2 out of 3
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse the outcomes of series of 'moves'. With a little encouragement from the teacher, a mathematical investigation is born.
2 out of 3
1 out of 3
In the process of working with some groups of teachers on using questions to promote mathematical thinking, the following table was developed. It provides examples of generic questions that can be used to guide children through a mathematical investigation, and at the same time prompt higher levels of thinking.
1 out of 3
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
1 out of 3
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
3 out of 3
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
