In maths a Year 5 child is expected to know:

• Read, write and order numbers to 1,000,000
• Count on and back in steps of 100,1,000, 10,000 up to 1,000,000
• Round any number to the nearest 10, 100, 1,000, 10,000 or 100,000
• Estimate and calculate additions involving 2, 3-digit numbers (to nearest 10)
• Estimate and calculate subtractions  involving 2, 3-digit numbers (to nearest 10)
• Estimate and calculate multiplications involving a 2-digit and a 3-digit numbers (to nearest 10)
• Estimate and calculate divisions of a 3-digit number by a 1-digit number (to nearest 10)
• Add 3, 5-digit numbers using column addition
• Subtract one 5-digit number from another, using column subtraction
• Rapid Recall: Mentally add a 2-digit number to a 3-digit number
• Rapid Recall: Mentally add a 1000s number to a 5-digit number
• Rapid Recall: Mentally subtract a 2-digit number from a 3 or 4-digit number
• Rapid Recall: Mentally subtract a 1000s number from a 5-digit number
• Know all factors that make up numbers to 100
• Recognise all prime numbers to 100
• Multiply a 4-digit number by a 2-digit number using formal methods
• Divide a 4-digit number by a 1-digit number (with remainders)
• Multiply numbers by 10, 100 and 1,000
• Divide number by 10, 100 and 1,000
• Recognise and use square numbers and square roots
• Know and use the symbols (²),(3) and (√) accurately
• Fractions: Compare and order fractions whose denominators are multiples of the same number
• Convert mixed numbers to improper fractions and visa versa
• Add and subtract fractions with the same denominator
• Multiple proper fractions and mixed fractions by whole numbers
• Decimal Fractions: Read and write decimal numbers as fractions (up to hundredths)
• Round decimals with two decimal places to nearest whole number and one decimal place
• Read, write, order and compare decimal numbers with up to three decimal places
• Percentages: Recognise the % symbol
• Understand that percentage is measured as part of 100
• Solve problems which require knowing percentage and decimal value of ½, ¼, ⅕, ⅖ and ⅘
• Measure angles in degrees
• Draw a given angle accurately
• Know and use reflex angles
• Construct shapes from given dimensions
• Identify 3D shapes from 2D representations
• Identify, describe and represent the position of a shape following reflection and translation
• Add, subtract, multiply and divide units of measure (using decimal notation)
• Understand and use basic equivalence between metric and common imperial units
• Calculate, estimate and compare areas of squares and rectangles using cm squared (cm²) and metre squared (m²)
• Recognise volume in practical contexts

A year 5 mathematician

Number, place value, approximation and estimation/rounding

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

Calculations

• I can add and subtract numbers mentally with increasingly large numbers.
• I can add and subtract whole numbers with more than 4 digits, including using formal written methods.
• I can use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.
• I can solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
• I can identify multiples and factors, including finding all factor pairs or a number and common factor pairs of two numbers.
• I use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers.
• I can establish whether a number up to 100 is prime and recall prime numbers up to 19.
• I recognise and use square numbers and cube numbers, and the notation for squared and cubed.
• I can multiply and divide numbers mentally drawing on known facts.
• I can multiply and divide whole numbers and those involving decimals by 10, 100 and 1000.
• I can multiply numbers up to 4 digits by a 1-digit or 2-digit number using a formal written method, including long multiplication for 2-digit numbers.
• I can divide numbers up to 4 digits by a 1-digit number using the formal written method of short division and interpret remainders appropriately for the context.
• I can solve problems involving multiplication and division including using knowledge of factors and multiples, squares and cubes.
• I can solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign.
• I can solve problems involving multiplication and division including scaling by simple fractions and problems involving simple rates.

Fractions, decimals and percentages

• I can recognise mixed numbers and improper fractions and convert from one form to the other.
• I can write mathematical statements >1 as a mixed number.
• I can identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.
• I can compare and order fractions whose denominators are multiples of the same number.
• I can add and subtract fractions with the same denominator and denominators that are multiples of the same number.
• I can multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.
• I can read and write decimal numbers as fractions.
• I recognise and can use thousandths and relate them to tenths, hundredths and decimal equivalents.
• I can round decimals with 2 decimal places to the nearest whole number and 1 decimal place.
• I can read, write, order and compare numbers with up to 3 decimal places.
• I can solve problems involving numbers up to 3 decimal places.
• I recognise the percent symbol and understand that percent relates to ‘number parts per hundred’.
• I can write percentages as a fraction with denominator hundred, and as a decimal.
• I can solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator or a multiple of 10 or 25.

Measurement

• I can solve problems involving converting between units of time.
• I can convert between different units of metric measure.
• I understand and use approximate equivalences between metric units and common imperial units, such as inches, pounds and pints.
• I can measure and calculate the perimeter of composite rectilinear shapes in cm and m.
• I can calculate and compare the area of rectangles (incl squares), and including using standard units (cm2 and cm3) to estimate the area of irregular shapes.
• I can estimate volume and capacity.
• I can use all four operations to solve problems involving money using decimal notation, including scaling.

Geometry – properties of shapes

• I can use the properties of rectangles to deduce related facts and find missing lengths and angles.
• I can distinguish between regular and irregular polygons based on reasoning about equal sides and angles.
• I can identify 3D shapes, including cubes and other cuboids, from 2D representations.
• I know angles are measured in degrees.
• I can estimate and compare acute, obtuse and reflex angles.
• I can identify angles at a point and one whole turn.
• I can identify angles at a point on a straight line and ½ a turn.
• I can identify other multiples of 90º.
• I can draw given angles and measure them in degrees.

Geometry – position and direction

• I can 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

• I can complete, read and interpret information in tables, including timetables.
• I can solve comparison, sum and difference problems using information presented in a line graph.