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Mathematics overview: Stage 7

Unit | Hours | Mastery indicators | Essential knowledge | Numbers and the number system | 9 | * Use positive integer powers and associated real roots * Apply the four operations with decimal numbers * Write a quantity as a fraction or percentage of another * Use multiplicative reasoning to interpret percentage change * Add, subtract, multiply and divide with fractions and mixed numbers * Check calculations using approximation, estimation or inverse operations * Simplify and manipulate expressions by collecting like terms * Simplify and manipulate expressions by multiplying a single term over a bracket * Substitute numbers into formulae * Solve linear equations in one unknown * Understand and use lines parallel to the axes, y = x and y = -x * Calculate surface area of cubes and cuboids * Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines | * Know the first 6 cube numbers * Know the first 12 triangular numbers * Know the symbols =, ≠, <, >, ≤, ≥ * Know the order of operations including brackets * Know basic algebraic notation * Know that area of a rectangle = l × w * Know that area of a triangle = b × h ÷ 2 * Know that area of a parallelogram = b × h * Know that area of a trapezium = ((a + b) ÷ 2) × h * Know that volume of a cuboid = l × w × h * Know the meaning of faces, edges and vertices * Know the names of special triangles and quadrilaterals * Know how to work out measures of central tendency * Know how to calculate the range | Counting and comparing | 4 | | | Calculating | 9 | | | Visualising and constructing | 5 | | | Investigating properties of shapes | 6 | | | Algebraic proficiency: tinkering | 9 | | | Exploring fractions, decimals and percentages | 3 | | | Proportional reasoning | 4 | | | Pattern sniffing | 3 | | | Measuring space | 5 | | | Investigating angles | 3 | | | Calculating fractions, decimals and percentages | 12 | | | Solving equations and inequalities | 6 | | | Calculating space | 6 | | | Checking, approximating and estimating | 2 | | | Mathematical movement | 8 | | | Presentation of data | 6 | | | Measuring data | 5 | | |

Numbers and the number system | 9 hours | Key concepts | The Big Picture: Number and Place Value progression map | * use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple * use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 * recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions | | Possible learning intentions | Possible success criteria | * Solve problems involving prime numbers * Use highest common factors to solve problems * Use lowest common multiples to solve problems * Explore powers and roots * Investigate number patterns | * Recall prime numbers up to 50 * Know how to test if a number up to 150 is prime * Know the meaning of ‘highest common factor’ and ‘lowest common multiple’ * Recognise when a problem involves using the highest common factor of two numbers * Recognise when a problem involves using the lowest common multiple of two numbers * Understand the use of notation for powers * Know the meaning of the square root symbol (√) * Use a scientific calculator to calculate powers and roots * Make the connection between squares and square roots (and cubes and cube roots) * Identify the first 10 triangular numbers * Recall the first 15 square numbers * Recall the first 5 cube numbers * Use linear number patterns to solve problems | Prerequisites | Mathematical language | Pedagogical notes | * Know how to find common multiples of two given numbers * Know how to find common factors of two given numbers * Recall multiplication facts to 12 × 12 and associated division factsBring on the Maths+: Moving on up!Number and Place Value: v6 | ((Lowest) common) multiple and LCM((Highest) common) factor and HCFPower(Square and cube) rootTriangular number, Square number, Cube number, Prime numberLinear sequenceNotationIndex notation: e.g. 53 is read as ‘5 to the power of 3’ and means ‘3 lots of 5 multiplied together’Radical notation: e.g. √49 is generally read as ‘the square root of 49’ and means ‘the positive square root of 49’; 3√8 means ‘the cube root of 8’ | Pupils need to know how to use a scientific calculator to work out powers and roots.Note that while the square root symbol (√) refers to the positive square root of a number, every positive number has a negative square root too.NCETM: Departmental workshop: Index NumbersNCETM: GlossaryCommon approachesThe following definition of a prime number should be used in order to minimise confusion about 1: A prime number is a number with exactly two factors.Every classroom has a set of number classification posters on the wall | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * When using Eratosthenes sieve to identify prime numbers, why is there no need to go further than the multiples of 7? If this method was extended to test prime numbers up to 200, how far would you need to go? Convince me. * Kenny says ’20 is a square number because 102 = 20’. Explain why Kenny is wrong. Kenny is partially correct. How could he change his statement so that it is fully correct? * Always / Sometimes / Never: the lowest common multiple of two numbers is found by multiplying the two numbers together | KM: Exploring primes activities: Factors of square numbers; Mersenne primes; LCM sequence; n² and (n + 1)²; n² and n² + n; n² + 1; n! + 1; n! – 1; x2 + x +41KM: Use the method of Eratosthenes' sieve to identify prime numbers, but on a grid 6 across by 17 down instead. What do you notice?KM: Square number puzzleKM: History and Culture: Goldbach’s ConjecturesNRICH: Factors and multiplesNRICH: Powers and rootsLearning reviewwww.diagnosticquestions.com | * Many pupils believe that 1 is a prime number – a misconception which can arise if the definition is taken as ‘a number which is divisible by itself and 1’ * A common misconception is to believe that 53 = 5 × 3 = 15 * See pedagogical note about the square root symbol too |

