Equation Game Dollar Words Algebra

After mastering the ABC valuation method (A=1, B=2 … Z=26) and the ZYX valuation method (Z=1, Y=2 … A=26), I introduced my newest valuation method I call the EAR method. E=26, A=25, R=24 since they are the most commonly used letters in the English language.  


See the pdfs attached for the full code.


The least common letters used in the English language are Q=1, J=2, Z=3, X=4, V=5 … This method was inspired by the board game, Scrabble, since it values letters with higher value if the letters are rare, and therefore, difficult to make words.


I created the Equation Game: Dollar Words Algebra to reinforce the algebraic concepts of using letters to represent numbers. Whether they are K or 7th grade, my Mathletes know that letters are just symbols like a smily face and we can give any number value to a letter. Here are the rules for grades 3 and up:


1. Establish a Target Number: Roll 6 sided dice twice. The first roll is your tens place and the second roll is your ones place (or units digit). For example, if you roll a 3 followed by a 5, your target number is 35. 

2. Identify your Value Method as ABC, ZYX, or EAR. After each new number, change your method. All three valuation methods are on the top of each sheet in the attached pdfs.

3. Create Algebraic Equations using different letters that equal your target number. 


For example, if your target is 35, choosing the Valuation Method: EAR, I can create equations: 35 = N + D using addition; 35 = WV using multiplication; 35 = 3B + V using multiplication and addition; 35 = 2N -- V using multiplication and subtraction; 35 = PB/4 using multiplication and division. Remember, a letter next to another letter or number means multiplication.

4. Point System: You get one point for each equation that is correct. Mr. Kramer (or your parents, if you are playing at home) can give you bonus points for creativity in your equations. More complex equations take more time so extra points reward your effort.

5. Collaboration: If you are playing with a partner, you can work together and check each other's calculations.

6. New Number: After you finish equations on a particular target number, roll again and repeat the steps.


The only difference with rules for K/1st grade is that I had them add the two rolls together to generate a target number from 2-12. So if they roll a 2 and a 5, their target number is 7. Same rules otherwise and I would only expect them to use addition, subtraction, and simple multiplication such as 10=2E=10A, if using the ABC method.


It was great to see each student’s mind working differently to reach the target number. Most started out with addition and when they would run out of equations, move to subtraction, additions opposite. Using multiplication is so much fun once you realize it is just addition repeated “that” many times. If the target number was 25 and they were using the ABC method, most started with Y=25; some said Y=25A since 25 ones equals 25. Then they moved to 10s, using 25=2J + E or even 25=BJ + E. The advanced students used division, exponents, and square roots, even factorials. There are so many equations that can be generated for each target number. 


Talk to your children using letters to represent numbers to keep the abstract/algebraic thinking alive. When they start formal algebra in 8th grade, they will be so comfortable with using letters to connect numbers. It’s like a second language or code.

Equation_Game_Dollar_Word_Algebra_3-7.pdf374.85 KB
Equation_Game_Dollar_Words_Algebra_k1st_.pdf265.97 KB