Displacement is the distance from the starting point when measured in a straight line.

Checking and securing understanding of drawing distance-time graphs

Maths

Checking and securing understanding of reading from context-based 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

Izzy travelled 12 km in half an hour. Then stopped for 15 minutes. Then travelled another 8 km in 25 minutes. If using these axes what would be the best scale for time?

The graph would be really small and not make use of the space.

The coordinates would be between gridlines and difficult to plot.

Izzy travelled 12 km in half an hour. Then stopped for 15 minutes. Then travelled another 8 km in 25 minutes. What would be the problem with using steps of 2 km on these axes?

Izzy travelled 12 km in half an hour. Then stopped for 15 minutes. Then travelled another 8 km in 25 minutes. What might be the difficulty with using steps of 5 km on these axes?

When all the travel is in the same direction.

When you want to know how long the journey has taken in total.

When you want to know how far the journey was in total.

When you want to know when the object has changed direction.

When might you use a displacement-time graph instead of a distance-time graph?

Moving away from a fixed start point at a constant speed.

Moving back towards a fixed start point at a constant speed.

On this displacement-time graph what does the line segment marked a) represent?

Moving away from a fixed start point in the opposite direction.

Moving towards a fixed start point from the opposite direction.

Travelling upwards from a position below ground.

An impossible journey as distance cannot be negative.

On this displacement-time graph what does the line segment marked b) represent?

What number is the arrow pointing to on this number line?

The coordinates of the point shown on the axes are (2, {{}}).

The coordinates of the point shown on the axes are ({{}}, 100).

Which graph shows a journey where speed is constant throughout?

How do we represent an object stopping for part of a journey on a distance-time graph?

Checking and securing understanding of drawing distance-time graphs

Lesson outcome