Year 7 Maths Revision Sheets

Year 7 Maths Revision Sheets

1. Expanded Notation

  • Meaning: Writing numbers to show the value of each digit.

  • Example:

    • For the number 4 582:

    • Expanded form is 4 000 + 500 + 80 + 2

  • Example with decimals:

    • For the number 3.47:

    • Expanded form is 3 + 0.4 + 0.07

  • Tip: Each digit represents place value.

2. Adding & Subtracting

  • Adding:

    • Line numbers up by place value.

  • Example:

    • 345 + 128 = 473

  • Subtracting:

    • Borrow if needed.

  • Example:

    • 502 - 187 = 315

  • Tip: Always line up ones, tens, hundreds.

3. Multiplying

  • Multiplication Example:

    • 23 × 4 = 92

  • Long multiplication example:

    • 34 × 12 = 68

    • 340 × 12 = 408

  • Tip: Multiply then add the rows.

4. Dividing

  • Division Example:

    • 24 ÷ 6 = 4

  • Long division example:

    • 96 ÷ 4 = 24

  • Tip: Think “how many groups?”

5. Rounding & Estimating

  • Rounding:

    • Look at the next digit to determine how to round.

  • Example:

    • 47 rounds to 50 (nearest 10)

    • 234 rounds to 200 (nearest 100)

  • Estimating:

    • Round numbers to make quick calculations.

  • Example of estimation:

    • 198 + 302 ≈ 200 + 300 = 500

6. Lowest Common Multiple (LCM)

  • Definition: Smallest number into which two numbers can both divide evenly.

  • Example for LCM of 4 and 6:

    • Multiples of 4:

    • 4, 8, 12, 16

    • Multiples of 6:

    • 6, 12, 18

    • Result: LCM = 12

7. Highest Common Factor (HCF)

  • Definition: Largest number that can divide both numbers without leaving a remainder.

  • Example for HCF of 12 and 18:

    • Factors of 12:

    • 1, 2, 3, 4, 6, 12

    • Factors of 18:

    • 1, 2, 3, 6, 9, 18

    • Result: HCF = 6

8. Factor Pairs

  • Definition: Two numbers that multiply together to give another number.

  • Example for factors of 24:

    • 1 × 24

    • 2 × 12

    • 3 × 8

    • 4 × 6

9. Index Notation (Powers)

  • Definition: A way to express repeated multiplication of the same number.

  • Example:

    • 3⁴ = 3 × 3 × 3 × 3 = 81

  • Parts:

    • 3 = base

    • 4 = index (also known as power)

10. Factor Tree

  • Definition: A diagram that shows how a number can be broken down into its prime factors.

  • Example for the number 24:

    24
   /  \
  6    4
 /\    /\
2  3  2  2

  • Prime factorisation:

    • 24 = 2 × 2 × 2 × 3

11. Factorisation & Primes

  • Prime number:

    • A natural number greater than 1 that is only divisible by 1 and itself.

  • Examples of prime numbers:

    • 2, 3, 5, 7, 11

  • Composite number:

    • A natural number greater than 1 that has more than two distinct positive divisors.

  • Example:

    • 12 = 2 × 2 × 3

12. Square Numbers

  • Definition: The product of a number multiplied by itself.

  • Examples:

    • 1² = 1

    • 2² = 4

    • 3² = 9

    • 4² = 16

    • 5² = 25

    • 6² = 36

13. Rounding Decimals

  • Tip: Look at the next digit to determine how to round the decimal number.

  • Examples:

    • 3.46 rounds to 3.5 (nearest tenth)

    • 7.382 rounds to 7.38 (nearest hundredth)

14. Good 30-minute Revision Routine

  1. Review notes: 10 minutes

  2. Practice questions: 10 minutes

  3. Test yourself without notes: 10 minutes