Mathematics
Intermediate
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+80 XP
What you need:
IWB/Projector/Large Screen

Square Numbers and Number Patterns

Explore square numbers by building area models and discover the hidden pattern in the odd-number gaps between consecutive squares.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at this square of dots on the board. Count how many dots there are along one side, then count the whole square. What do you notice — how does the number along one side connect to the total we counted?

    Key point

    We call the total a square number because it fills a perfect square exactly. Today we will build a few of them and hunt for the pattern hiding between them.

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Each square is built as an area model: dots along the bottom, dots up the side. When I ask you to predict, think it quietly and put your thumb up when you are ready. Watch what gets added each time the side grows by one.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~9 mins

    Key point

    Now we build together on the board: 7², then 8², then 9². One pupil drives the board while the rest of the class predicts each total aloud from the side length before it is built. Watch the gaps climb between each pair.

    Build the square

    +15 XP

    4 - Write the Squares in Your Copy ~4 mins

    COPYBOOK MOMENT

    In your maths copy, write each square number two ways — as 'squared' and as its product. For example: 6 squared = 6 × 6 = 36.

    Then list the first ten square numbers in a row, and underneath write the odd-number gap you notice between each one.

    +10 XP

    5 - Class Challenge ~7 mins

    Key point

    Now we work through fresh squares together, each one a step bigger: build 10², then 11², then 12², then 13². One pupil drives each build while the class predicts.

    Optional think-about-it: can you find two square numbers that add together to make another square number? Here is a way in — try combining a 9-square and a 16-square and count the total.

    Square number challenge

    +15 XP
    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 26 · Square Numbers and Number Patterns
    Download Activity Book page (PDF)
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