MATHEMATICS/

NUMERACY

Moments in Mathematics

Junior School

In Year 8 our students have been investigating algebra, starting with an introduction to pronumerals (letters representing unknown values), terms and expressions. From there students were able to substitute values, as well as expand, factorise, and simplify algebraic terms and expressions. A fun application of algebra is actually mind reading! Try this out: think of a positive whole number, add 3, double your answer, now subtract 4, halve it, and finally subtract your original number. What are you left with? I bet it’s the number one! How this works can be explored using algebra – if you represent the original number as “n”, then apply each operation in the order it is given, you can create an algebraic expression for the situation which lets you work out the solution. You can even use this method to create your own version of the “mind reading” trick; write down a series of operations which allow you to always get to a particular answer, then find a willing volunteer to impress!

Senior School

Our Year 11 Mathematical Methods students have been working on Circular Functions. This involves applying trigonometry – including the operations of sine, cosine, and tangent – to a unit circle (a circle with a radius of one that sits on the Cartesian plane with its centre at the origin). The graphs of these functions can be used to model a variety of scenarios, and students have been working together collaboratively to model daily temperatures, Ferris wheel motion, and a tsunami.

Family Fun

How did you go with last edition’s riddles? The answers were “977 animals” and “the match”. With the Olympics on at the moment here are some questions to get you in the spirit of the games; check out the next edition of Highlights for answers.

- You are participating in the swimming finals at the Olympics. In the final few seconds of the race you narrowly pass the swimmer who was in third place. What place did you get?

- Two athletes race each other in a 100 metre sprint. Athlete A wins by 10 metres. They decide to race again, but to make things fair Athlete A starts 10 metres behind. If both athletes run exactly the same speed as before, who win the race?