## Tuesday, January 12, 2016

### Factoring Game

It's been a while since I created a game and I had a chance to sit down today and do a little brainstorming.  My thoughts kept going back to factoring trinomials so that's where I landed.  I have not play-tested this game.  I won't get to factoring until later in the year.
I appreciate any feedback for this game, especially if any of you have a chance to play with current students.

Educational Objective:

Prep students for factoring trinomials.  This game asks students to think of two numbers that will add to _____ and multiply to ______.

Players:

Can be played as a whole-class game with 2 - 5 teams
or table top with 2 - 5 players.
I'm concerned about 5 teams or players since this is a turn-based game and there would be a lot of down time between turns.

Components:

31 cards -->  Write the following numbers on cards:

-25, -20, -16, -15, -12, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0
25, 20, 16, 15, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Game Set Up:

Shuffle the cards and turn the top 4 face up.
The left most cards is worth 4 points, the next is 3 points, the next is 2 points, and the card on the right is worth 1 point.

Game Play:

Player 1 uses any two numbers (any two numbers in the world, not the ones on the cards).  He adds his two numbers and multiplies his two numbers trying to create the numbers on the four cards.  If he is only able to get one of the numbers that's okay.  What ever number(s) he is able to create by adding and multiplying his two, he gets the point values associated with those cards.

 The numbers might be hard to seek, they are -10, 8, -3, and 2.

Player 1 comes up with the number -5 and 2.  When added the sum is -3 (worth 2 points) and when multiplied the product is -10 (worth 4 points).  Player 1 gets a total of 6 points this round.

The -10 and -3 are placed on the discard pile and two new cards from the draw pile are placed there.  It's player 2's turn.

 The numbers are -1, 8, -16, and 2.

Player 2 comes up with the numbers 1 and -1.  The sum is 0 and the product is -1.  Only -1 is on the board, so they get 4 points.

-1 is placed on the discard pile, and new card replaces it from the draw pile.  Play continues clockwise.

John Golden always has great suggestions for my games.  Check out this comment that he left about the game before you play.

To answer his question about the targets, those are all the sums and products of the integers from -5 to 5.  Initially I was going to have the students use cards in their hands to pick numbers from, but then decided to allow them to use what ever numbers they wanted.

Win Condition:

Option 1:  The first player to ____ points wins.

Option 2:  The player with the most points after _____ minutes is the winner.

Option 3:  After ____ rounds of play, the player with the most points is the winner.

Option 4:  The player with the most points once all the cards are gone from the draw pile, is the winner.

1. Another thought I just had was to have each player take a turn at the same time. The players each secretly write their two numbers. All players reveal their numbers at the same time, point values are assigned, and 4 new cards replace the current ones to begin the next round.

1. Great game. Used it today as you mentioned above, (and also with the 7,6,5,4 points suggestion), so there's no down time. Each group set a timer of a minute for each round, which worked well. Used groups of 4. Thanks for your ideas. Enjoy reading your blog.

2. I like gaming this factoring skill. What if the cards slid down so new cards come in at 1 point. Might get them to try for the larger point values. How did you choose the numbers for the targets?

I'm wondering a little bit about 1 to 4 points. Better to make a pair that adds to the 4 point card than get both the 2 and the 1 pt. 7,6,5,4 would have any two cards be more than one.

1. Thank you. This fixes the problem with students taking the easy way out with 4 points. I like the idea of cards sliding down so you can always see what's next. You always have great suggestions for my games. Thanks!!

3. I like the idea of the game but think you may run into issues with it the way it is currently set up. What is to stop students from picking 0 and the 4-point number each time as a pair with that sum?

A suggestion would be that they have to come up with numbers whose both sum AND product are among the 4 cards. You may have some rounds where there is no solution but I don't think that's a big problem if you have all the teams playing at once rather than taking turns as it wouldn't affect the fairness of the game and actually is a good lead into the idea that not all trinomials are factorable.

1. I agree. Why go for a 2-pointer and a 1-pointer when I can easily get 4 points? John has a solution for that with changing the point system to 7, 6, 5, 4 instead. That way 2 is always better than 1.

4. I think this is a great game! A good fluency builder for factoring. How would you increase the challenge for students who "get it"? Would using larger values be sufficient? Require them to find a sum AND product (as mentioned in another comment)?