Well done to Brooke, Alice, Toby, Jacob and George for correct answers this week. The prize goes to….Brooke!

- j2e – j2code – LOGO
- Start with: reset setpensize 4

**SQUARE**

- Draw a square using the repeat command

**SQUARE with VARIABLE**

- To make a spiral, we need to increase the length each time it repeats.
- To do this we will make a
called “length” that we can control.**variable** - Before the square code, type: make “length 30
- Replace your fd 40 by fd :length
- Try your code – try changing the number after make “length to make different sized squares.

**SPIRAL**

- Start with make “length 30
- Inside the repeat brackets put the following line:
- make “length :length +10
- NOTE the difference between “len and :len (“len is for changing it; :len is for using/calculating with it)
- Increase the number of repeats

What variations can you create? Save different versions for each one you do.

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.

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: https://scratch.mit.edu/projects/150578027/

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:

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

**Time:**

- Fact – a 1m long pendulum swings every 1 second.
- We made a 1m long pendulum using our 1m measure and tying the weight to the end.

**Speed of sound:**- Speed = distance divided by time
- 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)
- We measured 50m by using the 7m string 7 times then the 1m once.
- 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 - The real speed of sound is 340m/s so we were only 11m/s out – only using string to work it out!

Daniel C was inspired by some artwork, so he programmed this in LOGO: http://www.j2e.com/stmarks/bwilliams/Daniel+Cs+ultimate+pattern/

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 http://www.j2e.com/stmarks/bwilliams/Remix+Daniel+Cs+ultimate+pattern/

and made it into an animated GIF