Fractions: What are they? Are they just bits of something or are they much more. A fraction can be part of a whole or it can describe how a part of a group relates to the whole group. Think about the word fracture. If you were to drop a cup on the floor it might fracture into lots of small pieces. It's just the same - fractions show the parts of a complete group that has been fractured. We use fractions to help show how the pieces all fit together. There is a lot to learn about fractions, but we are going to learn about the basics first. It is important to learn the basics and have a good understanding before we can move onto the more complex aspects. So, let's give fractions a go.
There are some new words to use with this part of maths, so I will be asking Tiny later in the week to make a poster to help him remember. But for now we are just going to recap on what he already knows. We already covered fractions last year when he first started his home-schooling journey so he should be able to remember some of the things he learnt then. Even if he does remember more than I thought he would, going slowly is very important to build up his confidence. We all like to know the answers because it makes us feel good.
Remember - it never hurts to take it back to the basics for anyone that struggles with maths.
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 whitn one whole e.g. 5/7 + 1/7 = 6/7
So as you can see the expectations go up very quickly. There is no point me starting with Year 3 fractions (or Year 4 which is where he should be) if he hasn't got a very good grasp of what fractions are.
So - enough of all that. Let's get started.
Paper Play
We will be taking to strips of paper. One we will be folding carefully in half and cutting along the fold line. The other strip we will cut wherever we want.
Q. Are the parts equal?
Q. Do equal parts always have to look the same?
Q. Is there more than one way we could have cut the strip into two equal parts.
Q. Can you say what that part is called (1/2)
Images - equal and unequal
Now we are going to look at some images and decide which show equal parts and which show unequal parts. You can easily draw some images in their book or you can find some images on page one of Fractions. Found at the bottom of the topic page. https://www.whyplay.co/topics
Splitting into groups
Get sets of objects and split them into equal and unequal groups. We are going to use blocks and straws, then we are going to look at pictures of objects and do the same with that. If you want an example of the pictures we are using you will find them on page 2 https://www.whyplay.co/topics
Next ask - Q. How many different ways can you put these blocks into equal groups? (an easy number to start with is 12 because it can be split a few ways).
Problem solving
Understanding that sometimes the equal parts don't look the same is more difficult. Look at this problem yourself.
You will find a copy of this on page 3.
Some far we haven't looked at what a fraction looks like, rather we have been relating what we are doing to sharing (division). I am going to be talking to Tiny about how division and fractions are the same.
Recognise a Half
I know that Tiny is very aware of what a half is. When I ask him if I could have half of his smarties, then he will carefully count them out. Without fully understanding it he has already come to the realisation that division and fractions are related. But now, as a confidence booster we are going to look at half's again. We will not spend too long on this. Just long enough to put him in the frame of mind to go onto learning something new.
I will draw some pictures in his book and encourage him to draw some of his own. Then we will talk about which pictures represent 1/2. Something like this.
This ties in very nicely with the geometry work we have been doing and symmetry
Next I will ask him to shade in half of the shapes we have drawn and we will write the 1/2 notation down next to it. For those shapes we will put a lovely big cross.
Problem Solving
Now for a small problem where it would be very helpful to draw a line.
Tiny, Alex and Jacob are running a race. Tiny has run further than half way. Alex has only run half way and Jacob has run less than halfway.
Draw on your line where each boy could be.
Who do you think is going to win the race?
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.
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?
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.
Mum has 20 cakes. She is going to give half to Dad. How many will they have each?
Bob has 10 cars in the car lot. He sells half. How many cars does he sell?
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 ____
Our next task is going to be done with the help of our counters.
We are going to use counters to find half of the amounts. Then we are going to write a stem sentence for each amount.
The whole is ____. Half of ____ is ____.
Now the same thing in reverse.
I am going to write some questions for him in his book and he can use the counters to help him answer them.
1/2 of 10 = _______ 1/2 of ____ = 10
1/2 of 12 = _______ 1/2 of _____ = 12
You make them as easy or as difficult as you like - but remember the first few days is about building confidence.
I will be adding more to this tonight. This is just to get you started. Believe me its going to get harder. Hold onto your hats.