If you want something to keep your Y7s/Y8s busy for about 10 minutes, or amuse yourself for 3(ish), have a go at this:
Find, without a calculator, the sum of:
1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/14 + 1/15 + 1/18 + 1/22 + 1/24 + 1/28 + 1/33
(Hint at the end of the post)
Credit where credit is due and crucially, from the POV of fellow teachers, a very neat site for ideas to stretch/annoy your students: http://www.1000problems.org/index.htm It is not very attractive to look at, but there’s some really good content.
Speaking of ‘(not) attractive to look at’, I include this on the off-chance one of my pupils stumbles upon the blog:
Hint: Try to group the fractions so that they simplify easily