New
New
Year 11
Higher

Calculating the rate of change

I can calculate the gradient and interpret this as the rate of change for real life contexts.

New
New
Year 11
Higher

Calculating the rate of change

I can calculate the gradient and interpret this as the rate of change for real life contexts.

Lesson details

Key learning points

  1. For straight-line sections of a graph, it is easy to calculate the gradient.
  2. The gradient tells us the rate that one quantity changes with respect to the other.
  3. The gradient gives the rate that the $$y$$ variable changes with respect to the $$x$$ variable.
  4. The gradient can be interpreted in context and should be for real life contexts.

Common misconception

Gradient is change in $$y$$ divided by change in $$x$$.

The gradient is calculated by considering the change in $$y$$ when moving one unit in the positive $$x$$ direction.

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.

  • 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.

Learning cycle 2 involves interpreting the gradient within the context of the scenario. You may wish to provide more examples for pupils to practice with to ensure pupils are confident with how to interpret in context.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Loading...

6 Questions

Q1.
In this table there is a __________ rate of change in the $$y$$ values.
An image in a quiz
Correct answer: constant
negative
increasing
decreasing
Q2.
In this table for every change of $$+1$$ in $$x$$ there is a change of _________ in $$y$$.
An image in a quiz
$$-8$$
$$-6$$
$$+4$$
Correct answer: $$+6$$
$$+10$$
Q3.
How do we know there is not a constant rate of change between the $$x$$ and $$y$$ variables in this graph?
An image in a quiz
The graph is not decreasing.
Correct answer: It is not a linear graph.
The graph has a positive gradient.
The graph does not intercept the $$y$$-axis at the origin.
Q4.
What is the gradient of this line?
An image in a quiz
$$+2$$
$$+4$$
Correct answer: $$-3$$
$$-6$$
Q5.
When we find the gradient on a distance-time graph we have calculated the __________ of the particle being modelled.
An image in a quiz
distance travelled
displacement
Correct answer: speed
acceleration
deceleration
Q6.
What is the gradient of this line?
An image in a quiz
$$3$$
Correct answer: $$3\over2$$
$$2\over3$$
$$-{3\over2}$$
$$-2$$

6 Questions

Q1.
What is the gradient of this line?
An image in a quiz
$$+10$$
$$+2$$
$$-10$$
Correct answer: $$-5$$
Q2.
What is the gradient of this line?
An image in a quiz
$$1$$
$$2$$
$$4$$
Correct answer: $$8$$
$$0.25$$
Q3.
This is a conversion graph for British Pounds ($$£$$) to New Zealand Dollars ($${$}$$) and the gradient of the line is $$2$$. Which of the below statements are accurate?
An image in a quiz
Every one New Zealand Dollar is worth two British Pounds.
Correct answer: Every one British Pound is worth two New Zealand Dollars.
Correct answer: For every change of $$+1$$ in $$£$$ there is a change of $$+2$$ in $${$}$$
For every change of $$+1$$ in $${$}$$ there is a change of $$+2$$ in $$£$$
For every change of $$+10$$ in $${$}$$ there is a change of $$+20$$ in $$£$$
Q4.
What is the speed of the vehicle modelled in this distance-time graph?
An image in a quiz
$$2$$ km/h
Correct answer: $$60$$ km/h
$$120$$ km/h
$$240$$ km/h
Q5.
This graph shows the charges of a taxi firm in $$£$$ for every mile ($$m$$) travelled. Which of these statements are accurate about the rate of change for this taxi firm's charges?
An image in a quiz
Cost changes by $$£2$$
Correct answer: The rate of change of the cost is $$£2$$ per mile.
Journeys cost $$£2$$ per mile.
Correct answer: Every extra mile travelled adds $$£2$$ to the cost.
Q6.
How much faster is this vehicle travelling in the first hour of its journey versus the sixth hour?
An image in a quiz
$$60$$ km/h
Correct answer: $$50$$ km/h
$$40$$ km/h
$$10$$ km/h
$$110$$ km/h