The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.

Checking and securing understanding of reading from context-based graphs

Maths

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Estimating journeys from non-linear graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

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.

Real-life graphs

Here is a distance-time graph of a journey. When was the object moving the fastest?

Which sections of this graph are impossible?

Object is moving at a constant speed away from home.

Object is moving at a constant speed towards home.

On this 'distance from home' graph, which of these best describes what is happening at a)?

Object is moving at its fastest speed away from home.

Object is moving at its slowest speed away from home.

Object is moving at its fastest speed towards home.

Object is moving at its slowest speed towards home.

On this 'distance from home' graph, which of these best describes what is happening at b)?

Assuming it is filled at a constant rate, which of these could be a depth-time graph for this container?

Assuming they were filled at a constant rate, which container could this depth-time graph represent?

If the rate of change between two variables is constant, then the relationship between them is __________

Which of these shows a constant rate of change between $$x$$ and $$y$$?

Which of these lines have negative gradient?

Starting with the steepest, put these lines in order of steepness.

The solution to the equation $$2-\frac{3}{5}x = -1$$ is $$x = $${{}}. Use the graph to help you.

Using this distance-time graph, calculate the distance travelled after 4 hours.

Checking and securing understanding of reading from context-based graphs

Lesson outcome