The whole school are going to be **leading their own learning** to learn as much as they can about …FRACTIONS…!

How much do you know about fractions?

What pictures do you see what you think about fractions?

How can you explain what you understand to others?

We are going to be using this challenge – A FAIR FEAST – from the nrich website http://nrich.maths.org/2361

Have a look at the photo of our fair feast that was found at school this week.

What would be easy to share with 2 people? What would take a lot of thinking to share between two people?

What if there were more people to share with? What fraction of each food will you get? How much of each food will you get?

The drink are easy for two people as there are two drinks. The same for the cupcakes and the chocolate rolls.the chocolate bar can be shared with lots of people as you can break it into lots of pieces. The same with the cake, crisps. Tomatoes can be shared 10 ways. Three poeple can have the breadsticks or 6 people can have breadsticks if you break them in half

I would 1/2 the tomatoes because there are 10 so you would get 5 each . 1/2

The bread sticks i would chop them in 1/2 so you would get 3 each.

Would that mean you’d get 3 halves each Amie? Would you get the same amount if you had one whole stick each and split the final one in half? Mrs M

yes i think you would .

Why? Mrs M

The juce is easy because you can just have one each . The apple is more tricky because one of us would get the stork and the other will not get the stork so it is not fare.

Here’s my ‘What if? For KS2. What if this feast was for 2 people and you increased the amounts for 4 people to have the same. E.g. 10 tomatoes for two people so how many for four people making sure they got the same amount? What if there were 6 people? 8 people? Gold stickers for anyone wanting to take this thinking further? Mrs M

I have just cut up my apple in half then half making quaters tats fare because we got 2 each and you can pull the stork of.

Y ou would need 20 tomatoes to have 5 each .

If we carried on scaling up….what about the other items in the feast? How many cakes? How much juice? Ten see if you can use this to work out enough for 6 people. Mrs M

2 people can have 5 tomatoes each because 5+5=10. You need to cut the apple in the middle so it is equal. Each person has half an apple. You need to have one whole breadstick each and break the other one in half. You get one drink each. I found different ways of cutting the cake in half.

Great halving Alice.

How could you make sure that each person gets exactly half a breadstick?

Mr E

You could measure the breadstick. If the breadstick is 20cm long you need to break it into 10 and 10. Then it is the same.

Hi Alice, 🙂 what if there were 4 people? How would you share the tomatoes then? Mrs M

I shared out ten counters. Each person got two whole tomatoes and half of one. To start with I thought it wasn’t fair but then I thought about cutting the tomatoes.

I tried sharing the feast between 7 people. If you share 2 cartons of juice you get 2/7 each. If each carton has 250ml you have 500ml to share between 7 people. I did 500 divided by 7 using a number line. Each person gets 71 ml and 3/7. If you share the tomatoes you get one whole tomato and 3/7 of a tomato. This would be a bit difficult to cut up. If you share the chocolate you get 2 whole pieces and 1/7 of a piece. If you share the two cupcakes you get 2/7 of a cake. If you were sharing the feast in real life you would not share it out equally as sevenths are tricky.

Sevenths do seem quite tricky! How many of each food would you need to make it easier to share equally?

Think of your own ‘what if’ questions to lead other people’s learning.

Mr E

I think I’ve just suggested that Mr E (but in a much more complicated way!) Mrs M

Would you rather have …?

2/3 of the chocolate or 3/5 of the chocolate. 😉 🙂

Good question.

You could give some people some hints at school to help them think it through

Mr E

If you were allowed to increase the portions of all the items ( by the same amount) is there a slightly easier number of items that would share much more easily between 7 people? Or alternatively, if this is the feast for two people in total, can you scale the feast up to feed 7 people? Mrs M

To scale it up to feed 7 people you need 3.5 times as many! To feed 6 people you need 3x as many

and to feed 8 people you need 4x as many. 7 must be in between. 😉 🙂

Very clear explaining.

Have a think about your own what if questions for others to answer.

Mr E

The cakes would be easy because there is two cakes the same with the chocolate rolls and with the drinks. The chocolate bar you would have to exchang the piece into 4 half pieces .

You have 10 tomatoes so you would get 5 tomatoes each. If there was 4 people and they wanted the tomatoes they would have to exchange the last tomatoe two times.

