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

Repeating Patterns and Their Rule

Explore repeating patterns by identifying the unit that keeps coming back, then use it to predict shapes at any position without laying out every single one.

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    1 - Getting Started ~4 mins

    Look at this row of blocks: red, blue, red, blue, red, blue. Now hands up: what colour do you think the tenth block would be, without laying all ten of them out one by one? Have a think about how you could be sure.

    2 - Watch and Notice ~9 mins

    A two-shape unit

    Watch this pattern: triangle, square, triangle, square. The part that keeps coming back is triangle, square. That repeating part is called the unit, and here it is two shapes long. Notice how every second shape is a square.

    A three-shape unit

    Now watch a longer one: red, red, blue, red, red, blue, red, red, blue. The repeating unit is red, red, blue, which is three shapes long. Look hard at the blue ones, where do they keep landing?

    Skipping ahead in threes

    The blue ones land on the third shape, the sixth shape, the ninth shape, and so on. Those are the numbers we say when we count in threes. So to find the ninth shape we do not have to lay out nine blocks. We can count along in threes, three, six, nine, and land straight on blue. The unit length is the number we count in to skip ahead.

    3 - Try It Together ~11 mins

    Today we explore patterns together on the board. We will start a repeating unit, then continue it for two more full repeats, and ring the unit so everyone can see the part that keeps coming back. After each one, we'll say which shape comes next and why.

    Continue the repeating pattern

    4 - Design Your Own in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, design your own repeating pattern with a unit of three shapes. Draw two full repeats of your pattern, then underline the repeating part so anyone reading your copy can spot the unit at a glance.

    5 - Class Challenge ~8 mins

    Today we work through these patterns together, one at a time:

    1. First, a pattern that goes star, moon, star, moon. Name the sixth shape.
    2. Next, a pattern that goes red, blue, green. Name the ninth shape.
    3. Then a longer jump. A pattern that goes circle, triangle, star. We want the twentieth shape. We count along in threes, three, six, nine, twelve, fifteen, eighteen, which lands on star, then step on: nineteen is circle, twenty is triangle. So the twentieth shape is triangle.
    Tip

    The longer positions are where the unit really earns its keep, so we'll use it to skip ahead rather than count every shape.

    Name the shape at the position

    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Mixed
    Lesson 109 · Repeating Patterns and Their Rule
    Download Activity Book page (PDF)
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