Mathematics
Beginner
37 mins
Teacher/Student led
+80 XP
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Sorting 2D Shapes by Their Properties

Sort 2D shapes by one property at a time—such as number of sides, corners, or equal lengths. Discover that the same shape can belong to two different groups.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedLook at the shapes on the board: a triangle, a square, a rectangle, a circle and a hexagon. If I asked you to put just the shapes with four corners into one group, which ones would you choose?

    Hands up and tell me one shape that goes in, and one that stays out.

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    A square

    Watch as I check this square. I'll show its sides, then its corners. A square has four sides and four corners, and every side is the same length.

    A rectangle

    Now the rectangle. It also has four sides and four corners, but two sides are long and two are short, so not all its sides are the same length.

    A triangle

    The triangle has three sides and three corners. It would not go in our 'four corners' group.

    A circle

    The circle has no straight sides and no corners at all. Its edge is one smooth curve, so it is left out of any group about sides or corners.

    3 - Try It Together ~8 mins

    Now we sort together. I will name one sorting rule each time. A pupil comes to the board and taps a shape to reveal how many sides and corners it has. Everyone at your desks says yes or no out loud before we decide which group it belongs to.

    Our rules

    Our rules will be: shapes with three sides, then shapes with four corners, then shapes with all sides the same length.

    Check the property, then decide the group

    4 - Sort Into Two Boxes in Your Copy ~2 mins

    COPYBOOK MOMENT

    In your maths copy, draw two boxes. Label one box "4 corners" and label the other box "not 4 corners".

    Then write or draw three shapes into each box, choosing from the shapes we have looked at today.

    5 - Class Challenge ~8 mins

    Now sort your own cut-out paper shapes at your desk. I will give you one rule at a time, and each rule gets a little harder.

    The rule today

    Our first rule is: keep the shapes that have corners. A corner is a point where two straight sides meet, so the circle, with its smooth curved edge, stays out.

    For the next rule, keep the shapes that have exactly four sides. Then keep the shapes that have four sides and all of them the same length. Finally, find the shape that has four corners and four equal sides, and explain why it is the only one left.

    Hands-on Task

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    One pupil says the square belongs in the "4 sides" group. Another says it belongs in the "all sides equal" group. Could the same shape belong to two different groups at the same time? When?

    7 - What's Next ~3 mins

    What we learned

    • We can sort the same set of shapes in different ways by choosing one property to check.
    • A sorting rule must stay the same for every shape we test.
    • One shape, like a square, can belong to two groups at once.

    Coming up

    Coming up

    Next we look more closely at triangles and four-sided shapes, and find out why every square is also a quadrilateral.

    Pupil practice
    Module 7 · 2D and 3D Shapes and Angles Data & Chance
    Lesson 72 · Sorting 2D Shapes by Their Properties
    Download Activity Book page (PDF)
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