A Top Down Approach?

A new trimester is upon us in St. Francis, MN which means a new group of advanced algebra students as well as two classes full of squirrely 9th graders.  I’m amazed that these sets of students can have things in common and a lesson for one class can serve as a bell-ringer for another.  I have said in the past that my favorite activities are the ones that can be used across multiple ability levels and this task is no exception.

This week, in advanced algebra, we’ve been working on problems that allow the students to connect specific patterns and examples to general formulae.  I feel that this trimester, I have done a much better job of sequencing the class problems in a way that has help build student confidence in the problem solving process.  As I’ve done in the past, I chose some nrich problems that have a low barrier to entry and a high ceiling.  These problems feel like number play:  Pair ProductsAlways a Multiple, Think of Two Numbers, and Calendar Capers.  Although I’ve had the occasional moan from students who prefer their math to be in lecture/practice format, I’ve seen much more willingness to engage in the problem-solving process this time around.

One particularly memorable day, we used a Math Forum problem called Baffling Brother in which a brother is attempting to amaze his younger sister by having her choose a number, perform some operations on the number and then telling her the result.  I’m disappointed that I didn’t think at the time to have the students act out this scenario.  That could have been spectacular!

These being upper level students, I always encourage them to attempt the “extra” for these problems.  On this task, they needed to come up with a number puzzle of their own that resulted in an answer of 7 each time.  I told them that I would be giving these number puzzles to my 9th grade classes to amaze.

Here are some examples:

image (1) image

What happened next I could not have predicted and was not an iota shy of completely awesome!  I presented one of these number puzzles to my 9th grade class and stood in the back of the room as I read the steps to them.  When they arrived at their final answers, I had them compare with one another.  I wish I had a camera on the room to capture the amazed look on their faces when they realized they all got an answer of 7.  Icing on the cake:  the advanced algebra students were very satisfied that they were able to amaze 9th graders with problems that they created.  I’ll call that one a win for engaging kids in “boring” old, non-applicable, relevant Algebra.

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