As mentioned in my last post, Walking the walk, I recently completed a 2-week casual teaching block and agonised about walking MY walk. So, here’s another story…this time with Year 8s and on the topic of Rates and Ratios.

I had one lesson (yes ONE, the 3 with the year7s was a luxury in comparison) by the time I got my act together! Enter the Vitruvian Man again (yes, I’ve used him before, on Percentages and with more prep). Remixing my original idea was easier than starting from scratch! By the way, the previous time was with strugglers and this time with high achievers….note the differences in the activity, not just topic-wise but in also tasks…which also show how **my teaching approach is evolving towards inquiry and reflective practice.**

8mata1_vitruvian – have a squeeze (pdf) and remix if you like…the Vitruvian Man is a maths teacher’s friend!

**In a nutshell**, the students were meant to investigate the “accuracy” of the Vitruvian Man ratios, extrapolating their own, apply some ratio skills AND reflect on their leaning. That’s not too much to ask in one lesson, was it? And by the way, they were going to use 2 technologies they’ve never used before: Wallwisher (which turned out to be blocked. gah!) and Dropittome. They had to submit TO ME and they won’t see me again. CRAZY!

So, **I completely forgot about this** until a week later …. mostly, **I didn’t think any of them would submit work to a casual teacher** … I mean, really. No grades attached.

I finally remembered to check my Dropbox and – surprise! **I got submissions. **I wasn’t even going to blog about this activity but, how could I not?** ** Here are some excerpts:

### “New” ratios

- A man equals 96 fingers – 1:96
- A foot equals 16 fingers – 1:16
- Palm to foot: 4:1
- Length of outspread arms : 4 cubits

### Questions

- Is the theory 100% accurate?
- Is the growth of your arms in proportion to the growth of your height?
- Is the length of your foot, equivalent to the length of your forearm?
- Do these ratios work for everyone?
- What fraction of your body is one palm? (
*I love the use of the term fraction. yes!*) - What is the ratio of the length of a hand to a full arm span?
- When was the Vitruvian man first drawn/created?

### Reflections

- Ratios are good because they make it possible to work things out rather than have to measure them every single time.
- They may not always be 100% correct, as it was proven with my measurements.
- Although this task was reasonably difficult in the beginning, I found that it was reasonably accurate and correct, as we further investigated Da Vinci’s theory. My results displayed similar findings to the theory; I further developed my rates and ratio skills. Prior to this maths topic, I didn’t completely understand it, however now I find that I can use ratios in many other places to simplify, numerals I am given or to find and approve theory’s such as the Vitruvian theory.

I really enjoyed this lesson. I liked how we got a chance to put our maths into practice.

So yeah, I’m happy.

**That kid saying ‘reasonably difficult’ was being truthful! I nearly abandoned the activity! I’m glad I didn’t.** Unlike my strugglers before who were keen to get straight into measuring, this high-achiever class had to be prodded away from their calculations and musings. I’m sure there’s something there but I’m not going into it for this blogpost.