I did not have Geometry today because of a homecoming assembly but Algebra went great.
We opened up with Estimation180 then dove into Towering Numbers. This problem comes from Fostering Algebraic Thinking by Mark Driscoll. I was first introduced to this problem in a college class and it is deep.
I love this problem because you can present it in a low-entry high-exit sorta way.
The first thing I asked students to do was take a look and write down any patters/interesting pieces of the image.
There was some great discussion on this, some students who normally don’t speak up were talking about patterns they saw. Anything said was worth hearing by other students.
After I put up the first question:
Nothing too demanding here; but there are a TON of way to answer this question, which I wanted students to see/hear. Students drew pictures, used recursion, found equations, and used several other strategies; this was great to see!
After I ramped it up a bit and asked students to find how many bricks would be in the 25th row.
Students then answered the question “Using the same design another tower was built, this time the longest row had 299 bricks in it. How many rows of bricks did the tower have?”
This directed students towards the Undoing habit of mind.
We heard a lot of different solutions strategies; I was in a happy place.
Then I asked students to find how many bricks would be needed to build a 25 row tower.
I saw a lot of this happening:
All classes eventually reached an equation, n(n). Why does n(n) work though? Where do we see a square in our tower?
Crazy! Today was great.
Here are the goods