Math Campp - Day 3 & 4

For Wednesday and Thursday the focus moved from Proportional Reasoning to Patterning and Algebra.  We were treated to the lovely pair of Cathy Bruce and Ruth Beatty.  Ruth instructs at Lakehead University and Cathy at Trent University.  The main focus of their research is young students and their algebraic thinking. 

From the moment they began their plenary session, we were hooked!  They showed us a method for teaching patterning and algebra that may of us were unfamiliar with.  And yet, it is so simple and so hands on, that the learning for those of us in the room skyrocketed!  In fact, many of us can't wait to get back to the classroom to try it out.  The underlying concept of additive and multiplicative thinking is what really helps students gain not only more confidence when "doing" the math, but also makes a big difference as it shows us if they really have the conceptual knowledge they need in order to move forward as mathematicians.

Look at this photo below.  (It is upside down, so please read it from right to left).  Can you tell me what equation this model represents?

1n + 9  (where n=term) or position number x 1 +9

The first position is "Zero" - There are 9 green tiles.  If you look at the 9 green tiles they show up in every term.  Therefore, the 9 must be the constant.  Just by the pure look of it, the students are now more successful in identifying the constant.

The second position is "One" - You can see the 9 green tiles (the constant) but now there is 1 blue cube.  Hmm....what times "one" gives me one?  students can now begin to make conjectures about what they think the pattern rule is.  They can then look to the third position and see if that it is always "position number times 1".

The third position is "Two" - Two times one is two (hence the two little blue cubes). And then once again there are those 9 constant green tiles.

Here is another example:

Can you see it?  This one is a little more tricky, but you can probe the students with some questions like "What do you notice is the same about each position?"  "Is there any pattens that you notice?"  In fact, you can even use different colour tiles to lay on top of the pattern to help the students test their theories and prove and reason their conjectures.  What's the answer you ask?

4n + 5  (where n=term number)  or position number x 4 +5

Once we started doing these, we then made the jump to graphing the equations and predicting about what the "12th term would be" using graphing and our knowledge of co-ordinate points. 

Great stuff to think about!