Year 5 Maths
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Year 5 programme of study (statutory requirements) 
Notes and guidance (nonstatutory) 
Number, place value, approximation and estimation Pupils should be taught to:

Number, place value, approximation and estimation Pupils should identify the place value in large whole numbers. They should continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the termtoterm rule. 
Addition and subtraction Pupils should be taught to:

Addition and subtraction Pupils should practise using the efficient written methods of columnar addition and subtraction with increasingly large numbers to aid fluency. They should practise mental calculations with increasingly large numbers to aid fluency (e.g. 12 462 – 2 300 = 10 162). 
Multiplication and division Pupils should be taught to:

Multiplication and division Pupils should practise and extend their use of the efficient written methods of short multiplication and short division. They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations. They should use and understand the terms factor, multiple and prime, square and cube numbers. Pupils should interpret noninteger answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (e.g. 98 ÷ 4 = 24 r 2 = 24^{1}/_{2} = 24.5 ≈ 25). Pupils use multiplication and division as inverses to support the introduction of ratio in Year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres. 
Fractions Pupils should be taught to:

Fractions Pupils should connect equivalent fractions >1 that simplify to integers with division and fractions >1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions. Pupils should connect multiplication by a fraction to using fractions as operators, and to division, building on work from previous years. This relates to scaling by simple fractions. They should extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities, writing remainders as a fraction. Pupils should practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They should extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number. Pupils should read and write proper fractions and mixed numbers accurately and continue to practise counting forwards and backwards with mixed fractions. 
Decimals and fractions Pupils should be taught to:

Decimals and fractions Pupils extend counting from Year 4, using decimals and fractions including bridging zero, for example on a number line. They should add and subtract decimals including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (e.g. 0.83 + 0.17 = 1). They should mentally add and subtract tenths, and onedigit whole numbers and tenths. Pupils should say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and be confident in checking the reasonableness of their answers to problems. Pupils should go beyond the measurement and money models of decimals, for example by solving puzzles involving decimals. 
Percentages, decimals and fractions Pupils should be taught to:

Percentages, decimals and fractions Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing numbers. Pupils should make connections between percentages, fractions and decimals (e.g. 100% represents a whole quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to finding ‘fractions of’. They recognise that percentages are proportions of quantities as well as operators on quantities. 
Measures Pupils should be taught to:

Measures Pupils should use their knowledge of place value and multiplication and division to convert between standard units. Pupils should calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing number questions such as these are the beginning of algebraic understanding. They should also calculate the area of scale drawings using given measurements. Pupils should use all four operations in problems involving time and money, including conversions (e.g. days to weeks, leaving the answer as weeks and days). 
Geometry: properties of shapes Pupils should be taught to:
To identify:

Geometry: properties of shapes Pupils should become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils should use the term diagonal and make conjectures about the angles formed by diagonals and sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils should use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems. 
Geometry: position, direction, motion Pupils should be taught to:

Geometry: position, direction, motion Pupils should recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes. 
Data Pupils should be taught to:

Data Pupils should connect their work on coordinates and scales to their interpretation of time graphs using ICT tools, except where data are easily calculable. They should begin to decide which representations of data are most appropriate and why. 
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