# Maths Overview

#### How do we teach for Mastery for Maths in Early Years?

##### Fluency

In Reception we aim to teach so that children have a deep understanding of numbers.

##### Representing Numbers

We want to develop children’s number sense so that they understand the number rather than just recognising the numeral. Children need to understand that numbers can be represented in many ways, not just as a written numeral. We use many different objects and pictures to show that numbers can be represented in lots of ways.

__Some ways to represent five:__

Children sometimes need lots of practice to recognise numbers in different forms. We play matching games and encourage children to recognise and make different amounts in our indoor and outdoor areas.

##### Counting

When counting, children need to understand…

- That we need to say one number for each object counted (touch counting).
- The final number we say is how many altogether. Some children continue to count after they have reached the final object as they don’t connect the numbers they are saying to the objects in front of them.
- That we can count objects in any order and the total stays the same.

__The CPA Approach (Concrete, Pictorial, Abstract)__

**Concrete** is the ‘doing’ stage, using concrete objects to solve problems.

**Pictorial** is the ‘seeing’ stage, using representations of the objects involved in mathematical problems.

**Abstract** is the ‘symbolic’ stage, where children are able to use abstract symbols to model and solve mathematical problems.

##### Recognising amounts

Another skill that is very important is recognising small amounts without the need to count them. Initially this should be by using concrete objects such as those shown above but as children progress, allowing them to see groups of dots in different arrangements helps them to mentally ‘see’ how many objects are there without needing to count. This is a very important skill when children begin to add and subtract. Using dice is a good way to practice this skill before moving onto objects in different arrangements.

Understanding that the total stays the same even when the objects move.

When children first start to use numbers, they often do not understand that if we move objects into another arrangement the total stays the same. We practice this with many different types of objects but a useful tool is using a tens frame to be able to move counters around.

##### Problem Solving

Problem solving allows children to use their mathematical skills in lots of contexts and in situations that are new to them. It allows them to seek solutions, spot patterns and think about the best way to do things.

In Reception, problem solving might include:

- spotting, following and creating patterns
- estimating amounts of objects
- predicting how many times they can do something in a minute
- sharing objects between different groups – particularly when the amount of groups change and the amount of objects stays the same
- finding different ways to partition numbers e.g. 5 could be 5+0, 4+1, 3+2 etc.

##### Reasoning

Reasoning helps children to be able to explain their thinking, therefore making it easier for them to understand what is happening. It helps them to think about how to solve a problem, explain how they solved it and to think about what they could do differently.

In Reception, some examples of reasoning are:

- true and false statements e.g. adding one to a number always makes it smaller
- spotting incorrect number order e.g. 1, 2, 3, 4, 6, 5, 7, 8, 9, 10
- explaining how we know something or how we worked it out.

##### How can I help at home?

- Count – steps up the stairs, money into a money box etc.
- Ask children to say how many without counting (5 or fewer)
- Play games using dice/dominoes and encourage child to say how many spots without counting.
- Ask children to set the table with enough knives, forks and plates for everyone.
- Spot numbers in the environment – on phones, microwaves, clocks, registration plates, doors.
- Ask children to think of their own representations for numbers e.g. one of them, two hands, three bears, four wheels on a car, five toes, six sides on a dice, seven dwarves, eight legs on an octopus etc.
- Deliberately make mistakes. Children need to understand mistakes are normal and everyone makes them e.g. get mixed up when counting, muddle two numbers when ordering them.
- Watch Numberblocks on CBeebies. This programme is written by specialists to model mathematical concepts and represents number brilliantly. Also, Numberjacks is excellent for solving problems.
- Hide numbers around the house or garden for children to find.
- Play outdoor games like hopscotch and skittles. Even better, let children make up their own games and decide how to score points.
- Read books with mathematical concepts e.g. The Very Hungry Caterpillar, One is a snail, ten is a crab, What’s the time, Mr Wolf? The doorbell rang.
- Draw attention to more and less.
- Ask questions “How many more?”, “How many altogether?”, “How many would I have if?