Calculation Guidelines for Mathematics

INTRODUCTION The Primary National Strategy provides a structured and systematic approach to teaching number and there is a considerable emphasis on teaching mental calculation strategies. Up to Year 4 informal written recording and jottings should take place regularly and is an important part of learning and understanding. More formal written methods should follow only when the child is able to use a wide range of mental calculation strategies. A Whole School Approach We believe it is vital that children have a wide repertoire of mental strategies to support them when first solving a calculation.  We will ensure children are taught to choose the most efficient method of calculation when appropriate.  All calculations will be presented horizontally so as not to influence the method selected by the child. Children will be taught to: Attempt the calculation in their heads using an appropriate mental method Use jottings to support their mental calculations when needed Use a pencil and paper procedure (from Y4 onwards) Know when and how to use a calculator (Y5 and Y6) PLACE VALUE  A wide range of mental methods are established, refined and continue to be taught throughout the school, based on a good understanding of place value in numbers.  Place value is an important concept which must be taught mentally, first in the Reception year where number tracks and bead strings are used, progressing to beaded number lines, landmarked number lines and empty number lines to 10 or 20 or 100 as appropriate in key stage one and beyond. We follow this simple progression towards the ENL: Bead strings/ bead bars (dynamic number lines)

Beaded number lines (static number lines)

Landmarked number lines

An empty number line

0

20

20

Numbers such as the next 10, 100, 1000 we call landmark numbers.

90

 The empty number line (ENL) is introduced and used to aid mental calculations in all four operations throughout key stages one and two.  Pupils are taught the importance of locating and ordering numbers accurately on a landmarked and unmarked number line to aid calculation from key stage one.  Other place value resources are used regularly throughout key stage one and two, for example place value charts, place value arrow cards and various ICT applications and software. As underpinning skills, particularly for mental methods of addition and subtraction, children are taught:  Counting on and back in ones and tens  Pairs to ten, and using these to find complements to multiples of ten  Partitioning of single digits e.g. 7 = 5 + 2 and 8 – 5 = 3  Using place value to add/subtract a single digit to a multiple of ten  Using the ENL to help keep track ADDITION AND SUBTRACTION

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A range of models and images are used to support children’s early understanding of addition and subtraction. Some of these can be found on the models and images charts. We use two main mental strategies for addition and subtraction, called J10 (which includes the special case of OJ10) and T10, with a third for addition called the splits to support jottings and mental calculation.

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Within this, we teach children that there are two types of subtraction:

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Take-away Removing an amount from a total, usually one at a time and counting backwards on the number line. Numbers are far apart on the number line, e.g. 123 - 5 For example Mike has 43p and gives 4p to charity. How much did he have left?

-1-3

39 43 43p – 4p = 39p

Difference Comparing two numbers or quantities and counting forward on the number line. Numbers are closer on the number line, e.g. 1230 - 980 For example My flower is 24cm and your flower is 18cm. How much taller is my flower than yours?

+2 +4

18

24

24cm – 18cm = 6cm

J10 – Jumping in tens Addition

Subtraction What is 91 - 30?

What is 47 + 20?

91 - 37? 47 + 19? (OJ10) 91 - 19? (OJ10)

T10 – Target the tens Addition What is 8 + 5?

Subtraction As take-away: What is 22 – 4?

As difference: 32 – 27 = 5 or 27 +  = 32 What is 17 + 8?

What is 42 – 27?

What is 1023 – 487?

The Splits (Partition and recombine for addition only) This strategy cannot be modelled on the number line: both numbers are partitioned. The steps should be set out as below. Notice that each step is on a new line. This 36 + 27 = 30 + 6 + 20 + 7 helps to prevent the misuse of the equal sign. = 50 + 13 = 63  The aim is that children can add and subtract any pair of 2 digit numbers mentally by the end of year 4.  Note: Partition and recombine is not to be taught for subtraction as it gives rise to the common error 83 – 46 = 43

PROGRESSION TOWARDS A STANDARD WRITTEN METHOD OF CALCULATION We have developed an agreed and consistent approach to the teaching of written calculation methods which supports continuity and progression throughout the school. Reasons for using written methods  To aid calculation, particularly with larger numbers or decimals or when the problem is too difficult to be done mentally.  To help communicate methods and solutions.  To allow errors to be unpicked.  To aid mental calculation by writing down some of the numbers and answers involved.  To provide a record of work carried out. WHEN ARE CHILDREN READY FOR EXPANDED WRITTEN CALCULATIONS? (underpinning skills for Y1, Y2 and Y3)  Do they know how to add and subtract ones, tens or hundreds to numbers?  Do they know addition and subtraction facts for all numbers to 20?  Do they understand place value and can they partition and recombine numbers?  Can they add three or more single digit numbers mentally?  Can they add and subtract any pair of two digit numbers mentally, bridging through tens and hundreds when appropriate?  Can they use a number line to add and find the difference between pairs of numbers?  Can they explain their mental strategies orally and record them using informal jottings, such as the empty number line? The above lists are not exhaustive but are a guide for the teacher to judge when a child is ready to move from informal to more formal ‘pencil and paper’ methods of calculation. Stages in Addition 1.