Counting and comparing | 4 hours | Key concepts | The Big Picture: Number and Place Value progression map | * order positive and negative integers, decimals and fractions * use the symbols =, ≠, <, >, ≤, ≥ | | Possible learning intentions | Possible success criteria | * Compare numbers * Order numbers | * Place a set of negative numbers in order * Place a set of mixed positive and negative numbers in order * Identify a common denominator that can be used to order a set of fractions * Order fractions where the denominators are not multiples of each other * Order a set of numbers including a mixture of fractions, decimals and negative numbers * Use inequality symbols to compare numbers * Make correct use of the symbols = and ≠ | Prerequisites | Mathematical language | Pedagogical notes | * Understand that negative numbers are numbers less than zero * Order a set of decimals with a mixed number of decimal places (up to a maximum of three) * Order fractions where the denominators are multiples of each other * Order fractions where the numerator is greater than 1 * Know how to simplify a fraction by cancelling common factors | Positive numberNegative numberIntegerNumeratorDenominatorNotationThe ‘equals’ sign: =The ‘not equal’ sign: ≠The inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (more than or equal to) | Zero is neither positive nor negative. The set of integers includes the natural numbers {1, 2, 3, …}, zero (0) and the ‘opposite’ of the natural numbers {-1, -2, -3, …}.Pupil must use language correctly to avoid reinforcing misconceptions: for example, 0.45 should never be read as ‘zero point forty-five’; 5 > 3 should be read as ‘five is greater than 3’, not ‘5 is bigger than 3’.Ensure that pupils read information carefully and check whether the required order is smallest first or greatest first.The equals sign was designed by Robert Recorde in 1557 who also introduced the plus (+) and minus (-) symbols.NCETM: GlossaryCommon approachesTeachers use the language ‘negative number’ to avoid future confusion with calculation that can result by using ‘minus number’Every classroom has a negative number washing line on the wall | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Jenny writes down 0.400 > 0.58. Kenny writes down 0.400 < 0.58. Who do you agree with? Why? * Find a fraction which is greater than 3/5 and less than 7/8. And another. And another … * Convince me that -15 < -3 | KM: Farey SequencesKM: Decimal ordering cards 2KM: Maths to Infinity: Fractions, decimals and percentagesKM: Maths to Infinity: Directed numbersNRICH: Greater than or less than?Learning reviewwww.diagnosticquestions.com | * Some pupils may believe that 0.400 is greater than 0.58 * Pupils may believe, incorrectly, that: * A fraction with a larger denominator is a larger fraction * A fraction with a larger numerator is a larger fraction * A fraction involving larger numbers is a larger fraction * Some pupils may believe that -6 is greater than -3. For this reason ensure pupils avoid saying ‘bigger than’ |

