Calculation Booklet

Tranmere Park Primary

School

Progression in Calculations

Addition

Objective and Strategies

Concrete Pictorial Abstract

Combining two parts to make a whole: part- whole model

4 + 3 = 7 10= 6 + 4

Starting at the bigger number and counting on

Start with the larger number on the bead string and then count on to the smaller number 1 by 1 to find the answer.

12 + 5 = 17

Start at the larger number on the number line and count on in ones or in one jump to find the answer.

5 + 12 = 17 Place the larger number in your head and count on the smaller number to find your answer.

8 1

5

3

Use cubes to add

two numbers

together as a

group or in a bar.

Use pictures to

add two numbers

together as a

group or in a bar. Use the part-part

whole diagram as

shown above to

move into the

abstract.

Regrouping to make 10.

6 + 5 = 11 Start with the bigger number and use the smaller number to make 10.

Use pictures or a number line. Regroup or partition the smaller number to make 10.

7 + 4= 11 If I am at seven, how many more do I need to make 10. How many more do I add on now?

Adding three single digits

4 + 7 + 6= 17 Put 4 and 6 together to make 10. Add on 7.

Following on from making 10, make 10 with 2 of the digits (if possible) then add on the third digit.

Combine the two numbers that make 10 and then add on the remainder.

Column method- no regrouping

24 + 15= Add together the ones first then add the tens. Use the Base 10 blocks first before moving onto place value counters.

After practically using the base 10 blocks and place value counters, children can draw the counters to help them to solve additions. T O

Add together three groups of objects. Draw a

picture to recombine the groups to make 10.

+ +

+

Column method- regrouping

Make both numbers on a place value grid.

Add up the units and exchange 10 ones for one 10.

Add up the rest of the columns, exchanging the 10 counters from one column for the next place value column until every column has been added. This can also be done with Base 10 to help children clearly see that 10 ones equal 1 ten and 10 tens equal 100. As children move on to decimals, money and decimal place value counters can be used to support learning.

Children can draw a pictoral representation of the columns and place value counters to further support their learning and understanding.

Start by partitioning the numbers before moving on to clearly show the exchange below the addition.

As the children move on, introduce decimals with the same number of decimal places and different. Money can be used here.

Subtraction

Objective and Strategies

Concrete Pictorial Abstract

Taking away ones

Use physical objects, counters, cubes etc to show how objects can be taken away. 6 – 2 = 4

Cross out drawn objects to show what has been taken away.

18 -3= 15 8 – 2 = 6

Counting back Make the larger number in your subtraction. Move the beads along your bead string as you count backwards in ones. 13 – 4 Use counters and move them away from the group as you take them away counting backwards as you go.

Count back on a number line or number track

Start at the bigger number and count back the smaller number showing the jumps on the number line.

This can progress all the way to counting back using two 2 digit numbers.

Put 13 in your head, count back 4. What number are you at? Use your fingers to help.

Find the difference

Compare amounts and objects to find the difference.

Use cubes to build towers or make bars to find the difference

Use basic bar models with items to find the difference

Count on to find the difference.

Draw bars to find the difference between 2 numbers.

Hannah has 23 sandwiches, Helen has 15 sandwiches. Find the difference between the number of sandwiches.

Part Part Whole Model

Link to addition- use the part whole model to help explain the inverse between addition and subtraction.

If 10 is the whole and 6 is one of the parts. What is the other part?

10 - 6 =

Use a pictorial representation of objects to show the part part whole model.

Move to using numbers within the part whole model.

Make 10

14 – 9 =

Make 14 on the ten frame. Take away the four first to make 10 and then takeaway one more so you have taken away 5. You are left with the answer of 9.

Start at 13. Take away 3 to reach 10. Then take away the remaining 4 so you have taken away 7 altogether. You have reached your answer.

16 – 8= How many do we take off to reach the next 10? How many do we have left to take off?

10 5

Column method without regrouping

Use Base 10 to make the bigger number then take the smaller number away.

Show how you partition numbers to subtract. Again make the larger number first.

Draw the Base 10 or place value counters alongside the written calculation to help to show working.

This will lead to a clear written column subtraction.