Building on the splits, using partitioning and number facts to 20 with their related facts: 47 + 76

2.

= 40 + 7 + 70 + 6 = 110 + 13 = 123

Vertical layout, expanded working, moving to adding the least significant digit first through Y4: no carrying, adding up rows mentally. 47

47

368

368

+ 76

+76

+493

+493

110 13 123

(40+70) (6+7)

13 110 123

(6+7)

700

(300+400)

(40+70)

150

(60+90)

150

(60+90)

(8+3)

700

(300+400)

11 861

11

861

Note: pairs of numbers less than 100 should always be added mentally: – larger numbers should be used as soon as the method is secure

(8+3)

3.

Vertical layout, contracting the working to a compact, more efficient form by the end of Y5, always estimating first: No carries → one carry → two or more carries We have agreed the ‘carry numbers’ under the answer will be crossed when used

47

47

368

368

+76

+76

+493

+493

13

123

11

861

110

1

150

11

123

700 861

NB It is important for children to continue to make decisions about the most appropriate method of solving calculations. Children should always estimate and then decide whether they can find out the answer using a mental method first, whether to use jottings such as the use of the empty number line, or whether to use a more formal written method. All calculations will be presented horizontally. Stages in Subtraction A counting on method (the difference model of T10) using jottings will continue throughout KS1 and KS2 to aid mental calculation as appropriate. Subtraction by decomposition Underpinning skills must be in place throughout KS1 and Y3 before these stages are introduced, using both the difference and the take away models. The vocabulary of these methods must also be reinforced. We have chosen to use decomposition as the main written method for subtraction. Further partitioning skills must be in place before these stages are introduced; supported by the use of visual images, such as the 100 bead bar: e.g. 47

= (40 + 7), (30 + 17), (20 + 27), (10 + 37)…….

The following methods will be introduced with the aid of place value (arrow) cards from Y4 onwards, first with no exchange. For numbers less than 100, a mental method should always be used. 1.

563 - 241 500 - 200 300

2.

60 40 20

3 1 2

With one, then two exchanges… 593 - 278

623 - 469

80

500 - 200 300

90 13 70 8 10 5 =

500

315

110

600 120 - 400 60 100 50

1

3 9 4

= 154

3.

Moving to a more contracted method by Year 6 569 – 278 4 1

569 - 278 291 4.

Larger numbers and decimals in Year 6.

NB It is important for children to continue to make decisions about the most appropriate method of solving calculations. Children should always estimate and then decide whether they can find out the answer using a mental method first, whether to use jottings, such as the use of the empty number line, or whether to use a more formal written method. All calculations will be presented horizontally. MULTIPLICATION AND DIVISION WHEN ARE CHILDREN READY FOR EXPANDED WRITTEN CALCULATIONS? (underpinning skills for Y1, Y2 and Y3)  Do they know (at least) the 2, 5, 10, 3 and 4 times table by heart?  Can they use multiplication facts they know to derive mentally other multiplication facts that they do not know?  Do they know the result of multiplying by 0 and 1?  Do they understand 0 as a place holder?  Can they multiply two and three digit numbers by 10 and 100?  Can they double and halve numbers mentally or with jottings?  Do they understand place value and can they partition and recombine numbers?  Can they explain their mental strategies orally and record them using informal jottings?  Can they draw and use arrays and groups of objects / jumps on a number line to describe their multiplication / division sentences? Stages in Multiplication Begin by using arrays in KS1 and use a variety of language such as multiply, product multiple … 1.

Mental method using partitioning: 18 x 5, always modelled using the place value (arrow) cards, using arrays as appropriate 10 x 5

8x5

18 x 5 = (10 x 5) + (8 x 5) = 50 + 40 = 90 2.

Grid layout linked to partitioning and arrays: 30 8 x (30x7) = 210

7 3.

(8x7) = 56

38 x 7 = 266

266

Extend to bigger numbers: 56 x 27 = 1512, then with decimals 56 x 27 = (50 + 6) x (20 + 7) 50

6

20

1000

120

1120

7

350

42

392

x

1512

4.

