# Year 5 Mathematics

## Autumn

### Number and Place Value

• Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit.
• Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000.
• Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero.
• Round any number up to 1,000,000 to the nearest 10, 100, 1000, 10000 and 100000.
• Solve number problems and practical problems that involve all of the above.
• Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

• Add and subtract numbers mentally with increasingly large numbers.
• Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction).
• Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

### Statistics

• Solve comparison, sum and difference problems using information presented in a line graph.
• Complete, read and interpret information in tables including timetables.

### Multiplication & Division

• Multiply and divide numbers mentally drawing upon known facts.
• Multiply and divide whole numbers by 10, 100 and 1000.
• Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
• Recognise and use square numbers and cube numbers and the notation for squared (2) and cubed (3).
• Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.
• Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers.
• Establish whether a number up to 100 is prime and recall prime numbers up to 19.

### Measurement: Perimeter & Area

• Measure and calculate the perimeter of composite rectilinear shapes in cm and m.
• Calculate and compare the area of rectangles (including squares), and including using standard units, cm2,m2 estimate the area of irregular shapes.

## Spring

### Multiplication & Division

• Multiply and divide numbers mentally drawing upon known facts.
• Multiply numbers up to 4 digits by a one or two digit number using a formal written method, including long multiplication for 2 digit numbers.
• Divide numbers up to 4 digits by a one digit number using the formal written method of short division and interpret remainders appropriately for the context.
• Solve problems involving addition and subtraction, multiplication and division and a combination of these, including understanding the use of the equals sign.

### Fractions

• Compare and order fractions whose denominators are multiples of the same number.
• Identify, name and write equivalent fractions of a given fraction, represented visually including tenths and hundredths.
• 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 2/5 + 4/5 =6/5 = 1 1/5].
• 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 = 71/100]
• Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

### Decimals & Percentages

• Read, write, order and compare numbers with up to three decimal places.
• Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
• Round decimals with two decimal places to the nearest whole number and to one decimal place.
• Solve problems involving number up to three decimal places.
• Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal.
• Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

## Summer

### Decimals

• Solve problems involving number up to three decimal places.
• Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000.
• Use all four operations to solve problems involving measure [ for example, length, mass, volume, money] using decimal notation, including scaling.

### Geometry: Properties of Shape

• Identify 3D shapes, including cubes and other cuboids, from 2D representations.
• 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.
• Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.
• Draw given angles, and measure them in degrees.
• Identify: angles at a point and one whole turn (total 360°), angles at a point on a straight line and ½ a turn (total 180°) other multiples of 90°.

### Geometry: Position & Direction

• 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.

### Measurement: Converting Units

• Convert between different units of metric measure [for example, km and m; cm and m; cm and mm; g and kg; l and ml]
• Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.
• Solve problems involving converting between units of time.

### Measurement: Volume

• Estimate volume [for example using 1cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
• Use all four operations to solve problems involving measure.