Year 8 Maths

What does a child learn in Year 8 maths?

Curriculum scope

1. KS3.N (our numbering) · Teaching content · checked against the act

   Number

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number

2. KS3.N.1 (our numbering) · Teaching content · checked against the act

   understand and use place value for decimals, measures and integers of any size

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.1

3. KS3.N.2 (our numbering) · Teaching content · checked against the act

   order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.2

4. KS3.N.3 (our numbering) · Teaching content · checked against the act

   use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.3

5. KS3.N.4 (our numbering) · Teaching content · checked against the act

   use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.4

6. KS3.N.5 (our numbering) · Teaching content · checked against the act

   use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.5

7. KS3.N.6 (our numbering) · Teaching content · checked against the act

   recognise and use relationships between operations including inverse operations

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.6

8. KS3.N.7 (our numbering) · Teaching content · checked against the act

   use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

   National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.7

9. KS3.N.8 (our numbering) · Teaching content

   interpret and compare numbers in standard form A × 10ⁿ, 1 ≤ A < 10, where n is a positive or negative integer or zero

   our summary of the point · National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.8

10. KS3.N.9 (our numbering) · Teaching content

    work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)

    our summary of the point · National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.9

11. KS3.N.10 (our numbering) · Teaching content · checked against the act

    define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.10

12. KS3.N.11 (our numbering) · Teaching content · checked against the act

    interpret fractions and percentages as operators

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.11

13. KS3.N.12 (our numbering) · Teaching content · checked against the act

    use standard units of mass, length, time, money and other measures, including with decimal quantities

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.12

14. KS3.N.13 (our numbering) · Teaching content · checked against the act

    round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.13

15. KS3.N.14 (our numbering) · Teaching content · checked against the act

    use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.14

16. KS3.N.15 (our numbering) · Teaching content · checked against the act

    use a calculator and other technologies to calculate results accurately and then interpret them appropriately

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.15

17. KS3.N.16 (our numbering) · Teaching content · checked against the act

    appreciate the infinite nature of the sets of integers, real and rational numbers.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Number, statutory requirement KS3.N.16

18. KS3.A (our numbering) · Teaching content · checked against the act

    Algebra

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra

19. KS3.A.1 (our numbering) · Teaching content · checked against the act

    use and interpret algebraic notation, including:

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1

20. KS3.A.2 (our numbering) · Teaching content · checked against the act

    substitute numerical values into formulae and expressions, including scientific formulae

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.2

21. KS3.A.3 (our numbering) · Teaching content · checked against the act

    understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.3

22. KS3.A.4 (our numbering) · Teaching content · checked against the act

    simplify and manipulate algebraic expressions to maintain equivalence by:

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.4

23. KS3.A.5 (our numbering) · Teaching content · checked against the act

    understand and use standard mathematical formulae; rearrange formulae to change the subject

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.5

24. KS3.A.6 (our numbering) · Teaching content · checked against the act

    model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.6

25. KS3.A.7 (our numbering) · Teaching content · checked against the act

    use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.7

26. KS3.A.8 (our numbering) · Teaching content · checked against the act

    work with coordinates in all four quadrants

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.8

27. KS3.A.9 (our numbering) · Teaching content · checked against the act

    recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.9

28. KS3.A.10 (our numbering) · Teaching content · checked against the act

    interpret mathematical relationships both algebraically and graphically

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.10

29. KS3.A.11 (our numbering) · Teaching content · checked against the act

    reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.11

30. KS3.A.12 (our numbering) · Teaching content · checked against the act

    use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.12

31. KS3.A.13 (our numbering) · Teaching content · checked against the act

    find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.13

32. KS3.A.14 (our numbering) · Teaching content · checked against the act

    generate terms of a sequence from either a term-to-term or a position-to-term rule

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.14

33. KS3.A.15 (our numbering) · Teaching content · checked against the act

    recognise arithmetic sequences and find the nth term

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.15

34. KS3.A.16 (our numbering) · Teaching content · checked against the act

    recognise geometric sequences and appreciate other sequences that arise.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.16

35. KS3.A.1.a (our numbering) · Teaching content · checked against the act

    ab in place of a × b

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.a

36. KS3.A.4.a (our numbering) · Teaching content · checked against the act

    collecting like terms

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.4.a

37. KS3.A.1.b (our numbering) · Teaching content · checked against the act

    3y in place of y + y + y and 3 × y

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.b

38. KS3.A.4.b (our numbering) · Teaching content · checked against the act

    multiplying a single term over a bracket

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.4.b

39. KS3.A.1.c (our numbering) · Teaching content

    a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b

    our summary of the point · National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.c

40. KS3.A.4.c (our numbering) · Teaching content · checked against the act

    taking out common factors

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.4.c

41. KS3.A.1.d (our numbering) · Teaching content

    a/b in place of a ÷ b

    our summary of the point · National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.d

