Mathematics
Advanced
50 mins
Teacher/Student led
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Learning Outcomes
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+80 XP
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IWB/Projector/Large Screen

Representing Situations as Equations

Learn to turn word problems into equations using letters for unknowns, solve them by undoing operations backwards, and check your answers make sense in the original story.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    Example

    Here is a number trick. "I think of a number. I double it. I add 5. I get 17." What number did I start with?

    Illustration for Getting StartedHave a think: how could we work backwards from 17 to find the number I first thought of?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~10 mins

    We turn three number stories into equations, then solve them by undoing. In each one a letter stands for the number we are hunting for, and we work backwards to set it free.

    Number stories as equations

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~8 mins

    We walk through this worked example together on the interactive first, then work two more by hand on the board:

    • I think of a number, treble it, take away 4, and get 11.

    Then, together on the board:

    • A bag of apples has 6 apples — how many bags make 30 apples?
    • Four equal rows of chairs plus 3 extra chairs make 27 chairs — how many in each row?
    Key point

    For each one, name the unknown with a letter, write the equation, then undo step by step.

    Treble a number, take away 4

    +15 XP

    4 - Write It in Your Copy ~5 mins

    COPYBOOK MOMENT

    In your maths copy, for this problem write three things: the equation, your solution steps, and one sentence saying what the answer means in the real situation.

    Work this one:

    • I think of a number, double it, add 7, and get 19.

    Finish with a sentence like "So the number I thought of was ___."

    Done early? Try this one too:

    • Some €5 notes are worth €35 altogether — how many notes?
    +10 XP

    5 - Class Challenge ~8 mins

    Today we work through these Irish-context puzzles together, in order:

    • A taxi charges €4 to start plus €2 for every kilometre. The fare comes to €16 — how many kilometres was the trip?
    • Twenty-four pupils each put in the same amount and raise €120 for a class trip — how much did each pupil give?
    • Match tickets cost €9 each plus a €3 booking fee for the whole order. The total is €30 — how many tickets were bought?
    • I think of a number, multiply it by 5, take away 2, and get 18 — what is the number?
    Stretch

    Write your own number-trick puzzle, then hand it up to swap with the class.

    Form an equation for each Irish-context situation, solve it, and say what the answer means. The four core problems rise in difficulty; the final task is to invent your own.

    1. A taxi charges €4 to start plus €2 per km. The fare is €16. How many km? (Write and solve an equation.)
    2. 24 pupils each give the same amount and raise €120 for a trip. How much each? (Write and solve an equation.)
    3. Match tickets cost €9 each plus a €3 booking fee for the whole order. The total is €30. How many tickets? (Write and solve an equation.)
    4. I think of a number, multiply it by 5, take away 2, and get 18. What number? (Write and solve an equation.)

    Ways to start:

    • Name the unknown with a letter before you write anything else.
    • Turn each part of the story into a symbol: a starting amount, a 'per each' amount, a total.

    Stretch:

    • Write your own number-trick puzzle whose equation is 5x − 2 = 18, then check it solves to a whole number.
    • Can you write a situation whose equation needs two undos AND has a money answer to the nearest cent?
    Answers & strategies (teacher)
    1. A taxi charges €4 to start plus €2 per km. The fare is €16. How many km? (Write and solve an equation.) — 2k + 4 = 16, so 2k = 12, k = 6. The trip was 6 km.
    2. 24 pupils each give the same amount and raise €120 for a trip. How much each? (Write and solve an equation.) — 24a = 120, so a = 5. Each pupil gave €5.
    3. Match tickets cost €9 each plus a €3 booking fee for the whole order. The total is €30. How many tickets? (Write and solve an equation.) — 9t + 3 = 30, so 9t = 27, t = 3. Three tickets were bought.
    4. I think of a number, multiply it by 5, take away 2, and get 18. What number? (Write and solve an equation.) — 5x − 2 = 18, so 5x = 20, x = 4. The number was 4.
    +15 XP
    Pupil practice
    Module 10 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 122 · Representing Situations as Equations
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