You would have to cut the apple in half horasontaly for 2 people and for 4 people you would have to cut it in half 2 times horasontaly to get 2 pieces.

I like your use of the word ‘horizontally’ to explain your thinking.

I think it still might need a drawing to show your thinking a bit more clearly.

Mr E

If you had 6 people to feed you whould need

30 tomatoes for each child to have 5 .

In our class we have been answering different what if questions now I have got one for you.

What if…….there were three breadsticks and 12 hungry people.

what if 12 peopel came. what if 13 peopel came. what if 14 peopel came.

Good what if questions. I wonder how many people will reply to your thinking?

Try to get others in school to answer it so you can reply to them.

Mr E

I agree Mr Ellis and Harry’s answer is grate well done

Do you think it is easier to share the feast between an even amount or an odd amount of people?

Great What if questions Harry!

If you had 10 people each person would get 1 tomatoe each.

Good thinking. What if there were 20, 30 or 40 people? Do you notice a pattern?

Mr E

If there 20 people there would be half a tomatoe each. The pattern is the more people to share with is less tomatoes for the people.

Good understanding

Is there a pattern between the number of people and the fraction of tomatoes they would get?

Mr E

What if 66 people came? What if 798 people came? What if 333 people came? What if 75317 people came? What if 4321567 people came?

So what if 1 apple was shared between 798 people? What fraction of the apple would each person get?

Mr E

We have been having oranges and apples, mummy gave me 6 pieces of a whole apple 6/6, i ate it all but only had 1 apple so 6/6 = 1

This is really good explaining. It is a great way to show how 1 whole can be divided into parts. Mr E

What if there was 41 people

What if you had 1 cake.

What if i did not share them out proply.

We (my class) have been answering different what ifs we created at the beginning of the week. We investigated different amounts of foods, people and different lengths and sizes of food.

I worked about what if their were 5 people to share the feeast between then we found what if you shared between 7 people and then i throught this is going to be hard.

Lauren here. I worked out how much food there would be if 2 friends ate it and another friend came. It’s a what if question.

What if you ate 3/4 of the food. What fraction of the food is left?

I think that you made a great explanation. But what if she ate 1/2of her oranges and apples? What would she have left?

I have learnt how to divide fractions. The divider becomes the numerator ( The top number) and the number you’re dividing by becomes the denominator (The number underneath). For example

2 divided by 3 equals 2/3.

I have reaily in joid fractions week

I think that the crisps would be the hardest because there are lots of different sizes it wouldn’t be equal if I had a big crisp and my brother had a small. You would get the grams and half it twice which makes 150g.

I had tried shairing between 5 people

Mr Ellis what if you shared the food out eqully and everybody had ate 1/2 of their portion and then one other person comes along?

It’s so great to see so many of our class blogging; well done Abbie, C.Brooke, Keeley and Harry! Super thoughts so far.

I am wondering if you can explain to the other children what exchanging is? Can you give them an example to help them to understand?

Mrs Fallows

What if i shared the feast with 20 people will it be fare or not

be fare.

If we had 5 people and 2 drinks would it be equal if you put the 2 drink in a measuring jug then tip the equal amout in 5 glasses then the 5 people will have their own glass to drink

Good thinking. How would you make sure everyone gets an equal amount?

For example think about if there were two 200ml cartons of juice to share between 5.

Mr E

I have been learning about proper fractions and i throught they were hard

Yes I think it would be very esey I.

I wouldn’t like to do fractions week again because it is very hard

Half ing and quartering it is tayering

I’m really pleased to hear that you have been learning lots and you are up for a challenge. The more you challenge yourself, the more you learn.

Mr E

It is good to see year 5/6 on the blog

I agree!

Who do you think is best at leading your learning?

Mr E

Everybody is doing some great comments! I just can’t pick!:):)

There some good explanatoins on the school blog

Chaz d

Mrs Fallows I got the fair feast and it was so so fun.

if it was someone’s birthday and there was 5 items in each goody bag and 30 people came how many items would there be in total: 150

And what fraction of the 150 goodies would each person get?

Can you make this fraction any simpler?

Mr E

what is the theem of next week .

Good question!

What would you like the theme of next week to be?

Mr E

On fractions week i wasnt that conferied about fractions because some fractions are hard and some of them are hard specially impoper fractions there the hardest

I really enjoyed fraction week because if I got stuck others helped me so I would return the favour!!!