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50 mins
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Algebra Problem-solving and End-of-year Review

Pull together three algebra ideas from the year—generalising patterns, writing expressions, and solving equations—to crack a multi-stage challenge and reflect on which concept you trust most.

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    1 - Getting Started ~4 mins

    Key point

    Here is a pattern that grows: 4, 7, 10, 13 … What would the 100th number be? And is there a way to know without writing out all one hundred of them?

    Illustration for Getting StartedYou are not expected to know this yet. By the end of today you will be able to answer it. This is the last algebra lesson of primary school, so today we pull together three big ideas from the year: patterns, expressions and equations.

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~8 mins

    Two function machines are on screen. Together we will work out what the forwards machine does to each position in the pattern 4, 7, 10, 13, then how the backwards machine finds a position from a known value. Watch each step of the working.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~10 mins

    Today we work through one full challenge together. We take it one stage at a time. First we look at the pattern 5, 9, 13, 17. Then we say its rule in words. Then we write it as an expression. Finally we set up an equation to find which position gives 61.

    Find the rule for 5, 9, 13, 17

    +10 XP

    4 - Work the Stages in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, work the sample challenge through its stages and label each one as you go:

    • Table: positions 1, 2, 3, 4 with their values
    • Rule: in words
    • Expression: using n
    • Equation: to reach 61
    • Solution: the value of n

    Then check your solution by putting it back into the rule.

    +10 XP

    5 - Class Challenge ~8 mins

    Key point

    A five-stage algebra mystery. Solve each stage to unlock the next:

    • Find the step in the pattern 3, 5, 7, 9.
    • Write its rule as an expression.
    • Substitute to find the 10th term.
    • Solve a one-step equation.
    • Solve a two-step equation to reveal the mystery number.
    1. Stage 1: the pattern is 3, 5, 7, 9. What is the step from one term to the next?
    2. Stage 2: the pattern starts at 3 and steps up by 2. Write the rule as an expression using n.
    3. Stage 3: use the expression to find the 10th term.
    4. Stage 4: solve the one-step equation 2n = 20 to find n.
    5. Stage 5: solve the two-step equation 2n + 1 = 41 to reveal the mystery number.
    Answers & strategies (teacher)
    1. Stage 1: the pattern is 3, 5, 7, 9. What is the step from one term to the next? — 2
    2. Stage 2: the pattern starts at 3 and steps up by 2. Write the rule as an expression using n. — 2n + 1
    3. Stage 3: use the expression to find the 10th term. — 21 (because 2 × 10 + 1 = 21)
    4. Stage 4: solve the one-step equation 2n = 20 to find n. — n = 10
    5. Stage 5: solve the two-step equation 2n + 1 = 41 to reveal the mystery number. — n = 20 (take away 1 to get 2n = 40, then share by 2 to get n = 20)
    +15 XP
    Pupil practice
    Module 10 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 123 · Algebra Problem-solving and End-of-year Review
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