Graphs
Grade 3-5Real-Life Graphs
Real-life graphs represent situations rather than abstract equations, from converting currencies to describing a journey, and the key skill throughout is reading values off the graph accurately and understanding what the shape of the line represents. This lesson covers conversion graphs, interpreting distance-time graphs, finding average speed, and reading container-filling graphs.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Reading a conversion graph
A conversion graph is a straight line through the origin that lets you convert between two units. To convert a value, find it on one axis, trace across or up to the line, then read the corresponding value on the other axis.
A graph converting pounds to euros: to convert £24 to euros, find 24 on the pounds axis, trace up to the line, then across to the euros axis to read off the answer, €30.
Interpreting a distance-time graph
On a distance-time graph, a sloping line means the object is moving, a flat horizontal section means it has stopped, and a line sloping back down toward the horizontal axis means it is returning to the starting point.
A journey graph that rises steadily, stays flat for half an hour, then falls back to zero shows travelling away from the start, a stop of half an hour, and then travelling back to the start.
Finding average speed from a distance-time graph
Average speed is found by dividing the distance travelled by the time taken, which is the same as finding the gradient of a straight section of the graph.
A journey covering 90 km in 1.5 hours has an average speed of 90 ÷ 1.5 = 60 km/h.
Reading a container-filling graph
A graph showing the depth of liquid in a container over time rises more steeply when the container is filling quickly, and less steeply when it is filling more slowly. A change in the steepness of the line shows a change in the rate of filling.
A graph that rises steeply up to 2 minutes, then more gently afterwards, shows the container filling quickly at first and then at a slower steady rate.
Worked Examples
Three exam-style questions, fully solved.
The graph converts pounds (£) to euros (€). Use the graph to convert (a) £24 to euros, and (b) €35 to pounds.
Easy- 1.For (a), find £24 on the pounds axis, trace up to the line, then across to the euros axis
- 2.For (b), find €35 on the euros axis, trace across to the line, then down to the pounds axis
Answer: (a) €30, (b) £28
The graph shows the first part of a journey covering 90 km in 1.5 hours. Work out the average speed during this part of the journey.
Medium- 1.Read the total distance travelled from the graph: 90 km
- 2.Read the total time taken from the graph: 1.5 hours
- 3.Divide the distance by the time: 90 ÷ 1.5
Answer: 60 km/h
The graph shows a journey. Describe what is happening between 2 hours and 2.5 hours, and between 2.5 hours and 4 hours.
Hard- 1.Look at the shape of the line between 2 and 2.5 hours: it is flat, meaning distance is not changing
- 2.Look at the shape of the line between 2.5 and 4 hours: it slopes back down toward zero
Answer: Between 2 and 2.5 hours the person is stationary. Between 2.5 and 4 hours the person is travelling back to the start.
Avoid These
The most common mistakes students make.
Reading a conversion graph in the wrong direction, for example starting from the wrong axis when converting a value.
Describing a flat section of a distance-time graph as "moving slowly" instead of correctly identifying it as stationary, since distance is not changing at all.
Assuming a line sloping downward means the object is speeding up or slowing down, rather than recognising it as travelling back toward the starting point.
Finding average speed by reading a single point on the graph, instead of dividing the total distance travelled by the total time taken.
On a container-filling graph, assuming a steeper line always means a deeper container, rather than recognising it shows a faster rate of filling.
FAQ
Questions parents and students ask.
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