Year 5 Maths: Square Numbers Investigation

What are Square Numbers?

Hello, Year 5! Today, we are going to explore square numbers. A square number is a number that you get when you multiply a whole number by itself.

How to Find Square Numbers

To find a square number, you take a number (let’s say 3) and multiply it by itself:

$$

3 \times 3 = 9

$$

This means 9 is a square number.

Some Examples

Here are more examples of square numbers:

• 1: $$1 \times 1 = 1$$
• 4: $$2 \times 2 = 4$$
• 9: $$3 \times 3 = 9$$
• 16: $$4 \times 4 = 16$$
• 25: $$5 \times 5 = 25$$

Key Rules to Remember

1. Square Numbers: A square number is formed by multiplying a number by itself.
2. Counting: The first few square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
3. Even and Odd: The square of an even number is always even, and the square of an odd number is always odd.
4. Patterns: The difference between consecutive square numbers increases by 2 each time.

Tips and Tricks

• Memorise the First Ten Square Numbers: It will help you in many maths problems!
• Look for Patterns: Notice how square numbers are spaced apart as you go higher.
• Use a Number Line: Visualising square numbers on a number line can help you see their relationships.

Questions for Your Investigation

Easy Level Questions

1. What is the square of 1?
2. What is the square of 2?
3. What is the square of 3?
4. What is the square of 4?
5. What is the square of 5?
6. What is 6 squared?
7. What is 7 squared?
8. What is 8 squared?
9. What is 9 squared?
10. What is 10 squared?

Medium Level Questions

11. What is the square of 11?
12. What is 12 squared?
13. What is the square of 13?
14. Is 36 a square number? Why or why not?
15. What is the square of 14?
16. What is the difference between 16 and 25?
17. What is the square of 15?
18. Are all square numbers even? Give an example.
19. Which is smaller, 7 squared or 8 squared?
20. What is the next square number after 25?

Hard Level Questions

21. What is the square of 20?
22. What is the difference between 49 and 36?
23. Is 50 a square number? Explain.
24. What is the square of 18?
25. Which is the smallest square number greater than 20?
26. How many square numbers are there between 1 and 100?
27. What is the sum of the squares of 1 and 2?
28. If a number is squared, can it be negative? Why or why not?
29. What pattern do you see in the differences of consecutive square numbers?
30. If 5 is squared and then added to 4, what do you get?

Answers and Explanations

Easy Level Answers

1. 1
2. 4
3. 9
4. 16
5. 25
6. 36
7. 49
8. 64
9. 81
10. 100

Medium Level Answers

11. 121
12. 144
13. 169
14. Yes, because it is 6 x 6.
15. 196
16. 9
17. 225
18. No, square numbers can be odd. For example, 9.
19. 7 squared (49) is smaller than 8 squared (64).
20. 36

Hard Level Answers

21. 400
22. 13
23. No, 50 is not a square number.
24. 324
25. 25
26. 10 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)
27. 5
28. No, squaring a number gives a positive result or zero.
29. The differences increase by 2.
30. 29

Happy investigating square numbers, Year 5! Keep practising!