Mathematics in St. Ann’s school is creating mathematically literate children. This give them the skills needed to fully interact and grow in the modern world.

 

Our aims in teaching Mathematics include:

  • supporting all children in school to help them develop their skills and language in mathematics.
  • to apply and use the skills they have learnt to increase their ability to reason in a variety of contexts.

 

Number - Addition and Subtraction

 

 

 

For calculations that can be done wholly or partially by mental methods children should be taught to record their methods using:

 

  • Horizontal number sentences and
  • empty number lines.

 

Number sentences

 

Care should be taken that these are mathematically correct and do not make incorrect use of the equals sign.

 

Eg 42 + 35 = ! might be calculated by partitioning the second number to add the tens followed by the units.  This could be recorded as:

42 + 30 = 72

72 + 5 = 77

But not as 42 + 30 = 72 + 5 = 77

 

Empty Number Lines

 

As soon as children are ready they should learn to work with empty number lines.  They will need to work on empty lines alongside other lines before they are confident to rely on empty lines alone.  To make good use of empty lines children need to be able to:

 

  • Move forward and back confidently on the number line.
  • Make jumps of different sizes.
  • Use number complements to 10 and multiples of 10.
  • Partition and recombine numbers in appropriate ways e.g. see 7 + 5 as 7 + 3 + 2, or 28 + 9 as 28 + 10 – 1.

 

Teachers should demonstrate the use of number sentences and number lines to model the steps in calculations.  Children should be encouraged to record the steps in their mental calculations some of the time.  Recording is useful when explaining methods to others and to show which strategy has been used.  It is not necessary to always record, especially for those children who have efficient mental methods.  Teachers should use their judgement about when to require recording.  The following year-by-year charts give examples of the type of recording that should be used for mental calculations, based on the main strategies that are likely to be used.  They are by no means exhaustive and reference should be made to the documents listed above when planning mental calculation sessions.

 

The progression to compact standard written methods should be made using expanded written methods that build on mental methods and which continue to highlight understanding of the number system and number operations.  Children should continue to develop their mental calculation skills once written methods are introduced and should be given opportunities to identify which calculations might be done mentally, with reference to the nature rather than magnitude of the numbers involved.  They should continue to record mental calculations as described above.  Teachers need to judge when children are ready to move from mental to written calculations.  The following list offers some guidance.

 

Addition and Subtraction

 

  • Do they know addition and subtraction facts to 20?
  • Do they understand place value and can they partition numbers?
  • Can they add three single digit numbers mentally?
  • Can they add or subtract any pair of two digit numbers mentally?
  • Can they explain their mental strategies orally and record them using horizontal number sentences or an empty number line?

 

The following table gives an overview of expectations for each year group.  

 

Year

Addition and subtraction

1

Children in Year 1 should be taught to:

 

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.

 

2

Children in Year 2 should be taught to:

 

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.

 

3

Children in Year 3 should be taught to:

 

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.

 

 

 

4

Children in Year 4 should be taught to:

 

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.

 

5

Children in Year 5 should be taught to:

 

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.

 

 

 

Number - Multiplication and Division

 

Children should develop understanding of multiplication as:

 

  • repeated addition
  • describing an array
  • scaling

 

Children should develop an understanding of division as:

 

  • grouping
  • sharing

 

Up to Year 3 children can develop this understanding and perform calculations through recording in a variety of ways:

 

  • drawing pictures and making marks
  • drawing and partitioning arrays
  • drawing steps on number lines
  • writing number sentences.

 

The progression to standard methods should be made using informal written methods that build on mental methods and continue to highlight understanding of the number system and number operations.  Readiness for such methods might be judged by reference to the following criteria:

 

  • rapid recall of multiplication and division facts for 2, 3, 4, 5 and 10 times tables
  • understanding of what happens when a number is multiplied by 0 or 1
  • understanding of 0 as a place holder
  • ability to multiply two- and three-digit numbers mentally by 10 and 100
  • understanding of the commutative, distributive and associative laws (though not the names)
  • ability to double and halve two-digit numbers mentally
  • ability to explain mental strategies orally and in writing.

 

The following table gives an overview for each year group followed by examples for each year.

 

 

 

 

 

 

 

 

Year

Multiplication and division

1

Children in Year 1 should be taught to:

 

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.

 

2

Children in Year 2 should be taught to:

 

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.

 

3

Children in Year 3 should be taught to:

 

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.

 

4

Children in Year 4 should be taught to:

 

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.

 

5

Children in Year 5 should be taught to:

 

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