Linear Equations Card Sort - Day 2

If you missed day 1 of this card sort, you can read about it here.


Today when the students walked in, we were able to pick up right where we left off.  This is due in part to them writing down what they have matched so far.  FYI, yesterday we matched the slope-intercept equations with the tables.

The class decided to next determine which graphs would match.  As I walked around and listened to the groups, I noticed a few different methods...

Most groups were matching the ordered pairs from the table, to the lines on the graph.

One pair of students was matching the slope from the slope-intercept card with the slope of the graph cards.  We haven't discussed slope in the class yet, this is something they must remember from last year.

Organization was an issue for more than one group.  It seemed as though they wanted to only focus on two cards at a time rather than see all the cards as a whole.  I watched as one group would find a match, then throw the cards to the side and try to find another match.

At this point we have matched the slope-intercept, Table, and Graph cards.  I allowed the students to finish matching in whatever manner seems most natural to them.  This opened up a lot of conversations about everything going together.  We could match the intercepts to the graph, or the table, or even the standard form.  These connections are so important.

Overall, I think this was a success.  Many students wanted to know how this was going to effect their grade.  When I informed that it would help them master the next outcome, I swear I could hear crickets chirping.  You could see this little thought bubble above their heads saying, "You mean I did this for nothing?"  *Sigh*  Who cares about learning, let's just get a grade....

Linear Equation Card Sort - Day 1

Here is a link to the file:  Linear Equation Card Sort.




I started this card sort with my students yesterday and I always seem to forget that card sorting is a learned skill.  The students don't easily understand how this works.

I put students into pairs and gave each pair a set of laminated cards.  The laminating works well, so that students can write on them with dry-erase markers, then easily erase so that I can reuse them.

I started by asking the students to sort the 35 cards into 5 'logical' piles.  If I saw that a groups was struggling (some students just created 5 random piles), I would ask them to name each pile.  Groups that were using some type of logic were able to name piles such as graphs, intercepts, etc.

Once I felt that all students were done sorting the 5 piles, I gave them the paper with the headings: Slope-Intercept, Standard Form, Table, Intercepts, and Graphs.  I asked the students to physically place their cards on the paper under the column heading that matched that pile.
I needed students to do this, because in the past when I have done this card sort students starting writing numbers in the chart willy-nilly.

At this point I would love for student to individually pick two piles they want to match.  But in attempt to save my sanity, we decided as a class which to pile to match.  Interesting enough, both classes I did this with, picked the slope-intercepts and tables.  I asked the student to put the other piles to the side and not worry about them for now.  

Within these two piles there are two cards that have some blanks on them.  The #2 card and the #13 card.  I ask the students to match the cards and determine the missing pieces of information on the cards if they can.  Again, the students can write on the cards with dry-erase.  

At this point, many of my students were unable to determine the blanks for card #2.  I told them not to worry, as we match more cards, they will find a way to do this.  

That was the end of day 1.  Yes, an entire class period to match 7 cards.  

Stay tuned for day 2..

Absolute Value Equation Game - Exit Ticket Fail

After playing the Absolute Value Equation Game with my students.  I gave them an exit ticket, just to prove to myself that I'm awesome and games can solve every woe.  Little did I know that although they could easily solve the equations at the board while playing the game, they had difficulty making the connection on paper.  Take a look for yourself...

I don't feel that all hope is lost.  On the contrary, I feel that I have an easy entry point for working on this topic.  "Remember how you came to the board and blah, blah, blah, blah?"  Yes, I will keep you posted.  

Absolute Value Equation Game

When I teach my students about solving Absolute Value Equations I emphasize both the graphical and algebraic representations.

When students are confronted with an equation such as |x-4|=7 I require them to tell me:

• the meaning, "The distance between x and 4 is 7."
• to create the graph

• and to solve algebraically

Topics Covered:

Solving Simple Absolute Value Equations

Game Name:

Hmm.  I'll get back to you on this one.

Game Objective:

Be the team that collects the most points.

Materials:

Large Number Line from -20 to 20 (draw one on the class board).

Deck of playing cards, jokers removed.

Color paper cut into gem shapes (Blue, Green, Red, and Yellow) about 2 inches in diameter, at least 20 of each color.  If you have time to laminate that would be helpful.  

Small cheap magnets or tape.  Attach a small magnet to each gem or just a piece of tape to the gems so that they can stick to your board.  

