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KS2 Maths Reasoning Syllabus

Here you can find example questions covering the KS2 Maths Reasoning Syllabus. You can also try a demo test to get a better understanding of how BOFA works. The syllabus has been taken from the National Curriculum.

Component Strand Sub-strand Year 3 NC Ref / Description Year 4 NC Ref / Description Year 5 NC Ref / Description Year 6 NC Ref / Description
Number Number, place value, approximation and estimation/rounding Counting (in multiples) 3N1b Count from 0 in multiples of 4, 8, 50 and 100 4N1 Count in multiples of 6, 7, 9, 25 and 1000 5N1 Count forwards or backwards in steps of powers of 10 for any given number up to 1000000  
Number Number, place value, approximation and estimation/rounding Read, write, order and compare numbers 3N2a Compare and order numbers up to 1000. Read and write numbers to 1000 in numerals and in words. 4N2a Order and compare numbers beyond 1000 5N2 Read, write, order and compare numbers to at least 1,000,000 6N2 Read, write, order and compare numbers up to 10,000,000
Number Number, place value, approximation and estimation/rounding Read, write, order and compare numbers 3N2b Find 10 or 100 more or less than a given number 4N2b Find 1000 more or less than a given number    
Number Number, place value, approximation and estimation/rounding Place value; Roman numerals 3N3 Recognise the place value of each digit in a three-digit number (hundreds, tens, ones) 4N3a Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones) 5N3a Determine the value of each digit in numbers up to 1,000,000 6N3 Determine the value of each digit in numbers up to 10,000,000
Number Number, place value, approximation and estimation/rounding Place value; Roman numerals   4N3b 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 5N3b Read Roman numerals to 1000 (M) and recognise years written in Roman numerals  
Number Number, place value, approximation and estimation/rounding Identify, represent and estimate; rounding 3N4 Identify, represent and estimate numbers using different representations 4N4a Identify, represent and estimate numbers using different representations    
Number Number, place value, approximation and estimation/rounding Identify, represent and estimate; rounding   4N4b Round any number to the nearest 10, 100 or 1000 5N4 Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000 6N4 Round any whole number to a required degree of accuracy
Number Number, place value, approximation and estimation/rounding Negative numbers   4N5 Count backwards through zero to include negative numbers 5N5 Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero 6N5 Use negative numbers in context, and calculate intervals across zero
Number Number, place value, approximation and estimation/rounding Number problems 3N6 Solve number problems and practical problems involving 3N1–3N5 4N6 Solve number problems and practical problems involving 4N1–4N5 5N6 Solve number problems and practical problems involving 5N1–5N5 6N6 Solve number problems and practical problems involving 6N1–6N5
Number Calculations: Addition, subtraction, multiplication and division Estimate, use inverses and check 3C3 Estimate the answer to a calculation and use inverse operations to check answers 4C3 Estimate and use inverse operations to check answers to a calculation 5C3 Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy 6C3 Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Number Calculations: Addition, subtraction, multiplication and division Add / subtract to solve problems 3C4 Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction 4C4 Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why 5C4 Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why 6C4 Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Number Calculations: Addition, subtraction, multiplication and division Properties of number (multiples, factors, primes, squares and cubes)     5C5a Identify multiples and factors, including finding all factor pairs of a number and common factors of two numbers 6C5 Identify common factors, common multiples and prime numbers
Number Calculations: Addition, subtraction, multiplication and division Properties of number (multiples, factors, primes, squares and cubes)     5C5b Know and use the vocabulary of prime numbers, prime factors and composite (non- prime) numbers  
Number Calculations: Addition, subtraction, multiplication and division Properties of number (multiples, factors, primes, squares and cubes)     5C5c Establish whether a number up to 100 is prime and recall prime numbers up to 19  
Number Calculations: Addition, subtraction, multiplication and division Properties of number (multiples, factors, primes, squares and cubes)     5C5d Recognise and use square numbers and cube numbers, and the notation for squared and cubed  
Number Fractions, decimals and percentages Recognise, find, write, name and count fractions 3F1a Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 4F1 Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten    
Number Fractions, decimals and percentages Recognise, find, write, name and count fractions 3F1b Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators      
Number Fractions, decimals and percentages Recognise, find, write, name and count fractions 3F1c Recognise and use fractions as numbers: unit fractions and non- unit fractions with small denominators      
Number Fractions, decimals and percentages Equivalent fractions 3F2 Recognise and show, using diagrams, equivalent fractions with small denominators 4F2 Recognise and show, using diagrams, families of common equivalent fractions. ( 300/900 = 1/3 ; 4/5 = 8/10 = 80100 ) 5F2a Recognise mixed numbers and improper fractions and convert from one form to the other; write mathematical statements >1 as a mixed number [eg: 25 + 45 = 65 = 1 15 ] 6F2 Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Number Fractions, decimals and percentages Equivalent fractions     5F2b Identify name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths  
Number Fractions, decimals and percentages Comparing and ordering fractions 3F3 Compare and order unit fractions and fractions with the same denominators   5F3 Compare and order fractions whose denominators are all multiples of the same number 6F3 Compare and order fractions, including fractions >1
