Teacher notes on an investigation on areas of triangles, also covering topics such as simplifying surds, Pythagoras’ Theorem, congruency and algebraic formulae.
The problem the students must solve is ‘When the perimeter of a triangle is 20 cm and it is an isosceles triangle, how many possible triangles can there be?’. Students find this out through working out the area of each possible triangle and seeing a pattern.
An extension is also included in this resource which gets pupils to work out the total possible number of any triangle (not just isosceles) with a perimeter of 20 cm. Students then work to find a link between the base length of the triangle and the number of possible triangles which can be drawn with that base length.
A worksheet is included for each activity as well as notes and guidance on how to conduct the investigation with pupils.
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Huge Set of KS3/GCSE Maths Investigations
A set of 6 investigations (complete with teacher notes and worksheets) where students are set a challenging problem and work to find the solution. Each investigation should take up a whole lesson. The first investigation focuses mainly on probability and gets pupils to find the total possible number of half-time scores if given the full-time score, eventually finding a formula connecting the two. The second connects geometry and algebra, getting pupils to generate a formula which links the total possible number of triangles with a given perimeter. The third investigation gets pupils to discover the origins of square numbers whilst the fourth gets students to calculate the optimum rate (using compound interest) at which interest should be added to money in order to achieve maximum interest. The bundle concludes with a pair of investigations on triangular numbers, the first helping pupils to appreciate the properties of the sequence and the second which gets pupils to discover the derivation for the nth term of the triangular number sequence.
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