Mathematics
Advanced
50 mins
Teacher/Student led
+80 XP
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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    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 growing patterns together on the board. One pupil comes up to mark a count while the rest of the class watches and agrees or corrects out loud. The teacher re-sets the line for each new pattern.

    Example

    First the matchstick squares. The counts so far are 4, 7, 10. Find the jump, mark the next counts, and say the rule. Keep going on the line to reach step 6 without laying out six rows.

    Then a shrinking pattern starting 20, 16, 12. Find how the jump changes and mark what comes next.

    Key point

    Each time, mark the next count and say the rule out loud before we check it.

    Mark the next count

    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.

    5 - Class Challenge ~8 mins

    Now we investigate the "add 3 sticks" pattern all the way through, using the pattern record table you drew in your copy.

    1. Check your first four counts are 4, 7, 10, 13.
    2. Describe the rule in your own words: where it starts and how much it jumps.
    3. Keep adding 3 to reach step 6. How many sticks does step 6 have? You do not have to build it.
    4. Keep going in the table to step 10. Notice that each count is 3 lots of the step number, plus 1. Predict how many sticks step 10 has, and explain how the table helped you jump ahead.

    How many matchsticks does the row of squares need at each step, and what rule lets you predict a step you have not built?

    Check counts 4, 7, 10, 13 in the pattern record table; write the rule in words; keep adding 3 to reach step 6 (19); continue the table to step 10 (31) and notice the count is 3 × step number + 1; explain how the table helped.

    Record: the pattern record table (step number in one column, stick count in the other) plus a written rule and two predictions

    Share back: one group reads its rule and its prediction for step 10, and the class checks it against the table

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