Year 6 Algebra Reasoning Booklets
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Reasoning & Problem Solving
7 resources · All year groups · Free Resources · of 1,819
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Narrow it downby objective (224)
- 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
Same strand, other year groupsfor support and stretch
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Free download
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Free download
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Free download
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Free download
Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Free download
Free Reasoning Task- Compare and Classify Geometric Shapes – Triangles
Free download
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