Number and Place Value

Addition and Subtraction

• Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1.
• Know that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01.
• Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01.
• 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 through zero
• round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
• 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 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.

Multiplication and Division

Fractions

• Divide 1 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in units of 1 with 2, 4, 5 and 10 equal parts.
• Secure fluency in multiplication table facts, and corresponding division facts, through continued practice.

• identify multiples and factors, including finding all factor pairs of a number, and common factors of two 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 1000
• 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.

• 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 [e.g. ²/₅ + ⁴/₅ = ⁶/₅ = 1¹/₅]

• add and subtract fractions with the same denominator and 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 (e.g. 0.71 = ⁷¹/₁₀₀)
• 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
• read, write, order and compare numbers with up to three decimal places
• 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 hundred, 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 with a denominator of a multiple of 10 or 25.

Measurement

Geometry: properties of shape

• convert between different units of measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
• understand and use basic 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 [e.g. using 1 cm³ blocks to build cuboids (including cubes)] and capacity [e.g. using water]
• solve problems involving converting between units of time
• use all four operations to solve problems involving measure [e.g. length, mass, volume, money] using decimal notation including scaling

• identify 3-D shapes, including cubes and 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 one whole turn (total 360°)
• angles at a point on a straight line and ½ a turn (total 180°)
• 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

Statistics

• 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 line graphs
• complete, read and interpret information in tables, including timetables.