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SavannahYear 8
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MathsYear 9 Maths: standard form, modelling and Pythagoras30 min★★★ difficulty

Scatter graphs and correlation

Do taller people have bigger feet? Does revision time affect test scores? A scatter graph puts two measurements side by side and lets the pattern, if there is one, show itself.

Lesson overview

What you'll learn in this lesson

Describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs

Key learning points

  • • Building the graph
  • • Describing what you see
  • • Line of best fit and prediction
  • • Correlation is not cause

This lesson at a glance

  • 30 minutes
  • 18 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

simplemathematicalrelationshipsvariablesobservational

Scroll down — the lesson carries on below

Part 1 of 18 · Discover6%
1

Watch & discover

Part 1 of 18

Watch first

Scatter graphs and correlation

An English teaching video on this topic from Cognito. Watch it, then scroll down for the lesson.

In a nutshell

Describe simple mathematical relationships between two variables in observational and experimental contexts and illustrate using scatter graphs

2

What you already know

Part 2 of 18

Before we start

What you already know

You should already be able to plot coordinates and read the gradient of a straight line.

Recap: Straight-line graphs and what they mean
3

Key words

Part 3 of 18

Key words

Words you'll need today

Correlation
A pattern in how two variables change together.
Line of best fit
A straight line drawn through the middle of the pattern.
Outlier
A point that sits far away from the pattern.
Bivariate data
Data with two measurements for each item.
4

Learning cycle

Part 4 of 18

Learning cycle 1 of 2

Plotting and describing

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 18

Learn

Building the graph

Each item gives one point: the two measurements are its coordinates. Choose scales that spread the points across the grid, and label both axes with units. A scatter graph is never joined up dot-to-dot, because the points are separate observations rather than stages in one process. The shape of the cloud is the information.

6

Explore the idea

Part 6 of 18

Learn

Describing what you see

Correlation is described by direction and strength. Positive correlation means both rise together; negative means one rises as the other falls; no correlation means the points look scattered. Strength is about how tightly the points cluster around a line. Always describe correlation in the words of the context: 'as revision time increases, test score tends to increase'.

7

Quick check

Part 7 of 18

Quick check

As one variable increases the other decreases. This is...

8

Reset break

Part 8 of 18

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
9

Quick check

Part 9 of 18

Quick check

A line of best fit should...

10

Learning cycle

Part 10 of 18

Learning cycle 2 of 2

Best fit, prediction and caution

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 18

Learn

Line of best fit and prediction

A line of best fit follows the trend with roughly as many points above as below. It lets you estimate a missing value: read up from the x value and across to the y axis. Predicting inside the range of the data is called interpolation and is usually reasonable. Predicting well beyond the data is extrapolation, and it can be badly wrong because the pattern may not continue.

12

Explore the idea

Part 12 of 18

Learn

Correlation is not cause

Ice cream sales and swimming accidents rise together, but neither causes the other; hot weather drives both. A correlation shows an association, and a cause can only be argued from a controlled experiment or a clear mechanism. Outliers deserve attention too: an unusual point may be a recording error, or it may be the most interesting item in the data set.

13

Quick check

Part 13 of 18

Quick check

Predicting far outside the data range is called...

14

Quick check

Part 14 of 18

Quick check

A point far from the pattern is called...

15

Common mix-ups

Part 15 of 18

Common mix-ups

Things people often get wrong

  • People often join scatter points with straight segments. Points stay separate; only a single line of best fit is drawn.
  • People often say a correlation proves a cause. It shows a link, and a third factor is often responsible.
16

Challenge round

Part 16 of 18

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Mastery quiz

Part 17 of 18

Marked quiz

End of lesson quiz: Scatter graphs and correlation

6 questions, marked with the reasoning shown. No timer.

  1. 1. Each point on a scatter graph represents...

  2. 2. Height and shoe size rising together shows...

  3. 3. A tight cluster around the line means the correlation is...

  4. 4. Ice cream sales and sunburn cases correlate because...

  5. 5. Reading a value inside the plotted range is...

  6. 6. Scatter graph axes should always...

18

Lesson round-up

Part 18 of 18

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 18 · Watch & discover

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