Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+65 XP
Teacher-led from the board — pupils need no device
What you need:
IWB/Projector/Large Screen

Equality and the Balance

Use a balance beam to find the value of x that makes both pans level. Explore how the equals sign shows balance, not a signal for an answer.

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    Balance scales
    Balance scales

    1 - Getting Started ~4 mins

    Picture a balance beam with a pan on each side. On the left pan we have x + 3. On the right pan we have 7. We don't yet know what x is, so the beam might be tipping one way or the other.

    Key point

    What number would x have to be to make the two pans weigh the same and the beam sit perfectly level?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~10 mins

    Watch four balances on the board. In each one, x is set to the value that makes the beam sit level. Look at how the two pans match once x is right.

    This next one is different: the same letter appears twice on the left. Notice how the total is shared between the two copies.

    This last one is a new kind: a block of 4 is taken away on the left, and the right pan holds 9. Notice that x is bigger than the 9, because it has to cover the 4 that is taken off as well.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~8 mins

    Key point

    For each one, slide the x block until the beam sits level, then read off the value of x.

    Today we work through these together on the beam. First x + 4 = 9, then x + 6 = 15, then 3x = 12.

    Level the beam to find x

    +15 XP

    4 - Work It in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, work each find-x problem in three lines. Write the equation on the top line. On the middle line, write in words how you levelled the beam (for example, what the left pan came to, or how you shared the total between the copies of x). Write the value of x on the bottom line.

    Here is one worked out in full:

    • x + 3 = 7
    • Both pans come to 7, so the beam is level
    • x = 4

    Now work each of these the same way in your copy:

    • x + 5 = 12
    • 2x = 10
    • x + 7 = 11
    +10 XP

    5 - Class Challenge ~8 mins

    Key point

    For each one, slide the x block until the beam is level and press Check to confirm the value of x.

    Today we work through these numbers together on the beam. Start with x + 3 = 7. Then try x + 5 = 12. Next comes 2x = 10. After that, x − 4 = 9. Finish with 3x = 12.

    Find x so the beam levels

    +15 XP
    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 113 · Equality and the Balance
    Download Activity Book page (PDF)
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