Saturday, 29 September 2012

Lesson Sketch: A Deviation from Average Top Trumps *UPDATED*

Firstly, I have to admit that I haven't tried this one out yet. I just got the idea this weekend as I unearthed some 'fractions and decimals top trumps' I made for this Year 7 Maths Attack! I like the top trumps idea for a way to add a game element to practising maths skills (especially these on missing angles), but I also have two problems with them:
  • To have enough for a whole class, you need a whole lot of printing, laminating and cutting. Either you do it or it eats in to precious class time.
  • There's a low-limit to how hard you can make the problems before the time taken working out if you have won sucks all the fun out of playing.

Enter 'The Modal Group'; a set of Super-Average Super-Heroes!
http://3.bp.blogspot.com/__tiC-zE4tcU/Rg6BYVk5wGI/AAAAAAAAACo/Yp6j8MubFKU/s400/ah90.jpg

Before you start, let the class decide on the four stats that you will be comparing (e.g. Strength, Wits, Speed, Etc.). Then give them these, nicely laid out in playing-card-sized rectangles:

Picture
Hero No. 1
Name:  .......................................................
Description:  .........................................................
Skills:
Constraints: Their four skills must have a mean of 30.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 2
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their four skills must have a median of 30.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 3
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their four skills must have a mode of 30.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 4
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their four skills must have a range of 30.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 5
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their four skills must have a median of 25 and a mean of 35.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 6
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their four skills must have a median of 35 and a mean of 25.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................

Hero No. 7
Picture
Name:  .......................................................
Description:  .........................................................
Constraints: Their first three skills must have a mean of 10, but all four skills must have a mean of 20 and a range of 50.
Skills:
1:  ................................................
2:  ................................................
3:  ................................................
4:  ................................................


You could easily have more or make them easier/harder, but you get the idea. Pupils make their own Top Trumps cards and in the process:
  • Get a feel for the differences between the mean, median, mode and range, seeing which ones are most affected by outliers and which average it is best to have higher (in this case).
  • Solve more difficult problems involving averages, including finding the numbers when you know the averages, a moving average as data is added, and comparing data using averages.
  • Get a reason to experiment and play around with the numbers and not just go for 40, 40, 40, 40 to get a mean of 40.
  • Do something creative in class.
  • End up with something that they can take home which will remind them of the lesson.

There you have it: Let pupils make the cards, checking their partner's to make sure they don't cheat, cut them out, and play against each other.

But wait, there's more! How about these for great follow-up questions:
  • Which cards were the most/least constraining? Why?
  • Which could you 'cheat' on? How?
  • Next time I'll take those cards out to make it fair. Can you come up with some fairer constraints? Check that the problem you create is possible.
  • What about a harder problem? What about an easier one?

As always, suggestions are suggested :)

*UPDATE* Just as I posted this I saw a related post on twitter by @InteractMaths. Would make a great follow-up or plenary to this lesson.