Addition Subtraction Multiplication Division CPA for parents Addition Subtraction Multiplication Division

Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Combining two parts to make a whole (part whole model). Starting at the bigger number and counting on (using cubes). Regrouping to make 10 using tens frame. Key symbols + =

Year 1 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.

Addition: reception/year 1

- = Subtraction:reception/year 1 Key vocabulary Take away Less than The difference Subtract Minus Fewer Decrease Expectations Taking away ones Counting back Finding the difference Part whole model Make 10 using the ten frame Key symbols - =

Subtraction:reception/year 1

Subtraction:reception/year 1

Addition: year 2 Expectations Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Adding three single digits. Use of base 10 to combine two numbers. Key symbols + = Addition: year 2

Year 2 Addition and subtraction solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures 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: a two-digit number and ones a two-digit number and tens two two-digit numbers 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.

Addition: year 2

- = Subtraction: year 2 Key vocabulary Take away Less than The difference Subtract Minus Fewer Decrease Expectations Counting back Finding the difference Part whole model Make 10 Use the base of 10 Key symbols - =

Subtraction: year 2

Addition: year 3 Expectations Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Column method- regrouping. Using place value counters (up to 3 digits). Key symbols + = Addition: year 3

Year 3 Addition and subtraction add and subtract numbers mentally, including: a three-digit number and ones a three-digit number and tens 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.

Addition: year 3

- = Subtraction: year 3 Key vocabulary Take away Less than The difference Subtract Minus Fewer Decrease Expectations Column method with regrouping (up to 3 digits using place value counters) Key symbols - =

Subtraction: year 3

Addition: year 4 Expectations Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Column method- regrouping (up to 4 digits). Key symbols + = Addition: year 4

Year 4 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.

Addition: year 4

- = Subtraction: year 4 Key vocabulary Expectations Take away Less than The difference Subtract Minus Fewer Decrease Expectations Column method with regrouping (up to 4 digits) Key symbols - =

Subtraction: year 4

Addition: year 5 Expectations Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Column method- regrouping (up to 4 digits). Use of place value counters for adding decimals. Key symbols + = . Addition: year 5

Year 5 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.

Addition: year 5

- = . Subtraction: year 5 Key vocabulary Expectations Take away Less than The difference Subtract Minus Fewer Decrease Expectations Column method with regrouping Abstract for whole numbers Start with place value counters for decimals- with the same amount of decimal places. Key symbols - = .

Subtraction: year 5

Addition: year 6 Expectations Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’ Expectations Column method- regrouping (up to 4 digits). Abstract methods. Place value counters to be used for adding decimal numbers. Key symbols + = . Addition: year 6

Year 6 Addition and subtraction perform mental calculations, including with mixed operations and large 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.

Addition: year 6

- = . Subtraction: year 6 Key vocabulary Expectations Take away Less than The difference Subtract Minus Fewer Decrease Integer Decimal Expectations Column method with regrouping Abstract methods Place value counters for decimals - with different amounts of decimal places. Key symbols - = .

Subtraction: year 6

Multiplication and division

Year 1 multiplication 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.

x = Multiplication: reception/year 1 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Recognising and making equal groups. Doubling. Counting in multiples Use cubes, Numicon and other objects in the classroom Key symbols x =

Multiplication: reception/year 1

÷ = / Division: reception/year 1 Key vocabulary Share Group Divide Divided by Half Expectations Sharing objects into groups Division as grouping (e.g. I have 12 sweets and put them in groups of 3, how many groups?) Use cubes and draw round the same number of cubes at a time. Key symbols ÷ = /

Division: reception/year 1

Year 2 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.

x = Multiplication: year 2 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Arrays- showing commutative multiplication Key symbols x =

Multiplication: year 2

÷ = / Division: year 2 Key vocabulary Share Group Divide Divided by Half Expectations Division as grouping Division within arrays- linking to multiplication Repeated subtraction Key symbols ÷ = /

Division: year 2

Year 3 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.

x = Multiplication: year 3 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Arrays 2d × 1d using base 10 Key symbols x =

Multiplication: year 3

÷ = / Division: year 3 Key vocabulary Share Group Divide Divided by Half Expectations Division with a remainder-using lollipop sticks, times tables facts and repeated subtraction. 2d divided by 1d using base 10 or place value counters Key symbols ÷ = /

Division: year 3

Year 4 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.

x = Multiplication: year 4 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Column multiplication- introduced with place value counters. (2 and 3-digit multiplied by 1-digit). Key symbols x =

Multiplication: year 4

÷ = / Division: year 4 Key vocabulary Share Group Divide Divided by Half Expectations Division with a remainder. Short division (up to 3 digits by 1 digit- concrete and pictorial). Key symbols ÷ = /

Division: year 4 Year 4 Year 5

Year 5 Multiplication and division identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 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 1,000 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

x = Multiplication: year 5 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Column multiplication Abstract only but might need a repeat of year 4 first (up to 4 digit numbers multiplied by 1 or 2 digit numbers) Key symbols x =

Multiplication: year 5 Year4 Year 5

÷ = / Division: year 5 Key vocabulary Share Group Divide Divided by Half Expectations Short division (up to 4 digits by a 1 digit number including remainders) Key symbols ÷ = /

Division: year 5

Year 6 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.

x = Multiplication: year 6 Key vocabulary Double Times Multiply by The product of Groups of Lots of Equal groups (Area) Expectations Column multiplication. Abstract methods (multi-digit up to 4 digits by a 2 digit number). Key symbols x =

Multiplication: year 6

÷ = / Division: year 6 Key vocabulary Share Group Divide Divided by Half Expectations Short division. Long division with place value counters (up to 4 digits by a 2 digit number). Children should exchange into the tenths and hundredths column too. Key symbols ÷ = /

Year 6 also do short division as per year 5 Division: year 6 Year 6 also do short division as per year 5