Calculating | 9 hours | Key concepts | The Big Picture: Calculation progression map | * understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals) * apply the four operations, including formal written methods, to integers and decimals * use conventional notation for priority of operations, including brackets * recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) | | Possible learning intentions | Possible success criteria | * Apply understanding of place value * Explore written methods of calculation * Calculate with decimals * Know and apply the correct order of operations | * Use knowledge of place value to multiply with decimals * Use knowledge of place value to divide a decimal * Use knowledge of place value to divide by a decimal * Use knowledge of inverse operations when dividing with decimals * Be fluent at multiplying a three-digit or a two-digit number by a two-digit number * Be fluent when using the method of short division * Know the order of operations for the four operations * Use brackets in problem involving the order of operations * Understand and apply the fact that addition and subtraction have equal priority * Understand and apply the fact that multiplication and division have equal priority | Prerequisites | Mathematical language | Pedagogical notes | * Fluently recall multiplication facts up to 12 × 12 * Fluently apply multiplication facts when carrying out division * Know the formal written method of long multiplication * Know the formal written method of short division * Know the formal written method of long division * Convert between an improper fraction and a mixed numberBring on the Maths+: Moving on up!Calculating: v2, v3, v4, v5Fractions, decimals & percentages: v6, v7Solving problems: v2 | Improper fractionTop-heavy fractionMixed numberOperationInverseLong multiplicationShort divisionLong divisionRemainder | Establish level of understanding and ability based on expectations of pupils at primary schoolThe grid method is promoted as a method that aids numerical understanding and later progresses to multiplying algebraic statements.NCETM: Departmental workshop: Place ValueNCETM: SubtractionNCETM: Multiplication and divisionNCETM: GlossaryCommon approachesThe use of long multiplication is to be promoted as the ‘most efficient method’. Short division is promoted as the ‘most efficient method’.If any acronym is promoted to help remember the order of operations, then BIDMAS is used as the I stands for indices. | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Jenny says that 2 + 3 × 5 = 25. Kenny says that 2 + 3 × 5 = 17. Who is correct? How do you know? * Find missing digits in otherwise completed long multiplication / short division calculations * Show me a calculation that is connected to 14 × 26 = 364. And another, and another … | KM: Long multiplication templateKM: Dividing (lots)KM: Misplaced pointsKM: Maths to Infinity: Multiplying and dividingNRICH: Cinema ProblemNRICH: Funny factorisationNRICH: SkeletonNRICH: Long multiplicationLearning reviewwww.diagnosticquestions.com | * The use of BIDMAS (or BODMAS) can imply that division takes priority over multiplication, and that addition takes priority over subtraction. This can result in incorrect calculations. * Pupils may incorrectly apply place value when dividing by a decimal for example by making the answer 10 times bigger when it should be 10 times smaller. |

Visualising and constructing | 5 hours | Key concepts | The Big Picture: Properties of Shape progression map | * use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries * use the standard conventions for labelling and referring to the sides and angles of triangles * draw diagrams from written description | | Possible learning intentions | Possible success criteria | * Interpret geometrical conventions and notation * Apply geometrical conventions and notationBring on the Maths+: Moving on up!Properties of shapes: v3, v4 | * Know the meaning of faces, edges and vertices * Use notation for parallel lines * Know the meaning of ‘perpendicular’ and identify perpendicular lines * Know the meaning of ‘regular’ polygons * Identify line and rotational symmetry in polygons * Use AB notation for describing lengths * Use ∠ABC notation for describing angles * Use ruler and protractor to construct triangles from written descriptions * Use ruler and compasses to construct triangles when all three sides known | Prerequisites | Mathematical language | Pedagogical notes | * Use a ruler to measure and draw lengths to the nearest millimetre * Use a protractor to measure and draw angles to the nearest degree | Edge, Face, Vertex (Vertices)PlaneParallelPerpendicularRegular polygonRotational symmetryNotationThe line between two points A and B is ABThe angle made by points A, B and C is ∠ABCThe angle at the point A is ÂArrow notation for sets of parallel linesDash notation for sides of equal length | NCETM: Departmental workshop: ConstructionsThe equals sign was designed (by Robert Recorde in 1557) based on two equal length lines that are equidistantNCETM: GlossaryCommon approachesDynamic geometry software to be used by all students to construct and explore dynamic diagrams of perpendicular and parallel lines. | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Given SSS, how many different triangles can be constructed? Why? Repeat for ASA, SAS, SSA, AAS, AAA. * Always / Sometimes / Never: to draw a triangle you need to know the size of three angles; to draw a triangle you need to know the size of three sides. * Convince me that a hexagon can have rotational symmetry with order 2. | KM: Shape work (selected activities)NRICH: Notes on a triangleLearning reviewwww.diagnosticquestions.com | * Two line segments that do not touch are perpendicular if they would meet at right angles when extended * Pupils may believe, incorrectly, that: * perpendicular lines have to be horizontal / vertical * only straight lines can be parallel * all triangles have rotational symmetry of order 3 * all polygons are regular |

Investigating properties of shapes | 6 hours | Key concepts | The Big Picture: Properties of Shape progression map | * identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres * derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language | | Possible learning intentions | Possible success criteria | * Investigate the properties of 3D shapes * Explore quadrilaterals * Explore triangles | * Know the vocabulary of 3D shapes * Know the connection between faces, edges and vertices in 3D shapes * Visualise a 3D shape from its net * Recall the names and shapes of special triangles and quadrilaterals * Know the meaning of a diagonal of a polygon * Know the properties of the special quadrilaterals (including diagonals) * Apply the properties of triangles to solve problems * Apply the properties of quadrilaterals to solve problems | Prerequisites | Mathematical language | Pedagogical notes | * Know the names of common 3D shapes * Know the meaning of face, edge, vertex * Understand the principle of a net * Know the names of special triangles * Know the names of special quadrilaterals * Know the meaning of parallel, perpendicular * Know the notation for equal sides, parallel sides, right anglesBring on the Maths+: Moving on up!Properties of shapes: v1, v2 | Face, Edge, Vertex (Vertices)Cube, Cuboid, Prism, Cylinder, Pyramid, Cone, SphereQuadrilateralSquare, Rectangle, Parallelogram, (Isosceles) Trapezium, Kite, RhombusDelta, ArrowheadDiagonalPerpendicularParallelTriangleScalene, Right-angled, Isosceles, EquilateralNotationDash notation to represent equal lengths in shapes and geometric diagramsRight angle notation | Ensure that pupils do not use the word ‘diamond’ to describe a kite, or a square that is 45° to the horizontal. ‘Diamond’ is not the mathematical name of any shape.A cube is a special case of a cuboid and a rhombus is a special case of a parallelogramA prism must have a polygonal cross-section, and therefore a cylinder is not a prism. Similarly, a cone is not a pyramid.NCETM: Departmental workshop: 2D shapesNCETM: GlossaryCommon approachesEvery classroom has a set of triangle posters and quadrilateral posters on the wallModels of 3D shapes to be used by all students during this unit of work | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Show me an example of a trapezium. And another. And another … * Always / Sometimes / Never: The number of vertices in a 3D shape is greater than the number of edges * Which quadrilaterals are special examples of other quadrilaterals? Why? Can you create a ‘quadrilateral family tree’? * What is the same and what is different: Rhombus / Parallelogram? | KM: Euler’s formulaKM: Visualising 3D shapesKM: Dotty activities: Shapes on dotty paperKM: What's special about quadrilaterals? Constructing quadrilaterals from diagonals and summarising results.KM: Investigating polygons. Tasks one and two should be carried out with irregular polygons.NRICH: Property chartNRICH: Quadrilaterals gameLearning reviewwww.diagnosticquestions.com | * Some pupils may think that all trapezia are isosceles * Some pupils may think that a diagonal cannot be horizontal or vertical * Two line segments that do not touch are perpendicular if they would meet at right angles when extended. Therefore the diagonals of an arrowhead (delta) are perpendicular despite what some pupils may think * Some pupils may think that a square is only square if ‘horizontal’, and even that a ‘non-horizontal’ square is called a diamond * The equal angles of an isosceles triangle are not always the ‘base angles’ as some pupils may think |