Column method with regrouping

Use Base 10 to start with before moving on to place value counters. Start with one exchange before moving onto subtractions with 2 exchanges. Make the larger number with the place value counters

Start with the ones, can I take away 8 from 4 easily? I need to exchange one of my tens for ten ones.

Draw the counters onto a place value grid and show what you have taken away by crossing the counters out as well as clearly showing the exchanges you make.

When confident, children can find their own way to record the exchange/regrouping. Just writing the numbers as shown here shows that the child understands the method

and knows when to exchange/regroup.

Children can start their formal written method by partitioning the number into clear place value columns.

Moving forward the children use a more compact method.

Now I can subtract my ones.

Now look at the tens, can I take away 8 tens easily? I need to exchange one hundred for ten tens.

Now I can take away eight tens and complete my subtraction

Show children how the concrete method links to the written method alongside your working. Cross out the numbers when exchanging and show where we write our new amount.

This will lead to an understanding of subtracting any number including decimals.

Multiplication

Objective and Strategies

Concrete Pictorial Abstract

Doubling Use practical activities to show how to double a number.

Draw pictures to show how to double a number.

Partition a number and then double each part before recombining it back together.

Counting in multiples

Count in multiples supported by concrete objects in equal groups.

Use a number line or pictures to continue support in counting in multiples.

Count in multiples of a number aloud. Write sequences with multiples of numbers. 2, 4, 6, 8, 10 5, 10, 15, 20, 25 , 30

Repeated addition

Write addition sentences to describe objects and pictures.

Arrays- showing commutative multiplication

Create arrays using counters/ cubes to show multiplication sentences.

Draw arrays in different rotations to find commutative multiplication sentences.

Link arrays to area of rectangles.

Use an array to write multiplication sentences and reinforce repeated addition.

Use different

objects to add

equal groups.

Column multiplication

Children can continue to be supported by place value counters at the stage of multiplication.

It is important at this stage that they always multiply the ones first and note down their answer followed by the tens which they note below.

Bar modelling and number lines can support learners when solving problems with multiplication alongside the formal written methods.

Start with long multiplication, reminding the children about lining up their numbers clearly in columns. If it helps, children can write out what they are solving next to their answer.

This moves to the more compact method.

Division

Objective and Strategies

Concrete Pictorial Abstract

Sharing objects into groups

I have 10 cubes, can you share them equally in 2 groups?

Children use pictures or shapes to share quantities.

Share 9 buns between three people.

9 ÷ 3 = 3

Division as grouping

Divide quantities into equal groups. Use cubes, counters, objects or place value counters to aid understanding.

Use a number line to show jumps in groups. The number of jumps equals the number of groups.

Think of the bar as a whole. Split it into the number of groups you are dividing by and work out how many would be within each group.

28 ÷ 7 = 4 Divide 28 into 7 groups. How many are in each group?

8 ÷ 2 = 4

Division within arrays

Link division to multiplication by creating an array and thinking about the

number sentences that can be created. Eg 15 ÷ 3 = 5 5 x 3 = 15 15 ÷ 5 = 3 3 x 5 = 15

Draw an array and use lines to split the array into groups

to make multiplication and division sentences.

Find the inverse of multiplication and division sentences by creating four linking number sentences. 7 x 4 = 28 4 x 7 = 28 28 ÷ 7 = 4 28 ÷ 4 = 7

Division with a remainder

14 ÷ 3 = Divide objects between groups and see how much is left over

Jump forward in equal jumps on a number line then see how many more you need to jump to find a remainder.

Draw dots and group them to divide an amount and clearly show a remainder.

Complete written divisions and show the remainder using r.

Short division

Use place value counters to divide using the bus stop method alongside

42 ÷ 3= Start with the biggest place value, we are sharing 40 into three groups. We can put 1 ten in each group and we have 1 ten left over.

We exchange this ten for ten ones and then share the ones equally among the groups. We look how much in 1 group so the answer is 14.

Students can continue to use drawn diagrams with dots or circles to help them divide numbers into equal groups. Encourage them to move towards counting in multiples to divide more efficiently.

Begin with divisions that divide equally with no remainder.

Move onto divisions with a remainder.

Finally move into decimal places to divide the total accurately.

