Overview of progression in Year 5
Number and place value
Children work with numbers up to at least 1,000,000, using knowledge of place value to work out the value of digits.
They continue working with negative numbers in different contexts, and practise reading Roman numerals to 1000 (M), which helps them work out years written in Roman numerals. They continue using techniques introduced in earlier years for approximation and estimation.
Addition and subtraction
Children use columns in written addition and subtraction, accurately adding and subtracting numbers with more than four digits.
They use mental methods to add and subtract increasingly large numbers, and use rounding to check their answers. With support they choose appropriate operations and methods, and work ut the level of accuracy required to answer a particular problem. They will continue to develop this work in Year 6.
Multiplication and division
Children identify multiples and factors, and find all the factor pairs of a given number.
With support, they use factors to help solve multiplication and division problems involving larger numbers, and they confidently use written methods to multiply and divide large numbers. They extend their mathematical vocabulary and understanding, beginning to work with prime numbers, prime factors, composite (non-prime) numbers, square and cubed numbers.
Fractions (including decimals and percentages)
Children compare fractions with denominators that are multiples of the same number (comparing 3/7 with 6/14).
They also identify equivalent fractions of a given fraction including tenths and hundredths. They learn about mixed numbers and improper fractions, and understand how mixed numbers could be converted to improper fractions, and vice versa. With support and using practical equipment and diagrams, they multiply proper fractions and mixed numbers by whole numbers.
Children convert decimal numbers into fractions (0.65 = 65/100). Extending their work from previous years, they use thousandths and make connections between these and tenths, hundredths and their decimal equivalents. They round decimals to the nearest whole number, and to one decimal place, and begin to work with numbers with three decimal places.
Children begin to work with percentages and find solutions to problems using percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5, for example. This forms a basis for further work on percentages in Year 6.
In Year 4, children calculated the perimeter of rectilinear shapes; they now extend this to composite (or compound) rectilinear shapes, and calculate the area of squares and rectangles.
They begin to understand and estimate volume and capacity, and compare metric with common imperial units. They will build on this work in Year 6.
Geometry: properties of shapes
Children extend their work on angles from Year 4, estimating, measuring, comparing and drawing a variety of angles using degrees.
They use given dimensions to help them draw shapes accurately, and use techniques learnt in the context of missing number problems to help them work out missing angles.
Geometry: position and direction
Building on work with coordinate grids from Year 4, children work out the position of shapes following reflection or translation, in the first quadrant.
In Year 4, children were introduced to line graphs; now they use information from line graphs to solve problems.
They practise completing and reading tables, including timetables.