Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of
these numbers must be 1. Now for the complexity! When are the other
numbers real and when are they complex?
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]
This is one of a series of jumbled proofs. We think that sorting
the steps of the proof and the reasons, into the right order will
help people to understand and remember the derivation of the
formula for the roots of a quadratic equation.
hope this activity will be particularly useful in pair or group
work, where interpretation of the text can be shared and the
justification of choices can be tested on fellow
blue statement looks like a starter?
line of algebra looks like it belongs with that
look at the actions on offer : Subtract, Divide, Take and Complete.
Can you find a line of algebra to go with each of those?
there a sequence you can find by following the algebra?