Long division 2544 ÷ 12 How many groups of 12 thousands do we have? None

Exchange 2 thousand for 20 hundreds.

How many groups of 12 are in 25 hundreds? 2 groups. Circle them. We have grouped 24 hundreds so can take them off and we are left with one.

Exchange the one hundred for ten tens so now we have 14 tens. How many groups of 12 are in 14? 1 remainder 2

Exchange the two tens for twenty ones so now we have 24 ones. How many groups of 12 are in 24? 2

Instead of using physical counters, students can draw the counters and circle the groups on a whiteboard or in their books. Use this method to explain what is happening and as soon as they have understood what move on to the abstract method as this can be a time consuming process.

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Maths

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Maths

Maths Long terms Plans and Assessment

ContextIn the National Curriculum, objectives are given for each Year Group for mathematics. Those objectives are reflected here.

PlanningTeachers should plan to teach the objectives below for their year group, remembering that these should always be used and applied across a variety of contexts to give context to learning and bring in real life skills.

Teachers should plan a balance of number and non-number based maths each half term to give children an interesting, balanced curriculum and must revisit objectives throughout the year to consolidate and extend learning. Some of the objectives may need to be split into several sub-objectives, rather than being taught as one.

Objectives in bold are considered Key Learning Objectives (Key Performance Indicators from the NAHT, 2014) and therefore need more time spending on them.Objectives in grey are for pupils who have mastered the Year Group expectations and need some ‘exceeding ‘objectives to provide challenge.

AssessingRemembering that all groups are flexible, teachers should keep a copy of these grids for each group within their class and highlight the objectives in term colours to show achievement. Hashing can be used to show partial success. Names of children within groups should be recorded on the grids, as should movement between groups and dates.

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Maths

Year 1Number and place value• count to and across 100, forwards and backwards,

beginning with 0 or 1, or from any given number.• count, read and write numbers to 100 in numerals;

count in multiples of twos, fives and tens• given a number, identify one more and one less• 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, least

• read and write numbers from 1 to 20 in numerals and words

• Count reliably well beyond 100• Count on and back in 3s from any given number to

beyond 100

Addition and subtraction• read, write and interpret mathematical statements

involving addition (+), subtraction (–) and equals (=) signs

• represent and use number bonds and related subtraction facts within 20

• add and subtract one-digit and two-digit numbers to 20, including zero

• solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = - 9

• Say the number that is 10 more or 10 less than a number to 100

• Know the signs (+); (-); (=); (<); (>)• Apply knowledge of number to solve a one-step

problem involving an addition, subtraction• Add and subtract 1-digit and 2-digit numbers to 50,

including zeroMultiplication and division

• solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

• Apply knowledge of number to solve a one-step problem involving simple multiplication and division

Fractions• recognise, find and name a half as one of two

equal parts of an object, shape or quantity• recognise, find and name a quarter as one of four

equal parts of an object, shape or quantity

Measurement• compare, describe and solve practical problems

for: o lengths and heights [for example, long/

short, longer/shorter, tall/short, double/half] o mass/weight [for example, heavy/light,

heavier than, lighter than]o capacity and volume [for example, full/

empty, more than, less than, half, half full, quarter

o time [for example, quicker, slower, earlier, later]

• measure and begin to record the following:o lengths and heightso mass/weighto capacity and volumeo time (hours, minutes, seconds)

• recognise and know the value of different denominations of coins and notes

• sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]

• recognise and use language relating to dates, including days of the week, weeks, months and years

• tell the time to the hour and half past the hour and draw the hands on a clock face to show these times

• Recognise all coins and notes and know their value• Use coins to pay for items bought up to £1• Use knowledge of time to know when key periods of the day

happen, e.g., lunchtime, home time, etc.

