Fractions: Unit fractions - what are they? Is it true the larger the denominator - the smaller the fraction? Which fraction is bigger? Can you use division to work out a fraction of a quantity? What is a non-unit fraction?
These are just some of the problems we will be looking at this week. Join in and have fun with it. Remember, children need to have a good understanding of the foundations before they can move on.
We still have those days when we find it difficult to add basic numbers, but we have days where we can talk about the maths we are doing and show good understanding. But that's fine, because every time we have to take what seems like a step back - it is just helping to secure his knowledge a little more.
We have come so far in just one year by taking small steps and even though progress at times seems very slow - it is still progress. The wonderful thing about learning at home is that we have the time to make the understanding solid. Remember a lot of these ideas are taken from 'White Rose Maths' which is a very visual and hands on way of exploring maths. A lot more schools are using this programme now which I am very pleased about. It might mean that more of our children have less fear of numbers.
So let's look at what we managed to do last week.
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.
I will drew a grid with half the square coloured in but in a random order. I then asked -
I have been trying to shade just half my shape.
Have I shaded half?
Explain to me how you know.
It took a while before we could tell me that we would have to count all the squares and he wrote the number at the top of the page. Then we needed to use counters to work out what 1/2 of 12 was. In the end we agreed that there were 6 blue squares so it must be half shaded.
Then we talked about wanting new tiles for my kitchen. We had a grid and we discussed again that we would need to see how many square there were altogether. We worked out with the help of counters that he would need to shade in 12 squares. Even with encouragement and explaining that he could colour the squares in anywhere on the grid, he chose to stick to a half pattern he was more familiar with.
On the second grid he tried to do the same but just before he filled in the last square, he realised that the familiar half and half pattern was not going to work - so the last square was placed away from his pattern. This is very telling because he shows that he is not comfortable enough yet to take a leap into the unknown.
Colouring in 1/4 of each shape he found very easy.
Reasoning and 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?
He loved doing these - again we used our counters to help and 'shared' them out. We talked about sharing - and these problems were almost the same as the ones we had done before when we were doing division.
More paper cutting.
When I asked him about which would be bigger with the strips of paper - he said 'That's easy. The half will be bigger'. I asked him to show me using the two strips of paper. I was very pleased and surprised when he folder the strips very well and then showed me what half and a quarter looked like. We stuck the strips in his book and he was keen to move on to folding other bits of paper to make half's and quarters.
Because of time catching up with us this week and various hospital appointments that was as far as we managed.
I will start next week with the cutting ribbon problem - and then go onto thirds as well as the other problems from last week.
Now for the next lot of FRACTIONS:
We are going to talk about a unit fraction being just one part of a whole. We will also be starting to use the word denominator and talk about how it shows us the number of parts (bits) that a shape or a group of something is divided into.
First we will start off with a grid.
(There will be a copy of this on the topics page under the resources tab. Fractions 2)
We will talk about how we are going to be filling in the grid. As always - talking is very important - it helps to cement understanding.
Can I Make?
We are going to play with counters. We are going to start with 12 counters and we are going to find what
1/2 of 12 is.
1/4 of 12 is.
1/3 of 12 is.
Then we are going to repeat it with 24 counters.
We are going to look at our answers in the book and we are going to talk about - What is the same? What is different?
We can carry this on with different amounts. Then we can talk about some numbers not working for all three fractions.
In his book I will write some questions like this -
What is my number?
1/3 of my number is 12.
1/4 of my number is 3 less than 1/3 of my number.
What is 1/2 of my number?
I have 20 toy cars.
Can I find 1/2, 1/3, and a 1/4 of the cars without breaking any?
Now to go onto non-unit fractions:
We are going to talk about things like -
How many quarters make a whole?
How many quarters are there in 3/4?
In 3/4 what does the digit 3 represent? What does the digit 4 represent?
What is the difference between unit fractions and non-unit fractions?
So we will start off with another grid. (fractions 2)
I will talk to Tiny about what the number at the top of the fraction represents and introduce the word NUMERATOR. We will talk about the numerator being the 'normal' number and that it tells us how many bits were talking about. The DENOMINATOR lets us know how many bits there are altogether.
I'm not expecting Tiny to remember these words at this stage - I just want him to hear them.
Shading 3/4 of a shape:
We will be doing this with cut out paper shapes as well - looking at 2/3 as well as 2/4 and 3/4.
Lastly for this week we are going to look at whole numbers and how they are represented in fractions.
Lot's of talking and playing around with cutting paper this week as well as the book work.
We still have some of last weeks to catch up on - so its going to be a busy week for us.