Year 11 - Maths
Problem solving with real-life graphs
Real-life graphs
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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 expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.
Lesson Summary
You will learn to use your knowledge of interpreting real-life graphs to solve problems.
Key Notes
- Real life graphs present a visual model of a situation.
- Linear graphs are not always the best representation.
- The different parts of the graph describe different parts of the whole situation.
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. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.
Common Mistakes To Avoid
- When matching, or sketching, distance-time and speed-time graphs pupils may think these have a similar shape.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Real life graphs present a visual model of a situation. Linear graphs are not always the best representation.
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: When matching, or sketching, distance-time and speed-time graphs pupils may think these have a similar shape. Correction: Questioning helps. Ask pupils to explain what is happening on a variety of graphs. For example, "A diagonal line with positive gradient on a speed-time graph. What is happening?" "A horizontal line on distance-time graph. What is happening?".
More Lessons In This Unit
- Advanced problem solving with real-life graphs Study Guide
- Calculating journeys from linear speed-time graphs Study Guide
- Calculating the rate of change Study Guide
- Checking and securing understanding of drawing distance-time graphs Study Guide
- Checking and securing understanding of reading from context-based graphs Study Guide
- Distance-time graphs Study Guide
- Efficiently estimating journeys from non-linear graphs Study Guide
- Estimating journeys from non-linear graphs Study Guide
- Estimating the gradient of a curve Study Guide
- Finding the equation of a radius of a circle Study Guide
- Finding the equation of the tangent to a circle Study Guide
- Improving the estimate of the gradient of a curve Study Guide
- Interpreting and drawing more real-life graphs Study Guide
- Interpreting and drawing real-life graphs Study Guide
- Non-linear distance-time graphs Study Guide
- Speed-time graphs Study Guide
Browse all guides in the Year 11 Maths guide library.