Estimating journeys from non-linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

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

underestimate

overestimate ✓

miscalculation

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

$5$ metres

$16$ metres

$5\times16=80$ metres

${1\over2}\times5\times16=40$ metres ✓

${1\over2}\times5\times20=50$ metres
Which of the below is the formula for the area of a trapezium?

$A=b\times{h}$

$A={1\over2}\times{b}\times{h}$

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

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

$A={1\over2}\times({b}+{h})\times{h}$
How far has the particle modelled in this graph travelled after $5$ seconds? ______ metres.

'70' ✓
How far has the particle modelled in this graph travelled after $5$ seconds? ______ metres.

'55' ✓
How far has the particle modelled in this graph travelled after $5$ seconds? ______ metres.

'63' ✓

Exit quiz

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.

a large number

a small number

a calculation

an overestimate

an underestimate ✓
$Use the polygon mapped onto this graph to estimate the distance travelled by the vehicle. Distance <Math>\approx</Math> ______ metres.$

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

'76' ✓
The area of the polygon will estimate the distance travelled by the vehicle modelled in this graph but this will be __________.

an overestimate

an underestimate ✓

exact
Which of these groups of polygons will give us the best estimate for the distance modelled by this curve?
$Use these polygons to estimate the total distance travelled by the particle modelled by this curve. Distance <Math>\approx</Math> ______ metres.$

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

'51' ✓
$Use these polygons to estimate the total distance travelled by the particle modelled by this curve. Distance <Math>\approx</Math> ______ metres.$

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

'48' ✓

Worksheet

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Lesson Details

Key learning points

For non-linear graphs, this can be estimated by considering a trapezium.
The more trapezia used, the better the estimate.

Common misconception

When students find an area they are used to communicating the answer in units $^2$ . The area under a speed-time graph tells us the distance travelled though.

On the graph the base is time and the height is speed which is distance over time. Distance over time, multiplied by time, leaves just distance.

Keywords

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