For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Finally, algebraic or pictorial approaches used to justify earlier conjectures can be adapted to prove Pythagoras's Theorem.
Follow-up lessons could focus on working out the lengths of the sides of right-angled triangles when two lengths have been given.
Another possible follow-up task is Of All the Areas.
Start with Square It or Square Coordinates to help students become confident at drawing tilted squares.
"I used tilted squares as the basis of individual/group work with a top set (age 14). They were given time to explore this as an open ended question in groups in a brain storming session. Write ups were to be done individually, partly in class but completed at home. This is an important stage in the pupils' mathematical development where the idea of "proof" is coming to the fore. This
excellent investigation allows algebra to come to the fore as the language of generalisation and the means of "proof" of patterns. At this stage algebra skills are limited but we have now used this investigation as a springboard to developing necessary algebra skills - e.g. double brackets, squares, expressions etc."