## About our programmes

Our programmes help children to develop their reasoning skills which are important because they contribute to achieving a sound understanding of the world around us. We aim to build confidence, resilience and curiosity alongside skills through teaching reasoning in a non-threatening way. As children talk about their reasoning, they achieve independent thinking and understanding.

Two programmes are currently available to schools: Mathematical Reasoning in Year 2 and Reasoning about Fractions in Year 4. As a parent, you can give your child a jump start in Mathematical Reasoning, if your child is in Year 1 and in Reasoning about Fractions, if your child is in Year 3. If your child is or will be engaging with the programmes in Year 2 or Year 4, you can help to consolidate their learning. You can do this by playing at home games that support their reasoning. We have heard from parents who play games with their children that they all find it a rewarding experience. Check what is available to parents for each of the programmes.

## Mathematical Reasoning (Year 2)

Mathematical Reasoning in Year 2 focuses on promoting the children's understanding of numbers and problem solving.

This programme is important because it puts reasoning at the heart of mathematics lessons. Mathematics is much more than learning procedures and memorising facts: it is mostly about reasoning. Children need to be able to reason mathematically in order to make sense of the world and appreciate the beauty and power of mathematics. This programme will support them to achieve the aims of the National Curriculum.

The National Curriculum for mathematics aims to ensure that all pupils:

– become** fluent in the fundamentals of mathematics**, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

– **reason mathematically** by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

– can **solve problems** by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

This programme will help your child to solve problems and make decisions, to explain how they solved a problem and why they made a particular decision, to be more confident in problem solving and reasoning situations.

Your child will be learning to understand addition and how it relates to subtraction through actively solving problems and discussing their answers. For example, they will be reasoning that if you add and take away the same number of blocks from a row, the number in the row does not change. Your child will also be reasoning about what happens when you take away one less block than you added or when you take away one more block than you added.

Your child will be learning to reason about the different relationships that can be established between quantities by using objects to support their reasoning. For example, in additive relations problems they will be adding and taking away objets in problems such as *‘A girl has some sweets. Her Mum gives her two sweets and she now has eight sweets. How many did she have to start with?’ *In multiplicative relations problems, they will be using sharing to answer questions such as ‘*A boy is having a party and he has 18 balloons. He gives two balloons to each friend at his party and has no balloons left. How many friends are there at the party?’*

You can help at home by talking to them about mathematics in their environment so that they don’t just see mathematics as being numbers on a page. For example, if they have some sweets to share with friends or siblings, you can ask them to predict how many each one will get, then share them out, and then check their predicion.

Remember that mathematics is a language that can be developed through discussion, so ask questions and discuss their answers.

- What do we know?
*(How many***sweets altogether?**; how many**children sharing**?)

- What do we need to find out?
*(How many***sweets for each child?**)

- What would happen if…?
*(If there were***more children**? If there were**more sweets**?)

- How do you know that?
*(Can you***show me**using these sweets?)

## Fractions (Year 4)

Most children find fractions confusing, but fractions are crucial for further learning of maths and parents can help children make sense of fractions.

This novel approach to teaching fractions is research based. Research shows that children are often confused because 2, 3, 4, 5 and so on stand for increasing quantities but 1/2, 1/3, 1/4/ 1/5 and so on stand for decreasing quantities. This is because in whole numbers the digits 2, 3, 4, 5 etc. show how many things we added to a group of objects that we are counting. In fractions the same digits show the number of parts into which something was cut and, the more parts you cut a cake into, the smaller the parts will be.

Reasoning about Fractions is a programme that supports children’s thinking about division before they learn how to do fraction arithmetic. In only eight lessons, the programme improved children’s understanding of basic fraction concepts. At the end of the lessons, some children said that “fractions are the best thing in maths”.

The focus of the National Curriculum is on fractions as numbers. However, in order to understand numbers, children need to think about how the numbers relate to their experiences. If fractions are just symbols on a page or if they are seen as names for pieces of pizza or of chocolates, they cannot make sense of the fractions as numbers that indicate division.

Your child will develop confidence in understanding concepts that are actually quite difficult in maths and will have a solid basis for further learning of maths in later years. This is because your child will learn how everyday thinking about division helps them learn about fractions in school.

Your child will be making connections between ideas that they understand but cannot explain clearly in words or using numbers. For example, your child knows that, if two children share a cake, each one gets more than if three children were sharing the same cake. But your child may not be able to explain that, the more people sharing, the less each one gets, or may not connect this to the idea that 1/2 represents a quantity larger than 1/3.

The programme Reasoning about Fractions in Year 4 was created to help children make connections between ideas about sharing that they understand in everyday life and fractions.

The programme also aims to expand children’s understanding of how fractions are used in other situations. For example, if one child drinks a juice that is made with 1/2 orange concentrate and the rest is water and another child makes a juice that is made 1/3 concentrate and the rest is water, the first child’s juice tastes more orangey.

You can help at home by talking to them about mathematics in their environment so that they don’t just see mathematics as being numbers on a page. For example, if they have some sweets to share with friends or siblings, you can ask them to predict how many each one will get, then share them out, and then check their predicion.

Remember that mathematics is a language that can be developed through discussion, so ask questions and discuss their answers.

- What do we know?
*(How many***sweets altogether?**; how many**children sharing**?)

- What do we need to find out?
*(How many***sweets for each child?**)

- What would happen if…?
*(If there were***more children**? If there were**more sweets**?)

- How do you know that?
*(Can you***show me**using these sweets?)

## Activities to use at home

You can watch a video of the Caterpillar Game and then download it to play at home.