Geometry: position and direction• describe position, direction and movement, including

half, quarter and three quarter turnsGeometry: properties of shapes

• recognise and name common 2-D and 3-D shapes, including:o 2-D shapes [for example, rectangles

(including squares), circles and triangles] o 3-D shapes [for example, cuboids

(including cubes), pyramids and spheres]• Recognise different 2D and 3D shapes in the environment

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Number and place value• count in steps of 2, 3, and 5 from 0, and in tens

from any number, forward and backward• recognise the place value of each digit in a two-digit

number (tens, ones)• identify, represent and estimate numbers using

different representations, including the number line• compare and order numbers from 0 up to 100• use <, > and = signs correctly• read and write numbers to at least 100 in numerals

and in words• use place value and number facts to solve

problems• Count reliable up to 1000 in 2s, 5s and 10s• Count on and back in multiples of 4, 8, 25 and 0 and 100

from any given number to beyond 1000

Addition and subtraction• solve problems with addition and subtraction:

o using concrete objects and pictorial representations, including those involving numbers, quantities and measuresmass/weight

o applying their increasing knowledge of mental and written methods

• recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

• add and subtract numbers using concrete objects, pictorial representations, and mentally, including:o a two-digit number and oneso a two-digit number and tenso two two-digit numberso adding three one-digit numbers

• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

• recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

• Apply knowledge of number up to 100 to solve a one-step problem involving addition and subtraction.

• Add and subtract two 2-digit and numbers to 100• Use an appropriate strategy to add and subtract numbers that

move between and through 100, e.g., 97 + 7; 103 – 8

Multiplication and division• recall and use multiplication and division facts

for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

• show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

• Apply knowledge of number up to 100 to solve a one-step problem involving simple multiplication and division

Maths

Year 2Fractions• recognise, find, name and write fractions and of a length, shape, set of objects or quantity• write simple fractions for example, of 6 = 3 and

recognise the equivalence of and • Add and subtract fractions with a common denominator

Measurement• 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 vessels

• compare and order lengths, mass, volume/capacity and record the results using >, < and =

• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

• find different combinations of coins that equal the same amounts of money

• solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

• compare and sequence intervals of time• 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 times

• know the number of minutes in an hour and the number of hours in a day

• Apply knowledge of addition and subtraction to pay for items, up to £10, within a problem solving context

• Measure, compare, add and subtract using common metric measure

• Tell time to 5 minute intervals in both analogue and digital and relate one to the other

Geometry: properties of shapes• identify and describe the properties of 2-D shapes,

including the number of sides and line symmetry in a vertical line

• identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

• identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

• compare and sort common 2-D and 3-D shapes and everyday objects

Geometry: position and direction• order and arrange combinations of mathematics

objects in patterns and sequences• use mathematical vocabulary to describe position,

direction and movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three quarter turns (clockwise and anticlockwise)

• Know about right angles and where they can be seen in the environment

Statistics• interpret and construct simple pictograms, tally charts,

block diagrams and simple tables• ask and answer simple questions by counting the

number of objects in each category and sorting the categories by quantity

• ask and answer questions about totalling and comparing categorical data

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Maths

Year 3Number and place value• count from 0 in multiples of 4, 8, 50 and 100; find

10 or 100 more or less than a given number• recognise the place value of each digit in a three-

digit number (hundreds, tens, ones)• compare and order numbers up to 1000• identify, represent and estimate numbers using

different representations• read and write numbers up to 1000 in numerals and

in words• solve number problems and practical problems

involving these ideas• Recognise the value of each digit in a 4-digit number and

the value of a tenth• Being to have an understanding about negative numbers

recognising they are smaller than zero

Addition and subtraction• add and subtract numbers mentally, including:

o a three-digit number and oneso a three-digit number and teno a three-digit number and hundreds

• add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction

• estimate the answer to a calculation and use inverse operations to check answers

• solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

• Add and subtract numbers with any number of digits using formal written methods

Multiplication and division• recall and use multiplication and division facts

for the 3, 4 and 8 multiplication tables• 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 methods

• solve problems, including missing number problems, involving multiplication and

• division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

• Know all multiplication facts up to 10 x 10 and be able to instantaneously answer questions such as, how many 7s in 42?

