Estimating the gradient of a curve
I can estimate the gradient of a curved part of the graph by considering the gradient of a straight line connecting two points.
Estimating the gradient of a curve
I can estimate the gradient of a curved part of the graph by considering the gradient of a straight line connecting two points.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The gradient of a curve can be estimated.
- You can estimate by drawing a straight line between two points on the graph.
- The closer the points, the more accurate the estimate is.
Keywords
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
Pupils may estimate negative gradients incorrectly by drawing gradient triangles the wrong way round or ignoring the fact that the $$y$$ values are decreasing as $$x$$ increases.
Pupils should look at the shape of the graph between two points and decide if it is positive or negative before calculating. If $$y$$ is decreasing as $$x$$ increases then the gradient is negative.
To help you plan your year 11 maths lesson on: Estimating the gradient of a curve, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Estimating the gradient of a curve, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Real-life graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
Exit quiz
6 Questions
$$x=0 \ \text{to} \ x=1$$ -
$$4$$
$$x=1 \ \text{to} \ x=2$$ -
$$-4$$
$$x=2 \ \text{to} \ x=3$$ -
$$-6$$
$$x=3 \ \text{to} \ x=4$$ -
$$-2$$
$$x=4 \ \text{to} \ x=5$$ -
$$7$$