Mr. Jones’ Year 8 class has been learning how to apply Pythagoras’ theorem in 3 dimensions. Students are adept at using Pythagoras’ theorem: “The square of the hypotenuse is equal to the sum of the squares of the other two sides”, or a2 + b2 = c2, for those that like learning formulae, when the problems are presented in 2 dimensions. They have done very well at applying the formula and using their understanding of the theorem to check if their answers were reasonable or not.
In order to extend their learning and improve their understanding of this particular theorem, we have been investigating how to use it to work out “cross-diagonals” of cuboids. This requires a high level of spatial awareness as pupils have to see the 2-dimensional triangle inside the 3-dimensional shape. In order to help them visualize this, we have been working out the cross diagonals of physical objects around us so that they can actually see the triangles. Various objects measured were the classroom, the desk, and the corridor. The pupils enjoyed the challenging level 7 work and the opportunity to see a real life application of classroom theories.
Prime numbers are the building blocks of all the other numbers and so to represent this and to investigate the properties of prime numbers, Mr Dolan's Year 9 class has been building numbers out of Lego primes.
This sort of kinaesthetic learning allows students to turn abstract mathematical concepts into real world analogies. We can then take this idea and adapt it for use in more abstract mathematical situations.
By including extra factors, and adding bricks to the towers, we create multiples. By removing them we can create factors. This allowed students to see how we can connect the prime factor decompositions to the process of finding Highest Common Factors and Lowest Common Multiples of arbitrarily large numbers. You can see how this process works in the photos the students took.