Problem solving with real-life graphs | Maths | Quizalize & Oak National Academy

Starter quiz

A linear graph like this shows __________ between $x$ and $y$ .

no relationship

a constant rate of change ✓

indirect proportion
A constant rate of change on a distance-time graph shows __________.

constant speed ✓

increasing speed

acceleration

a stop
This distance-time graph shows the journey of a cyclist. When were they travelling fastest?

a ✓

b

c
This distance-time graph shows the journey of a cyclist. When did the cyclist stop?

a

b ✓

c
A horizontal line on this graph represents __________.

a constant speed ✓

a stop

acceleration

deceleration
This speed-time graph shows the journey of a car. When is it travelling fastest?

a

b

c

d ✓

Exit quiz

This graph shows __________ rate of change between speed and time.

a decreasing

an increasing

a fast

a constant ✓
Which speed-time graph matches this distance-time graph?
Which distance-time graph matches this speed-time graph?
Match these descriptions to the graph of this car journey.

Fastest constant speed

⇔

d ✓

Acceleration

⇔

c ✓

Deceleration

⇔

a ✓

Slowest constant speed

⇔

b ✓
Which moment represents the longest stop on this displacement-time graph?

a

b ✓

c

d

e
Which section shows the fastest speed?

a ✓

b

c

d

e

Worksheet

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Video

Lesson Details

Key learning points

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.

Common misconception

When matching, or sketching, distance-time and speed-time graphs pupils may think these have a similar shape.

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?"

Keywords

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.