Modelling with graphs | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ of change is how quickly one variable changes in relation to another.
- 'rate' ✓
Which of these lines has the steepest gradient?
- Line a ✓
- Line b
- Line c
Look at this graph. What is the value of $x$ when $y=5$ ?
- $x=1$
- $x=2$
- $x=3$ ✓
- $x=4$
This parabola models the flight of a cricket ball being thrown. Estimate the maximum height of the cricket ball.
- 9.8 metres
- 10 metres
- 10.2 metres ✓
- 11 metres
- 21 metres
Laura is plotting the graph of the line $3y + 4x=12$ . She only wants to plot two points. Which of these points would be the best points for Laura to use?
- When $x=0$ ✓
- When $x=1$
- When $x=2$
- When $x=3$ ✓
- When $x=4$
Jun wants to draw the graph of $y = 0.4x + 3.2$ for positive values of $x$ . The coordinates of the first point on the line that has positive integer coordinates are ______.
- '(2, 4)' ✓

Exit quiz

The ______ is a measure of how steep a line is.
- 'gradient' ✓
The distance-time graph shows Sofia's journey to a friend's house. $d$ is the distance in metres and $t$ is the time in minutes. Which part of the journey is Sofia moving at the greatest speed?
- Part a
- Part b
- Part c
The distance-time graph shows Andeep's journey to the shops. $d$ is the distance in metres from Andeep's house and $t$ is the time in minutes. Altogether Andeep's journey takes ______ minutes.
- '70' ✓
The distance-time graph shows Andeep's journey to the shops. $d$ is the distance in metres and $t$ is the time in minutes. Which segments show Andeep has stopped?
- A
- B ✓
- C
- D ✓
- E
The distance-time graph shows Andeep's journey to the shops. $d$ is the distance in metres from Andeep's house and $t$ is the time in minutes. Altogether Andeep has walked ______ kilometres.
- '2' ✓
Izzy has drawn this distance-time graph. Which of these statements explain what is wrong with Izzy's graph.
- A There should not be any sections with a positive gradient.
- B There should not be any sections with a negative gradien
- C There should not be any vertical sections. ✓
- D There should not be any horizontal sections.
- E There should not be any sections where time goes backward. ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Distance-time graphs tell you how far you have travelled over a period of time.
By reading the graph, you can tell if there is mistake with it.
You can sketch a graph based on the information you have been given.
Important given values should be marked on your sketch.

Common misconception

The line on a distance time graph can go in any direction.

The line may be horizontal, time changing without a change in distance, but it can not be vertical. That would be a change in distance without a change in time. Additionally, our line cannot go backwards; time is always moving forwards.

Keywords

Rate of change - The rate of change is how quickly one variable changes in relation to another.
Gradient - The gradient is a measure of how steep a line is, calculated by finding the rate of change in the $y$ -direction with respect to the positive $x$ -direction.