CREATE ALGEBRAIC EQUATIONS: Ascending Value of the Alphabet

Algebraic expressions are letters that we assign to unknown values or to specific values. 

For example, p people are sitting at a dinner table and each person is served 5 mussels for dinner. How many mussels were served for dinner? 5 times p or 5p.

People ask why do I teach algebra at the K-12th grade level? In this mathematician’s opinion, it is a flaw in our educational system that we wait until 7th grade to teach algebra. Algebra is the beginning of abstract thinking. We are so focused on teaching our kids concrete math (how to calculate or memorize math facts). Math facts and the ability to calculate are critical but these are all things we can look up or key-in on our calculators. If we teach children abstract thinking, they will be able to solve any problem using creativity and strategic techniques such as the combinatorics we learned over the last few weeks.

Take the example of asking a child what is 7 + 7, they automatically, “without thinking” answer 14. “How did you get that?” I ask. They usually say, “I just knew it.” Then, you ask the same child what is 87 + 7 and they are stuck in the mud. If they knew that 7 + 7 was really 10 + 4 then they would be able to apply that abstract concept to 87 + 7 to get 90 + 4. 

Alternatively, we could say that A = 1, B = 2, C = 3 ….Z = 26. This is the ascending order of the alphabet. If that is true, A + A + A = C or 1 + 1 + 1 = 3; A + B = C; Z — F = T and so on.

Without looking at the table of letters to numbers, you can use the acronym 

E J O T Y to represent 5, 10, 15, 20, and 25, respectively. It should be easy to find the value of each letter using these five multiples of five.

Try to use all four primary binary operations: + — x / and others if you like to create algebraic equations. Be as creative as you can. Start with your name. Use each letter at least once on the left side of the equation and use any of the 26 letters on the right side to make your each side of your equation equal.

Part of the objective of this lesson is to get our Mathletes thinking of equations as full sentences. B + C is interesting but B + C = E is a full sentence and when translated to numbers, it is 2 + 3 = 5 using our ascending code.

If K R A M E R have values of 11, 18, 1, 13, 5, and 18, you could use:

Algebraic Expression: Numerical Translation: 

M — K + R = T 13 — 11 + 18 = 20

R   — R  +  M — K  + E — A = F 18 — 18 + 13 — 11 + 5 — 1 = 6

Use any letters you want to create algebraic equations. For example,  just using the letters J and F worth 10 and 6, you could create:

Algebraic Expression: Numerical Translation:

J + F = P 10 + 6 = 16

J - F = D 10 — 6 = 4

J x F = D x O 10 x 6 = 4 x 15 = 60

J/F = T/L 10/6 = 20/12 = 5/3

J^F = (T x E)^C 10^6 = (20 x 5)^3 = 1,000,000

During the week, use the name of your family members, your dog, your teachers, your best friends, a favorite sport or book to create algebraic equations:

Algebraic Expression: Numerical Translation:

E + I + L + E + E + N =  Y X B = O X E 5 + 9 + 12 + 5 + 5 + 14 = 25 X 2 = 10 X 5 = 50

E — E + I — E + L — N = B 5 — 5 + 9 — 5 + 12 — 14 = 2