Here we continue the theme of parts of parts - or bits of pieces. We are shown a fraction, represented as part of a bar, and are asked to locate another fraction by operating on the given part. The tasks provide further opportunities for pupils to engage with ideas related to equivalent fractions and common denominators.
Task 06A: This is quite a tricky task - it is easy to fall into the trap of thinking that 1/6 will be exactly halfway between 1/8 and 1/4. However, if this happens it can lead to an interesting discussion: what is the fraction at that particular point? (A nice way to answer that is to divide the 1/4 interval into 4 equal parts - each mini-part will be a quarter of a quarter, or 1/16, and so the fraction midway between 1/8 and 1/4 is 3/16.)
(A sophisticated, qualitative argument, goes like this: Unit fractions with larger and larger denominators, get smaller and more tightly packed together. So 1/6 is closer to 1/8 than to 1/4.)
Falling into a trap occasionally, can be a useful experience for pupils - it's something that can happen to any of us, it doesn't make us poor mathematicians, and it can lead to an enriching discussion! However, the task is challenging even without the trap, so you might prefer to use the version below. To solve this, pupils need to realise, in effect, that we can form 12ths by splitting the quarter into 3 equal parts, and that 2 such parts are equivalent to 1/6.
Task 06B: This task connects more explicitly with the ideas in last Week's tasks and is fairly straightforward. The quarter has been split into 5 equal parts, so each of these is one 20th (4×5=20). 1/10 is equivalent to 2/20.
Task 06C: This is perhaps slightly more demanding than Task 06B because 1/4 >1/7 and so extra parts need to be drawn to locate the fraction. The mini-parts here are 28ths (7×4=28); 1/4 is equivalent to 7/28, so its location is 3 mini-parts to the right of 1/7.
Task 06D: Here the 0 to 1 scale has been split into 36 equal parts. However, we don't have to count them all to determine their size: the fraction 1/9 is split into 4 mini-parts so there are 9×4 altogether. The desired fraction, 1/6, is equivalent to 6 mini-parts, or 6/36.
Task 06E: We can solve this by finding the size of the mini-parts. If the green arrow is pointing to 1/8, the mini-parts are 40ths (8×5=40) and so the red arrow is pointing to 4/40 or 1/10.
If the green arrow is pointing to 1/12, the mini-parts are 60ths (12×5=60) and so the red arrow is pointing to 4/60 or 1/15.
A more formal way of solving the task is to argue that the fraction shown by the red arrow is 4/5 of that shown by the green arrow.
4/5 of 1/8 = 4/40 = 1/10.
4/5 of 1/12 = 4/60 = 1/15.