Number Fractions, decimals and percentages Fractions / decimals equivalence     5F6a Read and write decimal numbers as fractions [eg: 0.71 = 71/100] 6F6 Associate a fraction with division to calculate decimal fraction equivalents (eg: 0.375) for a simple fraction [e.g. 3/8]
Number Fractions, decimals and percentages Fractions / decimals equivalence   4F6b Recognise and write decimal equivalents of any number of tenths or hundredths 5F6b Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents  
Number Fractions, decimals and percentages Rounding decimals   4F7 Round decimals with one decimal place to the nearest whole number 5F7 Round decimals with two decimal places to the nearest whole number and to one decimal place  
Number Fractions, decimals and percentages Rounding decimals   4F8 Compare numbers with the same number of decimal places up to two decimal places 5F8 Read, write, order and compare numbers with up to three decimal places  
Number Fractions, decimals and percentages Solve problems with fractions and decimals 3F10 Solve problems that involve 3F1–3F4 4F10a 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 5F10 Solve problems involving numbers up to three decimal places 6F10 Solve problems which require answers to be rounded to specified degrees of accuracy
Number Fractions, decimals and percentages Solve problems with fractions and decimals   4F10b Solve simple measure and money problems involving fractions and decimals to two decimal places    
Number Fractions, decimals and percentages Fractions / decimal / percentage equivalence     5F11 Recognise the percent symbol (%) and understand that per cent relates to ‘number of parts per hundred’; write percentages as a fraction with denominator hundred, and as a decimal 6F11 Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
Number Fractions, decimals and percentages Solve problems with percentages     5F12 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  
Number Ratio and proportion Relative sizes, similarity       6R1 Solve problems involving the relative sizes of two quantities, where missing values can be found by using integer multiplication and division facts
Number Ratio and proportion Use of percentages for comparison       6R2 Solve problems involving the calculation of percentages [eg: of measures such as 15% of 360] and the use of percentages for comparison
Number Ratio and proportion Scale factors       6R3 Solve problem involving similar shapes where the scale factor is known or can be found
Number Ratio and proportion Unequal sharing and grouping       6R4 Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Number Algebra Missing number problems expressed in algebra       6A1 Express missing number problems algebraically
Number Algebra Simple formulae expressed in words       6A2 Use simple formulae
Number Algebra Generate and describe linear number sequences       6A3 Generate and describe linear number sequences
Number Algebra Number sentences involving two unknowns       6A4 Find pairs of numbers that satisfy an equation with two unknowns
Number Algebra Enumerate all possibilities of combinations of two variables       6A5 Enumerate possibilities of combinations of two variables
Measurement, geometry and statistics Measurement Compare, describe and order measures 3M1a Compare lengths (m/cm/mm) 4M1 Compare different measures, including money in pounds and pence    
Measurement, geometry and statistics Measurement Compare, describe and order measures 3M1b Compare mass (kg/g)      
Measurement, geometry and statistics Measurement Compare, describe and order measures 3M1c Compare volume / capacity (l/ml)      
Measurement, geometry and statistics Measurement Estimate, measure and read scales 3M2a Measure lengths (m/cm/mm) 4M2 Estimate different measures, including money in pounds and pence    
Measurement, geometry and statistics Measurement Estimate, measure and read scales 3M2b Measure mass (kg/g)      
Measurement, geometry and statistics Measurement Estimate, measure and read scales 3M2c Measure volume / capacity (l/ml)      
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4a Tell and write the time from an analogue clock; 12-hour clocks 4M4a Read, write and convert time between analogue and digital 12-hour clocks    
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4b Tell and write the time from an analogue clock; 24-hour clocks 4M4b Read, write and convert time between analogue and digital 24-hour clocks    
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4c Tell and write the time from an analogue clock, including using Roman numerals from I to XII >4M4c Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days 5M4 Solve problems involving converting between units of time  
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4d Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds minutes and hours; use vocabulary such as o’clock/a.m./p.m., morning, afternoon, noon and midnight      
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4e Know the number of seconds in a minute and the number of days in each month, year and leap year      
Measurement, geometry and statistics Measurement Telling time, ordering time, duration and units of time 3M4f Compare durations of events, [eg: to calculate the time taken by particular events or tasks]      
Measurement, geometry and statistics Measurement Convert between metric units   4M5 Convert between different units of measurement [eg: kilometre to metre; hour to minute] 5M5 Convert between different units of metric measure [eg: kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre] 6M5 Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit and vice versa, using decimal notation of up to three decimal places
Measurement, geometry and statistics Measurement Convert metric/imperial     5M6 Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints 6M6 Convert between miles and kilometres
Measurement, geometry and statistics Measurement Perimeter, area 3M7 Measure the perimeter of simple 2–D shapes 4M7a Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres 5M7a Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres 6M7a Recognise that shapes with the same areas can have different perimeters and vice versa
Measurement, geometry and statistics Measurement Perimeter, area   4M7b Find the area of rectilinear shapes by counting squares 5M7b Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes 6M7b Calculate the area of parallelograms and triangles
