# Mathematics

Our intention within the mathematics curriculum is for all pupils to attain the knowledge, skills and understanding necessary to be able to reason and problem solve both within maths and across other subjects.  We recognise that for children to be able to achieve this, they need to develop fluency and confidence across all aspects of mathematics, particularly with number, place value and quick recall of number facts (like number bonds and times tables).

We also focus on developing the children’s formal written methods for calculations alongside more practical exploration of maths through concrete and pictorial representations of their thinking.

### The three core strands to our mathematics curriculum are:

• Fluency - Pupils will become fluent in the fundamentals of mathematics. They will develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• Reasoning - Pupils will learn to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
• Problem solving -  Pupils will learn to seek solutions not just memorise procedures, explore patterns not just memorise formulas, and formulate conjectures, not just do exercises.

When introducing new learning we use the following three stages:

• Concrete - the children use resources and real objects to represent their thinking
• Pictorial - the children use pictures and images to represent their thinking
• Abstract - the children use mathematical symbols to show their thinking

To help the children progress to using formal, quick methods for maths calculations, we have produced  sheets to show the steps children will make as they become confident mathematicians. Please click on the written calculation progression tab.

### Tables challenge

Learning your times tables is a vital component of our mathematics curriculum. To help your child learn their tables, start by reciting them in order, and then randomly. Children learn in different ways, so it can be helpful to provide them with lots of ways to learn their tables:

• Have a large poster of the table being learnt in the kitchen.
• Have a CD of times table songs which your child can sing along to at bedtime or in the car.
• Some children benefit from writing out the table, or using a computer game.

For children in Year 1 and 2, start with the following tables: 2x, 5x and 10x. Once they have mastered these they can move onto 3x and 4x.

Older children need to ensure they keep these times tables fresh in their memory and move on to learning 6x, 7x, 8x, 9x, (and 11x and 12x when ready)

Occasionally we will test the children at school, but they will be using their tables knowledge all the time in their maths lessons.

### Mental Fluency

To enable pupils to master the skills and knowledge needed to become a competent mathematician, children need to be able to recall quickly a number of mathematical facts.

We have organised these quick recall facts in to expectations for each Year Group.  Pupils are taught these new concepts, skills or knowledge and then regularly tested to enable them to secure it in their long term memory.

Our Mental Fluency expectations fall in to 4 categories:

1. Bonds & Complements
2. Double & Half
3. Counting
4. More or Less

 EARLY YEARS Bonds & Complements Number bonds up to 5 a + b = c Double & Half Doubles to 5 Counting Counting to and across 20, forwards Counting to and across 20, backwards Skip counting in 10s to 100 One More One more to 20

 YEAR 1 Bonds & Complements Number bonds to 10 a+b=c, including adding zero (Aut) Double & Half Double and half within 10 (Spr) Counting Count from 0, 1 or any other number (Aut) Count to and across 100 forwards and backwards (Spr) Skip counting in 2s to 24 (Sum) Skip counting in 5s to 60 (Sum) Skip counting in 10s to 120 (Sum) More or less Identify one more & one less from a given number up to 20 (Spr) Identify one more from a given number up to 100 (Spr) Identify one less from a given number up to 100 (Spr)

 YEAR 2 Bonds & Complements reordering to find 10 e.g. 6+5+4= (6+4)+5 (Aut) addition & subtraction facts to 20 (Spr) addition facts of tens numbers 30+40 (Spr) Double & Half Double & Half within 20 (Spr) Counting count to and across 100 from any number (Aut) count forwards and backwards across 10 numbers (Aut) multiplication & division facts 2 (Aut) 10 (Aut) 5 (Spr) 4 (Sum) More or less 10 more or less than any given number up to 100 (Spr) find 9 &/or 11 more or less than any number (Sum)

 YEAR 3 Bonds & Complements Know number bonds to 20 and derive related facts e.g 13 + 5 = 18, so 23 + 5 = 28 (Aut) Partitioning of 2 digit numbers e.g. 27 = 20 + 7 (Aut) Can apply addition and subtraction up to 10 to multiples of 10 and 100. e.g. 3 + 4 = 7, 30 + 40 = 70 (Spr) Complements to 60 of multiples of 5 and 10 (time) e.g. 45 + ? = 60 (Sum) Complements of fractions with the same denominator that make 1. e.g 3/7 and 4/7 = 1 (Sum) Double & Half Doubles and halves of multiples of 10 e.g. 2 doubled = 4, 20 doubled = 40 (Aut) Near doubles within 20 6+7 = 6+6+1 (Spr) Counting Count to and across 1000 from any number (Aut) Count forwards and backwards across hundreds numbers (Aut) Skip count in 50s and 0.5s (Spr) Times table and division facts 5 (Aut) 10 (Aut) 2 (Aut) 4 (Spr) 8 (Spr) 3 (Sum) 6 (Sum) Division and multiplication by 10 (Spr) More, Less Identify 1 more or 1 less than any given number within 1000 (Aut) Identify 10 more or less of any number within 1000 (Spr) Identify 19 &/or 21 more or less than a number (add 20 and adjust by 1) (Sum)

 YEAR 4 Bonds & Complements Can apply addition and subtraction up to 10 to multiples of 1000. e.g. 3 + 4 = 7, 3000 + 4000 = 7000 (Aut) Know number bonds to 20 and derive related facts to two 2 digit numbers e.g 13 + 5 = 18, so 23 + 35 = 58 (Spr) Complements to 100 e.g. 37 + ? = 100 (Spr) Complements to 60 of any number (time) e.g. 47 + ? = 60 (Sum) Complements of tenths that make 1 e.g 0.3 + 0.7 3/10 + 7/10 (Sum) Double & Half Doubles and halves within 100 (Aut) Doubles and halves of multiples of 10, 100 or 1000 (6 + 6, 60 + 60, 600 + 600) (Aut) Counting Division and multiplication by 100 (Spr) All multiplication and division facts to 12 x 12 (including by zero and one) 2,5,10 (Aut) 3,4,8 (Aut) 6,7,9 (Spr) 11,12 (Spr) Count to and across 1 in tenths (0.8, 0.9, 1.0, 1.1 ..) (Sum) More or less Identify "multiples of 10" more or less of any number within 1000 e.g. 20 more or 30 less than a number (Spr)

 YEAR 5 Bonds & Complements Complements of hundredths that make 1 e.g. 0.75 + 0.25 2/100 + 98/100 Double & Half Doubles and halves within 1000 Know near doubles within 100 e.g. 45 + 46 Find the mid-point between 2 numbers e.g. what number is half way between 124 and 187 Counting Know square numbers and square roots up to 144 Skip count in 25s & 0.25s Skip count in 20s & 0.20s Count to and across 1 in hundreths (0.98, 0.99, 1.00, 1.01...) More or less Identify 99 or 101 more or less than a number

 YEAR 6 Bonds & Complements Know number bonds/complements to 1, 50, 100, 1000 Double & Half Know doubles and halves of 1000 Find the mid-point between 2 numbers e.g. what number is half way between 124 and 187 Counting Count forwards and backwards across zero Add and subtract negative numbers from -10 to 10 Rebalance to make calculations easier More or less Add or subtract any number from a given number up to 100

### Formal Written Calculations

We follow a specific plan in the way we teach written calculations in maths.  Please take a look at the documents below to see the progression in addition, subtraction, multiplication and division.