000)

Medium Level Answers

11. (2^3 + 3^3 = 8 + 27 = 35)
12. (4^3 – 1^3 = 64 – 1 = 63)
13. (3^3 \times 2 = 27 \times 2 = 54)
14. (5^3 \div 5 = 125 \div 5 = 25)
15. (6^3 – 5^3 = 216 – 125 = 91)
16. (1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36)
17. (x^3 = 4^3 = 64)
18. (7^3 + 1^3 – 3^3 = 343 + 1 – 27 = 317)
19. (8^3 – 2^3 = 512 – 8 = 504)
20. The next cube number after (3^3) is (4^3 = 64).

Hard Level Answers

21. (3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216)
22. (2^3 \times 3^3 = 8 \times 27 = 216)
23. (y^3 – 5^3 = 6^3 – 125 = 216 – 125 = 91)
24. (4^3 \times 2^3 = 64 \times 8 = 512)
25. (10^3 – (7^3 + 2^3) = 1000 – (343 + 8) = 1000 – 351 = 649)
26. (a^3 + b^3 = 3^3 + 2^3 = 27 + 8 = 35)
27. Average of the first five cube numbers (= (1 + 8 + 27 + 64 + 125) \div 5 = 225 \div 5 = 45)
28. (5^3 + 3^3 – 1^3 = 125 + 27 – 1 = 151)
29. (z^3 + 4^3 – 3^3 = 2^3 + 64 – 27 = 8 + 64 – 27 = 45)
30. Sum of all cube numbers from (1^3) to (4^3 = 1 + 8 + 27 + 64 = 100)

I hope this helps you understand cube numbers better! Now, let’s practice!