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Regular and irregular polygons

CONCEPTUAL
Mathematics›Geometry|Ages 9—10|ID: mt_8H2kO4k2B9

Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles

Mastery Evidence

  • Classify a set of polygons as regular or irregular
  • Explain that a regular pentagon has 5 equal sides and 5 equal angles
  • Identify that a rectangle is irregular (equal angles but not all equal sides) unless it is a square

Assessment Prompt

“If you show [child] a stop sign (regular octagon) and a wonky eight-sided shape, can they explain which is regular and which is irregular — and why?”

Prerequisites2

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  • Understanding angles (age 8+) hard

    Shape classification supports distinguishing regular from irregular

    • 2-D shapes (age 6+) hard

      Identifying 2D shape properties is prerequisite to classifying by shared attributes

      • Angles in triangles (age 6+) soft

        Understanding defining attributes supports describing shape properties formally

        • 2-D shapes hard

          Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

        • 3-D shapes (age 5+) hard

          Identifying defining attributes builds on informal analysis and comparison of shapes

          • 2-D shapes hard

            Analysing and comparing shapes requires being able to name them first

          • 3-D shapes hard

            Analysing 3-D shapes requires recognising and naming them

      • 2-D shapes hard

        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

      • 3-D shapes (age 5+) hard

        Formal property description extends informal analysis of sides and vertices

        • 2-D shapes hard

          Analysing and comparing shapes requires being able to name them first

        • 3-D shapes hard

          Analysing 3-D shapes requires recognising and naming them

    • Angles in triangles (age 7+) hard

      Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification

      • Angles in triangles (age 6+) hard

        Drawing shapes by attributes extends understanding defining vs non-defining attributes

        • 2-D shapes hard

          Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

        • 3-D shapes (age 5+) hard

          Identifying defining attributes builds on informal analysis and comparison of shapes

          • 2-D shapes hard

            Analysing and comparing shapes requires being able to name them first

          • 3-D shapes hard

            Analysing 3-D shapes requires recognising and naming them

      • 2-D shapes (age 6+) hard

        Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties

        • Angles in triangles (age 6+) soft

          Understanding defining attributes supports describing shape properties formally

          • 2-D shapes hard

            Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

          • 3-D shapes (age 5+) hard

            Identifying defining attributes builds on informal analysis and comparison of shapes

            • 2-D shapes hard

              Analysing and comparing shapes requires being able to name them first

            • 3-D shapes hard

              Analysing 3-D shapes requires recognising and naming them

        • 2-D shapes hard

          Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

        • 3-D shapes (age 5+) hard

          Formal property description extends informal analysis of sides and vertices

          • 2-D shapes hard

            Analysing and comparing shapes requires being able to name them first

          • 3-D shapes hard

            Analysing 3-D shapes requires recognising and naming them

  • Estimating Angles soft

    Classifying regular/irregular polygons benefits from angle estimation skills

    • Degrees and turns hard

      Estimating/comparing angles requires understanding the degree system

      • What Is an Angle? hard

        Degree measurement system requires understanding what an angle is

        • Types of angles hard

          Angle definition builds on understanding right angles

          • Right Angles & Turns hard

            Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse

            • Understanding angles hard

              Identifying right angles requires understanding what an angle is

              • 2-D shapes (age 6+) soft

                Understanding angles as shape properties requires knowing basic shape properties

                • Angles in triangles (age 6+) soft

                  Understanding defining attributes supports describing shape properties formally

                  • 2-D shapes hard

                    Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                  • 3-D shapes (age 5+) hard

                    Identifying defining attributes builds on informal analysis and comparison of shapes

                    • 2-D shapes hard

                      Analysing and comparing shapes requires being able to name them first

                    • 3-D shapes hard

                      Analysing 3-D shapes requires recognising and naming them

                • 2-D shapes hard

                  Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                • 3-D shapes (age 5+) hard

                  Formal property description extends informal analysis of sides and vertices

                  • 2-D shapes hard

                    Analysing and comparing shapes requires being able to name them first

                  • 3-D shapes hard

                    Analysing 3-D shapes requires recognising and naming them

              • Position, direction, and movement hard

                Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

            • Types of angles (age 8+) soft

              Identifying right angles and turns is supported by the convention of marking right angles with a small square

            • Position, direction, and movement hard

              Right angles as quarter turns extends Y2 turn vocabulary

              • Positional Language hard

                Position/direction vocabulary with right angles extends basic positional language

              • Turns & Directions hard

                Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

        • Right Angles & Turns hard

          Angle definition builds on classifying acute/obtuse angles

          • Understanding angles hard

            Identifying right angles requires understanding what an angle is

            • 2-D shapes (age 6+) soft

              Understanding angles as shape properties requires knowing basic shape properties

              • Angles in triangles (age 6+) soft

                Understanding defining attributes supports describing shape properties formally

                • 2-D shapes hard

                  Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                • 3-D shapes (age 5+) hard

                  Identifying defining attributes builds on informal analysis and comparison of shapes

                  • 2-D shapes hard

                    Analysing and comparing shapes requires being able to name them first

                  • 3-D shapes hard

                    Analysing 3-D shapes requires recognising and naming them

              • 2-D shapes hard

                Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

              • 3-D shapes (age 5+) hard

                Formal property description extends informal analysis of sides and vertices

                • 2-D shapes hard

                  Analysing and comparing shapes requires being able to name them first

                • 3-D shapes hard

                  Analysing 3-D shapes requires recognising and naming them

            • Position, direction, and movement hard

              Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

              • Positional Language hard

                Position/direction vocabulary with right angles extends basic positional language

              • Turns & Directions hard

                Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

          • Types of angles (age 8+) soft

            Identifying right angles and turns is supported by the convention of marking right angles with a small square

          • Position, direction, and movement hard

            Right angles as quarter turns extends Y2 turn vocabulary

            • Positional Language hard

              Position/direction vocabulary with right angles extends basic positional language

            • Turns & Directions hard

              Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

              • What Is a Half? soft

                Understanding half and quarter turns benefits from the concept of halves and quarters

                • Division as equal sharing hard

                  Finding a half requires equal sharing into 2 groups — a division concept

                  • Subtraction as taking away or separating hard

                    Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                    • How Many in Total? hard

                      Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                      • One-to-one counting hard

                        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

              • Positional Language hard

                Describing movement and turns builds on positional language

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