Pawns (8-12) two for each team with magnets attached if you have a magnetic white board.  My pawns are strips of color paper where I printed "Team 1" and laminated.

Set Up:

Divide the class into 3-6 teams.  This is a turn based game, therefore you don't want too many teams. 

Draw a large number line on the board so that all students can see it.  Number it from -20 to 20.

Under each number place a gem.  There will be many left over, but they are used as the game progresses.

Write each team name on the board.  Leave enough room underneath for them to place all the gems they collect.  

Deal 5 cards to each team.  

Game Play:

On a team's turn, they use two cards to create an Absolute Value Equation.  Ace through 10 represent the numbers 1-10, and a Jack represents 0.  I'll get to the Queen and King in a moment.  

Suppose a team decides to play the number 5 and 2.  They may create the equations |x-5|=2 OR |x+5|=2 OR |x-2|=5 OR |x+2|=5.  Have one of the team members come up to the board and write their equation on the board, hand in their two cards, and move their pawns to the corresponding values of x.  Remember to give the team 2 new cards at the end of the turn.

Once the team moves their pawns to the correct place on the number line, they take the gem from each number, if there are any, and place them under their team name on the board.

In the beginning of the game, I try to emphasize where the 'center' is (in the above example the center is -5) and the distance from the center (in this case the distance is 2).

If a team is able to create an equation with only one answer.  They move both of the pawns to that location and can take one gem.

If a team lands on the same number as another team, they must steal one gem from them (any color) and take the gem they land on.  Again, if they move both their pawns to one location they must steal 2 gems from that player.

One more "if".  If a team moves to a location that has multiple pawns on it, they must steal one gem from each of those teams.

After a team is finished, place new gems on the number line to replace the ones that were taken.  At some point in the game you may run out of gems.  That's okay, the teams will then have to focus on stealing gems.

What's with the Gems?

Initially the gems are worth 0 points, but the value may increase or decrease depending on what the queen and king decide.

A team may decide to play a queen or a king card on their turn rather than moving their pawns.  A queen card will decrease the value of a gem.  It is possible that gems are worth negative points.  A king card will increase the value of a gem.

Write/post this somewhere because the students will forget.

Suppose a team plays a king and a 7.  They may increase the value of any color gem by 7 points.

Also, if a team plays a queen and a 9, they may decrease the value of any color gem by 9 points.

If a team has all kings and queens in the hand, trade out those 5 cards with 5 new ones.


Winning the Game:

I play this game for about 35-40 minutes.  The team with the most points at that time is the winner.



For one of my classes the gems ended with the following values:

Team 1 has a total of 29 points...

Team 2 had a total of -97 points...

Team 3 had a total of -19 points...

Team 4 had a total of -20 points...

Story:

Another kingdom story.  I couldn't resist once I decided to use playing cards.  I mean a king and queen, come on!  Anyway, each team is a peasant in the kingdom trying to impress the king and the queen.  They mine anywhere and everywhere to find precious gems to win over the royalty.  Problem is, the king and queen keep changing their minds on the value of the gems.  Be the team to impress the royal couple and earn your bragging rights.


How Did it Go?

I played this game with two of my classes and it went well.  Initially, the students weren't sure why they were collecting gems (even though I told them) and just went for it.  But this went well to help them understand how to solve the equations.  Once the teams started to change the value of the gems that's when the magic started to take place.  The students were trying to create equations so that they would 'land' on certain colors or other teams.  They were strategizing as to when to play a King or a Queen.  EVERYONE was engaged and surprised when I told them the bell was about the ring.

Interview Assessments

I've been experiencing some growing pains with flipped mastery.

• Outside resistance 
• Procedures vs. really important stuff
• Test security
• Students who are falling behind
• Assessment feedback
• Some just need a little push

Test security:

Yesterday when I went to grade the day's tests, in the pile there was a test that I didn't remember handing out.  It had neat creases in it as it had been folded into fourths, and I wondered if I gave that student the test on the previous day.  Did he really take the test home to finish it and then hand it in today?!?!  When I asked him if that was the case, he admitted to it.  I gave him another version of the test to complete.  It's now the end of the school day and guess what I noticed?  Yes, he didn't hand the test in.  He took it with him again.  

I've started dating the tests in pen as I hand them out.  Now I'll know if a student took a test home with them.  

