Mathematics
Advanced
50 mins
Teacher/Student led
+70 XP
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Module Assessment: Pattern Hunt

Hunt for patterns around the school, identify whether each one grows or repeats, and write its rule in words clear enough for someone else to predict the next term.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at this illustration of patterns around the school, including a grid of classroom windows and a brick wall.

    Each hides a pattern. Which pattern would be easiest to describe to a friend on the phone, with no picture to help them?

    2 - Watch and Notice ~8 mins

    Illustration for Watch and NoticeHere is a pattern from around the school. We will work through two patterns, one that grows and one that repeats, writing a rule for each the way you will write yours today. As we work through each one, listen for how the rule lets you predict a term you cannot see.

    3 - Try It Together ~10 mins

    Today we work through one full pattern-hunt entry together on the board: the paving slabs outside the door.

    First we count the slabs step by step. Then we write the rule three ways. After that we decide which wording is clearest. Finally we test the best wording by predicting step 10 before anyone counts that far.

    Pattern-hunt entry: the paving slabs

    4 - Class Challenge ~12 mins

    Key point

    Find and tick one growing pattern and one repeating pattern, and write a position rule for at least one pattern (term n depends on n).

    Now you become a pattern hunter around the school. Work on your own with the checklist on your clipboard.

    For every pattern you find, write down what it is, count enough terms to be sure, and write its rule in words. There is one extra STRETCH target at the bottom of the checklist — that one is only for when you have finished the three you must find.

    1. A window grid: column 1 has 2 windows, column 2 has 4, column 3 has 6. What type of pattern, and what is the rule in words?
    2. A fence: tall, short, tall, short, repeating. What type of pattern, and how would a friend know if railing 9 is tall or short?
    3. Paving slabs: step 1 = 3 slabs, step 2 = 6, step 3 = 9. Write a position rule and use it to predict step 7.
    4. A brick row adds 12 bricks each time and the first row has 12. STRETCH: how many bricks in row 5?

    Ways to start:

    • Start by counting — write the first three or four terms before you guess any rule.
    • Decide first: does this pattern grow, or does it repeat?

    Stretch:

    • Design your own pattern from ONE shape and ONE rule, then swap it with the class and see if they can predict your next term.
    • Find a pattern where two rules act at once and describe both.

    Record: clipboard checklist: for each target, a box for a quick sketch, the counts, the pattern type, and one line for the rule in words

    Answers & strategies (teacher)
    1. A window grid: column 1 has 2 windows, column 2 has 4, column 3 has 6. What type of pattern, and what is the rule in words? — Growing pattern. Rule: column n has 2 × n windows (add 2 each column). Column 4 would have 8.
    2. A fence: tall, short, tall, short, repeating. What type of pattern, and how would a friend know if railing 9 is tall or short? — Repeating pattern, group of 2 (tall-short). Odd railings are tall, so railing 9 is tall.
    3. Paving slabs: step 1 = 3 slabs, step 2 = 6, step 3 = 9. Write a position rule and use it to predict step 7. — Rule: step n has 3 × n slabs. Step 7 = 3 × 7 = 21 slabs.
    4. A brick row adds 12 bricks each time and the first row has 12. STRETCH: how many bricks in row 5? — Growing pattern, add 12 each row (or row n has 12 × n bricks). Row 5 = 60 bricks.

    5 - Design Your Own Pattern ~8 mins

    Key point

    To finish your hunt, invent a brand-new pattern that nobody has seen. Choose one shape and one rule, then draw the first four terms in your maths journal on squared paper.

    Underneath, write the rule in words so clearly that a classmate could draw your fifth term without asking you a single question. Then note which pattern you met today was the hardest to put into words, and say why.

    Design your own pattern from one shape and one rule; draw the first four terms; write the rule in words a classmate could follow; then note which pattern was hardest to describe and why.

    Record: drawing on squared paper plus one rule sentence and one reflection sentence in the maths journal

    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 119 · Module Assessment: Pattern Hunt
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