### Happy Halving

Can you split each of the shapes below in half so that the two parts are exactly the same?

### Same Shapes

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

### Halving

These pictures show squares split into halves. Can you find other ways?

# A Bowl of Fruit

##### Stage: 1 Challenge Level:

We had a good selection of solutions submitted. Children from Mef School in Turkey explained it like this:

1+2+3= 6 Half of the total fruits is equal to the number of apples. They showed this in a picture:
 3 oranges, 2 pears and a banana apples

Year 1 from  St. Giles' Primary School in Shrewsbury wrote;

At first, we decided to draw the fruits that we knew were in the basket.
Delilah noticed that 2 (pears) + 1 (banana) =3, and 3 more (oranges) makes 6 fruits.
Some children suggested that there might be 12 apples but not everyone was convinced.
We decided to draw the bowl and draw a line through the middle to show two halves.
Some then drew the 6 fruit on one side, others wrote 3+2+1 or simply 6.
We then thought again about what it means if half are apples.
Now many more children could 'see' that there must be 6 apples... "because the two halves have to be equal".
We didn't all get it but we thought that drawing a picture was helpful.

Danny from Swarland Primary School sent this in

Hi, My Mum changed the fruit in the problem, hope you don't mind. It's because we take it in turns in our class to take Stuart (a Minion) home to have maths adventures and (as everyone knows) Minions LOVE bananas. I solved the problem using real fruit and by creating pictures. It was fun! I've sent you a picture of what I wrote in Stuart's diary. From Danny.

That is absolutely wonderful, one of the most lovely solutions to come in in the last 20 years since NRICH started.

Scott from Hagley Primary School sent in the following;

First, I wrote the question and drew the 3 oranges, 2 pears and the banana.
Then, I drew my bar and coloured 1 for banana, 2 for pears and 3 for oranges.
After that, I added 1,2 and 3. My answer was 6. I know that double 6 is 12 and doubling is the opposite of a half. So 6 more cubes makes 12, that is how many apples there will be.

Emily from Burrough Green Primary sent in a picture of her work.

Well done everyone. It was good to see different ways of expressing the solution.