We’ve been trying out some practical fractions challenges where we had to work out the fractions of different shapes when we had limited information. We investigated the shapes to discover which ones fitted exactly inside other ones. Then we used this information to work out the fraction each of the shapes were as a fraction of the blue square (the largest shape). Only the orange, red and yellow triangles fitted exactly inside the blue square. The other shapes we had to work out by comparing them to the triangles. We eventually discovered that the other shapes were the following fractions of the blue square:
Green square = 1/2 Orange triangle = 1/4
Red triangle = red square = pink triangle = 1/8
Yellow triangle = 1/32
Then we set ourselves some more challenges. We had to make some patterns using the different shapes and then work out the fractions of the whole shape each colour represented. The pictures below show some of our challenges. e.g. On this one, there are 10 yellow triangles so we know that yellow is 10/32 = 5/16 of the square. But, the yellow covers some of the red, so we need to work out the red base and then subtract the yellow to find the fraction that is red in the final shape. Then we could finally work out the fraction that is blue… Not as easy as it sounds!
These were tricky for different reasons but some of them are especially tricky because the pattern makes us think we have one fraction for a colour whereas the calculations show something different…. We found out that we always needed to check that the fractions of all the parts added up to make one whole one…
Using the information above, we worked out the fractions of all the colours in this ‘rainbow’ square made by laying other shapes on top of each other on top of the blue square..
This was another tricky one: We needed to check the information we started with very carefully to solve this one…
This one was especially tricky as the layout suggests that there are only three colours in the shape, but we discovered that there were, in fact, four… We ended up finding the fraction of the (almost) hidden colour too…