 ## Year 5 Areas of Study

Number and place value – students should be taught to:

• 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 0
• Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
• Solve number problems and practical problems that involve all of the above
• Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

Number – addition and subtraction – students should be taught to:

• Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
• Add and subtract numbers mentally with increasingly large numbers
• 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

Number – multiplication and division – students should be taught to:

• Identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
• 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
• Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
• Multiply and divide numbers mentally, drawing upon known facts
• 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
• Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
• 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
• Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
• Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Number – fractions (including decimals and percentages) – students should be taught to:

• Compare and order fractions whose denominators are all 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]
• 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 ½, 1/4, 1/5, 2/5, 4/5  and those fractions with a denominator of a multiple of 10 or 25

Measurement – students should be taught to:

• 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

Geometry – properties of shape- students should be taught to:

• 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 (°)
• Identify angles at a point and 1 whole turn (total 360°)
• Identify angles at a point on a straight line and half a turn (total 180°)
• Identify other multiples of 90°
• 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

Geometry – position and direction – students should be taught to:

• 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

Statistics – students should be taught to:

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

## Year 6 Areas of Study

Number and place value – students should be taught to:

• Count in multiples of 6, 7, 9, 25 and 100
• Find 1000 more or less than a given number
• Count backwards through zero to include negative numbers
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Order and compare numbers beyond 1000
• Identify, represent and estimate numbers using different representations
• Round any number to the nearest 10, 100 or 1000
• Solve number and practical problems that involve all of the above and with increasingly large positive numbers
• Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value

Addition and subtraction – students should be taught to:

• Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
• Estimate and use inverse operations to check answers to a calculation
• Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Multiplication and division – students should be taught to:

• Recall multiplication and division facts for multiplication tables up to 12 × 12
• Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
• Recognise and use factor pairs and commutativity in mental calculations
• Multiply two-digit and three-digit numbers by a one-digit number using formal written
• Layout solve problems involving multiplying and adding, including using the distributive law
• To multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

Fractions (including decimals) – students should be taught to:

• Recognise and show, using diagrams, families of common equivalent fractions
• Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
• Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• Add and subtract fractions with the same denominator
• Recognise and write decimal equivalents of any number of tenths or hundredths
• Recognise and write decimal equivalents to ¼, ½, ¾
• Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
• Round decimals with one decimal place to the nearest whole number
• Compare numbers with the same number of decimal places up to two decimal places
• Solve simple measure and money problems involving fractions and decimals to two decimal places

Measurement – students should be taught to:

• Convert between different units of measure (for example, kilometre to metre; hour to minute)
• Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
• Find the area of rectilinear shapes by counting squares
• Estimate, compare and calculate different measures, including money in pounds and pence
• Read, write and convert time between analogue and digital 12- and 24-hour clocks
• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days

Geometry – properties of shape – students should be taught to:

• Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• Identify acute and obtuse angles and compare and order angles up to two right angles by size
• Identify lines of symmetry in 2-D shapes presented in different orientations
• Complete a simple symmetric figure with respect to a specific line of symmetry

Geometry – position and direction – students should be taught to:

• Describe positions on a 2-D grid as coordinates in the first quadrant
• Describe movements between positions as translations of a given unit to the left/right and up/down
• Plot specified points and draw sides to complete a given polygon

Statistics – students should be taught to:

• Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs 