# Maths

Here at Highfield Hall we encourage our children to investigate and explore in maths. We use lots of concrete resources and real-life experiences to enable children to fully engage in maths and understand the concepts they encounter. This is an approach recommended by maths specialists and consultants across the globe to enable children to fully understand key underlying principles. In this way we are ensuring children learn through understanding and experience.

"All our experience and what we learn from research indicate that learning based on understanding is more enduring, more psychologically satisfying and more useful in practice than learning based mainly on the rehearsal of recipes and routines low in meaningfulness."  Derek Haylock and Ann Cockburn

## Autumn 1

We have been learning all about numbers and what they mean. We thought about what we saw in our heads when we thought of a number and talked about what numbers mean to us. We made numbers in lots of different ways and explored how numbers are different. We explored questions such as "What does 4 mean?" and "How are 4 and 7 different?"  We chose which resources we wanted to use to show our thinking and to explore numbers further.

## What does 4 mean?

After thinking about number and what they mean we were challenged to answer the question:

What is the difference between 4 and 7?

We use unifix to make the 5 and 7. We talked about how what we made was the same and how they were different. We could all tell our partner that one was smaller and one was bigger. Some children said that the difference between 4 and 7 was 3. They found this out by lining the two quantities up and finding that to turn the 5 into 7 they would have to add 3 more cubes. Some children said they one tower was bigger and one tower was smaller.

Singapore Bar Model

We have started learning about the bar model and how we can use this to represent addition. We used number facts we have already learnt to start thinking about how we can add parts together to make a whole! We are really good at our number bonds to 10 so we used raisins to make a bar model of number bonds to 10. We then found all the ways you can make 10 with 2 parts and wrote the numbers to show the size of each part and the whole. We did this really well and had lots of fun!

## Bar model 3.mp4

The children shared their raisins equally on their boards before sharing them with a partner.

We also use a song to help us understand the number bonds to 10. We love to sing along to Farmer Pete! If you use the link you can sing along at home too!

After making the bar model with raisins we thought about how to draw each number bond. We tried very hard to make our bars look like the correct value through their size. We found that all of our number bonds were equivalent to 10.

After learning how we can use a bar model to represent numbers and their relationships we started looking at other part, part, whole models. We have used the circle model to show how addition and subtraction are related and have also used them to find all the ways of making number bonds up to 20. Here we are generating our own numbers, using the model to understand what we need to do and why and using cubes to calculate the addition to find the 'whole' or total.

On Pirate Day we applied what we have learnt about equals, number bonds and part-part-whole to create biscuits! Some children said, "I’m going to share ours equally so we will get 5 and 5 sweets each.” We love maths – especially when it involves food!

## Autumn 2

We have been thinking about the history of numbers. Have they always existed? What did people do before numbers existed? Why do we use them? How difficult would it be without them? We thought about cavemen and building the best fire. How would they have known how many was ‘enough’ and used language such as fewer, more than and equal to compare amounts until we had ‘enough’. This was much harder than getting a given number of sticks. We also found that comparing could be tricky. How we lay out our sticks can change how many we think there are. We thought carefully about how we could know who had more without counting, Then we remembered ten frames. We used cavemen chalk to draw ten frames to compare quantities of sticks.

We have done lots of learning around subitising, addition, subtraction and ten frames. We have also been investigating the purpose of numbers and our number system! Today a some cavemen left us a puzzle to solve. When we arrived in school there was a mysterious box on the classroom floor. It was surrounded by sticks and leaves. We think the cavemen had left it because we have been learning about where counting and numbers began - looking at what cavemen would have done before numbers existed! We were very excited but we needed a code to open the box...it was locked!

The cavemen had left clues around our classroom. Cavemen don’t use numbers so they showed us the quantities using ten frames. We used the ten frames and our knowledge about addition to calculate which numbers might open the mysterious box. We recorded what we found.

We tried entering our numbers into the keypad on the box but it still wouldn’t open. We decided we might need a particular order so we worked together using number cards to try out various codes. It still wouldn’t work. Then we started to think the cavemen might have been logical with the order the numbers might be in. We tried sequencing the numbers from smallest to largest.

It worked! The code opened the box and we found treasure inside. We all shared the treasure. We are so pleased we could use our maths!

## Spring 1

Understanding and recall of number bonds to 10 is vital to future maths success so we have been checking our knowledge and skills in this area. We use what we knew to help Little Red Riding Hood. The wolf kept stealing buns from her basket and she had to deliver 10 buns to Grandma. We helped her know how many more she needed when he stole some from her. We were fantastic at this!

## Spring 2

This term started with the children being given a challenge from an inventor. He wanted to invent a new chocolate bar, we had the size of the chocolate bar he wanted to do invent and our job was to help him find out how many different ways he could split his chocolate up into pieces. But the pieces had to be equal to the size of the bar.

Then he rang again, giving them a challenge to make all the pieces of the bar equal to each other. The children were a great help! As Steve the inventor even changed the size of his chocolate bar a few times, as he wanted a snack sized bar and a super sized bar - meaning we had to find more answers for him.

The children found a great way to record their answers for him. They wrote their calculations using equations (the letters representing the colour of the bars they were using). Steve the inventor was so impressed with their work they received a chocolate button from him on the last day of their investigations!

## Dividing

This term the children have been learning about fractions and division. During this lesson the children were learning how to divide by 5.

The children had a very active lesson exploring measurement. The children had a carousel of activities:

• What can you do in a minute? E.g. How many jumps? How many hops? Etc..
• Which container holds the most cubes?
• Can you find items around the room larger and smaller than a metre?
• What items are heavier/lighter than a Kg?
• Can you make a play doh snake to specific cm measurements?

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