Algebraic proficiency: tinkering | 9 hours | Key concepts | The Big Picture: Algebra progression map | * understand and use the concepts and vocabulary of expressions, equations, formulae and terms * use and interpret algebraic notation, including: ab in place of a × b, 3y in place of y + y + y and 3 × y, a² in place of a × a, a³ in place of a × a × a, a/b in place of a ÷ b, brackets * simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket * where appropriate, interpret simple expressions as functions with inputs and outputs * substitute numerical values into formulae and expressions * use conventional notation for priority of operations, including brackets | | Possible learning intentions | Possible success criteria | * Understand the vocabulary and notation of algebra * Manipulate algebraic expressions * Explore functions * Evaluate algebraic statements | * Know the meaning of expression, term, formula, equation, function * Know basic algebraic notation (the rules of algebra) * Use letters to represent variables * Identify like terms in an expression * Simplify an expression by collecting like terms * Know how to multiply a (positive) single term over a bracket (the distributive law) * Substitute positive numbers into expressions and formulae * Given a function, establish outputs from given inputs * Given a function, establish inputs from given outputs * Use a mapping diagram (function machine) to represent a function * Use an expression to represent a function * Use the order of operations correctly in algebraic situations | Prerequisites | Mathematical language | Pedagogical notes | * Use symbols (including letters) to represent missing numbers * Substitute numbers into worded formulae * Substitute numbers into simple algebraic formulae * Know the order of operationsBring on the Maths+: Moving on up!Algebra: v1 | AlgebraExpression, Term, Formula (formulae), Equation, Function, VariableMapping diagram, Input, OutputRepresentSubstituteEvaluateLike termsSimplify / CollectNotationSee key concepts above | Pupils will have experienced some algebraic ideas previously. Ensure that there is clarity about the distinction between representing a variable and representing an unknown.Note that each of the statements 4x, 42 and 4½ involves a different operation after the 4, and this can cause problems for some pupils when working with algebra.NCETM: AlgebraNCETM: GlossaryCommon approachesAll pupils are expected to learn about the connection between mapping diagrams and formulae (to represent functions) in preparation for future representations of functions graphically. | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Show me an example of an expression / formula / equation * Always / Sometimes / Never: 4(g+2) = 4g+8, 3(d+1) = 3d+1, a2 = 2a, ab = ba * What is wrong? * Jenny writes 2a + 3b + 5a – b = 7a + 3. Kenny writes 2a + 3b + 5a – b = 9ab. What would you write? Why? | KM: Pairs in squares. Prove the results algebraically.KM: Algebra ordering cardsKM: Spiders and snakes. See the ‘clouding the picture’ approachKM: Use number patterns to develop the multiplying out of bracketsKM: Maths to Infinity: BracketsNRICH: Your number is …NRICH: Crossed endsNRICH: Number pyramids and More number pyramidsLearning reviewwww.diagnosticquestions.com | * Some pupils may think that it is always true that a=1, b=2, c=3, etc. * A common misconception is to believe that a2 = a × 2 = a2 or 2a (which it can do on rare occasions but is not the case in general) * When working with an expression such as 5a, some pupils may think that if a=2, then 5a = 52. * Some pupils may think that 3(g+4) = 3g+4 * The convention of not writing a coefficient of 1 (i.e. ‘1x’ is written as ‘x’ may cause some confusion. In particular some pupils may think that 5h – h = 5 |

Exploring fractions, decimals and percentages | 3 hours | Key concepts | The Big Picture: Fractions, decimals and percentages progression map | * express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 * define percentage as ‘number of parts per hundred’ * express one quantity as a percentage of another | | Possible learning intentions | Possible success criteria | * Understand and use top-heavy fractions * Understand the meaning of ‘percentage’ * Explore links between fractions and percentages | * Write one quantity as a fraction of another where the fraction is less than 1 * Write one quantity as a fraction of another where the fraction is greater than 1 * Write a fraction in its lowest terms by cancelling common factors * Convert between mixed numbers and top-heavy fractions * Understand that a percentage means ‘number of parts per hundred’ * Write a percentage as a fraction * Write a quantity as a percentage of another | Prerequisites | Mathematical language | Pedagogical notes | * Understand the concept of a fraction as a proportion * Understand the concept of equivalent fractions * Understand the concept of equivalence between fractions and percentagesBring on the Maths+: Moving on up!Fractions, decimals & percentages: v1, v2 | FractionImproper fractionProper fractionVulgar fractionTop-heavy fractionPercentageProportionNotationDiagonal fraction bar / horizontal fraction bar | NRICH: Teaching fractions with understandingNCETM: Teaching fractionsNCETM: Departmental workshop: FractionsNCETM: GlossaryCommon approachesAll pupils are made aware that ‘per cent’ is derived from Latin and means ‘out of one hundred’ | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * Jenny says ‘1/10 is the same as proportion as 10% so 1/5 is the same proportion as 5%.’ What do you think? Why? * What is the same and what is different: 1/10 and 10% … 1/5 and 20%? * Show this fraction as part of a square / rectangle / number line / … | KM: Crazy cancelling, silly simplifyingNRICH: Rod fractionsLearning reviewwww.diagnosticquestions.com | * A fraction can be visualised as divisions of a shape (especially a circle) but some pupils may not recognise that these divisions must be equal in size, or that they can be divisions of any shape. * Pupils may not make the connection that a percentage is a different way of describing a proportion * Pupils may think that it is not possible to have a percentage greater than 100% |

