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Coordinates (age 10+)

PROCEDURAL
Mathematics›Geometry|Ages 10—11|ID: mt_R4AY0LKxfl

Describe positions on the full coordinate grid (all four quadrants); use coordinates with negative values

Mastery Evidence

  • Plot points with negative coordinates such as (−3, 4) and (2, −5) on a four-quadrant grid
  • Identify the quadrant in which a given point lies
  • Describe the position of a shape using coordinates in all four quadrants

Assessment Prompt

“If [child] is playing a game where ships can be at negative coordinates too, can they correctly plot and read positions like (−3, 2) or (1, −4) on a grid?”

Prerequisites4

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  • Coordinates (age 8+) hard

    Working across the full coordinate grid requires first-quadrant plotting as a foundation

    • 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

  • Measuring temperature hard

    Negative coordinates require understanding of negative numbers

    • Negative numbers in context hard

      Calculating intervals across zero extends Y5 negative number context

      • Negative Numbers hard

        Counting through zero is prerequisite to interpreting negative numbers in context

        • Counting Within 1,000 hard

          Counting backwards through zero extends counting backwards within 1000

          • Counting in 2s hard

            Counting to 1000 by 5s/10s/100s extends skip counting from Year 2

          • The multiples of 100 soft

            Understanding multiples of 100 supports skip counting by 100s

            • A Hundred Is Ten Tens hard

              Multiples of 100 require understanding 100 as a unit

              • A Ten Is Ten Ones hard

                100 as ten tens extends understanding of 10 as ten ones

                • The teen numbers hard

                  Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'

                  • How Many in Total? hard

                    Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

                    • 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'

                  • Reading and writing numbers to 20 hard

                    Composing/decomposing teen numbers requires reading and writing those numerals

                    • How Many in Total? hard

                      Reading/writing numerals 0–20 requires understanding that numerals 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'

                    • Writing digits 0-9 hard

                      Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

              • The two digits of a two-digit number hard

                Must understand two-digit place value before extending to hundreds

                • A Ten Is Ten Ones hard

                  Understanding tens and ones place value requires the concept of 10 as a bundle

                  • The teen numbers hard

                    Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'

                    • How Many in Total? hard

                      Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

                      • 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'

                    • Reading and writing numbers to 20 hard

                      Composing/decomposing teen numbers requires reading and writing those numerals

                      • How Many in Total? hard

                        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)

                      • Writing digits 0-9 hard

                        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

                • The teen numbers hard

                  General two-digit place value extends from understanding teen number composition

                  • How Many in Total? hard

                    Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

                    • 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'

                  • Reading and writing numbers to 20 hard

                    Composing/decomposing teen numbers requires reading and writing those numerals

                    • How Many in Total? hard

                      Reading/writing numerals 0–20 requires understanding that numerals 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'

                    • Writing digits 0-9 hard

                      Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

  • Transformations on a grid soft

    Working with the full coordinate grid (all four quadrants) extends the transformation diagram to negative coordinates

  • Plotting points in the first quadrant hard

    Four-quadrant coordinates extend first-quadrant plotting

    • Numbers on a number line hard

      Plotting points requires understanding the coordinate system

      • Lines, Rays & Angles hard

        Coordinate system builds on understanding perpendicular lines

        • Types of angles hard

          Y4 acute/obtuse angle identification is prerequisite to drawing and labelling angle types

          • 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

        • Parallel and perpendicular lines hard

          Y3 horizontal/vertical/perpendicular/parallel lines is prerequisite to drawing and identifying them formally

          • Right Angles & Turns hard

            Perpendicular lines require understanding right 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

            • 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

          • Positional Language soft

            Horizontal/vertical builds on positional vocabulary

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