PROBLEM SOLVING

Patterns And Generalising

Learn the reliable method for patterns and generalising, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Pattern questions identify what stays constant and what changes between stages.

Picture itPlan, solve, then check
2 · THE METHOD

Follow these steps

  1. Record the change from one stage to the next.
  2. Separate the repeated growth from any fixed part.
  3. Write and test a general rule on more than one term.
3 · WORKED EXAMPLES

See the method in action

Example 1

The pattern starts at 3 and increases by 4. How much greater is term 8 than term 5?

  1. The positions are three steps apart, so the difference is 3 × 4 = 12.
Answer: 12
Example 2

Two separate joined-square patterns each grow from term 42 to term 50. How many additional sticks are needed altogether?

Terms 1, 2 and 3123
  1. Each pattern gains 8 squares, requiring 8 × 3 = 24 additional sticks.
  2. Two patterns require 24 × 2 = 48 additional sticks.
Answer: 48
4 · ELEVENSPRINT TIP

A useful shortcut

Write and test a general rule on more than one term.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.