During the last few weeks Phase 3 have been completing their work on shape by working on calculating area, perimeter and volume. They have then begun moving on to look at fractions, decimals and percentages.
To link this work together for Exhibition the students have undertaken a project on fractals. Each student constructed Sierpinski’s Triangle which consists of repeating patterns of triangles with each iteration resulting in smaller triangles with the sides half the length.
The students then carried out their own investigation into the properties of the triangles. Some students considered the fractions shaded at each iteration and discovered the amount of space shaded each time is ¾ of the previous iteration. Elias in year 7 was able to express this algebraically.
Other students considered the relationship between the areas of each subsequent triangle and found that although the sides were half the length, the area was a quarter. The students then managed to puzzle out that this was because in order to calculate area they had to multiply two sides together. They then were able to conjecture that volumes of a 3D Sierpinski tetrahedron would be eight times smaller each time.
This was a really exciting task that all students were able to undertake and to develop their thinking into different aspects of Mathematics. Through experiencing this type of project students can see how maths skills are related which enables them to begin to develop mastery in the subject.
“In order to fully master maths, you must understand it in lots of different ways. For example, you need to fully understand the inverse of an operation in order to understand it” – Shaya (Year 7) while explaining his reasoning for the sequence of the fraction shaded in each iteration.