Tag Archives: Math

Always, Sometimes, Never

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I used this Thoughtful Education strategy today with my Algebra I student.  I’ve attached the worksheet I used (ASN Graphing Equations and Inequalities).  I used this strategy as a refresher, since my student is going into the next chapter, and can always benefit from connecting topic areas.  I knew that she was absent a lot during the lessons on graphing inequalities, so I made up this worksheet for her to complete.  When I made up the statements to put on the page, I thought of all of the important things that she will need to remember from the previous chapter to take with her into the current chapter.  Her evaluation of these statements gave me a better idea of what she still needed to revisit.

First of all, she said something that told me she didn’t know what an inequality was.  Because I was having a discussion with her, instead of just giving her busy work, I was able to pick up on this and correct it right away.  Once she knew what an inequality was (a statement using < or > or “less than or equal to” or “greater than or equal to”), she was able to work through the statements on her own, and then we reviewed them together.  During our discussion, it was clear she was solid on many of the aspects of graphing, but when it came to the shading statement, I realized she didn’t know how to actually graph an inequality, and that we needed more time to practice and review that.

I will definitely use this tool again, both as a pre-teaching tool and a reviewing tool.  Both will help me to know what they have learned correctly, and what we still need to focus on.  In a larger group setting, this will be helpful to know who really understands a certain topic, and who is skating through.

Closed Properties

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I just taught a class on closed properties (ex. the set of Natural Numbers is closed under addition).  Unfortunately, not having a lot of time to plan, I just ran through the notes, and way over the kids’ heads.  Upon further thought, I would’ve explained it like this:

A set of numbers is like a classroom.  (this illustration works best for a finite set of numbers)

For example, I have a set {-1, 0, 1}.  Pretend that the {} are little doors into the room.  Now, we’re going to perform all the operations on these numbers.  If we come up with an answer that is still in this room, the doors stayed CLOSED (we didn’t have to open them to find the solution).

Let’s try it:

  • Addition: -1 +1 = 0; -1+ -1 = -2 **-2 wasn’t already in the room, therefore we had to OPEN the door to let it in (not closed!)
  • Subtraction: 0 – -1 = 1; 1-1 = 0; -1 – -1 = 0; 1 – -1 = 2 **2 wasn’t already in the room, therefore we had to OPEN the door to let it in (not closed!)
  • Multiplication: 0 x 0 = 0; 1 x 1 = 1; -1 x -1 = 1; -1 x 0 = 0; 1 x 0 = 0; 1 x -1 = -1 ** because I tried every possible combination of numbers, and my solutions were always already in the room, my door stayed CLOSED
  • Division: 0 / 1 = 0; 1 / 0 = does not exist **this answer obviously isn’t in the room, therefore we had to OPEN the door to let it in (not closed!)

Organization revisited

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Eventually, you may come to a point in the school year in which you are feeling burned out.  No worries, your collegues are right there with you. 

In our school, we have what is called Intervention time, which is basically an extra half hour of leveled reading time, focusing on students’ strengths and (mainly) their weaknesses in reading  – usually either fluency or comprehension. 

We also have leveled our math groups, so that those who need the extra help in math can receive it, and those who can power through problems faster than a speeding bullet have that opportunity as well.

As with any group of students, there are those that excell, and those that need more help.  Of course, those that need the most help are going to tire you out more because you have to put in more effort to come out with a comparable outcome to those students who excell.

Therefore, recently, my collegues and I have switched around Math groups and Intervention groups.  Here is where organization is key.  We needed to stay on the ball as to who was at what level, and the abilities of each person. 

My new math group is getting a folder for each student, so that I can better keep track of their work.  Also, because some of them are not from my classroom, I cannot simply ask them to put things in their desks, because they don’t belong to them.  We are also starting multiplication, so in each of their folders, they will be receiving multiplication fact flash cards as we move through the facts so that they can practice with any down time in the class.   

This will prove especially essential for multiplication, since most of that is drilling through facts.  This way every student will have a set of cards to drill through and practice during class time.  And (if well organized enough) they will have their OWN and know right where to find them!

The same holds true with my Intervention group.  Each student will have a folder containing any work they need to hand in, or still need to work on.  This way, it’s all in one central spot in the classroom.  I have a bin for Intervention, and a bin for Math so that any subs that might come in will also know where to find things.

Math games

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Today we were going over addition (again) in Math.  I have the slightly higher group of students that found this quite boring…yesterday.  So, I threw my plans out the window (yay for being flexible) and we played a game instead.  This game is quite simple, and of course adapted from another teacher.

I call it the Wipe-Board game.  Everyone in the class has a wipe-board, marker, and eraser.  I put them into teams of 2 and 3.  Then, I put a problem on the board that they must solve as a team.  Everyone is doing it on their own wipe-board because they don’t know whom I will tell to bring their board to the front for inspection.  Once everyone is done, and I’ve selected people to come up (i.e. the person whose first name is closest to A), then I have one of the students help me solve the problem on the board, and systematically check their wipe-boards for the correct answer and for neatness.  Everyone loves a little friendly competition, and I swear they don’t even realize they’re doing math work!

Of course, at the end, they always want to know who won, and I tell them we’re all winners (or something corny like that).