### What am I going to learn in Mathematics?

Reception

During the autumn term, the children will explore the composition of numbers within 5 before they compare sets of objects and use the language of comparison. They begin by subitising to 3 and counting using 1:1 correspondence. The children will focus on counting to 5 and the key representation of ‘5 fingers on one hand’, and the die-five pattern.

In the spring term, the children will develop their subitising and counting skills. Explore the composition of numbers within and beyond 5. Identify when two sets are equal or unequal and connect two equal groups to doubles before connecting quantities to numerals.

Year One

In the autumn term, the children will begin by sorting and grouping objects up to 10. They then count to 10 and focus on ‘one more’ and ‘one less’ before learning how to use a number line to count forwards and backwards. Next, they will extend their ability to count, compare and order numbers to 20, as they begin to learn the essential foundations of place value and recognise the place value of each digit in a 2-digit number. Their next step will be focusing on interpreting, ordering and comparing numbers to 50 as they extend their calculation skills and number knowledge to larger numbers and to an increasing range of situations. Children will then develop their understanding of, and ability to manipulate, numbers to 100. They will investigate patterns in 2-digit numbers, specifically 1 more and 1 less, and 10 more and 10 less, before moving on to partition numbers and identify the place value of digits within a number.

During the spring term, children are introduced to formal addition for the first time through the idea of ‘count all’ and ‘count on’ strategies. A ‘count all’ strategy is when all parts are added together to make a whole. A ‘count on’ strategy asks children to start with a number and count on. Next, children are introduced to formal subtraction for the first time: they count how many are left, break apart a whole and find the difference. Children will model each of these situations using concrete and pictorial representations: taking away cubes, crossing out pictures and counting back on a number-line. Children will then begin to develop their understanding of multiplication as repeated addition, understanding the difference between equal and not equal groups. They will use their knowledge of skip counting in 2s, 5s and 10s and will use concrete, pictorial and abstract representations to help them find the total of multiple equal groups and of doubles.

Year Two

In the autumn term, the children will focus on their ability to read and understand numbers to 100. They will use their growing understanding of place value to help them sort, compare and order numbers. They will explore the place value of each digit in two-digit numbers, and compose and decompose two-digit numbers using standard and non-standard partitioning. They will reason about the location of any two-digit number in the linear number system, including identifying the previous and next multiple of 10. Children are introduced to writing fact families of equations, and to relating addition and subtraction operations. As a result, children learn to use the inverse of one operation to check calculations using the other operation. Children will also be introduced to the concept of ‘make 10’ to aid mental calculations.

During the spring term, children will progress onto addition and subtraction involving two 2-digit numbers. They will start by representing the steps within these calculations visually with different resources. Children will then use the column method as a way to represent the mental calculation steps. Children will continue to use known number facts within mental calculations and use their understanding of the inverse as a way to check their calculations. The final stage of children’s learning allows the bar model to be used to represent a word problem, to allow children to self-identify the operation needed to complete the calculation.

Year Three

In the autumn term, the children will explore that 10 tens are equivalent to 1 hundred, and that 100 is 10 times the size of 10 before applying this to identify and work out how many 10s there are in other three-digit multiples of 10. They will learn to recognise the place value of each digit in three-digit numbers, and compose and decompose three-digit numbers using standard and non-standard partitioning. Children will then reason about the location of any three-digit number in the linear number system, including identifying the previous and next multiple of 100 and 10. Next, the children will divide 100 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in multiples of 100 with 2, 4, 5 and 10 equal parts. The children will then explore additions and subtractions gradually, beginning with adding and subtracting 1s, before moving onto adding and subtracting 2-digit numbers.

During the spring term, the children will develop a depth of understanding of the key skills of formal addition and subtraction through place value, checking strategies and mental methods. They will use their growing understanding to explore calculations which do or do not require exchange. Next, the children will explore in depth each of the times-tables that they need to know in Year 3. Children are reminded of the difference between equal sharing and equal grouping and then move on to look at when division problems may have a remainder.

Year Four

In the autumn term, the children will learn that 10 hundreds are equivalent to 1 thousand, and that 1,000 is 10 times the size of 100 before applying this to identify and work out how many 100s there are in other four-digit multiples of 100. They will learn to recognise the place value of each digit in four-digit numbers, and compose and decompose four-digit numbers using standard and nonstandard partitioning. The children will reason about the location of any four-digit number in the linear number system, including identifying the previous and next multiple of 1,000 and 100, and rounding to the nearest of each. Next, the children will divide 1,000 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in multiples of 1,000 with 2, 4, 5 and 10 equal parts. They will also use column addition and subtraction to add and subtract up to three-digit numbers.

During the spring term, the children will recall multiplication and division facts up to 12 x 12, and recognise products in multiplication tables as multiples of the corresponding number. They will solve division problems, with two-digit dividends and one-digit divisors, that involve remainders, and interpret remainders appropriately according to the context. Next, the children will apply place-value knowledge to known additive and multiplicative number facts before multiplying and dividing whole numbers by 10 and 100 before understanding this as equivalent to making a number 10 or 100 times the size. They will manipulate multiplication and division equations, and understand and apply the commutative property of multiplication. Additionally, they will understand and apply the distributive property of multiplication.

Year Five

In the autumn term, the children will develop their understanding of place value through decimal numbers. They will learn that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1. Next, they will learn that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01. Children will then make the links that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01. They will recognise the place value of each digit in numbers with up to 2 decimal places, and compose and decompose numbers with up to 2 decimal places using standard and non-standard partitioning. The children will reason about the location of any number with up to 2 decimals places in the linear number system, including identifying the previous and next multiple of 1 and 0.1 and rounding to the nearest of each. They will also divide 1 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in units of 1 with 2, 4, 5 and 10 equal parts. Children will then develop their understanding of decimal numbers in a real-life context through a unit of addition and subtraction involving money. They will also convert between units of measure, including using common decimals and fractions.

During the spring term, the children will multiply and divide numbers by 10 and 100 and understand how this is equivalent to making a number 10 or 100 times the size, or 1 tenth or 1 hundredth times the size. Next, they will find factors and multiples of positive whole numbers, including common factors and common multiples, and express a given number as a product of 2 or 3 factors. Children will multiply any whole number with up to 4 digits by any one-digit number using a formal written method and divide a number with up to 4 digits by a one-digit number using a formal written method. The children will begin their fractions unit by finding non-unit fractions of quantities before finding equivalent fractions and understanding that they have the same value and the same position in the linear number system. Next, they will recall decimal fraction equivalents for 1/2, 1/4, 1/5 and 1/10, and for multiples of these proper fractions.

Year Six

In the autumn term, the children will explore the relationship between powers of 10 from 1 hundredth to 10 million, and use this to make a given number 10, 100, 1,000, 1 tenth, 1 hundredth or 1 thousandth times the size. They will recognise the place value of each digit in numbers up to 10 million, including decimal fractions, and compose and decompose numbers up to 10 million using standard and non-standard partitioning. Children will reason about the location of any number up to 10 million, including decimal fractions, in the linear number system, and round numbers, as appropriate, including in contexts. Next, they will divide powers of 10, from 1 hundredth to 10 million, into 2, 4, 5 and 10 equal parts, and read scales/number lines with labelled intervals divided into 2, 4, 5 and 10 equal parts.

During the spring term, children we learn how 2 numbers can be related additively or multiplicatively, and quantify additive and multiplicative relationships. They will use a given additive or multiplicative calculation to derive or complete a related calculation, using arithmetic properties, inverse relationships, and place-value understanding. Children will solve problems involving ratio relationships and algebra when solving problems with 2 unknowns.