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Thursday, June 25, 2015

Operations with Monomials Game - Version 3

If you missed them, here are links to Version 1, Version 2, and the original game, Polynomial Pirates.

Who, What, When, Where, Why?

3-5 Players

Algebra 1 Students

After learning about operations with monomials

Anywhere you want

Because you want your students to practice operations with monomials.


Game Objective:

Be the first player to get rid of all his cards.


Materials:


  • 70 expression cards.  I wrote the expressions on index cards there were cut in half.  
Here are the 70 expressions that I used:


0, 1, 2, 1/2, 3, 1/3, 3/2, 2/3

x, 2x, 3x, 4x, 5x, 6x, x^2, 2x^2, 3x^2, 4x^2, 6x^2, 9x^2

y, 2y, 3y, 4y, 5y, 6y, y^2, 2y^2, 3y^2, 4y^2, 6y^2, 9y^2

x+y, x+2y, x+3y, 2x+y, 2x+2y, 2x+3y, 3x+y, 3x+2y, 3x+3y

x-y, y-x, x-2y, 2y-x, x-3y, 3y-x, 2x-y, y-2x, 2x-2y, 2y-2x, 3y-2x, 3x-y, 2y-3x, 3x-3y

xy, 2xy, 3xy, 4xy, 6xy, 9xy

x/y, y/x, 2y/x, x/3y, y/2x, 3y/2x, 2x/3y, y/3x, 3x/2y



  • 3 blank dice with these monomials written on each one.  x, 2x, 3x, y, 2y, and 3y





Set Up:

Deal all the cards to the players.  Make sure each player has the same amount of cards, the remaining ones can be set to the side.

Each player places their cards in a pile facedown in front of them and turns over the first three cards.

Place the three dice in the middle of the table.




Game Play:

Roll the three dice.  

Every player tries to create the expressions on their three face-up cards with two of the dice that have been rolled by adding, subtracting, multiplying, or dividing.  

Once a player is able to create an expression, he announces how to do it (add, subtract, multiply or divide the two monomials), places it to the side, then flips over another expression card from his pile.  
Players continue to do this until there are no moves left.  

Re-roll the dice and continue the process.



Example of game play:



Player 1 has the following expressions:


3x/2x gives up 3/2.  Player 1 moves that card to the side and replaces it with another one from his pile.



Player 1 uses 2y-3x to remove the middle card and replace it.
There are no more moves for player 1.







Winning the Game:

The first person to get rid of all his expression cards is the winner.


Monday, June 22, 2015

Updated Version of Tornado Inequality Game

A long time ago, I created a game for systems of linear inequalities.  Click here to read about it.  I gave it the catchy name of Tornado Inequality.  Well, it has a face lift.  Instead of little dots as trailers, I drew trailers.  Instead of nothing, I have a tornado inequality.  You can make the tornado go across the screen during game play if you like.  I have also included the rules right with the graph in case you need to refer to them.



This is the old:



And this is the new.  Here is the link.






Saturday, June 20, 2015

3rd Grade Math - The Distributive Property

Here's a post I started a few months ago, but never finished...


My step-daughter, Brianna is currently student teaching 3rd grade.  The other day she was expressing her frustration with teaching the distributive property to her students.  She felt that it was overwhelming due to the fact that many of them don't know their times tables, therefore they have difficulty finding the area of a rectangle, and ultimately struggle with the Distributive property.



I remember when my son, who is now in 4th grade, was struggling with this very topic last year.  He is a B student when it comes to math (go figure) and this was probably the most difficult math topic for him in 3rd grade.  

She asked for my opinion on some activities that she could do with her students to help them understand.  Here is what she came up with:

Each group of students is going to receive these rectangles: 5 x 1, 5 x 2, 5 x 3, 5 x 5, 5 x 6, and 5 x 7.  She cut these out and highlighted the edge of the rectangle to make them easier to identify.  For example, she highlighted all the 5 x 3 rectangles in orange.  Hopefully she took more pictures than I did.  This is all I have.  



Then she will give each group of students a paper with a 5 x 8 rectangle on it.  The students need to use the rectangles they have place two at a time without overlapping to create the 5x8 rectangle.  Very tactile, very hands on, excellent.  

