What fractions can you find between the square roots of 65 and 67?
Using the interactivity, can you make a regular hexagon from yellow
triangles the same size as a regular hexagon made from green
Tim Rowland introduces irrational numbers
The bisected equilateral triangle ($30-60-90$) is an important
shape for students to become familiar with. Each of the $4$
rectangles is made from $2$ equilateral triangles and $2$ isosceles
triangles. Together one of each of those two, makes the $30-60$
The switch from one quantity as the given unit to another,
emphasises that the choice of unit is a choice for the problem
solver and can be considered so as to make the relationships within
a problem as clear as possible.
Preceding these questions with 'playtime' using cut out
triangles to form patterns may be a very useful preliminary for
Include shapes that have holes, and suggest/invite challenges
with respect to that 'hole'.
And maybe include the challenge to lose the 'hole' but keep the
What is the area of the yellow equilateral triangle in terms of
its side length ?
There are a number of activities which can provide valuable
auxiliary experiences for students working on this problem :