Mar 232017

We used strips of paper to measure the diameter and circumference of various circular/cylindrical objects.

We noticed that the circumference was:

  • always bigger than the diameter
  • about 3 times bigger

Mr Williams then made a spreadsheet of our results.  Dividing the circumference of a circle by its diameter gives a special number called pi which is a never ending decimal that starts 3.141592…..

Person Iterm Diameter (cm) Circumference (cm) Circumference/ Diameter Pi Accuracy
Lola Paper roll 4.2 13 3.095238095 3.141592654 0.04635455835
Glue stick 3.1 10.2 3.290322581 3.141592654 0.1487299271
Umbrella handle 3.1 10.3 3.322580645 3.141592654 0.1809879916
Nailah Whiteboard pen 1.7 4 2.352941176 3.141592654 0.7886514771
Mug 8.5 26.7 3.141176471 3.141592654 0.0004161830016
Pipe 1.9 6.5 3.421052632 3.141592654 0.279459978
Wilf Whiteboard pen 1.7 5.2 3.058823529 3.141592654 0.08276912418
Hook 0.5 2 4 3.141592654 0.8584073464
Whiteboard cleaner 4.2 13.7 3.261904762 3.141592654 0.1203121083
Jake Headphones 3.4 12.1 3.558823529 3.141592654 0.4172308758
Cork 2 7.3 3.65 3.141592654 0.5084073464
Burger 7.5 27 3.6 3.141592654 0.4584073464
Jiyan Wipes 7.2 26 3.611111111 3.141592654 0.4695184575
Camera 13.4 39 2.910447761 3.141592654 0.2311448924
Fire extinguisher 11.2 35.3 3.151785714 3.141592654 0.0101930607

The spreadsheet shows how accurately we measured – Nailah was most accurate when measuring the mug!

We noticed that it was hardest to measure the smaller objects accurately.

Mar 162017

We looked at sum and difference problems like this one:

I buy a book and a pen.  In total, they cost me £5.  The book was £4 more expensive than the pen.  How much did each cost?

We did some more examples and came up with a general method of doing any question like it.  Then we looked at how we could program a computer to do it for us…

Here’s the link to see the code:

Apr 302016

We went out onto the playground to measure the speed of sound armed with only a piece of string and a weight – here’s how we did it:

  1. We figured that speed was something to do with time and distance, so we needed a way of measuring both.
  2. Distance:
      1. Mr Williams (stood on a few whiteboards!) is 1.75m so we measured that with string 4 times making 4 x 1.75 = 7m.
      2. Then we folded the string into 7 equal lengths to make 1m.  We cut another piece of string to this 1m length.
  1. Time:

    1. Fact – a 1m long pendulum swings every 1 second.
    2. We made a 1m long pendulum using our 1m measure and tying the weight to the end.
  2. Speed of sound:
      1. Speed = distance divided by time
      2. The aim was to use a pair of claves to make a sound and bounce the sound off a wall from 50m away continuously for 100 seconds.  The sound would travel 100m between hit and echo (and by hitting in a regular beat would travel another 100 before hitting the claves again)
      3. We measured 50m by using the 7m string 7 times then the 1m once.
      4.  The pendulum kept swinging off course and hitting the goalposts to which they were tied.  Eventually we managed 38 seconds, during which we had hit the claves 59 times which worked out to be 329m/s for the speed of sound
      5. The real speed of sound is 340m/s so we were only 11m/s out – only using string to work it out!
Dec 192015

Daniel C was  inspired by some artwork, so he programmed this in LOGO:


It’s an example of a mathematical never-ending picture called a fractal.

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

I remixed it using variables here

and made it into an animated GIF

Daniels LOGO fractal