When confident at using the above methods, move to a vertical format with expanded working, introduced alongside the grid method, then as shown to aid calculation:

x

4.

38 7 210 56 266

56 x 27 1000 120 350 42 1512

(30 x 7) (8 x 7)

(50 x 20) (6 x 20) (50 x 7) (6 x 7)

x 20 7

50

6

 

 

Vertical format, and with decimals towards the end of Y6, moving to more compact working when appropriate for the child involved. x

56 27 1120 392 1512

(56 x 20) (56 x 7) ->this stage for most able only

Stages in Division 1.

Informal methods, using multiples of the divisor or ‘chunking’, first without a remainder, then with a remainder. This is the grouping model of division which is used from KS1 onwards, using arrays, the number line and the grouping ITP: Always estimate first and check the reasonableness of the answer.

2.

From Y2 onwards 72 ÷ 5 72 50 22 20 2

3.

4.

(4 x 5)

Larger numbers from Y4 onwards 256 ÷ 7 256 70 (10 x 7) 186 140 (20 x 7) 46 42 ( 6 x 7) 4

Answer:

10 + 4 = 14 14 remainder 2

Answer:

10 + 20 + 6 = 36 36 r 4

Extend to simple decimals with up to 2 places by Year 6. 87.5 ÷ 7 -

5.

(10 x 5)

87.5 70.0 17.5 14.0 3.5 3.5 0.0

(10 x 7) (2 x 7) (0.5 x 7)

Answer:

Short method as appropriate by the end of Y6 36

4 7

7 256

10 + 2 + 0.5 = 12.5

Summary 

Written methods will be introduced from Y4 onwards in expanded form as set out above. The underpinning skills need to be in place before this, explicitly taught in reception, key stage one and consolidating in Year 3.

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Models and images are important tools for children, so they can visualise problems and calculations. We use the ‘models and images charts’ to help us support children with a range of models and images in six key concepts:  Addition and subtraction facts to 20.  Understanding addition and subtraction  Counting on and back in ones and tens  Partitioning and recombining  Ordering numbers to 100  Understanding multiplication and division

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Children will be taught the terminology of J10, T10 and the splits in KS1 and will have a broad range of experiences using bead strings, beaded number lines, landmarked number lines and the ENL. The Go Maths scheme will support progression in number at KS1.

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The main method of teaching division is by grouping and is linked closely to multiplication and the use of arrays.

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Children will always decide whether a mental method is appropriate and estimate first.

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Answers should usually be checked, preferably using a different method eg. the inverse operation, or an expanded way making sure their answer is reasonable.

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As teachers we will pay attention to mathematical vocabulary and the language we use and refer to the actual value of digits e.g. 56 = fifty and six or 60 + 70 is six tens and seven tens.

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Children who make persistent mistakes will return to the method that they can use accurately until ready to move on.

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Children need to know addition, subtraction, multiplication and division facts by heart and will be taught this throughout the school.

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Time will be spent discussing errors and diagnosing problems and then working through the problem, rather than re-teaching the method.

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When revising or extending to more complex numbers using a written method, we will refer back to expanded methods when appropriate. This helps reinforce understanding and reminds children that they have an alternative to fall back on if they are having difficulties.

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Problems will be set in a real life and/ or problem solving context where possible.

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End of year expectations and recording grids for each year group are set out in the key objective grids shown below:

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Reception

Use developing mathematical ideas and methods to solve practical problems. Talk about, recognise and recreate simple patterns. Say and use number names in order in familiar contexts. Count reliably up to 10 everyday objects. Use language such as ‘more’ or ‘less’ to compare 2 nos. Use language: ‘more’ to compare two numbers Use language: ‘less’ to compare two numbers. Recognise numerals 1 to 9. Find one more or one less than a number from 1 to 10 Find one more than a number from 1 to 10 Find one less than a number from 1 to 10 Begin to relate addition to combining two groups of objects, and subtraction to ‘taking away’ Begin to relate addition to combining two groups of objects Begin to relate subtraction to ‘taking away’ In practical activities and discussion begin to use the vocabulary involved in adding and subtracting. In practical activities and discussion, begin to use the vocabulary involved in adding In practical activities and discussion, begin to use the vocabulary involved in subtracting Use language such as circle or bigger to describe the shapes and size of solids and flat shapes Use everyday words to describe position Use language such as ‘greater’, ‘smaller’, ‘heavier’ or ‘lighter’ to compare quantities. Use language such as greater or heavier to compare two quantities Use language such as smaller or lighter to compare two quantities

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 1 Read and write numerals from 0 to 20, then beyond; use knowledge of place value to position these on a number track and number line. Read numerals from 0 to 20, then beyond. Write numerals from 0 to 20, then beyond. Use place value to position on a number track and number line. Derive and recall all pairs of numbers with a total of 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts.

