Education Technology

The Letter Product Game

Published on 06/09/2008

Activity Overview

This activity will encourage students' powers of deduction through a word game. This will allow a review of factoring integers. A simple extension allows a classroom discussion that will evolve into the Zero Product Theorem, essential to the technique of solving polynomial equations by factoring.

Before the Activity

Before class, store the value 7 for W, by typing 7 STO> ALPHA W. Also type 9 STO> ALPHA I, to store 9 in the variable I. Then clear the screen so students cannot see what was stored for W or for I.
During class, demonstrate how to store values in variables using the STO> key and ALPHA. For example, you could store 5 in A, 3 in R, and 4 in M. Also write these values on the chalkboard. Then type in those variables on their own to demonstrate how they are stored in the calculator. By typing in various expressions, such as A+M and 2^R, you can reinforce the use of variables on the calculator.
Then type in an expression like ARM. Ask them to predict the value generated by it, thereby reinforcing the use of juxtaposition for multiplication. Then ask them to predict values for AM and RAM, and verify their conjectures using the calculator.
Now type WARM and press enter. Ask students to explain what new information this gives them. Students should be able to conclude that since ARM had a value of 60, and WARM had a value of 420, that W must have a value of 420 ? 60 = 7. Be sure that student volunteers explain clearly how they reasoned that W had a value of 7.
Type in AIR, and ask students to write what they can conclude from this value. Circulate the room, checking for understanding. Students should now be ready for the game.

During the Activity

This game has several rules:
1. Each variable (A-Z) has an integer value stored in it between 1 and 10, inclusive.
2. Students may only type in English words that are three or more letters long. However, students may use the calculator by typing in an expression that does not contain any variables, like 135/15.
3. Students should keep a record of which words they have entered and what value was produced.
4. Students should try to type words so they would be able to figure out the meaning of each individual letter.
5. When a student (or team of students) think he/she/they know values for all of the letters, then they can verify their answers by typing in individual letters.
6. If all of the letters are correct, this is called solving the game. The team's score is the number of words they typed in to solve the game. The lowest score wins!
This game may be modified by having students work in teams, or by giving them some of the values before the game begins.
You may wish to let students that it would be very easy to cheat at this game, typing for example ALPHA A, and then pressing clear. This would destroy the value of the game.
Have students run the program LETTERS1. This program will set values for the 26 letters. Have students play the game. As students solve the game, you can challenge them with LETTERS2.
When most of the students are finished with the LETTERS1 challenge, call a "Time out" and discuss strategies. Then allow students to finish playing the LETTERS2 version.
If students wish to challenge each other with different values for the variables, they may store values in the first 26 spots in the List L1, and then run the program LETTLIST. This program will store the first value in the list as A, the second value in the list as B, the third as C, and so on.

After the Activity

The sample questions attached are helpful to assess student understanding, and some would make good discussion questions.
Allowing some variables to have the value of zero provides some interesting twists. It is recommended that if some variables can have the value of zero, the person who developed the game is required to say how many zeroes there are, such as "There are four zeroes in this game."
If you allow the value of zero to be stored as a variable, it makes the game more difficult, but questions like Okay, RED has a value of zero, what does that mean? can lead naturally into a discussion of the Zero Product Theorem, and the use of factoring to solve polynomial equations.
Negative values for the variables and/or decimal values for the variables can make the game more challenging!
Please Note: I don't recall if this idea is original with me. I may have seen it before, but I don't recall where or when. If you have any information about the history of this activity, please contact me.