A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

Estimating journeys from non-linear graphs

Maths

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.

Real-life graphs

The curve models the movement of a particle. If we had scales on the axes and could find the area of the triangle it would give us __________ for the distance travelled.

Use the polygon mapped onto this graph to estimate the distance travelled by the vehicle. Distance $$\approx$$ {{}} metres.

The area of the polygon will estimate the distance travelled by the vehicle modelled in this graph but this will be __________.

Which of these groups of polygons will give us the best estimate for the distance modelled by this curve?

Use these polygons to estimate the total distance travelled by the particle modelled by this curve. Distance $$\approx$$ {{}} metres.

An ________ is an estimate for a calculation which is greater than the exact answer.

How far has the particle modelled in this graph travelled after $$5$$ seconds?

$$A={1\over2}\times({a}\times{b})\times{h}$$

Which of the below is the formula for the area of a trapezium?

How far has the particle modelled in this graph travelled after $$5$$ seconds? {{}} metres.

Estimating journeys from non-linear graphs

Lesson outcome