Checking and securing understanding of reading from context-based graphs | Maths

Starter quiz

If the rate of change between two variables is constant, then the relationship between them is __________

linear ✓

parabolic

regular

variable
Which of these shows a constant rate of change between $x$ and $y$ ?
Which of these lines have negative gradient?

A (black) ✓

B (blue)

C (green) ✓

D (pink)

E (purple)
Starting with the steepest, put these lines in order of steepness.

1

⇔

B (black)

2

⇔

A (blue)

3

⇔

D (pink)

4

⇔

C (green)

5

⇔

E (purple)
$The solution to the equation <Math>2-\frac{3}{5}x = -1</Math> is <Math>x = </Math><span class="blank">______</span>. Use the graph to help you.$

The solution to the equation $2-\frac{3}{5}x = -1$ is $x =$ ______. Use the graph to help you.

'5' ✓
Using this distance-time graph, calculate the distance travelled after 4 hours.

'120 km' ✓

Exit quiz

Here is a distance-time graph of a journey. When was the object moving the fastest?

Between 0 and 2 hours.

Between 2 and 3 hours. ✓

Between 3 and 4 hours.

Between 4 and 6 hours.
Which sections of this graph are impossible?

a ✓

b

c ✓

d

e
On this 'distance from home' graph, which of these best describes what is happening at a)?

Object is moving at a constant speed away from home.

Object is stationary. ✓

Object is moving at a constant speed towards home.

Object is accelerating.

Object is decelerating.
On this 'distance from home' graph, which of these best describes what is happening at b)?

Object is accelerating.

Object is moving at its fastest speed away from home.

Object is moving at its slowest speed away from home.

Object is moving at its fastest speed towards home. ✓

Object is moving at its slowest speed towards home.
Assuming it is filled at a constant rate, which of these could be a depth-time graph for this container?
Assuming they were filled at a constant rate, which container could this depth-time graph represent?

Worksheet

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Video

Lesson Details

Key learning points

Distance-time graphs can tell you about a journey.
By reading the graph, you can tell if there is mistake with it.

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 cannot 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 one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.