Mathematics

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50 mins

Teacher/Student led

Learning Goals

Learning Outcomes

Lesson Files

+80 XP

What you need:
IWB/Projector/Large Screen
Multilink cubes

The Mean as a Measure of Centre

Learn to find the mean of a set of values by sharing them equally. Use cube towers to picture the mean as levelling, then practise with adding and dividing.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Work the Mean in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started

Key point

Here are five towers of cubes, and they are all different heights. Imagine we knocked them down and shared every cube out equally, so all five towers became the same height. Roughly how tall would each one be? Have a guess before we work it out.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

We will level three sets of cube towers until each set sits at one equal height — that height is the mean. Watch how levelling the towers and adding-then-dividing land on the very same number. For the last two sets, predict the equal height in your head before it is revealed.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Key point

At your tables, level a fresh set of cube towers so they are all the same height, then check your answer against adding-and-dividing. Today's set is 5, 7, 3, 9 cubes. Level them together, count how many cubes are in each equal tower, then work out (5 + 7 + 3 + 9) ÷ 4 to see if it matches.

Hands-on Task

+15 XP

4 - Work the Mean in Your Copy ~2 mins

COPYBOOK MOMENT

In your maths copy, write out the lesson's data set. Show the total, then divide by the number of values, and underline the mean.

+10 XP

5 - Class Challenge ~8 mins

Worked example

Two players scored a mean of 5 points across 2 games. What was their total? Multiply the mean by how many games: 5 × 2 = 10 points in total. That is the move you need for the last problem below.

Now we work through four mean problems together, each a step harder than the last:

Rainfall over three days: 4 mm, 6 mm and 8 mm. What was the mean daily rainfall?
A hurler scored 3, 5, 5 and 7 points in four matches. What was his mean score?
Five pupils saved €2, €3, €0, €4 and €6. What was the mean saving?
The tricky one: three friends have a mean of 8 sweets each. Two of them have 6 and 11. How many does the third one have?

Four mean problems in Irish contexts, rising from a plain three-value mean to a reversed missing-value stretch, after a short worked example of working backwards.

Rainfall over three days was 4 mm, 6 mm and 8 mm. Find the mean daily rainfall.
A hurler scored 3, 5, 5 and 7 points across four matches. Find his mean score.
Five pupils saved €2, €3, €0, €4 and €6. Find the mean saving.
Three friends have a mean of 8 sweets each. Two of them have 6 and 11. How many does the third friend have?

Ways to start:

Add all the values first, then decide how many there are to divide by.
Remember every value counts, even a zero.

Stretch:

For the missing-sweets problem, multiply the mean by the number of friends to get the total, then take away the values you already know.

Answers & strategies (teacher)

Rainfall over three days was 4 mm, 6 mm and 8 mm. Find the mean daily rainfall. — 6 mm
A hurler scored 3, 5, 5 and 7 points across four matches. Find his mean score. — 5 points
Five pupils saved €2, €3, €0, €4 and €6. Find the mean saving. — €3
Three friends have a mean of 8 sweets each. Two of them have 6 and 11. How many does the third friend have? — 7 sweets

+15 XP

Pupil practice

Module 9 · Data and Chance Data & Chance

Lesson 105 · The Mean as a Measure of Centre

Download Activity Book page (PDF)

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