Mathematics
Advanced
50 mins
Teacher/Student led
+95 XP
What you need:
IWB/Projector/Large Screen

Letter-symbols: Using a Letter for an Unknown

Learn how letters hold the place of unknown numbers in equations. Use a balance to find what value makes each equation true, then solve puzzles by reasoning out the hidden number.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a puzzle: n + 3 = 7.

    The letter n is standing in for a number we cannot see yet. What number could n be, so that when you add 3 you land on 7?

    2 - Watch and Notice ~12 mins

    Each balance below shows an equation. One pan holds a letter that stands for a hidden number; the other holds a known amount, and when the beam sits level the letter has found its value. Watch the interactive work through five balances — look for where the letter's value comes from each time.

    3 - Try It Together ~11 mins

    Today we work these out together on the board, and the beam tells us when the letter is right. Remember the take-away trick from before: put the number we took off back beside the answer, so the letter's pan balances both together. We'll do:

    • n + 5 = 12
    • x − 4 = 9
    • 2y = 14 (remember, 2y means two lots of y)
    • Aoife had some sweets, got 5 more, and now has 12: s + 5 = 12

    Slide the letter until the beam sits level, then read off its value.

    Find the hidden number

    4 - Write the Letters in Your Copy ~2 mins

    COPYBOOK MOMENT

    In your maths copy, write each of the lesson's equations on its own line and put the value of the letter underneath, like this:

    • n + 3 = 7 → n = 4
    • x − 5 = 12 → x = 17
    • y + y = 8 → y = 4
    • s + 5 = 12 → s = 7

    Circle the letter on each line so you can see where the hidden number was.

    5 - Class Challenge ~8 mins

    Now the practice round. Find the hidden number for each equation.

    • n + 3 = 7
    • x − 4 = 9
    • 2y = 10
    • p + 6 = 15
    • 3m = 12 (3m means m + m + m, three lots of m)
    • 2k + 1 = 11 (the tricky one — take the 1 off first, then halve, just like we did together)

    Predict the value before you slide the letter, then use Check to confirm.

    Find the hidden number

    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 103 · Letter-symbols: Using a Letter for an Unknown
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