Year 9 - Maths
Extending thinking about sequences
Graphical representations
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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 pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.
Lesson Summary
You will learn to appreciate that abstract sequences can have negative values.
Key Notes
- When you move away from physical representations of sequences, you can think abstractly.
- You can consider what happens if there was not a first term.
- The sequence could extend forward and backwards.
- You can generate previous terms using the inverse of the term-to-term rule.
Vocabulary To Learn
- Arithmetic sequence: An arithmetic (or linear) sequence is a sequence where the difference between terms is a constant.
- Geometric sequence: A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
Common Mistakes To Avoid
- All sequences can go on infinitely.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When you move away from physical representations of sequences, you can think abstractly. You can consider what happens if there was not a first term.
2. Use this key word in a maths sentence and explain it clearly. 'Arithmetic sequence'
An arithmetic (or linear) sequence is a sequence where the difference between terms is a constant. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: All sequences can go on infinitely. Correction: When we think abstractly and start a sequence such as 8, 10, 12, 14, 16, ... it is possible that it goes on infinitely. However, if we applied this sequence to a context such as pairs of pupils getting on a bus, then a physical limit will apply.
More Lessons In This Unit
- Checking and securing understanding of non-linear sequences Study Guide
- Efficiently drawing linear graphs Study Guide
- Equations and their graphs Study Guide
- Exploring the shapes of graphs using technology Study Guide
- Graphically solving two linear graphs that intersect Study Guide
- Modelling with graphs Study Guide
- Problem solving with graphical representations Study Guide
- Reading from graphs Study Guide
Browse all guides in the Year 9 Maths guide library.