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

Number Patterns and Sequences: Find the Rule

Learn to find the repeating step in a number pattern, then use it to predict the next numbers without counting every single one.

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    1 - Getting Started ~4 mins

    Here are three short patterns. Look hard at each one.

    • 2, 4, 6, 8, …
    • 5, 10, 15, …
    • 20, 18, 16, …

    What number do you think comes next in each one? And here is the real question: how did you know?

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    2, 4, 6, 8

    Watch as we mark each number on the number line. Look at the size of each jump. They are all the same hop, aren't they? That equal hop is the step.

    5, 10, 15, 20

    Now a different pattern. The hops are bigger this time. What is each one worth?

    30, 40, 50, 60

    This time we start at 30 and the hops are bigger again. What is the step here?

    20, 18, 16, 14

    This last one is different. The numbers are getting smaller. Which way are the hops going now?

    3 - Try It Together ~9 mins

    On screen is our hundred square — all the numbers from 1 to 100 laid out in rows. A pattern shows up on it as a path: start at a number, count on by the step, and shade every number you land on.

    We will do four rounds. Each round, a starting number and a step are called out. One of you comes up and shades the pattern across the grid while the rest of us say each number as it is shaded. Then we agree the rule together — or fix it.

    Shade the count-on pattern

    4 - Write the Rule in Your Copy ~4 mins

    COPYBOOK MOMENT

    In your maths copy, write the first six numbers of a "count on in 4s from 0" pattern, one after the other.

    • 0
    • 4
    • 8
    • 12
    • 16
    • 20

    Then write the rule beside it in words: add 4 each time.

    5 - Class Challenge ~9 mins

    Today we work through these patterns together on the number line. Find the missing number or the next number each time, and be ready to say the rule:

    • Continue 3, 6, 9, …
    • Continue 50, 45, 40, …
    • Fill the gap: 10, ?, 20, 25
    • Continue 100, 90, 80, 70, and be ready to name the rule

    We show every answer the same way: drag the marker to that number on the 0100 line. The pattern lives in the question; the line is where we show the answer.

    Find the missing number

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    How does finding the step help you say what comes next without counting every single number?

    7 - What's Next ~2 mins

    Today we learned

    • Every number pattern is built by repeating the same step.
    • Once you spot the step, you can say what comes next without counting every number.
    • Patterns can count on (the step is added) or count back (the step is taken away).

    Coming up

    Next we look at growing patterns made from shapes, and how to predict a stage we have not even built yet.

    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Mixed
    Lesson 107 · Number Patterns and Sequences: Find the Rule
    Download Activity Book page (PDF)
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