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

Homework, Oh Homework

(Note #1:  The title of this post is inspired by this poem by Jack Prelutsky my sister had to memorize in second grade)

(Note #2:  This is my fiftieth post and it is coming exactly one year after I started blogging :)

Homework is a big deal.  It is something I have a lot of thoughts about.  It is also something I have trouble organizing in my head...so this may be an unorganized post :)

I give almost no homework.  Rarely (like maybe twice this year) I have asked a specific period to complete ONE thing outside of class.  Also once this year I gave all students a "project".  I gave lots of class time, but it may have been necessary to do work outside of class as well.

I am often asked why I don't assign homework.  Actually I was recently asked, "How can you not assign homework in math class?"  My answer to this question is multi-dimensional.

What is the Purpose?
(Man, this issue is so complicated.  I have put it off for a year, and I'm considering just deleting this post right now...)
I guess this right here is the critical issue.  All the other stuff doesn't matter.  What is the purpose of homework?  Traditionally, homework in mathematics was used as additional practice.  I prefer to do practice in class so that:

• I can ensure it is getting done
• I can ensure students are doing their own work
• I can ensure it is getting done correctly
• I can question and guide when necessary
• Students can have conversations about what they are learning

So I'm going to discuss the other issues as well, but I do think this is the biggest.  What do you see the as the purpose of homework?  (Please leave comments, because I truly am curious.)

Who Will Do It?
When I first started in my district, I assigned maybe 5 additional problems a night.  Maybe 10% of my students completed them.  MAYBE.  Which students were they?  The students who did not need additional practice.  The students who needed more practice chose not to do it.

How Will It Get Done?
Previously, in a different district, I assigned homework almost nightly.  Ranging closer to 10 to 15 problems a night.  I would say my completion rate was closer to 80% there, but by completion I mean students who had the work written out on their own paper by the time class came.  What was happening right before school?  Massive copying sessions in the halls.

I do not want to put my students in a situation where they are going to want to copy.  I want them to see the value in what they are doing (one reason why I think they copy) and I want them to believe that they are capable of doing it themselves (another reason why I think they copy).

What is the Consequence?
If students choose not to complete homework, what is an appropriate consequence?  I firmly believe that it should not affect their grade directly.  That is something I am not willing to compromise on.  So what other options do I have?  Without an entire school-wise system, the only option I can think of is to assign a detention.  What happens then?  I spend extra time (and a lot of if) for several days tracking down students who need to serve a detention to get their work done.  And what if they refuse to serve it?

Do They Have Time?
I am so grateful for all of the time that I get to spend with my students.  I see them and interact with them for 51 minutes each school day.  I think that is more than what some parents get to spend with their children.  High school students can get so involved.  I think some of them stretch themselves too thinly, but I do think it is good for them to be involved.  So if I get more time with my students than their parents, who I am to take away some of the time they might actually get?

Societal Views
Initially I wanted to tackle some of the views society has about homework (including the one exhibited by the poem linked at the beginning of the post), but I'm too worn out right now.  Perhaps another time.

Please feel free to comment away.  I would be happy to hear both your agreements and disagreements.
-Kathryn

Coteaching--For Real!

At semester, when schedules were rearranged, I got a new opportunity.  We fiddled with a few things so that a special education teacher and I would be able to coteach an intervention class.  She has been involved in our project with the AEA, and as we were continuing to have conversations about how to help the students, it became evident that this was something we both thought would be good for the students.

It has allowed me to serve more students during the intervention time than I did previously; and with less stress.  We arranged it so that some of our lowest students are in the intervention class together.  We have 12 students and 2 teachers.  It is such an awesome opportunity for me (as a gen ed teacher) to have so few students at a time!

We had some conversation about how best to coteach, because it is not very common in our school or even in our area of the state.  But this teacher is also a reading teacher, so we thought it would work well to have her do vocabulary and then I can work on the content for each of our weekly units.  Here is a breakdown of what our week looks like:

THURSDAY:

• Opening Task:  fluency practice
• Vocabulary (as a class we make flashcards for our vocabulary words for the week)
• Very simple intro to the content

FRIDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

MONDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

TUESDAY

• Opening Task:  fluency practice
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

WEDNESDAY

• Opening Task:  counting circle
• Vocab and Content assessment
• (every other week we progress monitor)

Most of the ideas for how to structure this came from the project with the AEA.  We just manipulated it to fit our situation best.  Let me know what you like or what you would change if it was you!

-Kathryn