Proportional reasoning | 4 hours | Key concepts | The Big Picture: Ratio and Proportion progression map | * use ratio notation, including reduction to simplest form * divide a given quantity into two parts in a given part:part or part:whole ratio | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Ratio and proportion: v1 | | NCETM: The Bar ModelNCETM: Multiplicative reasoningNCETM: GlossaryCommon approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * Many pupils will want to identify an additive relationship between two quantities that are in proportion and apply this to other quantities in order to find missing amounts * |

Pattern sniffing | 3 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * generate terms of a sequence from a term-to-term rule | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Number and Place Value: v5 | | NCETM: AlgebraCommon approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Measuring space | 5 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.) * use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate * change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts * measure line segments and angles in geometric figures | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Measures: v3 | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Investigating angles | 3 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles | | Possible learning intentions | Possible success criteria | * Bring on the Maths+: Moving on up!Properties of shapes: v5 | * | Prerequisites | Mathematical language | Pedagogical notes | * | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Calculating fractions, decimals and percentages | 12 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers * interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively * compare two quantities using percentages * solve problems involving percentage change, including percentage increase/decrease | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Fractions, decimals & percentages: v3, v4, v5Ratio and proportion: v2 | | NCETM: The Bar ModelNCETM: Teaching fractionsNCETM: Fractions videosCommon approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | NRICH: Would you rather?Learning reviewwww.diagnosticquestions.com | * |

Solving equations and inequalities | 6 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) * solve linear equations in one unknown algebraically | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Algebra: v2 | | NCETM: The Bar ModelNCETM: AlgebraCommon approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Calculating space | 6 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * use standard units of measure and related concepts (length, area, volume/capacity) * calculate perimeters of 2D shapes * know and apply formulae to calculate area of triangles, parallelograms, trapezia * calculate surface area of cuboids * know and apply formulae to calculate volume of cuboids * understand and use standard mathematical formulae | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Measures: v4, v5, v6 | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Checking, approximating and estimating | 2 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * estimate answers; check calculations using approximation and estimation, including answers obtained using technology * recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions) | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Mathematical movement | 8 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * work with coordinates in all four quadrants * understand and use lines parallel to the axes, y = x and y = -x * solve geometrical problems on coordinate axes * identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation * describe translations as 2D vectors | | Possible learning intentions | Possible success criteria | * Carry out transformations of shapes * | * Carry out a reflection in a diagonal mirror line (45° from horizontal) * | Prerequisites | Mathematical language | Pedagogical notes | * Carry out a reflection in a given vertical or horizontal mirror line * Carry out a translationBring on the Maths+: Moving on up!Position and direction: v1, v2 | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Presentation of data | 6 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data and know their appropriate use | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Statistics: v1, v2, v3 | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

Measuring data | 5 hours | Key concepts | The Big Picture: xxx progression map INSERT LINK | * interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range) | | Possible learning intentions | Possible success criteria | * | * | Prerequisites | Mathematical language | Pedagogical notes | * Bring on the Maths+: Moving on up!Statistics: v4 | | Common approaches | Reasoning opportunities and probing questions | Suggested activities | Possible misconceptions | * | Learning reviewwww.diagnosticquestions.com | * |

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