IWB Raw: Demonstrating similar triangles

Here's my first ever (be kind!) screencast showing how I work with my Interactive Whiteboard + SMARTNotebook software to turn static diagrams into something that hopefully shows ideas more clearly:

IWB Tips: Making invisible algebra visible

Second in a series on quick easy tips to get more from your Interactive Whiteboard + SMART Notebook software - mostly for maths teachers but might apply to other subjects too.

A perennial challenge when teaching algebra is getting students used to the conventions - and in particular, the conventions of what we don't show.  When I look at the algebraic expression "3x", I don't just see a '3' and an 'x' - I see, or at least I know, this is 3 times x.  And when I see x on its own, I know it's the same as 1x.  The challenge is to help our students see and understand the presence of these implied algebraic ideas amongst the more visible characters.

In my class, we have names for these algebra conventions:

If you're wondering about that hat ... see my post
on how the royal wedding helps teach algebra.

The joy with an IWB + SMART Notebook is you can show the invisible symbols. Here's how....

Mr Zuber:  " ...and don't forget the invisible one. Can you see it? I can see it". 

Step 1: Can you see the "invisible 1" ? It's there! Really!

Student#1: "I can't see it! Where is it?"

Student#2: "Show it! Show it!"  (they all know what is coming now!)

I switch my SMART Notebook pen to the Magic Pen, 

and write in the 'invisible' part of the expression.

Step 2: Use the Magic Pen to write the 'invisible 1'. 

The whole class holds their breath in anticipation .... waiting, waiting ....  and sure enough, five seconds later, the Magic Pen marking fades - and my invisible 1 is gone.

Step 3: Five seconds later - the 'invisible 1' has disappeared.
Back to where we were - but with the 'invisible 1' in place!

But I can now quite reasonably continue talking as if it's really there - it was there wasn't it? Did you miss it? Maybe you weren't watching? :-)

Any time I want to show 'invisible' elements, or hidden, assumed conventions, I use the Magic Pen to temporarily write them in. It really grabs the class attention and drives the point home.  OK - it's only a little gimmick - but it seems to have a real impact. Something about the anticipation of waiting for the fade, and seeing it fade automatically, combined with just the sheer fun of the trick really does seem to drive the point home.  I've been using the Magic Pen this way for six months now and my Year 8 class still  hasn't tired of it - they still watch, wait, and then ooh and ah and laugh when the text disappears. Indeed, whenever I mention the invisible one or the invisible multiple sign, they usually insist I demonstrate it. Funny thing is, even Year 11 students, who are "way beyond childish things" still get a chuckle from the Magic Pen.

My thanks to my wonderful colleague Ms Tran who gave me some early lessons on using SMART Notebook and showed me the power of the Magic Pen. The Magic Pen changes function depending how you use it: if you write with it, you get disappearing ink. Try drawing a circle or a rectangle to see some other fun tricks.

Demonstrating angle sum of triangle using an IWB

Here is a quick demo of how to show the angle sum of a triangle using an Interactive Whiteboard and SMART Notebook, starting with blank screen. It's surprisingly quick and fun to do - my Year 7 class hooted in delight.

Grab a triangle from the shapes menu.

Use three different colour pens to mark the angles -
can be as messy as you wish!

Group the triangle with the three coloured paint patches
 to make a single object.

Clone the group twice to make three identical triangles.

Grab the second triangle by the rotation handle and start rotating it.

Drag the second triangle to join the first triangle, aligning
so two different coloured angles are adjacent.

Bring in the third triangle, aligning so
the third angle is adjacent to the other two.

The three angles line up to form a straight line = 180 degrees. QED!

My Year 7 class loved this - they half-jokingly suggested I was rigging it - and insisted I try out different triangles and watched very intently to see if I was sneakily stretching or adjusting the triangles.  Enjoy - but don't miss out doing it the traditional way with a paper triangle and cutting off the angles - nothing beats hands on feel for maths.

Next in this series: IWB Tips: Making invisible algebra visible