We can do Maths 11

More Fractions

Fractions: The denominator is the bottom number of a fraction. It tells you the number of equal parts into which something is divided. The numerator is the top number and its job is to tell you how many of those equal parts you have. Sounds complicated - but it isn't when you take it step by step.

We had great fun looking at fractions again. I started to introduce the words denominator and numerator - but I didn't spend too much time on that.

We did do a lot of talking during the week on cutting cakes in half and how would we cut them into quarters. It's always more fun when you include food with maths.

I'm going to leave the expectations for year 2 and 3 on here so that you can refer back to them.

Just in case you want to know -

Year 2 expectations for fractions include:

  • Recognise, find, name and write the fractions 1/3 - 1/4 - 2/4 and 3/4 of a length, shape or set of objects.

  • Begin to recognise and find one half of shapes and small numbers of objects

  • Begin to recognise and find one quarter of shapes and small numbers of objects

  • Write a simple fractions e.g. 1/2 of 6 = 3

  • Recognise the equivalence of 2/4 and 1/2

  • Count in fractions up to 10 using a number line

Year 3 expectations for fractions include:

  • Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one digit numbers or quantities by 10

  • Recognise and use fractions as numbers

  • Recognise 1/2 - 1/3 - 1/4 - 1/5 - 1/10 and use them to find fractions of shapes and numbers

  • Know that 1/2 lies between 1/4 and 3/4

  • Estimate a simple fraction of a shape

  • Compare and order unit fractions, and fractions with the same denominators

  • Rounding decimals to the nearest 1 decimal place

  • Begin to recognise simple equivalent fractions, e.g. 5/10 is equivalent to 1/2 and 5/5 = 1 whole

  • Add and subtract fractions with the same denominator

  • e.g. 5/7 + 1/7 = 6/7

Review of what went well and things that did not.

All the things that went well.

Paper Play. Images - equal and unequal, Splitting into groups, Problem solving

Understanding that sometimes the equal parts don't look the same is more difficult. Look at this problem yourself. We had to cut out the images to make sure.

Are these equal?

You will find a copy of this on page 3.

Recognise a Half This went very well.

Problem Solving

He enjoyed the problem solving with the race and we ended up thinking of other problems that were similar.

Problem Solving

Granddad says that the shaded part of the shape does not show a half because there are four parts, not two equal parts.

Does the shaded part show half?

Ask Q. Does the green show half of the shape?

Q. Do you think that Granddad is right?

Q. What fraction of the shape is orange?

this one was a bit more difficult.

Finding a Half

Next we will be finding a half of a given number. this is where Tiny can apply his understanding of whole and two equal parts to quantities. It is important for him to understand that the total amount equals the whole and in order to find a half, this must be split into 2 equal parts.

Again this is linked to dividing by 2

The types of questions I'm going to be asking.

  1. Mum has 20 cakes. She is going to give half to Dad. How many will they have each?

  2. Bob has 10 cars in the car lot. He sells half. How many cars does he sell?

  3. Jane has 30 biscuits. She wants to save half for later. How can we work out half of 30?

We will be writing it out like this:

The whole is ____. Half of ____ is ____

For this we had to use counters.

Overall the first week went very well and his confidence in himself is growing.

Now to move on

Our next task is to understand the concept of a whole being one object or one quantity more fully.

We will stick to half's for the first part.

we will start with Problem Solving. (you will find the sheets you need on page 4 and 5 of the fractions booklet https://www.whyplay.co/topics )

I will draw a grid with half the square coloured in but in a random order. I will then ask

I have been trying to shade just half my shape.

Have I shaded half?

Explain to me how you know.

Then I am going to talk about wanting some new tiles for my kitchen. Again I will draw a grid and I will ask Tiny to fill in the grid with two colours, making sure that the pattern is half and half.

Now at last to move onto quarters:

Starting simple in the same way as before - it is the beginning of the week after all.

You will find a copy of this in the booklet

Reasoning and Problem Solving - These questions I will write in his numeracy book at the beginning of the week leaving lots of space for out answers or to glue in strips of paper that we have been working with.

More paper cutting for this one.

Take two identical strips of paper and say;

"I think 1/4 of the strip will be bigger the 1/2 because 4 is bigger than 2. What do you think?

We will then fold and cut the strips to see if I was correct.

Now we will talk about the relationship between halves and quarters and that to get a quarter you half something and then half it again.

Problem Solving:

Who has more? Work through some problems about 'Who has more'. Here is an example:-

Bob has 1/4 of £8

Jane has 1/2 of £6

Who has more?

Jed has 1/2 of 10 toy cars

Mike has 1/4 of 12 toy cars

Who has more?

Cutting Ribbon:

Mary and Sue each have a piece of ribbon that they have cut into quarters.

Mary's cut piece of ribbon is 5cm long.

Sues's cut piece of ribbon is 4cm long.

How long was Mary's whole piece of ribbon?

How long was Sue's whole piece of ribbon?

Whose ribbon was the longest?

We will be thinking of some more questions like this and then move on when we are ready.

Thirds next:

Tackle thirds in the same way and to be sure of understanding ask a question like -

"I have one third of a cake. I know its one third because I have one and there are three pieces left."

Talk about whether or not this is correct.

For this next task I am going to prepare some strips of coloured paper to help demonstrate.

Work out the answers together.

David will have the longest because he will have 4 pieces and Jo will have the shortest because he will only have 2 pieces.

Grouping objects into thirds:

In the same way we worked with the halves - we will now be grouping blocks and counters into thirds.

In the book I am going to write:

John is going to give away 1/3 of his marbles. He has 9 marbles all together.

How many marbles will he have left?

We will work through the problem using counters or blocks and we will write the answer down in the book.

At the bottom of the page I will ask him to complete the following:

1/3 of 9 = ______

1/3 of 12 = ______

1/3 of 15 = ______

1/3 of 18 = ______

More Reasoning and Problem Solving:

In the book write this problem:

Jane has a piece of string.

She cuts it into three equal parts.

One third of the string is 5cm long.

How long was the piece of string before it was cut?

This is a difficult one for some children - and it might prove very challenging for Tiny because it involves bigger numbers, but with will use counters and work it out practically.

I am thinking of a number.

One third of my number is greater than 8 but smaller than 15.

My number is even.

My number has an odd amount of tens.

What could my number be?

Remember a lot of these task can be done practically and for some children they will need to be.

So far we have been looking mainly at unit fractions - working on just one part of the fraction - 1/2. Next week we will start to look at non-unit fractions - 3/4 etc. We can make a fraction wall to help us with this. I hope you will join us.

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