• Multiply and divide any 2-digit number by a single digit number and have an understanding of ‘remainder’

Fractions• count up and down in tenths; recognise that a tenth

arises from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

• recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

• recognise, find and write fractions as numbers: unit fractions and non-unit fractions with small denominators

• recognise and show, using diagrams, equivalent fractions with small denominators

• add and subtract fractions with the same denominator within one whole

• compare and order unit fractions, and fractions with the same denominators

• solve problems that involve all of the above• Can find fractional values (from to ) of amounts up to 1000

Measurement• measure, compare, add and subtract: lengths (m/

cm/mm); mass (kg/g); volume/capacity (l/ml)• measure the perimeter of simple 2-D shapes• add and subtract amounts of money to give

change, using both £ and p in practical contexts• tell and write the time from an analogue clock,

including using Roman numerals from I to XII, and 12-hour and 24-hour clocks

• 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

• know the number of seconds in a minute and the number of days in each month, year and leap year

• compare durations of events [for example to calculate the time taken by particular events or tasks]

• Use knowledge of number to solve problems related to money, time and measures

• Measure, compare, add and subtract more complex problems using common metric measures set out in Kg, g; Kl, l: Km and m, etc

• Can relate knowledge of time to problems related to timetables

Geometry: properties of shapes• draw 2-D shapes and make 3-D shapes using

modelling materials; recognise 3-D shapes in different orientations and describe them

• recognise angles as a property of shape or a description of a turn

• 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

• identify horizontal and vertical lines and pairs of perpendicular and parallel lines

• Know that the total internal angles of a triangle measure 180°

Statistics• interpret and present data using bar charts,

pictograms and tables• 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 tables

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Maths

Year 4Number and place value

• count in multiples of 6, 7, 9, 25 and 1000• find 1000 more or less than a given number• count backwards through zero to include negative

numbers• recognise the place value of each digit in a four-digit

number (thousands, hundreds, tens, and ones)• order and compare numbers beyond 1000• identify, represent and estimate numbers using

different representations• round any number to the nearest 10, 100 or 1000• solve number and practical problems that involve all of

the above and with increasingly large positive numbers• 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

• Use tenths, hundredths and thousandths when comparing values and solving addition and subtraction problems

• Relate tenths and hundredths to fractional values• Round any number to 100,000 to the nearest 10, 100, 1000

or 10000

Addition and subtraction• add and subtract numbers with up to 4 digits using

the formal written methods of columnar addition and subtraction where appropriate

• estimate and use inverse operations to check answers to a calculation

• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

• Solve multi-step problems involving more than one of the operations

Multiplication and division• recall multiplication and division facts for

multiplication tables up to 12 × 12• use place value, known and derived facts to multiply

and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

• recognise and use factor pairs and commutativity in mental calculations

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout

• solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

• Rapidly recall answer when multiplying and dividing a whole or decimal number by 10

• Solve multi-step problems involving more than one of the operations

Fractions (including decimals)• recognise and show, using diagrams, families of

common equivalent fractions• count up and down in hundredths; recognise that

hundredths arise when dividing an object by one hundred and dividing tenths by ten

• 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

• add and subtract fractions with the same denominator• recognise and write decimal equivalents of any

number of tenths or hundredths• recognise and write decimal equivalents to • 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 hundredths

• round decimals with one decimal place to the nearest whole number

• compare numbers with the same number of decimal places up to two decimal places

• solve simple measure and money problems involving fractions and decimals to two decimal places

• Work out simple percentage values of whole numbers as is related to on-going learning in science, history and geography

• Compare and add fractions whose denominations are all multiples of the same number

• Use a 24-hour timetable to find out times for a journey between various places

Measurement• convert between different units of measure [for

example, kilometre to metre; hour to minute] • measure and calculate the perimeter of a rectilinear

figure (including squares) in centimetres and metres• find the area of rectilinear shapes by counting squares• estimate, compare and calculate different measures,

including money in pounds and pence• read, write and convert time between analogue and

digital 12- and 24-hour clocks• solve problems involving converting from hours to

minutes; minutes to seconds; years to months; weeks to days

• Use knowledge of perimeter to work out perimeter of large areas around school using meters and centimetres

Geometry: properties of shapes• compare and classify geometric shapes, including

quadrilaterals and triangles, based on their properties and sizes

• identify acute and obtuse angles and compare and order angles up to two right angles by size

• identify lines of symmetry in 2-D shapes presented in different orientations

• complete a simple symmetric figure with respect to a specific line of symmetry.