Measurement, geometry and statistics Measurement Volume     5M8 Estimate volume [eg: using 1cm3 blocks to build cuboids (including cubes)] and capacity [eg: using water] 6M8a Calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm3) and cubic metres (m3), and extending to other units [eg: mm3 and km3]
Measurement, geometry and statistics Measurement Volume       6M8b Recognise when it is possible to use the formulae for the volume of shapes
Measurement, geometry and statistics Measurement Solve problems (a, money; b, length; c, mass / weight; d, capacity / volume) 3M9a Add and subtract amounts of money to give change, using both £ and p in practical contexts 4M9 Calculate different measures, including money in pounds and pence 5M9a Use all four operations to solve problems involving measure [money] using decimal notation, including scaling 6M9 Solve problems involving the calculation nd conversion of units of measure, using decimal notation up to three decimal places where appropriate
Measurement, geometry and statistics Measurement Solve problems (a, money; b, length; c, mass / weight; d, capacity / volume) 3M9b Add and subtract lengths (m/cm/mm)   5M9b Use all four operations to solve problems involving measure [eg: length] sing decimal notation, including scaling  
Measurement, geometry and statistics Measurement Solve problems (a, money; b, length; c, mass / weight; d, capacity / volume) 3M9c Add and subtract mass (kg/g)   5M9c Use all four operations to solve problems involving measure [eg: mass] using decimal notation, including scaling  
Measurement, geometry and statistics Measurement Solve problems (a, money; b, length; c, mass / weight; d, capacity / volume) 3M9d Add and subtract volume / capacity (l/ml)   5M9d Use all four operations to solve problems involving measure [eg: volume] using decimal notation, including scaling  
Measurement, geometry and statistics Geometry – properties of shapes Describe properties and classify shapes 3G2 Identify horizontal, vertical lines and pairs of perpendicular and parallel lines 4G2a Compare and classify geometric shapes, including quadrilaterals and triangles based on their properties and sizes 5G2a Use the properties of rectangles to deduce related facts and find missing lengths and angles 6G2a Compare and classify geometric shapes based on their properties and sizes
Measurement, geometry and statistics Geometry – properties of shapes Describe properties and classify shapes   4G2b Identify lines of symmetry in 2–D shapes presented in different orientations 5G2b Distinguish between regular and irregular polygons based on reasoning about equal sides and angles 6G2b Describe simple 3–D shapes
Measurement, geometry and statistics Geometry – properties of shapes Describe properties and classify shapes   4G2c Complete a simple symmetric figure with respect to a specific line of symmetry    
Measurement, geometry and statistics Geometry – properties of shapes Draw and make shapes and relate 2–D to 3–D shapes (including nets) 3G3a Draw 2–D shapes     6G3a Draw 2–D shapes using given dimensions and angles
Measurement, geometry and statistics Geometry – properties of shapes Draw and make shapes and relate 2–D to 3–D shapes (including nets) 3G3b Make 3–D shapes using modelling materials; recognise 3–D shapes in different orientations and describe them   5G3b Identify 3–D shapes including cubes and other cuboids, from 2–D representations 6G3b Recognise and build simple 3D shapes, including making nets
Measurement, geometry and statistics Geometry – properties of shapes Angles – measuring and properties 3G4a Recognise that angles are a property of shape or a description of a turn 4G4 Identify acute and obtuse angles and compare and order angles up to two right angles by size 5G4a Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles 6G4a Find unknown angles in any triangles, quadrilaterals and regular polygons
Measurement, geometry and statistics Geometry – properties of shapes Angles – measuring and properties 3G4b Identify right angles, recognise that two right angles make a half- turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle   5G4b Identify: (i) angles at a point and one whole turn (total 360) (ii) angles at a point on a straight line and 1/2 a turn (total 180) (iii)other multiples of 90 6G4b Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
Measurement, geometry and statistics Geometry – properties of shapes Angles – measuring and properties     5G4c Draw given angles and measure themin degrees (o)  
Measurement, geometry and statistics Geometry – properties of shapes Circles       6G5 Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
Measurement, geometry and statistics Geometry – position and direction Describe position, direction and movement   4P2 Describe movements between positions as translations of a given unit to the left/right and up/down 5P2 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 6P2 Draw and translate simple shapes on the co-ordinate plane, and reflect them in the axes
Measurement, geometry and statistics Geometry – position and direction Coordinates   4P3a Describe positions on a 2–D grid as co-ordinates in the first quadrant   6P3 Describe positions on the full co-ordinate grid (all four quadrants)
Measurement, geometry and statistics Geometry – position and direction Coordinates   4P3b Plot specified points and draw sides to complete a given polygon    
Measurement, geometry and statistics Statistics Interpret and represent data 3S1 Interpret and present data using bar charts, pictograms and tables 4S1 Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs 5S1 Complete, read and interpret information in tables, including timetables 6S1 Interpret and construct pie charts and line graphs and use these to solve problems
Measurement, geometry and statistics Statistics Solve problems involving data 3S2 Solve one-step and two- step questions [eg ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts, pictograms and tables 4S2 Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs 5S2 Solve comparison, sum and difference problems using information presented in a line graph 6S3 Calculate and interpret the mean as an average
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