Angles in triangles (age 12+)

CONCEPTUAL

Mathematics›Geometry|Ages 12—14|ID: mt_167X6Ax8P7

Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

Mastery Evidence

State which congruence criterion (SSS, SAS, ASA, or RHS) applies to a given pair of triangles
Use the notation △ABC ≅ △DEF and match corresponding sides and angles
Determine whether given measurements produce a unique triangle, more than one, or none

Assessment Prompt

“If [child] is shown two triangles where all three sides of one match all three sides of the other, can they explain why those triangles must be identical in shape and size?”

Curriculum Standards2 alignments

8.G.2Common Core State Standards for Mathematics

Congruence via rigid motions

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

KS3.Maths.Geo.6The national curriculum in England

Labelling Conventions and Triangle Congruence

use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

Mathematics · Key Stage 3

Prerequisites2

Measuring angles (age 11+)
hardAges 11—13
Types of angles (age 11+)
hardAges 11—13

Show full prerequisite tree

Measuring angles (age 11+) hard
Determining congruence requires constructing triangles from given conditions
- Measuring angles hard
  KS3 drawing/measuring extends KS2 protractor and ruler skills
  - Types of angles (age 8+) hard
    Measuring and drawing angles with a protractor requires knowing how to mark and label angles using standard notation
  - Degrees and turns hard
    Using a protractor requires understanding degree measurement
    - 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
        
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
      - 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
        
        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
        
        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)
        
        Positional Language hard
        Describing movement and turns builds on positional language
- 2-D shapes (age 10+) hard
  Drawing figures with given dimensions extends KS2 drawing 2D shapes accurately
  - Measuring angles hard
    Drawing shapes with given angles requires protractor skills from Y5
    - Types of angles (age 8+) hard
      Measuring and drawing angles with a protractor requires knowing how to mark and label angles using standard notation
    - Degrees and turns hard
      Using a protractor requires understanding degree measurement
      - 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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        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
        
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
  - Regular and irregular polygons soft
    Drawing regular/irregular polygons benefits from property knowledge
    - 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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
Types of angles (age 11+) hard
Triangle congruence criteria require standard labelling conventions
- Regular and irregular polygons hard
  Describing regular polygons requires knowing the distinction from KS2
  - 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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        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
        
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
- Classifying shapes by properties hard
  KS3 geometric notation builds on KS2 shape classification and property language
  - Regular and irregular polygons hard
    Hierarchy includes regular/irregular distinction from Y5
    - 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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        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
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
  - Classifying shapes by line properties hard
    Property-based hierarchy extends Y5 classification by parallel/perpendicular lines
    - Lines, Rays & Angles hard
      Must draw/identify geometric elements before classifying shapes by them
      - 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
        
        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
        
        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
        
        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
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Positional Language soft
        Horizontal/vertical builds on positional vocabulary
    - Understanding angles (age 8+) hard
      Y4 quadrilateral classification supports classifying by lines/angles
      - 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

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