Year 9 - Maths
Problem solving with graphical representations
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 use your knowledge of graphical representations to solve problems.
Key Notes
- When presented with a real-life problem, it can help to sketch what is happening.
- A sketch can provide a visual aid for understanding.
- In there is a context to the problem then the solution should be given in context.
Vocabulary To Learn
- Linear: The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
- Gradient: The gradient is a measure of how steep a line is.
- Intercept: An intercept is the coordinate where a line or curve meets a given axis.
- Parabola: A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).
Common Mistakes To Avoid
- A distance time graph will always be constructed with straight lines.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When presented with a real-life problem, it can help to sketch what is happening. A sketch can provide a visual aid for understanding.
2. Use this key word in a maths sentence and explain it clearly. 'Linear'
The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A distance time graph will always be constructed with straight lines. Correction: A straight line represents a consistent rate of a change, a consistent speed. In reality we need to model acceleration and deceleration which will involve curved lines.
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
- Extending thinking about sequences Study Guide
- Graphically solving two linear graphs that intersect Study Guide
- Modelling with graphs Study Guide
- Reading from graphs Study Guide
Browse all guides in the Year 9 Maths guide library.