Sunday, January 31, 2016

Start a Lesson With a Question

Whenever possible I try to start any lesson with a question to lead into what we are learning that day. This is a real shift from when I started teaching in the 80s - teaching training then focused on "tell tell tell" while students listened. Being the kind of learner that needs to understand I was never a big fan of that and figured out how to make questioning a bigger focus of my teaching. Marilyn Burns was a great mentor for this and I used her book

Collection of Math Lessons, A: Grades 6-8 a great deal when I taught middle school.

Anyhow back to this blog post...Here I am focusing on the 3rd week of the MTSoB blogging initiative

So to repeat myself - Whenever possible I try to start any lesson with a question.

Algebra One last week we were starting systems of equations. I knew that students had dabbled in this in 8th grade - they had solved systems of equations using graphing and perhaps had been exposed to some algebraic methods. But did they really know what a system was? I love really knowing what certain math concepts ARE and what they are good for (not always real life applications, just how they interconnect with other things I know about math), It's really the only way I can learn math.

So I started class with this question..

What are some mathematical models that we can use to solve problems?

Students came up with great responses (almost like there were cue cards or something) - Graphs, Tables, Equations. Yay! But this wasn't really the question to lead the lesson, this was the warm up. Next I asked them

You have a bunch of quarters and dimes.

The value of your coins is $3.00.

How many of each coin do you have?

My students sit in small groups so I let them work on that. They gathered up some graph paper and made beautiful linear graphs of this situation with a lovely equation to accompany it. We talked about whether this graph was continuous or discrete and whether we would consider values in all four quadrants. Also with some prodding they came up with a table showing the possible solutions. Great work!

Then I told them that this question presented them with a situation that had two unknowns (number of quarters & number of dimes) and one condition that established a relationship between the unknowns. It resulted in a number of possible solutions. What if I gave them another condition to partner with this information?

What if the number of dimes is two more than the number of quarters?

Then students worked on narrowing things down with this condition. They added on to the models they already created (another line on the graph, another equation for that condition). They found that this second condition resulted in a unique solution. Cool.

These initial questions allowed us to explore situations with two unknowns and two conditions that would have a unique solution. From here we could define systems of equations (after we did a few more examples) and keep in mind that is what drives a system of equations in two variables. Two unknowns and Two conditions.

I put all our questions on a powerpoint. I also have a homework sheet to accompany this. We created a cool foldable for our notebook of an example (this was used the next class block as our warm up). All supporting materials can be found at this link.

Here's the foldable I used with my students to illustrate these models. It's a cool "4 square fold" that my student teacher found last year (thanks Tess!). So it allows you to get a lot of information down in once place.

Here is the front all folded up into 4s (see how it folds up to use only half the page?):