For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. Pupils extend their understanding of the language of addition and subtraction to include sum and difference. Pupils connect their work on coordinates and scales to their interpretation of time graphs. Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. The national curriculum for mathematics aims to ensure that all pupils: ... Year 5 programme of study Number - number and place value. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money. Year 1; Year 2; Year 3; Year 4; Year 5. By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study. Put your child's learning into practice with our Year 5 maths worksheets, which cover all the topics taught as part of the curriculum, or try our Y5 mental maths mini-test. ☐ Know that a right angle is 90 degrees, a straight angle is 180 degrees and a full circle is 360 degrees. They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10). Pupils learn decimal notation and the language associated with it, including in the context of measurements. * 10 thousands = 1 ten thousand Stage 3 content and outcomes for the K–10 syllabuses on the NSW Syllabuses site. simplify and manipulate algebraic expressions to maintain equivalence by: expanding products of 2 or more binomials, understand and use standard mathematical formulae; rearrange formulae to change the subject, model situations or procedures by translating them into algebraic expressions or formulae and by using graphs, use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement), recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane, interpret mathematical relationships both algebraically and graphically, reduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically, 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, find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs, generate terms of a sequence from either a term-to-term or a position-to-term rule, recognise arithmetic sequences and find the nth term, recognise geometric sequences and appreciate other sequences that arise, change freely between related standard units [for example time, length, area, volume/capacity, mass], use scale factors, scale diagrams and maps, express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1, use ratio notation, including reduction to simplest form, divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio, understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction, relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions, solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics, solve problems involving direct and inverse proportion, including graphical and algebraic representations, use compound units such as speed, unit pricing and density to solve problems, 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), calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes, draw and measure line segments and angles in geometric figures, including interpreting scale drawings, 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, 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, use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles, derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies, identify properties of, and describe the results of, translations, rotations and reflections applied to given figures, identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids, apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles, understand and use the relationship between parallel lines and alternate and corresponding angles, 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, 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, use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles, use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D, interpret mathematical relationships both algebraically and geometrically, 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, understand that the probabilities of all possible outcomes sum to 1, enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams, generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities, 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), 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, describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs, the mathematical content that should be taught to all pupils, in standard type, additional mathematical content to be taught to more highly attaining pupils, in braces { }, consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}, select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy, consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}, extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities, move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal, {exponential and trigonometric} functions, use mathematical language and properties precisely, extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically, extend their ability to identify variables and express relations between variables algebraically and graphically, make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}, reason deductively in geometry, number and algebra, including using geometrical constructions, explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally, assess the validity of an argument and the accuracy of a given way of presenting information, develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts, make and use connections between different parts of mathematics to solve problems, model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions, select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems; interpret their solution in the context of the given problem, apply systematic listing strategies, {including use of the product rule for counting}, {estimate powers and roots of any given positive number}, calculate with roots, and with integer {and fractional} indices, calculate exactly with fractions, {surds} and multiples of π {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}, calculate with numbers in standard form A × 10n, where 1 ≤ A < 10 and n is an integer, {change recurring decimals into their corresponding fractions and vice versa}, identify and work with fractions in ratio problems, apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}. Mathematical language An important aim of the mathematics programme is to enable the child to use mathematical language effectively and accurately. Year 5 maths worksheets, interactive activities and resources covering the 2014 mathematics curriculum. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. Skills available for New Zealand year 5 maths curriculum IXL's year 5 skills will be aligned to the New Zealand Curriculum soon! This establishes addition and subtraction as related operations. By the end of year 5, students will be achieving at early level 3 in the mathematics and statistics learning area of The New Zealand Curriculum. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word-reading knowledge and their knowledge of spelling. Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals. recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, add and subtract fractions with the same denominator, and denominators that are multiples of the same number, multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams, read and write decimal numbers as fractions [for example, 0.71 =, recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents, round decimals with 2 decimal places to the nearest whole number and to 1 decimal place, read, write, order and compare numbers with up to 3 decimal places, solve problems involving number up to 3 decimal places, recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction, solve problems which require knowing percentage and decimal equivalents of, convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre], understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints, measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres, calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes, estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water], solve problems involving converting between units of time, use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling, identify 3-D shapes, including cubes and other cuboids, from 2-D representations, know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles, draw given angles, and measure them in degrees (°), angles at a point and 1 whole turn (total 360°), angles at a point on a straight line and half a turn (total 180°), use the properties of rectangles to deduce related facts and find missing lengths and angles, distinguish between regular and irregular polygons based on reasoning about equal sides and angles, identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed, solve comparison, sum and difference problems using information presented in a line graph, complete, read and interpret information in tables, including timetables, read, write, order and compare numbers up to 10,000,000 and determine the value of each digit, round any whole number to a required degree of accuracy, use negative numbers in context, and calculate intervals across 0, solve number and practical problems that involve all of the above, multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication, divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context, divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context, perform mental calculations, including with mixed operations and large numbers, identify common factors, common multiples and prime numbers, use their knowledge of the order of operations to carry out calculations involving the 4 operations, solve problems involving addition, subtraction, multiplication and division, use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy, use common factors to simplify fractions; use common multiples to express fractions in the same denomination, compare and order fractions, including fractions >1, add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. National curriculum in England: mathematics programmes of study - key stages 1 and 2 Ref: DFE-00180-2013 PDF , 488KB , 47 pages National curriculum in England: mathematics programme of … Year 5 Mathematics: Australian Curriculum in Queensland provides an overview of the Australian Curriculum learning area within the context of a Kindergarten to Year 12 Professional Maths teaching resources. Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’. Check with your local education authority to find out their requirements. The Year 5 maths curriculum will introduce new concepts and calculations involving multiplication of fractions, measurement conversions and greater numbers up to 1,000,000. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems. Year 5 Recovery Curriculum - Autumn - Week 2 Welcome to IXL's year 5 maths page. 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