Geometry: position and direction• describe positions on a 2-D grid as coordinates in the

first quadrant• describe movements between positions as translations

of a given unit to the left/right and up/down• plot specified points and draw sides to complete a

given polygon

Number and place value• count in multiples of 6, 7, 9, 25 and 1000• find 1000 more or less than a given number• count backwards through zero to include negative

numbers• recognise the place value of each digit in a four-digit

number (thousands, hundreds, tens, and ones)• order and compare numbers beyond 1000• identify, represent and estimate numbers using

different representations• round any number to the nearest 10, 100 or 1000• solve number and practical problems that involve all of

the above and with increasingly large positive numbers• 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

• Use tenths, hundredths and thousandths when comparing values and solving addition and subtraction problems

• Relate tenths and hundredths to fractional values• Round any number to 100,000 to the nearest 10, 100, 1000

or 10000

Addition and subtraction• add and subtract numbers with up to 4 digits using

the formal written methods of columnar addition and subtraction where appropriate

• estimate and use inverse operations to check answers to a calculation

• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

• Solve multi-step problems involving more than one of the operations

Multiplication and division• recall multiplication and division facts for

multiplication tables up to 12 × 12• use place value, known and derived facts to multiply

and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

• recognise and use factor pairs and commutativity in mental calculations

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout

• solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

• Rapidly recall answer when multiplying and dividing a whole or decimal number by 10

• Solve multi-step problems involving more than one of the operations

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Statistics• interpret and present discrete and continuous data

using appropriate graphical methods, including bar charts and time graphs

• solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

• Collect own data on given project and present information in graphical formats of their choosing

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Maths

Year 5Number and place value

• 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, including 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

• Have a concept of numbers well beyond 1,000,000 and their relative association to distances to planets; historical data and geographical aspects

• Use rounding as a strategy for quickly assessing what approximate answers ought to be before calculating

• Link working across zero for positive and negative numbers to work time between BC and AD in history

Addition and subtraction• 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.

• Calculate number problems algebraically, e.g., 2x – 3 = 5

Multiplication and division• 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

• Divide whole numbers (up to 4 digits) by 2-digit numbers, using preferred method

• Recognise the symbol for square root (√) and work out square roots for numbers up to 100

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Maths

Year 5 (continued)Fractions (including decimals and percentages)

• 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

[for example, ] • add and subtract fractions with the same denominator

and denominators that are 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 [for example, 0.71 = ] • 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 100, and as a decimal

• solve problems which require knowing percentage and decimal equivalents of and those fractions with a denominator of a multiple of 10 or 25.

Measurement• convert between different units of metric measure

(for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

• understand and use approximate 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), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

• estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]

• solve problems involving converting between units of time

• use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

• Use knowledge of measurement to create plans of areas around school, such as classroom, field, outside play area, etc

• Relate imperial measures still used regularly in our society to their metric equivalents, e.g. miles to KM and lbs to Kg

• Use a range of timetables to work out journey times on a fractional journey around the world, e.g. how long would it take to reach the rainforests in the Amazon

Geometry: properties of shapes• identify 3-D shapes, including cubes and other 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:

o angles at a point and one whole turn (total 360°)

o angles at a point on a straight line and 21 a turn (total 180°)

o 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• 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• Solve comparison, sum and difference problems using

information presented in a line graph• complete, read and interpret information in tables,

including timetables• Collect own data on personal project and present information

in formats of their choosing, charts, graphs and tables

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Maths

Year 6Number and place value

• read, write, order and compare numbers up to 10 000 000 and determine the value of each digit• round any whole number to a required degree of

accuracy• use negative numbers in context, and calculate

intervals across zero• solve number and practical problems that involve all of

the aboveAddition, subtraction, multiplication and division

• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

• 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 context

• divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

• perform mental calculations, including with mixed operations and large numbers

• identify common factors, common multiples and prime numbers

• use their knowledge of the order of operations to carry out calculations involving the four operations

• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

• solve problems involving addition, subtraction, multiplication and division

• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

• Multiply all integers, (using efficient written methods) including mixed numbers and negative numbers

Ratio and proportion• solve problems involving the relative sizes of two

quantities where missing values can be found by using integer multiplication and division facts

