This worksheet teaches students to find and use the rules behind growing shape patterns and number patterns, including patterns with decimals and fractions, and to predict terms further along. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A pattern (sequence) is a list of numbers that follows a rule. Each number is called a term.
- An additive pattern adds or subtracts the same amount each time: 2.5, 5, 7.5, 10 (add 2.5).
- A multiplicative pattern multiplies or divides by the same amount each time: 3, 6, 12, 24 (× 2).
- A "position rule" links a term to its position: for toothpick triangles, toothpicks = number of triangles × 2 + 1.
- Patterns can use decimals and fractions as well as whole numbers.
What your child will practise:
- Continueing number patterns with whole numbers, decimals and fractions.
- Describing a pattern's rule in words.
- Using a position rule to find any term without listing them all.
- Working backwards from a term to find its position.
- Spotting and explaining patterns in shapes and in calculator results.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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