# Stage 4 -number – ratio and rates: distance-time graphs

## Strategy

Students can:

• write or tell a story that matches a given distance/time graph
• match a distance/time graph to a description of a particular journey and explain the reasons for the choice
• compare distance/time graphs of the same situation, decide which one is the most appropriate, and explain why

## Activities to support the strategy

Students need to correctly interpret distance time graphs which involve a series of straight line segments. Students need to understand that the steepness (or gradient) of each straight line segment determines the speed of travel. The steeper the line segment, the faster the speed, the shallower the line segment the slower the speed, a horizontal line indicates a zero speed. Also a line with a positive gradient (i.e. Increasing as we move left to right), indicates that the position is moving away from its initial position and a line with a negative gradient (i.e. Decreasing as we move left to right), indicates that the position is moving back towards its initial position. View/print (PDF 899.62KB)

### Activity 1

Students should begin be watching the Reading a distance-time graph activity. The video allows students see how to interpret a journey by car from a starting point to a location and see it described on a distance-time graph. Find out how to answer four questions about the journey. See how the gradient of a distance-time graph enables you to work out the speed.

### Activity 2

The Triathlon: distance-time graphs activity examines distance-time graphs in the context of the three legs of a triathlon. Students see how distance-time graphs are used to represent and compare race performances. For example, notice that a flat line on a graph shows that an athlete is resting or preparing for the next stage. This activity also explores distance-time graphs which have non-straight segments indicating an athlete is speeding up ar slowing down.

### Activity 3

As an extension, students can be asked to write a story for almost any line graph. The example below shows the height of water in a bath and students need to write a story explaining the graph. It is an open-ended method for exploring line graphs. View/print (PDF 907.81KB)

More such activities can be found at Broadbent maths - teaching data handling creatively using graph stories.

## References

### Australian curriculum

ACMNA180: Investigate, interpret and analyse graphs from authentic data

### NSW syllabus

MA4-7NA: Operates with ratios and rates, and explores their graphical representation

## Student resources

Distance-time graphs - This interactive multimedia website helps students learn how to plot a distance-time graph and understand what it shows. It includes an animated presentation, a short quiz and a review.