The students will be able to use the rectangles 5 x 1 and 5 x 7 to complete the activity, also 5 x 2 and 5 x 6, or 5 x 3 with 5 x 5.

One word of caution from Bri: She didn't create the rectangles 5 x 4 for the students.  She found that when she was trying to talk to the students about two congruent rectangles, the student were confused as to which one she was referring.  

That's her lesson for today and she will build on this foundation, but I can't help but keep thinking about this 3rd grade topic.  My son struggled with it, her students are struggling with it, I remember a frustrated Facebook post about this from a friend of mine, and I'm sure there are many others who struggle with this.  


What do you do when a math topic is proving difficult for students?  Why you create a game of course.

I'm not all that familiar with a group of 3rd graders, please keep that in mind.

I like the idea where Bri gave her students different rectangles to manipulate, so I think that should be a component of the game.  There are 15 different rectangles 1 x 1  up to 5 x 5.  And I like that she gave her students a target 5 x 8, so for the game I see the target changing.  

Each team of students is given 15 random rectangles.  Some will be repeats and that's okay.  The teacher displays the target and the students try to create as many as they can with the rectangles they have.  It is possible that the students won't be able to create the target since the rectangles given are random.  

Here are all the different rectangles.  The teachers will need to create as many sets as there are students plus at least one extra set. 23 students means 24 of each rectangle below.

1x1  1x2  1x3  1x4  1x5

2x2  2x3  2x4  2x5

3x3  3x4  3x5

4x4 4x5

5x5


Here are all the different targets that can be created with any 2 of the rectangles.  The teacher will need to create just one of each target.

1x2    2x2      

1x3    2x3    3x3   

1x4    2x4    3x4    4x4   

1x5    2x5    3x5    4x5    5x5

1x6    2x6    3x6    4x6    5x6

1x7    2x7    3x7    4x7    5x7

1x8    2x8    3x8    4x8    5x8

1x9    2x9    3x9    4x9    5x9

1x10  2x10  3x10  4x10  5x10



For each pair or rectangles that a team successfully creates the target, they get 2 points.  
If a team can use 3 rectangles to create the target, then they receive 3 points.  And so on.  
After that round is over, the students hand in the rectangles they just used and replace them with new random ones.  

The team with the most points after a certain amount of time (teacher's choice), is the winner.



Or How About This Game?

Students are given still given the 15 random rectangles (is 15 too many?), but this time 36 of the 39 targets are written on the board in a 6x6 array randomly.  

Teams take turns using at least 2 rectangles to make a target.  That target is circled in that team's color.  The team then hands in the rectangles they just used and are replaced with random rectangles.  

The first team to get 4 (maybe 3?) in a row wins.  

If the 6 x 6 board is too small, some targets could be written more than once.


How about some photos?

Again, sorry about the lack of photos.  I was so excited to create this game, that when I did I proceeded to give the 'game pieces' to Bri immediately and forgot to take a picture.  Sorry :(






Friday, June 19, 2015

Operations with Monomials Game - Version 2

If you are just tuning in and missed Version 1, click here to read about that version.  I am creating different versions of games that reinforce operations with monomials.  Here is version 2.

Who, What, When, Where, Why?

4 Players

Algebra 1 Students

After learning about operations with monomials

Anywhere you want

Because you want your students to practice operations with monomials.


Game Objective:

Be the first player to move all of your pawns to the opposite side of the board.


Materials:


  • 70 Expression cards.  I wrote the following expressions on index cards that were cut in half.  You may find it useful to write the expression twice so that it can be read from opposite directions.



The 70 expressions:

0, 1, 2, 1/2, 3, 1/3, 3/2, 2/3

x, 2x, 3x, 4x, 5x, 6x, x^2, 2x^2, 3x^2, 4x^2, 6x^2, 9x^2

y, 2y, 3y, 4y, 5y, 6y, y^2, 2y^2, 3y^2, 4y^2, 6y^2, 9y^2

x+y, x+2y, x+3y, 2x+y, 2x+2y, 2x+3y, 3x+y, 3x+2y, 3x+3y

x-y, y-x, x-2y, 2y-x, x-3y, 3y-x, 2x-y, y-2x, 2x-2y, 2y-2x, 3y-2x, 3x-y, 2y-3x, 3x-3y

xy, 2xy, 3xy, 4xy, 6xy, 9xy

x/y, y/x, 2y/x, x/3y, y/2x, 3y/2x, 2x/3y, y/3x, 3x/2y


  • 6 blank dice or 6 dice with stickers.  Write the monomials x, 2x, 3x, y, 2y, and 3y on the six sides.


