Coordinate Transformations

PROCEDURAL

Mathematics›Geometry|Ages 11—14|ID: mt_K0Y15w48SY

Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

Mastery Evidence

Reflect a shape in a given mirror line (including diagonal lines) and state the coordinates of the image
Rotate a shape about a given centre by 90° or 180° and describe the result
Translate a shape by a given vector and verify that lengths and angles are preserved

Assessment Prompt

“If [child] is asked to rotate a triangle 90° clockwise around a fixed point, can they work out where each corner ends up — and confirm the triangle is still the same size and shape?”

Curriculum Standards5 alignments

8.G.1aCommon Core State Standards for Mathematics

Properties of transformations: Lines

Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length.

8.G.1bCommon Core State Standards for Mathematics

Properties of transformations: Angles

Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure.

8.G.1cCommon Core State Standards for Mathematics

Properties of transformations: Parallel lines

Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.

8.G.3Common Core State Standards for Mathematics

Coordinates and transformations

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

KS3.Maths.Geo.8The national curriculum in England

Transformations

identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Mathematics · Key Stage 3

Prerequisites2

Coordinates (age 11+)
hardAges 11—12
Translating and reflecting shapes
hardAges 10—11

Show full prerequisite tree

Coordinates (age 11+) hard
Transformations on coordinate grids require confident four-quadrant coordinate work
- Coordinates (age 8+) hard
  Plotting in all four quadrants extends first-quadrant coordinate grid plotting skills
  - 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
- Coordinates (age 10+) hard
  KS3 coordinates work extends KS2 four-quadrant coordinate skills
  - 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
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
  - 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
        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
        
        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
        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
        
        Positional Language soft
        Horizontal/vertical builds on positional vocabulary
- Fractions on a number line (age 11+) hard
  Plotting coordinates in all four quadrants requires understanding positive and negative values on both axes
  - Positive and Negative Numbers hard
    Ordering all number types (integers, decimals, fractions) on a number line extends the negative-number number-line representation
    - Measuring temperature hard
      Negative number arithmetic extends Y6 using negative numbers in context
      - 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
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
        
        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'
        
        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
        General two-digit place value extends from understanding teen number composition
  - Fractions on a number line hard
    Ordering all number types requires understanding place value across the full system
    - Reading and writing numbers to 10,000,000 hard
      Extending place value to any size builds directly on Y6 reading/writing/ordering numbers to 10,000,000
      - Place Value × 10 and ÷ 10 soft
        ×10 relationship supports understanding of larger numbers
        
        Tenths (age 9+) soft
        Understanding 1/10 of requires familiarity with thousandths
        
        Decimals for Tenths & Hundredths hard
        Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
        
        Converting tenths to hundredths hard
        10ths as 100ths supports using decimal notation for both
        
        Tenths (age 8+) hard
        Understanding hundredths is prerequisite to working with 10ths and 100ths together
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Equivalent fractions (age 9+) hard
        Generating equivalent fractions supports converting 10ths to 100ths
        
        Equivalent fractions on a number line hard
        Understanding equivalence conceptually is prerequisite to explaining algebraically
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Equivalent fractions (age 8+) hard
        Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
        
        Equivalent fractions on a number line hard
        Must understand equivalence before generating equivalent fractions
        
        Decimal equivalents of tenths and hundredths hard
        Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
        
        Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
        
        Decimal & Percent Notation hard
        Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
        
        Place Value × 10 Pattern hard
        ×10 both directions extends Y5 ×10 relationship
        
        Place value of each digit hard
        Four-digit place value is prerequisite to understanding ×10 relationship between places
        
        The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires 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'
        
        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
        General two-digit place value extends from understanding teen number composition
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
      - Reading and writing numbers (age 9+) hard
        Numbers to 10M extends Y5 numbers to 1M
        
        Comparing Large Numbers hard
        Comparing beyond 1000 is prerequisite to comparing up to 1,000,000
        
        Ordering Numbers to 1000 hard
        Comparing beyond 1000 extends comparing to 1000
        
        The three digits of a three-digit number hard
        Comparing three-digit numbers requires three-digit place value
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires 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'
        
        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
        General two-digit place value extends from understanding teen number composition
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Comparing and ordering numbers hard
        Comparing to 1000 extends comparing two-digit numbers
        
        The two digits of a two-digit number hard
        Comparing two-digit numbers using PV requires understanding tens and ones
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Two written numerals between 1 and 10 soft
        Comparing two-digit numbers extends from comparing single-digit written numerals
        
        Comparing groups: more or fewer soft
        Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required
        
        Counting objects to 20 soft
        Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
        
        Place value of each digit hard
        Comparing four-digit numbers requires four-digit PV
        
        The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires 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'
        
        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
        General two-digit place value extends from understanding teen number composition
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Numbers to 10,000 hard
        Ordering and comparing numbers over 1000 requires the full 10,000 representations toolkit
        
        Representing Numbers hard
        Representing to 10,000 extends representing to 1000
        
        The three digits of a three-digit number hard
        Representing numbers requires place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        Representing numbers with objects hard
        Representing and estimating numbers on a number line builds on Y1 number representations
        
        How Many in Total? hard
        Representing numbers with objects/pictures/number line requires understanding that 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'
        
        The two digits of a two-digit number soft
        Estimating placement on a 0-100 number line benefits from place value understanding
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Place value of each digit hard
        Representing four-digit numbers requires knowing their place value
        
        The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        Place Value × 10 Pattern hard
        Understanding ×10 place-value relationship supports reading/writing larger numbers
        
        Place value of each digit hard
        Four-digit place value is prerequisite to understanding ×10 relationship between places
        
        The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires 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'
        
        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
        General two-digit place value extends from understanding teen number composition
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
  - Measuring temperature hard
    Ordering with inequality symbols extends Y6 work with negative numbers in context
    - 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
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
Translating and reflecting shapes hard
KS3 transformations extend KS2 translation and reflection on coordinate plane
- Transformations on a Grid hard
  Coordinate-plane translations/reflections extend Y5 informal transformations
  - 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
- Coordinates (age 10+) hard
  Transformations on coordinate plane require four-quadrant coordinates
  - 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
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
  - 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
        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
        
        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
        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
        
        Positional Language soft
        Horizontal/vertical builds on positional vocabulary
- Transformations on a grid hard
  Drawing and describing translations and reflections on coordinate planes is the direct application of transformation diagram skills

Unlocks1

Coordinates (age 12+)
hardAges 12—14