Mathematics
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50 mins
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+85 XP
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Multilink cubes

Investigation: the Staircase Pattern

Investigate how a staircase pattern grows by examining how each size is built from the one before, then use the rule to predict cube counts for staircases you haven't constructed.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a staircase built from cubes. Look at how many cubes each size needs:

    • Size 1 → 1 cube
    • Size 2 → 3 cubes
    • Size 3 → 6 cubes
    • Size 4 → 10 cubes

    Roughly how many cubes do you think the size-5 staircase needs, before we work it out?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~8 mins

    Illustration for Watch and NoticeThe staircase grows in a special way. Let's look at the counts side by side and work out what gets added each time.

    • Size 1 → 1
    • Size 2 → 3
    • Size 3 → 6
    • Size 4 → 10
    Key pattern

    Look at the jumps between the counts. What gets added each time, and how do the jumps change? What do you think we add to a size-4 staircase to reach the next size?

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Sketch the Staircases in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, sketch staircases of size 1, 2, 3 and 4 and write the cube count underneath each one:

    • 1
    • 3
    • 6
    • 10

    Underline the pattern you see in the four counts, then write in words the rule that gives the next staircase.

    +10 XP

    4 - Try It Together ~9 mins

    Key point

    Now we extend the staircase table together on the board. We already have 1, 3, 6, 10 and 15. Predict the count for size 7, then size 8, then size 10, each time, add the next counting number and write the new total in the table before we agree on it.

    Illustration for Try It TogetherCheck size 7 with your hands: at your desk, build seven columns with cubes from the tub, then count. If your group has no cubes, sketch the seven columns on squared paper and count the squares.

    +10 XP

    5 - Class Challenge ~8 mins

    Key point

    First, predict the cube count for a staircase of size 12 using the rule, add the next counting number each time. Write out the running steps from a size you already know so size 12 is easy to reach.

    Then we play a target round. We use the staircase numbers 1, 3, 6, 10, 15 and 21 as our starter chips and combine them to hit each target.

    Hit the target from staircase numbers

    +15 XP
    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 117 · Investigation: the Staircase Pattern
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