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Transformations on a Grid

PROCEDURAL
Mathematics›Geometry|Ages 9—10|ID: mt_efOeaGFyGM

Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed

Mastery Evidence

  • Reflect a triangle in a vertical mirror line on a coordinate grid and state the new coordinates
  • Translate a shape 3 units right and 2 units up and describe the movement
  • Explain that a reflected/translated shape is congruent to the original

Assessment Prompt

“If [child] slides or flips a shape on squared paper, can they describe exactly where it ends up and confirm the shape itself hasn't changed size or angles?”

Prerequisites4

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  • Lines of symmetry hard

    Completing symmetric figures supports understanding reflection

    • 2-D shapes (age 8+) hard

      Must identify lines of symmetry before completing symmetric figures

      • 2-D shapes (age 6+) hard

        Vertical line symmetry in Y2 is prerequisite to finding symmetry lines in multiple orientations

        • 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

      • Transformations on a grid hard

        Identifying lines of symmetry requires the ability to draw and interpret reflection on a grid

    • Transformations on a grid hard

      Completing a symmetric figure requires performing a reflection on a grid accurately

  • Coordinates (age 8+) hard

    Performing reflections and translations on a coordinate grid requires the ability to plot specified points

    • First Quadrant Coordinates hard

      Must read/understand coordinates before plotting points

      • Position, direction, and movement soft

        Position/direction vocabulary supports understanding coordinate grid

        • 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

    • Understanding angles (age 8+) soft

      Shape classification supports completing polygons on grid

      • 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

  • Transformations on a grid hard

    Describing and representing reflections and translations requires the grid-based transformation diagram

  • Describing Movements hard

    Y4 translations on a grid is prerequisite to formal reflection and translation

    • First Quadrant Coordinates hard

      Must understand coordinates before describing translations between positions

      • Position, direction, and movement soft

        Position/direction vocabulary supports understanding coordinate grid

        • 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

    • Transformations on a grid hard

      Describing translations on a grid requires the grid-based transformation diagram representation

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