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The Leigh Academy Blackheath Maths department have been impressed by how our students have started the new academic year despite the obvious challenges. We have continued to deliver our curriculum in order to advance our students' understanding of mathematics. For example, Year 7s have worked to understand the conceptual underpinnings of negative numbers; Year 8s have grappled with straight line graphs; Year 9s have faced the challenge of simultaneous equations and our Year 10s have explored trigonometry for the first time (more on that below!). Our KS4 students have started their maths GCSE with enthusiasm and determination.
The maths department is committed to excellence and when the Year 9 Criteria B&C Assessment demonstrated the relationship between the Fibonacci Sequence and The Golden Ratio, Mr. Natufe was curious as to what this also had to do with the human body.
Should you know what Mr. Natufe is currently trying to ascertain about himself and how this links with a very famous artist and piece of art, please drop me an email!
The maths and the computer science teams are very conscious of the cross-over between our subject areas and it is particularly amazing when our students are able to transfer their knowledge and skills between the two curriculum areas.
For example, Tomaz in 10D used his new knowledge of trigonometry to calculate accurately for his coding class the angles and distances required to be able to complete a computer science coding challenge set by Mr. Hughes. Please have a read of the outstanding work explained by Tomaz below:
Tomaz 10D:
The code in this program draws a Christmas themed, spiked bauble. The program uses Turtle, a graphics library for python. Turtle has basic functions, such as moving forward, and turning left and right. And of course, it can draw. Image to the right:
The outline of the shape is drawn first. The triangles use a loop so they are drawn repeatedly. They are arranged in circular shape because every time the turtle finishes a triangle, it turns 20 degrees before moving on to the next one.
The issue is when the red circle is drawn. To make the shape, Turtle first moves to the centre of the canvas, before changing colour and pen size. The larger pen size means that, rather than having to move back and forth repeatedly to draw the circle, it only has to move forward once, immediately filling in the area around it. However, given that the shape is not at the centre of the canvas (0,0), we need to calculate the coordinates for the centre of the shape.
To do this we must use trigonometry. Each of the triangles around the shape are isosceles triangles, and within these, two right-angled triangles facing opposite each other. The line separating the two right-angled triangles is the centre of the shape. Since the right-angled triangles line up with the centre of the shape, the base of one right-angled triangle would be equal to the difference between the centre of the canvas and the centre of the shape.
To calculate the base, you need the hypotenuse (the diagonal, or longest, side of the triangle) and an angle. There are 90 degrees in a right angle, and the turtle turned right 5 degrees to draw the triangles. With this information we know the interior angle is 85 degrees. When drawing the triangle, the turtle also moved forward 100, so the hypotenuse is 100. The base, then, is cos(85) x 100, which equals 8.7.
If the base of the triangle is 8.7, then the difference between the centre of the canvas and the centre of the shape is also 8.7. To draw the circle in the centre of the shape, we need to change the coordinates the turtle moves to from (0,0) to (0,-8.7). Now the circle is in the centre of the shape. And, this is an example of you needing to use maths in real life.
Student Report
"Since starting Year 10, I have really enjoyed studying Maths, particularly building upon topics that I have previously studied in Key Stage 3, like linear graphs and quadratic equations. So far in the past 3 or 4 months, we have learnt about similarity, volume and surface area, trigonometry, solving equations and linear graphs. My favourite topic so far has been solving equations. Although there is a big difference between Key Stage 3 and higher tier Key Stage 4, I have found that completing more difficult mathematical problems has pushed me to be more interested in Maths.
As we are tested regularly, after finishing each topic, using GCSE style questions I feel more confident about approaching my mocks, and later my GCSEs. I can recognise how a GCSE exam might be structured and how questions might be laid out to trick me. In addition, this year I have discovered how maths can be applied to different topics, notably physics. This application has helped me learn each topic more comprehensively, by not only knowing the knowledge based around the topic but also the way in which it is used by scientists today."
By Khushi 10E
From the Maths Team, we would like to wish you all a Merry Christmas, Happy Holidays and a Happy New Year!
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