Year 9 - Maths
Problem solving with non-linear relationships
Non-linear relationships
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit we explore geometric and special number sequences like the Fibonacci sequence. We develop strategies to recognise types of sequence and continue them.
Lesson Summary
You will learn to use your knowledge of non-linear relationships to solve problems.
Key Notes
- If you can spot a sequence, it is possible to predict behaviour.
- By predicting future behaviour, you can plan how to react.
- As with all predictions, it is not a guarantee.
Vocabulary To Learn
- Geometric sequence: A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
- Triangular number: A triangular number (or triangle number) is a number that can be represented by a pattern of dots arranged into an equilateral triangle.
Common Mistakes To Avoid
- If you combine two sequences of the same type the resulting sequence will still be that type.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If you can spot a sequence, it is possible to predict behaviour. By predicting future behaviour, you can plan how to react.
2. Use this key word in a maths sentence and explain it clearly. 'Geometric sequence'
A geometric sequence is a sequence with a constant multiplicative relationship between successive terms. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: If you combine two sequences of the same type the resulting sequence will still be that type. Correction: Adding corresponding terms of two sequences will be good preparation for future units but it also a way to explore what sequences can be generated by combining other sequences.
More Lessons In This Unit
- Checking understanding of arithmetic sequences Study Guide
- Extrapolating a sequence Study Guide
- Features of geometric sequences Study Guide
- Features of special number sequences Study Guide
- Graphing special number sequences using technology Study Guide
- Recognising geometric sequences Study Guide
- Recognising special number sequences Study Guide
- Representing geometric sequences graphically Study Guide
- Securing understanding of arithmetic sequences Study Guide
Browse all guides in the Year 9 Maths guide library.