Math isn't so tough if you have workable strategies.

I find that often when teaching a new strategy in math, some of the students feel that the strategy is not needed as they have other ways to solve the problem or they can calculate it mentally.  So, when will students have to use a strategy?

When the question is really difficult!!

So, I was in England and visited some experimental neolithic structures that archeologists are building for the new visitors center at Stonehenge.  I was showing the children the pictures and we saw that many of the building styles were similar to the ones we had built.  We then talked about the way all native materials were used and also native tools of the time.

Then came the provocation:

It took 2 hours and 48 minutes and 11, 477 blows of a flint axe to chop down a 30cm diameter tree.  A number of volunteers took two minute turns to chop.  So, how many axe blows per turn?

This immediately led to discussion of we can't possibly know, some people would chop faster than others, some would be stronger and be able to make deeper cuts.  As a class we came up with finding the average (arithmetic mean) axe blows per turn.

So, how do we do that?

We first figured out that 2 hours and 48 minutes divided into 2 minute turns would be 84.

First what is the equation?    11,477 / 84 =   ?

Well, we haven't tackled this type of problem in 4th grade, how could we possibly find out the answer - was it too difficult?

No - not with patience and strategy.

So what strategies do we have that we could use?

Counting with pop cubes
Landmark numbers
Multiplication
Building up
Coming down
Estimation

How did they do it?

Using landmark numbers and then adding on.
Also showing an understanding that even though the answer isn't exact, it cannot be a fraction because of course you cannot have "half a blow!"

 Again, starting with 84 x 100.  An estimate to get close.

This group started very high, then used halving to get to a closer estimate.


None of the groups had ever tackled a problem like this, but with the aid of learned strategies and a sense of adventure, even the seemingly impossible was very much within reach.