42. KS3.A.4.d (our numbering) · Teaching content · checked against the act

    expanding products of two or more binomials

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.4.d

43. KS3.A.1.e (our numbering) · Teaching content · checked against the act

    coefficients written as fractions rather than as decimals

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.e

44. KS3.A.1.f (our numbering) · Teaching content · checked against the act

    brackets

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Algebra, statutory requirement KS3.A.1.f

45. KS3.R (our numbering) · Teaching content · checked against the act

    Ratio, proportion and rates of change

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change

46. KS3.R.1 (our numbering) · Teaching content · checked against the act

    change freely between related standard units [for example time, length, area, volume/capacity, mass]

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.1

47. KS3.R.2 (our numbering) · Teaching content · checked against the act

    use scale factors, scale diagrams and maps

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.2

48. KS3.R.3 (our numbering) · Teaching content · checked against the act

    express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.3

49. KS3.R.4 (our numbering) · Teaching content · checked against the act

    use ratio notation, including reduction to simplest form

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.4

50. KS3.R.5 (our numbering) · Teaching content · checked against the act

    divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.5

51. KS3.R.6 (our numbering) · Teaching content · checked against the act

    understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.6

52. KS3.R.7 (our numbering) · Teaching content · checked against the act

    relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.7

53. KS3.R.8 (our numbering) · Teaching content · checked against the act

    solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.8

54. KS3.R.9 (our numbering) · Teaching content · checked against the act

    solve problems involving direct and inverse proportion, including graphical and algebraic representations

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.9

55. KS3.R.10 (our numbering) · Teaching content · checked against the act

    use compound units such as speed, unit pricing and density to solve problems.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Ratio, proportion and rates of change, statutory requirement KS3.R.10

56. KS3.GM (our numbering) · Teaching content · checked against the act

    Geometry and measures

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures

57. KS3.GM.1 (our numbering) · Teaching content · checked against the act

    derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.1

58. KS3.GM.2 (our numbering) · Teaching content · checked against the act

    calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.2

59. KS3.GM.3 (our numbering) · Teaching content · checked against the act

    draw and measure line segments and angles in geometric figures, including interpreting scale drawings

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.3

60. KS3.GM.4 (our numbering) · Teaching content · checked against the act

    derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.4

61. KS3.GM.5 (our numbering) · Teaching content · checked against the act

    describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.5

62. KS3.GM.6 (our numbering) · Teaching content · checked against the act

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

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.6

63. KS3.GM.7 (our numbering) · Teaching content · checked against the act

    derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.7

64. KS3.GM.8 (our numbering) · Teaching content · checked against the act

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

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.8

65. KS3.GM.9 (our numbering) · Teaching content · checked against the act

    identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.9

66. KS3.GM.10 (our numbering) · Teaching content · checked against the act

    apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.10

67. KS3.GM.11 (our numbering) · Teaching content · checked against the act

    understand and use the relationship between parallel lines and alternate and corresponding angles

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.11

68. KS3.GM.12 (our numbering) · Teaching content · checked against the act

    derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.12

69. KS3.GM.13 (our numbering) · Teaching content · checked against the act

    apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.13

70. KS3.GM.14 (our numbering) · Teaching content · checked against the act

    use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.14

71. KS3.GM.15 (our numbering) · Teaching content · checked against the act

    use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.15

72. KS3.GM.16 (our numbering) · Teaching content · checked against the act

    interpret mathematical relationships both algebraically and geometrically.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Geometry and measures, statutory requirement KS3.GM.16

73. KS3.P (our numbering) · Teaching content · checked against the act

    Probability

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Probability

74. KS3.P.1 (our numbering) · Teaching content · checked against the act

    record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Probability, statutory requirement KS3.P.1

75. KS3.P.2 (our numbering) · Teaching content · checked against the act

    understand that the probabilities of all possible outcomes sum to 1

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Probability, statutory requirement KS3.P.2

76. KS3.P.3 (our numbering) · Teaching content · checked against the act

    enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Probability, statutory requirement KS3.P.3

77. KS3.P.4 (our numbering) · Teaching content · checked against the act

    generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Probability, statutory requirement KS3.P.4

78. KS3.S (our numbering) · Teaching content · checked against the act

    Statistics

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Statistics

79. KS3.S.1 (our numbering) · Teaching content · checked against the act

    describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Statistics, statutory requirement KS3.S.1

80. KS3.S.2 (our numbering) · Teaching content · checked against the act

    construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Statistics, statutory requirement KS3.S.2

81. KS3.S.3 (our numbering) · Teaching content · checked against the act

    describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

    National Curriculum in England, mathematics, Key stage 3 (Years 7-9), Statistics, statutory requirement KS3.S.3

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