Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
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+80 XP
What you need:
IWB/Projector/Large Screen

Using a Letter or Word for the Unknown

You'll learn to use a letter to stand for a missing number in a number sentence, then find its value by keeping both sides of the balance equal. You'll check your answer by putting the number back in and reading the sentence.

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    1 - Getting Started ~4 mins

    Illustration for Getting Started

    Key point

    Here is a puzzle on a balance: a + 3 = 10. The letter a is hiding a number. Both pans have to weigh the same, so the beam stays level. What number do you think a is hiding?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Watch these balanced sentences on the scales. In each one a letter is standing in for a missing number. See how the letter is just a name for the number that keeps both pans level.

    In the next one the total is on the left — the balancing job is still the same.

    In the last one the same letter appears twice. That means two of the same hidden number added together.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~9 mins

    Key point

    Each time we say the value of the letter aloud. Then we read the whole sentence back with the number in place of the letter to check both sides match.

    Let us find the value of the letter together. First we work e + 4 = 9 on the balance, sliding the letter block until the beam is level. Then we work three more the same way at the board: g − 3 = 8, then 7 + h = 16, then 13 = k + 5.

    Find the value of the letter

    +15 XP

    4 - Find the Letters in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, find the value of the letter in each of these, then write the full sentence with the number in place of the letter:

    • a + 5 = 12
    • n − 4 = 6
    • 9 = m + 2

    Read each finished sentence back to yourself to check both sides match.

    +10 XP

    5 - Class Challenge ~8 mins

    Now we work through these together at the board, sliding the letter block until both pans balance. First is a + 4 = 13. Then b + 4 = 18. Then c + 7 = 6 + 8. Last is d + d = 14.

    Tip

    The last two are the ones to slow down for. For c + 7 = 6 + 8, work out the right pan first — 6 + 8 = 14 — then find c to match it. For d + d = 14, the same letter appears twice, so it means two of the same hidden number added together — each d must be the same.

    Find the value of the letter

    +15 XP
    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Algebra
    Lesson 122 · Using a Letter or Word for the Unknown
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