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.]
What fractions can you find between the square roots of 56 and 58?
Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
In silence, write three lengths on the board (for example 3
units, 6 units, 7units) and accurately draw a triangle with sides
of corresponding lengths. You could use a dynamic geometry package
to do this.
Do it again with three more lengths.
And again but instead of drawing the triangle put a question
mark. After some thinking time, encourage a member of the group to
come up and draw the triangle.
Finally, list three lengths that will not work followed by a
question mark and after time has been taken to realise the
impossibility, discuss why this is the case as a group.
Now pose the problem.
Working in small groups the challenge will be to employ
systematic approaches as well as applying the triangle
Take opportunities to pull together different ideas for
recording, including the use of nets and working