In some of my larger classes, students are taking tests right next to people who are working on other things.  It's been challenging to notice who is taking a test and should not be talking or have their notes out vs. those who are not testing and should be collaborating and have their notes out.  In these large classes I don't have the space to create a testing area.  One solution is to print the tests on color paper to make it more noticeable.  

Students who are Falling Behind:

There are some students who are not motivated enough for this program.  They will do anything to avoid doing the work.  I suppose that happens in any program.  So I had this great idea (or so I thought).  I created a google sheet where the students would type in their plan for the week.  It worked great for the first few weeks.  Can you figure out why?  Because I was staying on top of the students.  I was nagging them to type in their plan.  And if they didn't, I went to them individually and then made them type it in.  This was just another form of babying the students.  And these same students would type in their plan and then not do it.  

Assessment Feedback:

While I'm grading tests I will notice that a certain student has this misconception or that misconception.  I write my comments on the test, file them away, and then they are never seen again.  Hold on.  That's not entirely true.  If a students asks to see his test, we will go over his mistakes, I'll tell his what to work on, then I'll send him on his merry way.  Effective right?  Bah!

Some Just Need a Little Push:

I sat with a student yesterday as he was taking a test.  His initial complaint was that he could correctly do all of the practice problems, but then he would fail the test. And he was right.  I sat with him before and he did amazing, I gave the test and he failed.  So this time I sat and watched.  I noticed a little error in the beginning of the test and from there he was fine.  Passed like a pro.

There's a Common Theme Here:

Do you see the common theme among many of these complaints?  Assessments.  

The other week my 4 year old son came home from pre-school with a DVD for us to watch.  The director of the pre-school took each student one by one into a room, assessed the child on the recommended skills for Kindergarten, recorded each session, and sent the DVD home for the parents to watch with their child.  As a parent I loved this.  It made my child's education so transparent.  I want to do this in my own classroom.  

Interview Assessments:

I've decided that I'm going to try assessment interviews with my students.  I will still have the paper and pencil tests available, but volunteers can chose to take their test with me.  This is how I see it in my head:  The student and I are sitting at a table with an iPad and using the educreations app to record our session. I write a question on the iPad, then the student answers it in writing and verbally.  During the recording I can tell the student where they need more work.  I can redirect them and clear up misconceptions immediately.  Students who are unable to prove that they possess all the skills necessary for that outcome can reassess.  Once the recording is over, I can email it to the student and his parents.  I can even post these recordings to my website.  Students who are not yet on that outcome can see what the assessment is like and what it looks like to have those necessary skills.  

Here is a skills sheet that I created for an outcome on Slope and Graphing with Slope-Intercept:

I'm trying to make a list of all the problems this will solve for me.

• Test security will no longer be an issue.  Since I only teach Algebra 1, creating problems on the spot isn't that difficult.
• Those who just need a little push to be successful will have this.
• I'm wondering if this will help with some students who are falling behind.  Will it create some pressure for them to be ready?  
• Feedback will be immediate.  

A list a new problems.

• I'm not sure I have enough time to interview every student on every outcome.  I suppose that's where the paper and pencil versions will come in.  
• I think educreations has limited space.  I can't save recordings forever.  

There's Something Here I Just Know It - Take Away Game

I don't know the name of this game, but I have always enjoyed it.  The game play is where two players have a bunch of objects in front of them (I used pennies) and they take turns taking away pennies.  They can take away up to a certain amount on their turn and the person who takes the last penny loses.

Here is the version I played:

We started with 43 pennies and the players could take away up to 5 pennies on their turn.  I won every single time.  The reactions I got from the students is something I want to bottle.  They were fighting over who got to play next.  They got their calculators and were doing crazy things there.  They were watching me closely.  They wanted to watch what I did over and over again.  They were playing against each other to try out their strategies (without being asked!).  And the same question again and again, "How are you winning?"  (answer at the bottom of the post)

There were other questions formulating in their heads that they weren't asking aloud.  Questions such as how many pennies should be remaining on the 2nd to last turn? and Does the number of pennies a player take depend on how many were taken on the last turn? 

They were shouting out ideas to each other during game play.  "She always takes 1 more than you do!", "She's doing math in her head!", "Just take the same amount she takes.",  "If she takes 5 you take 1!"

