Clock flowers in Year 4

In the course of our counting circle sessions we looked at clock counting (mod 60 counting).

We took this a bit further. using a Scratch project to generate these easily. 

It was a great opportunity for mathematical noticing, reasoning and claim-making. For instance

1. 
   Rose15 December 2014 at 02:33

   The odd numbers go to every stop
   
   
   

   1. 
      Justus15 December 2014 at 02:38

      I do not think so, because 15 is a odd number and it does not meet every stop

and

Justus15 December 2014

I notice that all of the prime number under 22 meet all of the numbers under 59 on the clock.It looks so cool!

1. 
   Mr Grgg15 December 2014

   What you say is almost true, Justus, but what about 2, 3 and 5?
   
   What do you think?
2. 
   Justus16 December 2014

   3 5 7 do not visit all of the numbers because are the factors of 60

The class also had a go at creating some of the "clock flowers" by hand:

and looked at the same thing in terms of division:

There's a lot more mileage in these clock patterns. Who knows where we'll take it next time... maybe string patterns?

As if by magic, a right angle appeared...

Year 5 looked at a certain kind of triangle. It's one inside a circle where the long side of the triangle is the diameter of the circle. The opposite corner is on the circle too.

At first we looked at these triangles on a big scale. The school pitch, like every football pitch, has a very convenient circle, with a straight line right through its middle. If that line is the long side of a triangle, what angle would the opposite corner have?



Next we used a pair of compasses and a ruler to recreate the situation:

We've also started using GeoGebra  in Year 5. It's great for showing how the angle is always 90°:

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com I didn't take it on to this with Year 5, but there is a fairly simple proof that this will be always the case...