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Wednesday, October 7, 2015

Expression Polygons

In the August 2015 issue of Mathematics Teacher the article Expression Polygons by Colin Foster caught my attention.  A quick google search lead me to a PDF of the article if you'd like to read it.

Just this morning my colleagues and I were talking about the struggle that students have when faced with an expression.  They are programmed to solve, so they insert an equal sign where ever they can.  Even Algebra II students.  I feel that this activity is a great way to help students understand the difference between expressions and equations.

In a nutshell, the students create 4 expressions and set each one equal to the others, so that there are a total of 6 equations:

Try it myself:

Before I try a new activity with students I like to try the activity for myself.  Here are the requirements I'd like to give the students:

  • Create 4 expressions where the 6 solutions will all be different integers.
  • Two of the expressions are of the form __x +- ___.
  • One of the expressions are of the form x +-____.
  • One of the expressions is a constant. 
It took me 6 minutes to come up with this, so I think it's a reasonable assignment for my students.  

For the Students:

I introduced the project to the students, put them into groups of 2 or 3 students, and gave them this link for a copy of the template.  Click here for template.  

I gave each student a copy of the rubric.  Click here for the rubric.

There was a lot of productive struggle going on in my classes.  One thing many groups were doing was not getting an integer answer, so they erased the entire equation rather than working backwards for a solution.  

Many times I hear the students say that the assignment was hard (not as a complaint though) and I was ready for them to give up and say that it was impossible.  But, this assignment must have had the right amount of flow to keep them going because not one group of students gave up.  

I also like all the bonus stuff we got to talk about other than solving equations.  First was vocabulary: expressions, equations, vertex, and polygon.  Students had many questions as to what an integer was since all the solutions had to be an integer.  And believe it or not, in high school the students wanted to know if there was a difference between 5 divided by 1 and 1 divided by 5.  

Action Shots:


Here are some of the students' work ,worts and all.

I found this one interesting with all the same solution of 5.  

Monday, October 5, 2015

How to Implement Games in the Classroom

Since playing more games in my classroom, I've been stumbling though the implementation part of it.  Trial and error really.  My hope with this post is two-fold.  For one, I want to reflect on my lesson/game planning.  And two, if any of you are considering using games in the classroom perhaps you can learn from my trials (and errors).

This is a little tricky, since different games have different objectives.  For instance, some games are created to introduce a topic and should be played before the lesson.  However, other games are meant as more of a review or reinforcement and would be played after the lesson.  Here is my flowchart of a unit of study.


The idea of previewing a topic before pre-testing is new to me.  Typically I would start by giving students a pre-test.  I read about previews in the book Mindsets in the Classroom by Mary Cay Ricci.  The book suggests that before giving a pre-assessment, to quickly preview the material.  It even states that 5 minutes or less will do.  We could show a few examples on the board, watch a short video clip, or have a class discussion.


I teach Algebra 1 and most of the material that I cover has already been touched in to some degree in previous courses.  But how much was covered and how much do they remember?  You won't know unless you pre-test them.  Remember to share the results with the students, but be careful with their egos the first time.  I seem to get students who are not accustomed to pre-assessments.  They often tell me they feel stupid.  Once they become familiar with pre-assessments they understand that they will feel better once they have the chance to compare the pre- and post- test results.

Play the Game:

Most of the games that I play with the students introduce the topic so I'm going to focus on game play that takes place before the lesson.  I generally don't tie the game to curriculum with introductory games until after game play.  Every once in a while a students will say something like, "I enjoy playing this game, but shouldn't we be learning some math?"  Ah, but you are.  I like this element of surprise when I show them how the game is actually teaching some math concept or at least a connection to a math concept.  I think this sudden and surprising learning experience is effective.

Teach the Lesson:

When game play is over and it's time to teach the lesson, I often refer back to the game.
"What numbers would you use to capture this city?"
"Pretend this ordered pair is one of the character in the game.  How would you get him to this ordered pair?"
Just as it is important to help student make connections between topics in our curriculum, it's also important to help them make connections between the game and the topic it covers.