  • 16 pawns in four different colors.  I used water bottle caps with color paper glued on and arrows drawn.  I believe the arrows are necessary to keep track of which pawns are moving in which direction.


Set Up:

Shuffle the expression cards and place them in a 6x6 array with the four corners missing.  Along each side place four pawns.  See image below:





Place the pawns so that each arrow is pointing toward the nearest card.  That is the direction the pawns need to move to get to the opposite side of the board.





Game Play:

Player 1 rolls all six dice.  He is trying to use two dice at a time to create the expression in the direction of the arrow.  A player may add, subtract, multiply, or divide to create the expressions.  Players may make up to two moves per turn, either one move with two pawns or two moves with once pawn.

From the image below, you can see that the yellow player has the following expressions he can move to; x/3y, y-2x, 3xy, and x-y.



He rolls the following monomials:



Using 3y * x, he gets 3xy and can move his pawn ahead one space.  And with 2x-2x, he gets 0 and can move that same pawn ahead one space.



After rolling the 6 dice, a player may keep any dice that he likes and re-roll the rest.  A player can only re-roll once per turn.  

Play moves to the next player.



Take a look at the green pawn that is still off the board.  pawns may 'jump' over other pawns that are in their way.  


The green player rolls the follow monomials:


Using 2y*y he gets 2y^2 and moves his pawn.



Then using x*2x he gets 2x^2 and 'jumps' over the yellow pawn to the next space.




As the game continues, the middle of the board will get congested and pawns may 'jump' over multiple pawns on their turn.  This is a good strategy to get to the opposite side faster.






The yellow player was the winner this round . he was able to get all 4 pawns to the opposite side of the board before the rest of the players.  



Hints, Tips, and Suggestions:

Make sure the arrows are pointing in the correct direction at all times.  

There will be times when players will only be able to move once on their turn or in some cases not at all.  In the image above, the red player was moving left and was unable to move because the green pawn was in the way.

Writing the expression twice on each card is recommended so that it's easier for all players to read them.

Since you are creating 70 cards but only need 32, you could have two simultaneous games running with one deck.

Players may move their pawns in any direction as long as they only move to adjacent spaces.

To create a longer version of the game, start with a 7x7 array of expression cards with the corners missing and 20 pawns, 5 of each color.

Thursday, June 11, 2015

Operations with Monomials Game - Version 1

I can see so many version of this game, I just need to sit down and make them happen.  So, this morning I did just that (for 1 version at least).  I created a game previously with operations of monomials and you can read about that here.  But that game is complicated and requires a lot a stuff.  The following game will cover the same topic, but is easier to set up.

The inspiration of this game came from Sequence.


If you see this game at a yard sale, buy it.  Not only do you get two decks of cards with it, but there are colorful game pieces and a folding game board.  So, even if you don't like the game itself you can us the components for a different game.  I, however, do like the game, but wish for more player options.  



To make this game you will need index cards (cut in half) and color chips for each player.  I play tested this game with 3 players.  


The monomials that are used for this game are x, 2x, 3x, y, 2y, and 3y.  I wrote these on the playing cards (index cards) in red.  Make a few sets of these, they will be the cards that they players hold in their hands.  



If you add, subtract, multiply, or divide the above monomials you get the expressions that make up the game board.  I wrote out those expressions on some more index cards in black.  To create the game board place them in a 7 x 10 array.  At the bottom of this post is a list of the expressions that I used in the game.



To begin, the dealer shuffles the playing cards (the red ones) and deals 4 to each player and the rest are placed facedown so all players can reach them.  The first player uses two of his cards to create an expression.  He can either add, subtract, multiply, or divide them.  Two cards must be used for each player's turn (not 3, not 1).  The player discards the two cards he used, places one of his color chips on one of the corresponding black cards, and picks up two more red cards.  Play continues around the table.  The first player to get 2 sets of 4 in a row is the winner.  The winning player must use 8 different chips to count as his four in a row.  He cannot use the same chip twice in two rows (Does that make sense to you?)   



Blue is the winner with two sets of 4 in a row.


Here are the expressions that I used:

0, 1, 2, 1/2, 3, 1/3, 3/2, 2/3

x, 2x, 3x, 4x, 5x, 6x, x^2, 2x^2, 3x^2, 4x^2, 6x^2, 9x^2

y, 2y, 3y, 4y, 5y, 6y, y^2, 2y^2, 3y^2, 4y^2, 6y^2, 9y^2

x+y, x+2y, x+3y, 2x+y, 2x+2y, 2x+3y, 3x+y, 3x+2y, 3x+3y

x-y, y-x, x-2y, 2y-x, x-3y, 3y-x, 2x-y, y-2x, 2x-2y, 2y-2x, 3y-2x, 3x-y, 2y-3x, 3x-3y

xy, 2xy, 3xy, 4xy, 6xy, 9xy

x/y, y/x, 2y/x, x/3y, y/2x, 3y/2x, 2x/3y, y/3x, 3x/2y









Wednesday, June 10, 2015

Writing Linear Equations Given Two Ordered Pairs

Here is an activity I forgot to write about.  My students were learning how to write linear equations when given two ordered pairs.  I wanted to help them make the connection between the algorithm and what was happening graphically.  On some index cards, I wrote an ordered pair, laminated them, cut hole in them, and put a string in them to make them necklaces.  I also wrote a letter in the bottom corner of each index card.



As the students walked into the room, I handed them a necklace, and asked them to wear it.  The students were then instructed to work with a partner to write the equation of the line that passed through both of their points.  They also needed to record the letter of the person they were working with (this is pointless, but I did it so the students thought I had an answer key).  Once they had their equation, they found another partner and repeated the process.




It all seems rather straightforward and very much like a worksheet.  But what happens as they keep changing partners blows their minds.  THEY KEEP GETTING THE SAME EQUATION.  And not only that, everyone in the room is getting the same equation.  Every. Single. Time.

They begin to wonder what is going on.  Of course I don't tell them.  One student finally spoke up and said that if we were to plot all of the points, they would fall on the same line.  So we did.  

Tuesday, June 9, 2015

Algebra 1 Curriculum Next Year

I'm tired of trying to cover all of the Algebra 1 material.  Mostly because it never happens and I always feel like a failure.  Thinking that I can cover all of the material and then not doing it is really crushing my ego.  Our school uses a traditional schedule of 45 minutes periods and 4 marking periods a year.  I'm going to eliminate some outcomes and try to cover the remaining ones really well.  So, here's my plan for next year:

Quarter 1 (Solving Linear Equations and Inequalities)

Outcome 3 - Combining Like Terms and One-Step Equations
Outcome 4 - Multi-Step Equations
Outcome 5 - Equations with Variables on Both Sides
Outcome 7 - One-Variable Inequalities
Outcome 8 - Compound Inequalities
If there's time:  Outcome 9 - Absolute Value Equations and Inequalities


Quarter 2 (Graphing)

Outcome 15 - Patterns
Outcome 16 - Domain and Range
Outcome 17 - Graphing with Tables and Intercepts
Outcome 18 - Slope and Slope-Intercept
Outcome 19 - Writing Linear Equations


Quarter 3 (Systems)

Outcome 20 - Applications of Writing Linear Equations (I hope I can fit this in the 2nd Quarter)
Outcome 21 - Graphing Two-Variable Inequalities
Outcome 24 - Systems of Graphing
Outcome 25 - Systems of Inequalities
Outcome 26 - Systems by Substitution
Outcome 27 - Systems by Elimination


Quarter 4 (Polynomials)

Outcome 28 - Applications of Systems (I hope to move this to Quarter 3)
Outcome 29 - Operations with Polynomials
Outcome 30 - GCF & LCM of Monomials, Factoring
Outcome 31 - Solving Polynomial Equations
Outcome 32 - Operations with Rational Expressions