Once a student determined what I was doing and was able to beat me (okay so I didn't win every single time), I changed the rules.  Now it was 41 pennies and each player could take away up to 4 pennies.  If that student won again I knew they understood the how-to-win rules.  

Here's the thing.  This felt like a 1st act.  But I'm not exactly sure what the 2nd and 3rd acts are.  I'm not even sure of the math topic this is covering.  Patterns??  Linear Equations?  Developing formulas?? All of the above??  Please help me here.  What do I do next with my students?

Here is how I develop a version of the game.  I decide the maximum number of pennies a person could take on their turn.  Let's call this p.  Then I need to determine the total number of pennies needed to play this game.  There are many answers to this, but here is the formula g = t(p+1) + 1 where g is the total pennies in the game, and t is the number of turns each player would have before the end of the game.  

*Spoiler Alert*  Below is how to win.  

Remember that number p?  Add 1 to that.  That is the sum of the pennies that need to be taken during 2 turns.  For example, if you are playing a game where you can take up to 4 pennies, then 5 pennies need to be taken between you and the other player.  Allow the other player to go first.  If they take 1 penny, you take 4.  If they take 2 pennies, you take 3.  If they take 3 pennies, you take 2. And if they take 4 pennies you take 1.  

Sometimes the other player will insist that you go first.  If so just make sure you get back to being the one that takes the 5th penny.  

Rolling Throne: An Exponent Game - The Results

For the past three days I have been doing some informal research on my game Rolling Thrones.  I often wonder if playing games is worth my time, or any activity for that matter, and created a pre/post test to help me determine.

Link to the Game

Pre/Post-Test on socrative.com  #soc14351941

Period 1:  Playing Rolling Thrones

The Pre-Test:

19 Students took the pre-test
The class average was 46.7%
6 students scored above 70%
1 student scored 100%

The Post-Test:

21 Students took the post-test
The class average was 75.9% (a change of +29.2%)
15 students scored above 70% (a change of +9 students)
4 students scored 100%

3 students' scores stayed the same (1 of them was the 100%)
2 students' scores dropped




Period 4:  Lecture and a Worksheet

The above information doesn't tell me too much if I don't have a control group.  So, for the other class, instead of playing a game, I gave a lecture and a worksheet.  The results were very similar.

The Pre-Test:

19 students took the pre-test
The class average was 45.6%
4 students scored above 70%
0 students scored 100%

The Post-Test:

19 students took the post-test
The class average was 77.2% (a change of +31.6%)
13 students scored above 70% (a change of +9 students)
0 students scored 100%

2 students' scores stayed the same
2 students' scores dropped


My Conclusion:

Since there wasn't too much difference in the amount of learning that takes place, I would personally play the game because it was more fun.

Engagement:

Students who played the game were involved, out of their seats, yelling (if you like that sort of thing), asking questions and advice (more than I can count), and awake.  Compare that to the student who had the lecture; I noticed at one point that 3 students put their heads down and weren't taking notes, students complained that they had to do the problems on the worksheet, and only 2 students asked me for help/advice with their problems.

Amount of problems:

During the game we perhaps did a total of 6 or 7 problems (I should have kept track), while the students with the worksheet were required to complete 40 problems.

Amount of time:

The students playing the game reluctantly stopped playing when there were 4 minutes left in class, while the lecture/worksheet students finished as quickly as they could and went to work on something  else.  Depending on how you look at it, the lecture/worksheet students were able to accomplish more in a class period than the game students.

The Next Day:

The day after we played the game in class, the students asked if we could do that more often.  The students in the lecture/worksheet class did not ask for more lectures/worksheets.



Game Tweaks:

There are a few things that I would change about the game next time.

Hardly any groups purchased dice with their points.  The teams that did, lost too many points to be able to come back from that and possibly win.  Next time, I will make the price of new dice 2 points each.

Groups of 2 or 3 worked just fine.  It seemed as though all students were engaged especially with the smaller groups.  I was not frustrated with the number of teams.

I did keep track of team rank on the board.  That went over well with the students and they kept me honest as to what team was at what rank.

There wasn't a team that reached the royalty status, so the team with the highest amount of points was crowned.  The students loved the story line with the game.  I was tempted to leave it out because high school students are too old for that stuff.  <--sarcasm.  

If you play this game DO NOT forget to award the winners their crown!

The winners: