2
Sorting shapes by rules
Discover Mathematics P2: Term 1, Lessons 41–50
GoalSort plane shapes by rules about sides, vertices and equal sides.
New words
rule · a sentence that tells which shapes belong in a groupattribute · something that describes a shape, like its number of sidesequal sides · sides that are the same lengthcurved · round, not straight
Explanation
We can sort shapes by a rule. A rule uses an attribute, such as the number of sides or vertices. Read the rule, then check each shape one by one. The square and the rhombus have 4 sides that are all the same length. The rectangle has 4 sides, but only the opposite sides are the same length. The circle and the oval have no straight sides and no vertices at all.
| Rule | Shapes that fit |
|---|---|
| 3 sides | triangle |
| 4 sides and 4 vertices | square, rectangle, trapezoid, rhombus |
| more than 5 vertices | hexagon |
| 4 equal sides | square, rhombus |
| no straight sides | circle, oval |
Worked examples
Rule: 4 sides and 4 vertices. Check each shape. A is a triangle (3), B is a rectangle (4), C is a hexagon (6), D is a rhombus (4). B and D fit the rule.
Rule: no straight sides. The circle (A) and the oval (C) fit. The square (B) has straight sides, so it does not fit.
Rule: more than 5 vertices. The pentagon (A) has exactly 5, so it does not fit. The hexagon (B) has 6, so it fits. The triangle (C) has only 3.
Class activity
Sorting game with paper shapes. The grown-up cuts out about 8 shapes from paper: triangles, squares, rectangles, a pentagon, a hexagon and a circle. Make two bowls. The grown-up says a secret rule, such as ‘4 vertices’ and puts the first few shapes in the bowls. The child guesses the rule and sorts the rest. Swap roles and try a new rule.
Practice
1
Which shape has exactly 3 sides?
B, the triangle.
2
Rule: 4 equal sides. Which shapes fit?
A and C (the square and the rhombus). The rectangle has two long and two short sides.
3
Which rule fits the pentagon and the hexagon but not the square: ‘more than 4 sides’ or ‘4 vertices’?
‘More than 4 sides’.
4
Hana sorts shapes with no vertices. She picks the circle and the square. Which one is wrong?
The square. It has 4 vertices.
5
How many of these shapes have 4 vertices?
2: B (square) and D (trapezoid).