Friday, February 27, 2015

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....


Thursday, February 26, 2015

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..


Friday, February 13, 2015

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.  

Thursday, February 5, 2015

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.