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

Patterns and Rules Investigation

Investigate growing patterns by building each stage, spotting the rule, and using it to predict stages you haven't built yet. Discover how patterns grow in different ways.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedCount the seats around the tables on screen. One square table seats four people. Push two square tables together and more people can sit. Push three together for a longer table.

    How many seats do you think each new table adds when we join one more? Hands up with your guess.

    2 - Watch and Notice ~9 mins

    Here are three growing patterns on the number line. Look at where the markers sit, and be ready to say the jump between each pair.

    For the first two, what is the same jump happening every time — and where would the very next marker go? The last one is different: its jump does not stay the same size. To double means to make something twice as big, so 1 doubles to 2, 2 doubles to 4, 4 doubles to 8. Watch how those jumps get bigger and bigger.

    3 - Try It Together ~8 mins

    We record each stage as a marker on the line, then predict the next one. Work in order:

    • Grow by 2: 2, 4, 6, predict the next
    • Grow by 5: 5, 10, 15, predict the next
    • 1, 4, 7, predict the next
    Key point

    Before each new marker, tell us where you think it will land. Then we check.

    Where does the next marker land?

    4 - Build the Table in Your Copy ~4 mins

    COPYBOOK MOMENT

    In your maths copy, make a small table for a grow-by-3 pattern over four stages. The rule is the same jump the pattern makes every time.

    • Stage 1: 3
    • Stage 2: 6
    • Stage 3: 9
    • Stage 4: 12

    Write the rule beside it in words, then predict what stage 5 would be.

    5 - Class Challenge ~8 mins

    Key point

    Place the next marker for four growing patterns and find each rule:

    • Chairs around 1, 2, 3 tables: 4, 6, 8 — place the next
    • Dots in a growing L: 2, 4, 6 — place the next
    • Matchstick squares: 4, 7, 10 — place the next
    • Double each time: 1, 2, 4, 8 — place the next. This one's jump is not the same each time; remember it doubles, so watch it grow.

    Which one grows the fastest? Say your prediction before each check.

    Find the rule, place the next marker

    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Mixed
    Lesson 118 · Patterns and Rules Investigation
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