Reasoning & Problem Solving
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- Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)51
- solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures39
- Mixed Maths26
- choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels21
- Identify, represent and estimate numbers using different representations21
- Identify, represent and estimate numbers using different representations, including the number line21
- read, write, order and compare numbers up to 10,000,000 and determine the value of each digit21
- read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit20
- Use place value and number facts to solve problems20
- Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why18
- compare and order numbers from 0 up to 100; use <, > and = signs17
- Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line16
- Order and compare numbers beyond 1,00016
- Round any whole number to a required degree of accuracy16
- Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)15
- write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 1/2 and 2/415
- compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes14
- Compare, describe and solve practical problems for capacity and volume14
- Read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs14
- Recognise, find and name a half as one of two equal parts of an object, shape or quantity14
- Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity14
- solve problems involving number up to three decimal places14
- Use simple formulae14
- count forwards or backwards in steps of powers of 10 for any given number up to 1,000,00013
- identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces13
- Identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least13
- recognise, find, name and write fractions 1/3, 1/4, 2/4, 3/4 of a length, shape, set of objects or quantity13
- Use common factors to simplify fractions; use common multiples to express fractions in the same denomination13
- use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns13
- Compare and order unit fractions, and fractions with the same denominators12
- count in multiples of 6, 7, 9, 25 and 1,00012
- Multiply and divide numbers mentally, drawing upon known facts12
- Order and arrange combinations of mathematical objects in patterns and sequences12
- read Roman numerals to 1,000 (M) and recognise years written in Roman numerals12
- Recognise and use fractions as numbers12
- recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators12
- Solve comparison, sum and difference problems using information presented in a line graph12
- Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change12
- Use negative numbers in context, and calculate intervals across 012
- Add and subtract one-digit and two-digit numbers to 20, including zero11
- count in multiples of twos, fives and tens11
- Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number11
- given a number, identify one more and one less11
- interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 011
- Recognise the place value of each digit in a two-digit number (tens, ones)11
- round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,00011
- Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times11
- Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 111
- add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and ones10
- Add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and tens10
- add and subtract numbers using concrete objects, pictorial representations, and mentally, including two two-digit numbers10
- Choose and use appropriate standard units to estimate and measure length/height in any direction10
- Compare, describe and solve practical problems for mass/weight10
- Count, read and write numbers to 100 in numerals10
- identify 2-D shapes on the surface of 3-D shapes10
- Know and use the vocabulary of prime numbers, prime factors and composite (non- prime) numbers10
- multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers10
- Represent and use number bonds and related subtraction facts within 2010
- Round any number to the nearest 10, 100 or 100010
- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems10
- Add and subtract whole numbers with more than 4 digits, including using formal written methods9
- compare and sort common 2-D and 3-D shapes and everyday objects9
- Count backwards through zero to include negative numbers9
- Find 1,000 more or less than a given number9
- 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 value9
- Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction9
- Express missing number problems algebraically8
- Identify common factors, common multiples and prime numbers8
- identify lines of symmetry in 2-D shapes presented in different orientations8
- Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.8
- Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents8
- Recognise and write decimal equivalents to 1/4, 1/2, 3/48
- Solve number and practical problems that involve all of the above and with increasingly large positive numbers8
- write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods8
- Add and subtract amounts of money to give change, using both £ and p in practical contexts7
- Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions7
- Add and subtract fractions with the same denominator7
- Add and subtract numbers using concrete objects, pictorial representations, and mentally, including adding three one-digit numbers7
- Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity7
- Calculate and interpret the mean as an average7
- Calculate the area of parallelograms and triangles7
- Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]7
- Compare and order fractions whose denominators are all multiples of the same number.7
- complete a simple symmetric figure with respect to a specific line of symmetry7
- Divide numbers up to 4 digits by a 2-digit whole number using the formal written method of long division7
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes7
- Find different combinations of coins that equal the same amounts of money7
- Generate and describe linear number sequences7
- identify acute and obtuse angles and compare and order angles up to two right angles by size7
- identify horizontal and vertical lines and pairs of perpendicular and parallel lines7
- Interpret and construct pie charts and line graphs and use these to solve problems7
- Interpret and construct simple pictograms, tally charts, block diagrams and simple tables7
- Interpret and present data using bar charts, pictograms and tables7
- Measure and begin to record time7
- plot specified points and draw sides to complete a given polygon7
- Read and write numbers to at least 100 in numerals and in words7
- recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.7
- Recognise and know the value of different denominations of coins and notes7
- Recognise and show, using diagrams, families of common equivalent fractions.7
- Recognise that shapes with the same areas can have different perimeters and vice versa7
- Recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)7
- recognise when it is possible to use formulae for area and volume of shapes7
- Recognise, find and write fractions of a discrete set of objects: unit fractions and non- unit fractions with small denominators7
- round decimals with two decimal places to the nearest whole number and to one decimal place7
- solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher7
- Solve problems involving addition, subtraction, multiplication and division7
- Solve problems involving converting between units of time7
- solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days7
- Solve problems involving similar shapes where the scale factor is known or can be found7
- Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts7
- Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples7
- use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling7
- Add and subtract fractions with the same denominator and denominators that are multiples of the same number6
- Add and subtract fractions with the same denominator within one whole6
- add and subtract numbers mentally with increasingly large numbers6
- Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition where appropriate6
- angles at a point on a straight line and half a turn (total 180°)6
- Ask-and-answer questions about totalling and comparing categorical data6
- Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication, division and equals (=) signs6
- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons6
- Compare and order numbers up to 1,0006
- compare durations of events [for example, to calculate the time taken by particular events or tasks]6
- Convert between different units of measure (for example, kilometre to metre, hour to minute)6
- Convert between miles and kilometres6
- Count from 0 in multiples of 4, 8, 50 and 1006
- count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number6
- Count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward6
- Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.6
- 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 106
- 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 context6
- divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context6
- Divide proper fractions by whole numbers6
- draw given angles, and measure them in degrees6
- Estimate and use inverse operations to check answers to a calculation6
- estimate the answer to a calculation and use inverse operations to check answers6
- Find pairs of numbers that satisfy an equation with 2 unknowns6
- identify 3-D shapes, including cubes and other cuboids, from 2-D representations6
- Identify angles at a point and one whole turn (total 360)6
- Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn6
- Identify whether angles are greater or less than a right angle6
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius6
- know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles6
- Know the number of minutes in an hour and the number of hours in a day6
- know the number of seconds in a minute and the number of days in each month, year and leap year6
- Measure and begin to record lengths and heights6
- Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres6
- Measure the perimeter of simple 2-D shapes6
- Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,0006
- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication6
- Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams6
- perform mental calculations, including with mixed operations and large numbers6
- Read and write decimal numbers as fractions6
- Read, write and convert time between analogue and digital 12- and 24-hour clocks6
- read, write, order and compare numbers with up to three decimal places6
- Recall and use addition and subtraction facts up to 20 fluently6
- Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables6
- Recognise 3-D shapes in different orientations and describe them6
- Recognise and use language relating to dates, including days of the week, weeks, months and years6
- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems6
- Recognise and write decimal equivalents of any number of tenths or hundredths6
- Recognise angles as a property of shape or a description of a turn6
- 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 ]6
- Recognise the place value of each digit in a two-digit number (10s, 1s)6
- Round decimals with one decimal place to the nearest whole number6
- Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.6
- solve number and practical problems that involve all of the above6
- solve number problems and practical problems that involve all of the above6
- Solve one step addition and subtraction problems6
- solve one-step and two-step questions [for example ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables6
- Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate6
- Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison6
- Solve simple measure and money problems involving fractions and decimals to 2 decimal places6
- Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks6
- Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.6
- understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints6
- Use estimation to check answers to calculations and determine in the context of a problem, an appropriate degree of accuracy6
- Use their knowledge of the order of operations to carry out calculations involving the four operations6
- use written division methods in cases where the answer has up to two decimal places6
- Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]5
- combine amounts to make a particular value5
- Compare and order fractions, including fractions > 15
- Compare numbers with the same number of decimal places up to two decimal places5
- Compare, describe and solve practical problems for time5
- complete, read and interpret information in tables, including timetables5
- Describe position, direction and movement, including whole, half, quarter and three- quarter turns5
- describe positions on the full coordinate grid (all 4 quadrants)5
- distinguish between regular and irregular polygons based on reasoning about equal sides and angles5
- 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 hundredths5
- identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers5
- Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs5
- Mixed Arithmetic5
- multiply one-digit numbers with up to two decimal places by whole numbers5
- Multiply simple pairs of proper fractions, writing the answer in its simplest form5
- Read and write numbers from 1 to 20 in numerals and words5
- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 1005
- recall multiplication and division facts for multiplication tables up to 12 × 125
- Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)5
- Sequence events in chronological order5
- show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot5
- Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number5
- solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes5
- solve problems which require answers to be rounded to specified degrees of accuracy5
- Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy5
- Use, read, write and convert between standard units, converting measurements of length, mass, volume and time5
- Add and subtract numbers mentally, with increasingly large numbers4
- compare and order lengths, mass, volume/capacity and record the results using >, < and =4
- Compare, describe and solve practical problems for lengths and heights4
- enumerate possibilities of combinations of two variables.4
- Multiply two-digit and three-digit numbers by a one-digit number using formal written layout4
- Recognise and name common 2D shapes4
- Recognise and name common 3D shapes4
- solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates4
- Use simple algebra4
- Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/24
- add and subtract numbers mentally, including a three-digit number and ones3
- Compare and order lengths and record the results using > =3
- Measure and begin to record mass and weight3
- Read and write numbers to at least 1000 in numerals and words3
- read and write numbers up to 1000 in numerals and in words3
- recall and use equivalences between simple fractions, decimals and percentages including in different contexts.3
- recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers3
- Recognise and use factor pairs and commutativity in mental calculations3
- Solve number problems and practical problems involving these ideas3
- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts3