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Numbers on a number line

CONCEPTUAL
Mathematics›Geometry|Ages 10—11|ID: mt_oDlduFnemk

Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin

Mastery Evidence

  • Identify the x-axis, y-axis, and origin on a coordinate grid
  • Explain that (3, 5) means go 3 along the x-axis and 5 up the y-axis
  • Distinguish (2, 4) from (4, 2) by explaining each coordinate's meaning

Assessment Prompt

“If [child] looks at a map with a grid and you describe a location as "3 across and 5 up from the origin", can they find the exact point — and explain what each of the two numbers tells you?”

Curriculum Standards1 alignment

5.G.1Common Core State Standards for Mathematics
Coordinate System

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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Prerequisites1

Show full prerequisite tree
  • 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

            • 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

        • 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

    • 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

            • 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

        • 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

      • Positional Language soft

        Horizontal/vertical builds on positional vocabulary

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