Fractions in a Box
Fractions in a Box
We have a game which has a number of discs in seven different colours. These are kept in a flat square box with a square hole for each disc. There are $10$ holes in each row and $10$ in each column. So, there would be $100$ discs altogether, except that there is a square booklet which is kept in a corner of the box in place of some of the holes.
We haven't drawn a grid to show all the holes because that would give the answer away!
There is a different number of discs of each of the seven colours.
Half ($\frac{1}{2}$ ) of the discs are red, $\frac{1}{4}$ are black and $\frac{1}{12}$ are blue.
One complete row (of $10$ holes) of the box is filled with all the blue and green discs.
One of the shortened rows (that is where the booklet is) is exactly filled with all the orange discs.
Two of the shortened rows are filled with some of the red discs and the rest of the red discs exactly fill a number of complete rows (of $10$) in the box.
There is just one white disc and all the rest are yellow.
How many discs are there altogether?
What fraction of them are orange?
What fraction are green? Yellow? White?
Why do this problem?
This problem gives practice in calculating with fractions in a challenging setting. It also requires the use of factors and multiples. While doing the problem learners will need to express a smaller whole number as a fraction of a larger one and find equivalent fractions. This activity will require some estimating and trial and improvement, combined with working systematically.Possible approach
In the plenary, you could invite the class to look at each other's posters and ask each other questions about the methods used.
Key questions
Possible extension
Learners could find out possible fractions for the differently coloured discs if the square booklet was larger, say $6 \times 6$.Possible support
Some children my find it helpful for you to structure the approach a little. You could suggest making a list of the possible sizes for the square booklet then working out the number of remaining small square holes for the coloured discs.You may also like
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