Post Test:

Once I feel that almost everybody will be successful, I give the post-test.  However, once in a while I will give the students a test even when I know they're not ready.  I use it as formative assessment to see what areas still need reinforcement.  Sometimes this includes the game and sometimes it doesn't.

Repeat as Necessary:

I feel it's important for students to know that the teacher will work at their pace.  If a class is struggling with a topic, the teacher will go back and help them.

There you have it.  This is my general guideline for playing games in the classroom.

Thursday, September 24, 2015

Hidden Squares Activity Goes Digital

Remember my hidden squares activity that I wrote about last year.

Click here to read about that.  You won't be sorry, it's a great activity.

We just finished this activity with 3 of my classes, roughly 65 students.  As much as I enjoy this activity, I do not enjoy the little scraps of paper all over the floor, the students who still cut paper as skillfully as a Kindergartener, and the  s l o w n e s s  of the students' pace with just creating the posters.  Not to mention the grading.  I don't mind the grading, it's just that I'm not willing to drag them all home to grade, I try to get them done at school.  Oh and I almost forgot to complain about buying the supplies.

Then I received an email from our tech coach about making virtual posters with Google Drawing.  If only she had sent this one week sooner.  Better yet:  why didn't I think of this?

4(x + 2) + 3x + 5 = 34
4x + 8 + 3x + 5 = 34
7x + 13 = 34
7x = 21
x = 3

Here is a link for you.

Monday, September 14, 2015

Never Give Up, Never Never Give Up, Never Never Never Give Up

Never Give Up,
Never Never Give Up,
Never Never Never Give Up

-Winston Churchill

These words were and are displayed in the high school where I graduated.  I was on the basketball team and before each home game we ran through that hallway to the gym and would jump up to touch those words.  Never Give Up!

I was a young 17 years old when I graduated from high school, what does a teenager know about hanging in there and not giving up?  My 17-year-old self didn't know too much about that.  I know quite a bit more about the long haul (I still have a lot to learn), but that's not the focus of this post.  I would rather focus on my students.

Many of my students are quick to throw in the towel.  I see this often in math class and I can't help but wonder if they give up so easily in other aspects of their lives.  How many people easily give up on their spouse?  How many give up on their friends?  How many....give up on their dreams?  Here's something unexpected:  How many give up on getting gas for their car?  What?  Just watch this clip.

I've been showing this short video to my classes and while they watch it I listen to and note their comments:

"She should just drive away."
"Wow!  I can't believe someone is that stupid."
"Why didn't she ask for help?"
"Is she going to drive around again?"
"Finally!  She figured it out."

After we watch this, I like to make the connection to the classroom.
"Do you ever feel like you're driving around in circles?"
"Do YOU ever feel like you look like a fool and others are laughing at you?"
"Did this woman give up even though she may have looked foolish and stupid?"
"At what point do you ask for help?"

And then may favorite analogy is if she were to give up and drive away without getting any gas:
"What would happen if she drove away without getting fuel?"
Then we talk about how she would run out of gas, or she would need to come back to the gas station at a later point.  This is like quitting on a challenging class assignment, but then having to come back and try it later.  This takes a lot of time.  It could even have a bigger meaning, like dropping out of school and having to go back when you're older.

And what if she was too embarrassed to come back?  The students say she would have to walk or get a ride with someone else.  Walking is one way, but it sure isn't as convenient for efficient as driving (aside from pollution and exercise).  And other people are going to get tired of driving you around all the time, you have to be more independent.

Now, when I see a student give up on an assignment I say, "Ah, little Bobby just drove away from the station without gas."

Sunday, September 13, 2015

Guess My Number - Python

In the beginning of August I wanted to learn a little bit about coding.  I mean I took a semester of computer programming in college and struggled, but it was interesting.  Insert MOOCs and I'm all set.  I signed up for the Coursea course An Introduction to Interactive Programming in Python (Part 1).  I am in love.  I am only in the 3rd week of class, but I can't get enough.  I finish the assignments during the 2-day weekends, then wish for more the rest of the week.

For me, the assignments are just challenging enough that I have productive struggle and a real feel of accomplishment when finished.  I'm also learning a lot about being a student again.

