Monday, 22 October 2012

Making Shapes Puppets

Earlier I mentioned the start of the Shapes Puppet Show idea. We are making good progress. Song lyrics are written (courtesy of their music teacher) and we have focused our making on the shapes needed for the songs, and a few extra cool ones to be judges on "Which Shape's Got Talent?".

I beleive this character is performing "I'm Hexy and I know it".

Sadly there is no song for the dodecahedron. But he is very good at eating other puppets. Perhaps he'll be a judge.

Starting with cardboard bodies, we have been adding coloured paper and fabric to give them a stylish look. It's amazing what some cute eyes will suddenly do for a puppet.

 Aren't they just adorable?

A lot of songs feature cubes.

We've had lots of discussions about different ways to make the puppet best represent the shape, especially for 2D shapes. The two paths seem to be to either keep it in 2D or make it into a prism, where the front face is the 2D shape of the character.

This circle is really a cylinder, but with the outer sides covered in black the focus is kept on the circle of the face.

This square, on the other hand, is kept as 2D as possible and controlled using sticks from below.

This fellow was originally Sherlock Cones. Can't remember his name now. Coney McSomething I think.

Today they were mostly finished so we paraded around a small section of the school showing them off to some teachers and senior maths classes we found. I think they are something to be proud of.

Tuesday, 16 October 2012

A trial of expert groups

A topic I find interesting to teach is graphs. I like graphing at pretty much all levels, although once you get away from just straight lines it is exponentially better (pun intended).

Teaching graphs I try to focus on linking features of the graph and features of the equation, and piecing together what the graph looks like one clue at a time.

 What type of equation is it? 
Looks like a parabola.
Is the x positive or negative? What does that tell us?
It's negative, so it curves down.
It's got a number added to the end? What does that tell us?
It moves up the y axis.

I favour matching activities and assigning "possible" equations to graphs rather than dealing with definites where they can check points or use a table of values.

I've also focused on categorising graphs and exploring their features by looking at a lot of graphs and equations to help make those links. There's a great exploration of this idea at exzuberant (A Visit to the Function Zoo). With a lower-achieving General Maths class I've used Geogebra printouts of graphs with their equations on them in a hands-on categorising activity. I just get them to put them into groups of graphs that they think are similar. Then look at what is similar, and what is different. Where do those differences come from in the equation? What do they look like in the graph?

Today I tried another approach. It was with a Year 10 5.1 class, so they don't really need to know about these graph types, but they are supposed to have seen them or graphed them using tables of values or something, so I figured we'd try this anyway. Extra knowledge can't hurt, and lots of them will do General Maths and it might help to have seen these wacky graphs before.

Here's how it worked:

  • Students are given a card with a letter-number coordinate. Letters are from A-E and numbers are from 1-5. 
  • (I was going to add this in but realised there wasn't enough time) Whole class to place a series of images of graphs into 5 categories based on the shape of the graphs. 
  • Assign a letter to each group of tables.
  • Students go to the table with a letter that matches their coordinate. Each table has a different type of graph to become ‘experts’ on. They have a worksheet with questions (each) and a set of graphs (to share) with their equations written on them. Students have to work together (and with the teacher’s help when needed) to answer the questions and learn all about that type of graph. The questions are all about the properties of the graph and links between graph and equation.
  • Students now move to tables based on the number in their coordinate. This is arranged in such a way that each table has at least one expert on each type of graph. Each person has 5 minutes to share their knowledge about the graph type.

The Good:

  • Some students who were not usually engaged in their work were more serious because they knew they would have to explain it to others.
  • Many students benefited from working with people they didn't usually work with.
  • Some students made the connections between the transformations of different graph types very well. (and what does adding or subtracting a constant do to this graph? What a surprise.)
  • It changed our routine up a bit. Always worth doing.
The Bad:
  • Some students seemed to understand well enough in their first group, but were not confident enough to explain it to others without any support.
Next Time:
  • I think I'd prefer using expert groups for an idea that is well within the ability range of the kids rather than something at the edge of what's expected of them, just for the confidence thing. Although it certainly showed which students could cope with these new and challenging ideas.
  • On that note it might also be a good revision activity - break the topics down into small bits and share those around. Then most students should already have some idea of the content and just need the extra time to fine tune their knowledge.
  • More time if possible. Maybe a good activity for a double period rather than a single. This would leave time to do some prep activity (like the categorising that I left out) and add other elements.
  • After the expert sharing time, I went over things together as a class. This meant that weaker groups had an opportunity to fill in gaps of knowledge, and it acted as a nice summary. I would then like to follow this up with an individual activity like a little quiz or worksheet, to check their understanding. Maybe the group with the highest score could get a prize, to show what good experts and teachers they are.

Friday, 5 October 2012

Subtracting a Negative - The Third Umpire

My Lovely Year 7s are starting their topic on directed numbers/integers at the moment. Over the years we have had a lot of discussions about how to get them to really understand about adding a negative and especially subtracting a negative.

With some help from my lovely husband, it seems that sport or some kind of game is the way to go. He played a version of cricket where each batsman stays in for a fixed number of overs, but gets a negative score added if they get "out". I thought it was a great idea, and had lots of potential for negative numbers - what if the third umpire overturns an out?

Here's the game we played today:

Students came up in pairs, one pair at a time, to play. They had 30 seconds to throw a bean bag between them (from behind marked lines) as many times as they could.

1 point for each successful catch.
-1 points for each time the bean bag hit the ground but was picked up again in less than 2 seconds.
-5 points for each time the bean bag stays on the ground for 2 seconds or more.

Also I stopped them mid-game so we could discuss the scores on the board.

I considered the penalties for dropping as negative numbers, rather than subtractions, so that we could write our number statements that way. That also allowed us to subtract a negative score if a penalty was overturned.

For example:

A pair of students catch the bean bag 22 times, then drop it. I rule that it is on the ground for more than 2 seconds.

So I write 22 + (-5) =

Here we can talk about the use of brackets, how they may or may not appear and why we might use them. We can also talk about how we would say it. Do we say "22 plus minus 5" or "22 plus negative 5" or can we say "22 plus take-away 5"? Which ones make sense? Which is the most clear?

Now they know that the pair have lost points, because they did something wrong, so 22 + (-5) = 17.

But they did appeal that it was less than 2 seconds. We took a vote. My decision was overruled.

So I write 17 - (-5) =

I'm removing the negative score. They all know already that the result should be back at 22. So we can now discuss why that is.

In summary at the end of the games we talked about adding and subtracting positive numbers, and adding and subtracting negative numbers, since we had done a bit of all of these.

After we played that version a few times, we switched to a system where the scores started at -20. This allowed us to do the same types of calculations, but in the negative numbers and crossing zero. I have a number line across the front of my room which helps a lot in these situations.