I wrote this series of five circuits for my own child who wanted to "do some algebra". The skills covered are: addition, subtraction, multiplication and division (all within mostly 20 and occasionally within 40). The idea is not to learn the procedure "subtract two from both sides" (or whatever) but rather to be able to read the mathematical sentence "x + 2 = 7" and realize from the student's conceptual knowledge that x must be 5. Each circuit contains 14 self-checking equations and each circuit is progressive in nature (builds from easiest to hardest).
Here are the opening directions for the addition circuit: Begin in cell #1. Read the equation out loud and then imagine what number the variable (letter) is the same as. For example: a + 2 = 7 means some number “a” plus two equals 7, so “a” must be 5. Search for your answer and call that cell #2. Continue in this manner until you complete the circuit.
I do not include answer keys with my circuits because the answers are imbedded in the circuit, but should you get stuck or find a mistake, please let me know!
I could imagine 2nd - 6th graders working on these five circuits.