Here is a screen recording for this week's mini project.  Nothing earth shattering here, but still cool.  It's called Guess the Number.


Would you like to play?  Click here to try it out.

To start, click on the play button in the upper left of the screen.  
Then click on either 0 to 100 or 10 to 1000.
Type your guesses in the box and press enter.  

Thursday, August 27, 2015

First Day Wordle

Yesterday was our students' first day of class.  I'm very excited about what I saw so far.  The students were very respectful and I think I'm going to have a great year!

I usually start the year with a survey for the students to fill out about themselves.  The first question asks the students to fill in the blank with one word.  Algebra is __________.  Then I take the words from all classes and create a Wordle.  This is the result:

My plan to to give the same fill-in-the-blank later in the year to see the change.  I'm hoping that "Boring" will get smaller.  It would be great if it disappeared all together.  

Here are the questions that I give to my students.  Feel free to steal this if you like.

As far as question #2 goes.  Here are the results of that:

This bar graph was create at Create A Graph

The one year almost all of the boys wrote that "The Maze Runner" was the favorite book.  I had to go out and buy that book right away.

There is one thing that happened this year that never happened before.  One of the students asked me what my answers were to these questions.  I was flattered.  Never did a student show interest in how I would respond.  See?  I told you it was going to be a great year.

Monday, August 24, 2015

Connect Games to Curriculum - Don't Make my Mistake(s)

I use to believe that the games I play in my classroom could stand alone.  In other words, the students could play the game and *poof* they knew the material without any further instruction from me. Let me give some examples.

Bounty Hunter:

Last school year, I had students comes to my room four at a time during homeroom.  I asked them to come there to play Bounty Hunter so I could pre-test them, watch them play, and post-test them without losing class time.  Most importantly, the students were struggling with determining slope from a graph and needed this reinforcement.

I was amazed at how quickly they 'learned' the material for the game.  They were correctly placing the numbers in the "fraction" for the game and moving their pawns in the right direction.  I was so impressed.  Then I gave them the post-test and although their scores increased, I expected scores to be much higher due to their competence in the game.

After this happened with 16 students (4 groups) I decided to figure out what was going on.  When the 5th group came during homeroom I took some time between the game and the post-test to talk with the students.  During the game, the students did spectacular just like the other groups.  Then I gave them a graph like the one on the right in the image above and asked them to tell me the slope.  I got blank stares from all 4 of them.  After some discussion with the students I found out that they didn't see the pawns in the game as points on a graph.  In fact, they didn't even see the grid lines on the game board as grid lines on the graph.  Once I took 30 seconds (literally) to make those connections for the students, the light bulbs went on.  The difference really showed on the post test. 

Pre- to Post-Test results without making connections for students --> 18% increase

Pre- to Post-Test results with making connections for students --> 35% increase

The Absolute Value Equation Game:

In our building, the administration team allows us to decide what day and period we want to be formally observed.  I chose to play a game with the class on the day of my observation.  (You think I would have learned my lesson from Bounty Hunter, but I'm a little thick in the head.)  My plan was to play the game with the class, then give the students an exit ticket before leaving, and showing my Assistant Principal what a genius I am. Ha!  Not one single student got the exit ticket question correct.  Not one.  

So what happened this time?  We played the game and the students were doing extremely well.  They could create absolute value equations that would place their pawns exactly where they wanted them.  In the example above, the student created the equation |x+5| = 2 with their cards, then moved their pawns to -7 and -3 to collect their gems.  They were doing with without assistance from me.
The exit ticket was a problem similar to the one above.  "Solve |x+5| = 2 for x".  Most students gave an answer of x = -3 and quite a few of the remaining students wrote IDK on their exit slips (The correct answers are x = -7, -3).
The Assistant Principal asked to see the exit slips and noticed that not one student was correct. "What happened Mrs. Oswald?"  Oh, I'm certain that I didn't connect the game to the curriculum.  *sigh*
The next day I took some time again to talk with the students.  In less than a minute I was able to help the students understand the connection between the game and the problem.  For my own sanity, I needed to give another formative assessment on this.  This time all but one of the students were able to get the correct answers.