Derive all pairs of numbers with a total of 10. Recall all pairs of numbers with a total of 10. Work out the corresponding subtraction facts. Derive all pairs of numbers for totals to at least 5. Recall all pairs of numbers for totals to at least 5. Work out the corresponding subtraction facts. Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentences. Use the vocabulary related to addition. Use the vocabulary related to subtraction. Use symbols to describe and record addition and subtraction number sentences.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 1 Visualise and name common 2D shapes and 3D solids and describe their features. Visualise and name common 2D shapes. Describe features of common 2D shapes. Visualise and name common 3D solids. Describe features of 3D solids Estimate, measure, weigh and compare objects, choosing and using suitable uniform non-standard or standard units and measuring instruments (e.g. a lever balance, metre stick or measuring jug). Estimate, measure and compare length of objects. Estimate, measure and compare weight of objects. Estimate, measure and compare capacity of containers. Choose and use suitable uniform non-standard or standard units. Choose and use suitable measuring instruments. Answer a question by recording information in lists and tables; present outcomes using practical resources, pictures, block graphs or pictograms. Answer a question by recording information in lists and tables. Present outcomes using practical resources or pictures. Present outcomes using block graphs or pictograms.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 2 Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a two-digit number represents, including numbers where 0 is a place holder; partition 2-digit numbers in different ways, including into multiples of 10 and 1.

Count objects by grouping and counting in twos. Count objects by grouping and counting in fives. Count up to 100 objects by grouping and counting in tens. Explain what each digit in a 2-digit number represents. Partition 2-digit numbers into multiples of 10 and 1. Partition 2-digit numbers in different ways. Derive and recall all addition and subtraction facts for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100. Derive and recall all addition and subtraction facts for each number to at least 10. Derive and recall addition and subtraction facts for all pairs with totals to 20. Derive and recall addition and subtraction facts for all pairs of multiples of 10 with totals up to 100. Add or subtract mentally a one-digit number or a multiple of 10 to or from any 2-digit number; use practical and informal written methods to add and subtract 2-digit numbers. Add or subtract mentally a one-digit number to or from any 2-digit number. Add or subtract mentally a multiple of 10 to or from any 2-digit number. Use practical and informal written methods to add 2digit numbers. Use practical and informal written methods to subtract 2-digit numbers.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 2 Use the symbols + - x ÷ and = to record and interpret number sentences involving all four operations: calculate the value of an unknown in a number sentence (e.g.  ÷ 2 = 6, 30 -  = 24).

Use the symbols +, - and = to record and interpret number sentences. Use the symbols x, ÷ and = to record and interpret number sentences. Calculate the value of an unknown in addition and subtraction number sentences (e.g. 30 -  = 24). Calculate the value of an unknown in multiplication and division number sentences (e.g.  ÷ 2 = 6). Visualise common 2D shapes and 3D solids; identify shapes from pictures of them in different positions and orientations; sort, make and describe shapes, referring to their properties.

Visualise common 2D shapes and identify them from pictures in different positions. Visualise common 3D solids and identify them from pictures in different positions and orientations. Sort, make and describe shapes, referring to their properties. Use units of time (seconds, minutes, hours, days) and know the relationship between them; read time to the quarter hour; identify time intervals, including those that cross the hour. Use units of time (seconds, minutes, hours, days). Know the relationship between units of time (seconds, minutes, hours, days). Read the time to the quarter hour. Identify time intervals, including those that cross the hour. Use lists, tables, and diagrams to sort objects; explain choices using appropriate language, including ‘not’ [in Carroll diagrams, e.g. magnetic : not magnetic].

Use lists, tables and diagrams to sort objects. Explain choices using appropriate language, including ‘not’.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 3 Partition three-digit numbers into multiples of 100, 10 and 1 in different ways. Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100. Derive and recall all addition and subtraction facts for each number to 20. Derive and recall sums and differences of multiples of 10. Derive and recall number pairs that total 100. Add and subtract mentally combinations of one-digit and two-digit numbers. Add mentally combinations of one-digit and two-digit numbers. Subtract mentally combinations of one-digit and twodigit numbers. Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side. Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy. Read, to the nearest division and half-division, scales that are numbered or partially numbered. Use the information to measure and draw to a suitable degree of accuracy. Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion. Use Venn diagrams to sort data and objects using more than one criterion. Use Carroll diagrams to sort data and objects using more than one criterion.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 4 Use diagrams to identify equivalent fractions (e.g. 6 /8 and ¾, or 70 /100 and 7/10 ); interpret mixed numbers and position them on a number line (e.g. 3½)

