Year 9 - Maths
Features of special number sequences
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 appreciate the features of special number sequences, such as square, triangular and cube.
Key Notes
- Square number sequences are formed by squaring the position within the sequence.
- Cube number sequences are formed by cubing the position within the sequence.
- Triangular number sequences are formed by increasing the difference by one between each consecutive term.
- These special number sequences can be represented visually.
Vocabulary To Learn
- Triangular number: A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle
Common Mistakes To Avoid
- Square numbers are any number that can be squared.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Square number sequences are formed by squaring the position within the sequence. Cube number sequences are formed by cubing the position within the sequence.
2. Use this key word in a maths sentence and explain it clearly. 'Triangular number'
A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Square numbers are any number that can be squared. Correction: Give students counters or let them draw dot patterns to explore square numbers geometrically as well as numerically.
More Lessons In This Unit
- Checking understanding of arithmetic sequences Study Guide
- Extrapolating a sequence Study Guide
- Features of geometric sequences Study Guide
- Graphing special number sequences using technology Study Guide
- Problem solving with non-linear relationships 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
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