• solve problems involving the calculation of percentages [e.g. of measures, and such as 15% of 360] and the use of percentages for comparison

• solve problems involving similar shapes where the scale factor is known or can be found

• solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Algebra• use simple formulae• generate and describe linear number sequences• express missing number problems algebraically• find pairs of numbers that satisfy an equation with two

unknowns• enumerate possibilities of combinations of 2 variables• Move beyond squared and cubed numbers to calculate

problems such as X x 10n where n is positive• Use +, ≠, ≤, ≥ correctly• Recognise an arithmetic progression, and find the nth

term

Measurement• solve problems involving the calculation and

conversion of units of measure, using decimal notation up to three decimal places where appropriate

• 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 to up to three decimal places

• convert between miles and kilometres• recognise that shapes with the same areas can have

different perimeters and vice versa • recognise when it is possible to use formulae for area

and volume of shapes• calculate the area of parallelograms and triangles• 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]

• Use four operations with mass, length, time, money and other measures, including with decimal quantities

• Crease a scaled model of a historical or geographical structure showing an acceptable degree of accuracy using known measurements

• Calculate costs and time involved to visit a destination in another part of the world

Geometry: properties of shapes• draw 2-D shapes using given dimensions and angles• recognise, describe and build simple 3-D shapes, including

making nets• compare and classify geometric shapes based on their

properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

• illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

• recognise angles where they meet at a point, are on a straight line, or vertically opposite; find missing angles

Fractions• use common factors to simplify fractions; use common

multiples to express fractions in the same denomination• compare and order fractions, including fractions > 1 • add and subtract fractions with different denominators

and mixed numbers, using equivalent fractions• multiply simple pairs of proper fractions, writing the

answer in its simplest form [for example, ] • divide proper fractions by whole numbers [for example, ] • associate a fraction with division and calculate decimal

fraction equivalents [for example, 0.375] for a simple fraction [for example, ]

• identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

• multiply one-digit numbers with up to two decimal places by whole numbers

• use written division methods in cases where the answer has up to two decimal places

• solve problems which require answers to be rounded to specified degrees of accuracy

• recall and use equivalences between simple fractions, decimals and percentages, in different contexts

• Compare, order and convert between fractions, decimals and percentages in contexts related to science, history or geography learning

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Ratio and proportion• solve problems involving the relative sizes of two

quantities where missing values can be found by using integer multiplication and division facts

• solve problems involving the calculation of percentages [e.g. of measures, and such as 15% of 360] and the use of percentages for comparison

• solve problems involving similar shapes where the scale factor is known or can be found

• solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Algebra• use simple formulae• generate and describe linear number sequences• express missing number problems algebraically• find pairs of numbers that satisfy an equation with two

unknowns• enumerate possibilities of combinations of 2 variables• Move beyond squared and cubed numbers to calculate

problems such as X x 10n where n is positive• Use +, ≠, ≤, ≥ correctly• Recognise an arithmetic progression, and find the nth

term

Measurement• solve problems involving the calculation and

conversion of units of measure, using decimal notation up to three decimal places where appropriate

• 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 to up to three decimal places

• convert between miles and kilometres• recognise that shapes with the same areas can have

different perimeters and vice versa • recognise when it is possible to use formulae for area

and volume of shapes• calculate the area of parallelograms and triangles• 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]

• Use four operations with mass, length, time, money and other measures, including with decimal quantities

• Crease a scaled model of a historical or geographical structure showing an acceptable degree of accuracy using known measurements

• Calculate costs and time involved to visit a destination in another part of the world

Geometry: properties of shapes• draw 2-D shapes using given dimensions and angles• recognise, describe and build simple 3-D shapes, including

making nets• compare and classify geometric shapes based on their

properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

• illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

• recognise angles where they meet at a point, are on a straight line, or vertically opposite; find missing angles

Maths

Year 6 (continued)Geometry: position and direction

• describe positions on full coordinate grid (4 quadrants)• draw and translate simple shapes on the

coordinate plane, and reflect them in the axes

Statistics• interpret and construct pie charts and line graphs and

use these to solve problems• calculate and interpret the mean as an average• Collect own data on personal project and present information

in formats of their choosing, charts, graphs and tables and answer specific questions related to their research