Fruit in a Bowl
Problem
Here is a bowl of fruit.
Half of the pieces of fruit in the bowl are apples. There are also $3$ oranges, $2$ pears and a banana.
How many apples are there in the bowl?
If, instead, one quarter were apples and one quarter were oranges and there were also $4$ bananas, $3$ pears and $3$ plums how many would be apples?
Getting Started
In total, what fraction of the fruit in the bowl are oranges, pears and bananas?
How many pieces of fruit which are not apples are there altogether?
In the second part of the problem, what fraction of the fruit in the bowl are bananas, pears and plums?
How many bananas, pears and plums are there altogether?
Student Solutions
Alistair aged 5 who goes to Histon Infants School said there are 6 apples in the bowl because there are six other fruits.
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
In the second question, Alistair wrote: There are ten other fruits, so there are 5 apples (and 5 oranges).
Pupils at Mef School said:
4+3+3 = 10 (half of the total fruits)
10/2= 5 so a quarter of the total fruits is equal to the number of apples
Teachers' Resources
Fruit in a Bowl
Here is a bowl of fruit.
Half of the pieces of fruit in the bowl are apples. There are also $3$ oranges, $2$ pears and a banana.
How many apples are there in the bowl?
If, instead, one quarter were apples and one quarter were oranges and there were also $4$ bananas, $3$ pears and $3$ plums how many would be apples?
Why do this problem?
This problem requires a sound understanding of the relationship between part and whole. It could be used as part of a lesson on finding fractions of numbers and quantities.
Possible approach
Key questions
What fraction of fruit in the bowl is apples?
What fraction of fruit in the bowl is not apples?
Possible extension
Possible support
Those experiencing difficulty with this problem may find it easier if they use this sheet along with counters to represent the fruit.