Mathematics
Advanced
50 mins
Teacher/Student led
+80 XP
Teacher-led from the board. Pupils do not need a device, but can follow on one.
What you need:
IWB/Projector/Large Screen
Pattern blocks

Algebra Investigation, Patterns and Rules

Investigate growing patterns made from matchsticks. Record counts in a table, find the rule, and use it to predict steps you haven't built yet.

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    Number line jumps

    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a row of squares built from matchsticks. One square takes 4 sticks. Two squares side by side take 7 sticks, because the middle stick is shared. Three squares take 10.

    Key point

    How many sticks will the fourth square row need? Have a guess before we build it.

    2 - Watch and Notice ~9 mins

    Here are two growing patterns marked out along the number line. Each mark shows a count, and the gap between one mark and the next is the jump.

    Here is a second pattern. Look at how big each gap is.

    One of these grows by the same jump every time. The other grows by a jump that gets bigger. See if you can tell which is which from the gaps.

    3 - Try It Together ~9 mins

    Now we work two patterns on the same number line, one after the other. One pupil comes up to mark a count while the rest of the class watches and agrees or corrects out loud. Press Reset to clear the line before the second pattern.

    Example

    First, the counts from the matchstick-square pattern. The line starts at 4 and two jumps of 3 are already drawn, landing on 7 and 10: that is one, two and three squares. Say the rule, then tap +3 to add the next jump. Keep going to reach step 6 without laying out six rows of matchsticks.

    Then press Reset and try a shrinking pattern: 20, 16, 12. Set the start to 20, find the jump, and jump back to land on each count. What comes next?

    Continue the pattern

    4 - Build the Pattern Record Table in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, draw the first four steps of the "add 3 sticks" square pattern — one square, then two joined, then three, then four. Beside your drawing, make a pattern record table: one column for the step number and one column for the stick count. Fill in 4, 7, 10, 13. Then write the rule you found underneath.

    Pupil practice
    Module 10 · Algebra: Patterns, Rules and Number Sentences Algebra
    Lesson 127 · Algebra Investigation, Patterns and Rules
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