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New
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Year 11
Foundation

Problem solving with real-life graphs

I can use my knowledge of interpreting real-life graphs to solve problems.

icon-background-square
New
New
Year 11
Foundation

Problem solving with real-life graphs

I can use my knowledge of interpreting real-life graphs to solve problems.

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These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

Lesson details

Key learning points

  1. Real life graphs present a visual model of a situation.
  2. Linear graphs are not always the best representation.
  3. The different parts of the graph describe different parts of the whole situation.

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.

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?"


To help you plan your year 11 maths lesson on: Problem solving with real-life graphs, download all teaching resources for free and adapt to suit your pupils' needs...

There is a great opportunity here to get pupils physically active. Take the pupils outside and ask one pupil to model a journey. "I'd like you to go slow for ten metres, fast for ten metres, stop a short time, then go slow for ten metres". Then, ask the rest of the class to sketch the graphs.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
A linear graph like this shows __________ between $$x$$ and $$y$$.
An image in a quiz
no relationship
Correct answer: a constant rate of change
indirect proportion
Q2.
A constant rate of change on a distance-time graph shows __________.
An image in a quiz
Correct answer: constant speed
increasing speed
acceleration
a stop
Q3.
This distance-time graph shows the journey of a cyclist. When were they travelling fastest?
An image in a quiz
Correct answer: a
b
c
Q4.
This distance-time graph shows the journey of a cyclist. When did the cyclist stop?
An image in a quiz
a
Correct answer: b
c
Q5.
A horizontal line on this graph represents __________.
An image in a quiz
Correct answer: a constant speed
a stop
acceleration
deceleration
Q6.
This speed-time graph shows the journey of a car. When is it travelling fastest?
An image in a quiz
a
b
c
Correct answer: d

6 Questions

Q1.
This graph shows __________ rate of change between speed and time.
An image in a quiz
a decreasing
an increasing
a fast
Correct answer: a constant
Q2.
Which speed-time graph matches this distance-time graph?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
Which distance-time graph matches this speed-time graph?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q4.
Match these descriptions to the graph of this car journey.
An image in a quiz
Correct Answer:Fastest constant speed,d
tick

d

Correct Answer:Acceleration,c
tick

c

Correct Answer:Deceleration,a
tick

a

Correct Answer:Slowest constant speed,b
tick

b

Q5.
Which moment represents the longest stop on this displacement-time graph?
An image in a quiz
a
Correct answer: b
c
d
e
Q6.
Which section shows the fastest speed?
An image in a quiz
Correct answer: a
b
c
d
e