Thursday, August 16, 2007

Sample 5e Lesson Plan: a Card Game for Combining Like Terms

A few weeks ago I discussed learning the 5e instructional model at a workshop this summer, but neglected to include the sample 5e lesson plan I had created using the model.

I started with an unfinished idea I had last year for teaching simplifying equations using a card game where the cards would be algebraic terms. My sister and I used to play rummy, spit and every other card game during summers at home when we were young. (We also used to play board games like Monopoly, but it inevitably ended badly). Reflecting on these memories as this summer started, I came up with "Like Terms".

Like Terms

Like Terms is played like rummy, but with a special deck of cards made up of sets of like terms: a, 2a... through 10a and so on for b, c, a2, b2, c2 and the integers 1-10.

The game follows the normal rules of rummy:
  • Each player is dealt 7 cards.
  • The remaining cards are placed face down--this is the draw pile.
  • The top card is flipped over to a new pile--this is the discard pile.
  • Each player draws a card, looks for a 3 or 4 card set of like terms, and places that face up on the table in front of them if they have it (7a, 3a and a or 6c2, 2c2, 4c2, and 10c2 would be two playable hands).
  • Whether they have something to play or not, they must then discard one card to end their turn.
  • Play continues until someone discards their last card and has no cards left.
  • The winner adds everything they placed on the table together. Everyone else subtracts what's in their hand from what they had placed on the table.
At this point in the real game of rummy, players would tally their score based on a point system. You could assign points to each variable in this game, I suppose, but I think that defeats the purpose. I would rather have the "scores" look like 15a2 + 16b2 + 9b + 6c + 7 for the winner and -5b2 - a - 6c - 11 for the loser and jump directly to giving students problems where they have to simplify expressions.

If you only explained the rules of Like Terms and told your students they would use only the game rules to solve math problems afterwards, it would make a sometimes boring and easily forgettable operation fun and easy to remember.

How to make a deck of cards for Like Terms the easy way:
  • Use white 3x5 index cards and at least 4 different colors of highlighters or flip chart markers (so the terms won't bleed through). Each term gets a different color (a and a2 are blue, b and b2 are red, etc), OR...
  • Use colored index cards for the sets and one marker that won't bleed through, OR...
  • Cut up scratch paper and use trusty blue, black and red pens, OR...
  • If you want to really get fancy, you can get card stock and print out cards on the computer.
Whichever method you choose, remember that you'll need multiple decks since a typical game should be 4 players (max 6).

How to use this in your classroom

I designed this with my 9th grade Algebra I students in mind, because they usually come to me unable to simplify expressions. This little problem, like so many little problems, gets compounded as we move into more complicated equations and make things infinitely more difficult than it needs to be. This is appropriate for the first few weeks of school when you're working on review, basic skills and procedures.

Some teachers may find this more appropriate for middle school, and I'd be interested to see how this would fare in a Pre-Algebra classroom. If you try it please share your results!

Here is the full sample lesson plan based on the 5e model to help you plan a complete lesson around this activity.

UPDATE 9/3/07: Since I will be using this lesson in class this week, I am adding 2 documents I will be handing out to my students as a one page back and front handout:
  1. Like Terms rules and scoring - Simplified for student consumption.
  2. Like Terms score sheet - This is a simple graphic organizer that they can hand in or you can refer to while monitoring the games so you can identify problems (and/or give them a grade for participation). I had to reformat this document for Google Docs, because it didn't like the tables I used for the score sheets or the columns I used to fit 2 on the same page. You might have to cut and paste to save paper. Or, email me at teachforeverATgmailDOTcom and I can send you the original document in OpenOffice, Word or PDF format.
Please leave comments or email me with feedback.

UPDATE #2 7/22/11: Check out Combining Like Terms Game Revisited for an alternate version of this game. I've expanded upon this lesson idea and many more in my book Ten Cheap Lessons: Second Edition.


Carly Albee said...

I am going to use this brilliant game today in class. Thanks for posting.

Anonymous said...

Please help me understand how do I make the scores MEANINGFUL to the students at the end (other than saying that we just learned how to combine like terms).

Anonymous said...

You can assign numbers to the variables. For example, a = 2, b = 3, and c = 4.

ER said...

This is a brilliant game. I am planning on using a regular deck of cards with the face cards pulled out. Red suits will be negative and black cards will be positive. That way they are practicing adding/subtracting integers. Especially subtracting a negative (major issues here) when they have lost the hand.

thanks for sharing!!!

Anonymous said...

I used the rules that someone else posted, with a few minor changes.

I also included negative coefficients with the variables and integers.

For scoring, I'm making different points for different variables.
Ex: If you have the highest A value, get 8 points, the highest B value get 6 points. If you got rid of your cards first, 10 points. Etc!
Hope that helps

Jason said...

I am constantly looking for games to play in my math classroom.

I got tired of looking so, like you, I created my own. I know it may be cheaper to make your own cards (I have bought blank cards at my local teacher supply store) but I have found a company where you can get cards made inexpensively.

If you are interested in taking your game to the "next level" you ought to check out the site The Game Crafter.

I created a game called Solve and Settle using the site to use in my Algebra class.

Alyson said...

I have a question about the rules. If you deal 7 cards and pick up and discard 1 each turn and also take away groups of 3 or 4 - and you start with a group of 3, next you could ONLY make a group of three first (because if you didn't give away as an initial group of 4 you'll get to three before you get 4), which would leave you with 1, picking up and discarding one per turn would mean you never get rid of all your cards. Has no one had that problem?

I tried it with my husband and he won because he was dealt 4 (of a suit, we were using regular cards and I was just going to make the variables c, s, h, and d after the suits.) I also tried it with picking up a card each turn without a discard..but then I wondered how you pick a winner because I could have 25h as my high suit and you could have 25d as your high suit and someone else could have 25s and 25c. Do you just add coefficients at the end?

I think it's a great idea and my Algebra II kids REALLY need it based on the ridiculous things they were doing with unlike terms on their first test!

Mr. D said...


I have had this happen, so I would use a "house rule" I always used in rummy.

If you're left with a single card, you can add it to an existing group of 3 (yours or someone else's), as long as it's a like term.

Charlie Gramatges said...

This game is great!!! I have added some embellishments, which I am sure most have already discovered...but check it out:

To Win the Game: have a stack of cards available with the values of a, b, and c on them for each player to use to evaluate his or her expression (so sometimes a winner may become the loser!)

Special Cards: multipliers! have random instant cards in the deck that must be placed on one group of like terms already played. That multiplier may help (or hurt, depending on what the multiplier does to the expression played)!

ryan said...

came up with a version with a deck of cards that helps with the snag or keeping score. Played with a regular deck of cards. Variables are D,S,H,C for names of the faces...variation black and red, one of the blacks being a squared same with the red.'s played the same way, except the winner of the game will get an expression with all four suits. First one wins, but with each round you must subtract like stated in original directions. They have a running expression the entire game, after the first round they begin with an expression and every round after that adds to that expression. At the end, if there's a tie, you just add the coefficients of all the terms and the highest one wins....It's a combo of phase ten, and hearts...

Anonymous said...

I love this idea and am definitely going to use it! Just a few thoughts: has anyone tried using "Go Fish" style rules? I think that is a game more kids would be familiar with.
Also, if the cards are color coded, then a student could play the game successfully just by matching the colors, but having no clue how to actually combine like terms. I think I'm going to make my deck all the same color.