Class-to-Class Adjustments

The other day I was working on substitution with my students and I wanted them to try three problems that were similar to what we had been working on, but one had no solution, one had infinite solutions, and one had one solution.  They had seen these ideas when solving graphically and numerically, but this was the first time with substitution.

Thinking back at the end of the day, I realized that although I had taught the same lesson three times, I had made slight adjustments each period.  I thought it was interesting, so I wanted to summarize it here.

In my 4th period, my first Algebra 1 class of the day, I only have 14 students and generally 2-3 of them are absent.  So I split the students into 3 groups and had each group focus on one question.  Then after 5 minutes, I had each group share out with the class.  I think it might have been a little better if I had made the groups jigsaw to share at the end, but I guess I'll save that idea for next time.

In 5th period there are 22 students.  Some of the students are very quick learners, others are slow learners, and others are "I don't want to learn" learners.  So I gave them some time to work independently or in partners on the three problems, then I went over each one with the class.

In 6th period there are 18 students who are generally slow learners and easily distracted.  They are all capable, but not very many of them are used to seeing success in the classroom.  I decided for some reason (this was not pre-planned) to get three students to each be a "professional" on one of the problems.  I focused my attention getting them on the right track, and then encouraged the other students to ask them for help.  After 10 minutes or so, the three students presented their solutions to the class.

I can't say that I preferred one method over the other, but I'm going to side note on one of my classes now...

I have struggled a lot to keep the students focused on learning this semester, but this past week was the best yet.  The day about included.

I had begun to realize these students are all very dependent on me as the source of information, processes, and answers.  A few of them like to work together, but they tend to get off task and lead each other astray when problem solving.  I need to get them to think, problem solve, discuss, justify, share, and ask questions.

I think in order for them to do this they need more of an opportunity to be in charge, so I am going to continue to try to provide that for them little bits at a time.  Including by having students present the solutions to bellwork...why did I never think of this before?  That was a student-suggested thing we tried this week that worked really well.  I think we will continue with it this week...

-Kathryn

Setting up Systems of Equations

As I was desperately searching (for a while) for something to boost my systems of equations unit with, I came across this post by Mimi at I Hope This Old Train Breaks Down.  It proved to be a great resource.  Please check it out!

Things I liked about it:

• There was more than one way to "solve" each puzzle
• The scaffolding was wonderful! Puzzle 1 and 2 were similar, puzzle 3 and 4 were similar, and puzzle 5 and 6 were similar
• The questioning at the end of puzzle 1 would help students more easily solve puzzle 2 (etc.)
• Shapes are much more friendly than x, y, and z.  Students were solving systems without knowing it

Because of all that I didn't want to just give my students the giant (8 page?) packet and have them work alone, so I made some formatting changes before using with my students:

• I put each puzzle 4/page
• I typed the questions up on powerpoint
• I printed each puzzle on a different color of paper

So in class it looked a little like this:

• We set up a bit of speed-dating scenario so they could rotate partners
• I passed out Puzzle 1 to all students
• If they completed it they were asked to answer the projected question on the back
• After 5-10 minutes I asked students to share out how they found the solution (I made sure to call on many students each time for various perspectives.)
• We rotated partners
• I passed out Puzzle 2 
• Etc.

Here is what it looked like as a quarter piece of paper.  After we were all finished I did have students staple all six together and keep them in their pocket for this section.  As we got into solving systems using substitution and elimination we kept coming back to this idea of the shape puzzle.

Some things I ran into as we worked:

• Students were using guess-and-check to find their solution.  Some kids have super-awesome number sense and could do this easily, but were then not being stretched to think about substitution or elimination.
• Students really struggled to explain clearly their solution method
• In Puzzle 3, some really struggled with that conceptual elimination that needed to happen.  I drew it out to help, but that wasn't enough for everyone.  Here is something similar to what I had on the board

My files:

• Puzzles 1-6 (4/page)
• Puzzle Questions

Note:  The link will open in drive.  You will want to download to see the full version in word.

Overall, I LOVED this as an introduction to systems of equations.  I'm not sure that I will change much about it when I do it next year.  And I have seen it benefiting students as we continue to work on solving systems of equations.

-Kathryn