Mathematics
Intermediate
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+95 XP
Teacher-led from the board. Pupils do not need a device, but can follow on one.
What you need:
IWB/Projector/Large Screen
Multilink cubes

The Mean: A Fair, Even Share

Explore the mean as a fair, even share by levelling towers of cubes and using the add-then-share method to find the answer for small sets of numbers.

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    Manipulative task
    Worked example

    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at these four towers of cubes: one is 3 high, one is 5, one is 2, and one is 6. They belong to four friends.

    Key point

    If the four friends shared all their cubes fairly, so everyone had the same, how many would each one get?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Illustration for Watch and NoticeWatch what happens when we make the four towers the same height. We move cubes off the tall towers and put them onto the short ones, taking care not to add or lose any.

    Key point

    When every tower is level, that even height is the fair share for everyone. We call this fair share the mean.

    There is also a quicker way to reach the same answer: add all the heights together, then share the total between the towers.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~9 mins

    Key point

    We take one set at a time. For each set, build the towers first: use your own cubes, or shade the towers on your cube-tower strip. Then move cubes from the tall towers to the short ones until every tower is the same height. A pupil does the same at the board.

    • 2, 4, 6
    • 4, 4, 4, 8
    • 5, 1, 3
    • 3, 5, 2, 6

    When every tower in a set is the same height, read off that even height together. That is the fair share: the mean.

    Hands-on Task

    +15 XP

    4 - Watch the Working ~8 mins

    Example

    Here is the add-then-share method written out for the four friends' towers, so you can see each step clearly before you use it on your own.

    Mean of four cube towers

    +15 XP
    Pupil practice
    Module 9 · Data and Chance Data & Chance
    Lesson 110 · The Mean: A Fair, Even Share
    Download Activity Book page (PDF)
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