Use diagrams to identify equivalent fractions (e.g. 6 /8 and ¾, or 70 /100 and 7/10 ) Interpret mixed numbers and position them on a number line (e.g. 3½) Derive and recall multiplication facts up to 10 x 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple. Derive & re-call x facts and corresponding ÷ facts: x 2 Derive & re-call x facts and corresponding ÷ facts: x 3 Derive & re-call x facts and corresponding ÷ facts: x 4 Derive & re-call x facts and corresponding ÷ facts: x 5 Derive & re-call x facts and corresponding ÷ facts: x 6 Derive & re-call x facts and corresponding ÷ facts: x 7 Derive & re-call x facts and corresponding ÷ facts: x 8 Derive & re-call x facts and corresponding ÷ facts: x 9 Derive & re-call x facts and corresponding ÷ facts: x 10 Add or subtract mentally pairs of two-digit whole numbers (e.g. 47 + 58, 91 – 35) Add mentally pairs of two-digit numbers (e.g. 47 + 58) Subtract mentally pairs of two-digit numbers (e.g. 91 – 35)

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 4 Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders (e.g. 15 x 9, 98 ÷ 6)

Develop and use written methods to record, support and explain multiplication of two-digit numbers by a one-digit number (e.g. 15 x 9) Develop and use written methods to record, support and explain division of two-digit numbers by a one-digit number, including with remainders (e.g. 98 ÷ 6) Know that angles are measured in degrees and that one whole turn is 360°; compare and order angles less than 180°. Know that angles are measured in degrees and that one whole turn is 360° Compare and order angles less than 180°. Choose & use standard metric units & their abbreviations when estimating, measuring & recording length, weight & capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg) Choose & use standard metric units & their abbreviations when estimating, measuring and recording length. Choose & use standard metric units & their abbreviations when estimating, measuring and recording weight. Choose & use standard metric units & their abbreviations when estimating, measuring and recording capacity. Know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.3 m or 0.6 kg). Answer a question by identifying what data to collect; organise, present, analyse & interpret the data in tables, diagrams, tally charts, pictograms & bar charts, using ICT where appropriate.

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 5 Explain what each digit represents in whole numbers and decimals with up to two places and partition, round and order these numbers. Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences and doubles and halves of decimals (e.g 6.5 ± 2.7, half of 5.6, double 0.34). Derive sums and differences of decimals (e.g. 6.5 ± 2.7) Derive doubles and halves of decimals (e.g. half of 5.6, double 0.34) Use efficient written methods to add and subtract whole numbers and decimals with up to two places. Use efficient written methods to add whole numbers and decimals with up to two places. Use efficient written methods to subtract whole numbers and decimals with up to two places. Read and plot co-ordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides Read and plot co-ordinates in the first quadrant Recognise parallel & perpendicular lines in grids & shapes Use a set-square and ruler to draw shapes with perpendicular or parallel sides Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle's area

Draw and measure lines to the nearest millimetre Measure and calculate the perimeter of regular and irregular polygons Use the formula for the area of a rectangle Construct frequency tables, pictograms and bar and line graphs to represent the frequencies of events and changes over time

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 6 Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000); find equivalent percentages, decimals and fractions

Express one quantity as a percentage of another (e.g. express £400 as a percentage of £1000) Find equivalent percentages, decimals and fractions Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6) Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer Use efficient written methods to add integers and decimals Use efficient written methods to subtract integers and decimals Use efficient written methods to multiply integers and decimals by a one-digit integer Use efficient written methods to divide integers and decimals by a one-digit integer Use efficient written methods to multiply two-digit and three-digit integers by a two-digit integer

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.

Refined key objective grids for the renewed Primary Strategy Framework

Key Objectives: Year 6 Visualise and draw on grids of different types where a shape will be after reflection, after translations, or after rotation through 90° or 180° about its centre or one of its vertices Visualise and draw on grids of different types where a shape will be after reflection Visualise and draw on grids of different types where a shape will be after translations Visualise and draw on grids of different types where a shape will be after rotation through 90° or 180° about its centre or one of its vertices Select and use standard metric units of measure and convert between units using decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa) Select and use standard metric units of measure Convert between units using decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa) Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask

Where appropriate, objectives have been broken down into smaller steps (shown in italics below each objective). Pupils need to achieve all the steps below an objective before they can be assessed as having met that objective.