Monday, 14 November 2011

The Chopped Cubes

We'd done a lesson or two on volume/surface area of a cube & cuboid.

We began Monday showing the kids this wicked GIF of a dude/dudette slicing a large cube:

We chatted about how to create it (some were familiar with online stop-motion software that i'd never heard of!) before one of them asked the question i'd missed:

"It doesn't work though, does it?"

I asked what he meant, and he just said simply that the guy/guyette ends up with 9 little cubes, but you couldn't stick them back into the original shape.

Why? (I said as i face-palmed, having intended to ask them a question about the surface area that would be near impossible for them to answer... *)










He said you could put them in a square, but not 3D unless they were all different sizes, but they seemed the same size.

A couple of the kids spotted that 9 isn't a cube number - we'd need to get rid of one little cube, or get another boatload from somewhere.

One suggested we could make a video that made mathematical sense, i thought this was a great idea and scrapped my lesson.

The kids split into teams and used card to draw nets and build themselves big and small cubes.
One team even went to the trouble of having stages of increasingly small shapes (eg actual size after 1 cut, them after 2 cuts etc) whereas most just went for 1 big cube, and 8 small ones.

We plan to upload and create our own GIFs tomorrow, will post the results when we get done.

Really excited me this one, cos it hits loads of maths, is pretty creative, and came entirely from the kids.

*I was going to ask how much larger the total surface area of all the small cubes was compared to the large cube - could they answer this or am i just being thick?!

Monday, 10 October 2011

Blood Spatter

 Spent some time this week after watching season 1 reruns of Dexter:
From October 10, 2011


Showed the kids this, asked what the hell they thought he was doing.

I'd also seen this infographic over summer:

And we chatted about why a 10 degree angle of impact would leave a different shape etc.

Kids correctly surmised that it was related to the height/width of the droplet, so i dropped the formula on them, and we did some investigatin'!

After drawing some random blood droplets and swapping with neighbors, we jumped in and messed around in Geogebra creating the activity below (with some help from me in terms of the input aspect):

BloodSpatter - GeoGebra Dynamic Worksheet

BloodSpatter

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
OG, Created with GeoGebra


Most entertaining if slightly bloodthirsty, led into using arcsin etc in trig very nicely.

We also created crime scenes that we could analyse, by drawing huge drops of blood on paper and tacking them to the walls, then going all Dexter with bits of string!

This basically works out the angle of elevation from the surface - not sure how we could find the "horizontal" angle to the surface though... Any thoughts?!

Sunday, 16 January 2011

Online Dating # 2




(Again, data shamelessly ripped from OK Trends.com)

Started with the Question:
Which of these options would you rather be true:
people either think you are beautiful or cute
people either think you are beautiful or ugly
people either think you are cute or unattractive
people either think you are beautiful or unattractive

We voted, with unsurprising results (R asking if he could choose "unattractive to everyone" as an option aside..)

Flashed over to some data from OK Trends:

Nice scatter, posed a couple of questions - and ended up identifying a couple of points with the same attractiveness but wildly different numbers of messages received.

Invented two sets of stats about these two women, and asked kids to give me some possible ratings they could have had to give them an average rating of "7" (for our purposes, the average was the mean):

Started talking about the differences between the two sets of ratings - pleasingly, words like "range" started coming up with only minor prompting.

They decided that by and large, the first girl had a larger range (the boys also decided by and large that they preferred the first girl!)

We then talked about what we could do to examine the "spread" of our data, and I gave them some data that we constructed histograms from (always surprised how difficult our little ones find histograms!)

One of the kids piped up that the first graph didn't make sense, that she should get more messages as basically no-one finds her unattractive.
We agreed, but then again, more people thought the second girl was super hot.

We compared a few other comparable women from the site:

and saw the pattern repeated.

We formed a hypothesis: you're more attractive if men argue about you.

again, from the data set given, the kids this time found the standard deviation of each woman of a similar level of attractiveness (i.e. all rated 7), and compared this to the number of messages received per week (the thick grey line is the average messages per week.
and came to the conclusion that if everyone thinks your hot, you get less messages, if there's disagreement, you get loads.
Hypothesis confirmed!

We didn't really get time to head on to the equation that OK Trends proposed, which explicitly shows that some types of ratings detract from your message possibility, which was a pity (as i say, histograms, damn!) but a good, eye opening lesson drawn (largely) from the real world that had kids arguing, which i generally take as a good sign!


The lesson PPT and Handout can be found at the links.