Year 4 Maths: Square Numbers

What Are Square Numbers?

Hello Year 4! Today, we’re going to learn about square numbers. A square number is a special kind of number that you get when you multiply a number by itself.

Understanding Square Numbers

Let’s break it down:

• Multiply a number by itself: For example, if we take the number 3 and multiply it by 3 (which is the same as adding 3 three times), we get 9. So, 9 is a square number because it is 3 times 3.
• Square numbers look like this:
  • 1 × 1 = 1 (1 is a square number)
  • 2 × 2 = 4 (4 is a square number)
  • 3 × 3 = 9 (9 is a square number)
  • 4 × 4 = 16 (16 is a square number)
  • 5 × 5 = 25 (25 is a square number)

List of Some Square Numbers

Here are some square numbers you should remember:

• 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Key Rules for Square Numbers

1. The number multiplied by itself: Always remember that square numbers come from multiplying a number by itself.
2. Always positive: Square numbers are always positive because multiplying two positive numbers gives a positive result.
3. Perfect squares: The numbers we get (like 1, 4, 9) are called perfect squares.

Tips and Tricks

• Visualisation: You can think of square numbers as forming a perfect square shape. For example, if you have 4 objects arranged in a 2 by 2 square, that’s 2 × 2 = 4!
• Counting Squares: You can also use a number line to see where square numbers appear. Every time you reach a square number, mark it!
• Practice: The more you practice finding square numbers, the easier it will become. Try writing down the squares of numbers from 1 to 12!

Questions About Square Numbers

Easy Level Questions

1. What is 1 squared?
2. What is 2 squared?
3. What is 3 squared?
4. What is 4 squared?
5. What is 5 squared?
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?
11. Are square numbers always positive? (Yes/No)
12. What is the next square number after 16?
13. Which is a square number: 15 or 16?
14. What is 0 squared?
15. What is 11 squared?
16. Is 25 a square number? (Yes/No)
17. What number do you multiply by itself to get 36?
18. What is the square of 12?
19. Is 49 a square number? (Yes/No)
20. What is 2 squared plus 2 squared?

Medium Level Questions

1. What is 3 squared minus 1?
2. How many square numbers are between 1 and 30?
3. What is the smallest square number?
4. Write down the first five square numbers.
5. What number is squared to get 64?
6. Write the square of 9 and 10.
7. What is the square of 8 minus the square of 7?
8. Is 30 a square number? (Yes/No)
9. What is the sum of the squares of 2 and 3?
10. What is 5 squared plus 4 squared?
11. Can you find a square number that is 20?
12. What is 6 squared minus 3 squared?
13. How many digits does 100 have?
14. What is the square of 15?
15. Are there any square numbers between 50 and 60? (Yes/No)
16. What is the difference between 7 squared and 5 squared?
17. What is 8 squared plus 1 squared?
18. What is the square of 11 minus the square of 10?
19. How many square numbers are less than 50?
20. What number squared gives you 81?

Hard Level Questions

1. Find the sum of the first ten square numbers.
2. What is the difference between 12 squared and 10 squared?
3. If a number squared equals 144, what is the number?
4. How many square numbers are there between 1 and 100?
5. What is the product of 2 squared and 3 squared?
6. If a number is squared and the result is 49, what could the number be?
7. What is 13 squared minus 12 squared?
8. Find a square number that is also a multiple of 10.
9. If you add 1 to 25, is the result a square number? (Yes/No)
10. What is the square of the sum of 2 and 3?
11. Are there any square numbers that are three digits? (Yes/No)
12. If you take the square root of 36, what number do you get?
13. What is the square of 9 divided by the square of 3?
14. What is the smallest square number greater than 50?
15. If you subtract 1 from 16, what is the square root of the result?
16. What is the square of 14?
17. Can you find two square numbers that add up to make 50?
18. If 7 squared is 49, what is 8 squared?
19. Find the square of 5 and then double it.
20. What is the product of the square of 4 and the square of 5?

Answers

Easy Level Answers

1. 1
2. 4
3. 9
4. 16
5. 25
6. 36
7. 49
8. 64
9. 81
10. 100
11. Yes
12. 25
13. 16
14. 0
15. 121
16. Yes
17. 6
18. 144
19. Yes
20. 8

Medium Level Answers

1. 8
2. 5
3. 1
4. 1, 4, 9, 16, 25
5. 8
6. 81 and 100
7. 15
8. No
9. 13
10. 41
11. No
12. 27
13. 3
14. 225
15. No
16. 24
17. 65
18. 11
19. 7
20. 9

Hard Level Answers

1. 385
2. 44
3. 12
4. 10
5. 36
6. 7 or -7
7. 25
8. 100
9. No
10. 25
11. Yes
12. 6
13. 9
14. 64
15. 3
16. 196
17. Yes (25 and 25)
18. 64
19. 100
20. 80

Happy learning about square numbers, Year 4! Keep practicing and you’ll become a square number expert in no time!