Mathematics
Advanced
50 mins
Teacher/Student led
+65 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.

Teacher Class Feed

Load previous activity

    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.

    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.

    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

    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.

    • 5
    • 7
    • 3
    • 9

    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.

    1. Rainfall over three days was 4 mm, 6 mm and 8 mm. Find the mean daily rainfall.
    2. A hurler scored 3, 5, 5 and 7 points across four matches. Find his mean score.
    3. Five pupils saved €2, €3, €0, €4 and €6. Find the mean saving.
    4. 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)
    1. Rainfall over three days was 4 mm, 6 mm and 8 mm. Find the mean daily rainfall. — 6 mm
    2. A hurler scored 3, 5, 5 and 7 points across four matches. Find his mean score. — 5 points
    3. Five pupils saved €2, €3, €0, €4 and €6. Find the mean saving. — €3
    4. 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
    Pupil practice
    Module 9 · Data and Chance Mixed
    Lesson 97 · The Mean as a Measure of Centre
    Download Activity Book page (PDF)
    123learn · Online learning platform

    Unlock the full learning experience

    You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

    Hundreds of curriculum-aligned lessons
    Interactive activities in every lesson
    Printable resources & progress tracking
    Copyright Notice
    This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.
    🍪 Our website uses cookies to make your browsing experience better. By using our website you agree to our use of cookies. Learn more