One-Step Equations with an Unknown Number
One-step equations in Grade 3 formalize the change-in-quantity thinking from Grades 1 and 2. n + 15 = 20 asks: what number, when 15 is added, gives 20? Students who have experience with build-and-change tasks and unknown-addend problems already know how to reason about this. The symbolic equation is the formal notation for that reasoning. Verifying by substitution is a habit of mind that transfers to all of algebra: the answer must make the equation true.
All three equation structures
Start unknown: n + 15 = 20 (what did I start with?). Change unknown: 12 + n = 20 (what was added?). Result unknown: 6 + 13 = n (what is the total?). Grade 3 students work with all three, now written formally with a box or variable. The inverse operation solves each: n + 15 = 20 means n = 20 - 15 = 5. Check: 5 + 15 = 20. Correct.
Verify by substitution
The verification step is non-negotiable. After solving n + 15 = 20 to get n = 5, replace the n with 5: 5 + 15 = 20. True. This is the definition of a solution: a value that makes the equation true. Students who verify every solution are building the most important habit in all of algebra. It also catches errors before they become wrong answers.
Even and odd number investigation
The BC curriculum notes that equation work can be connected to investigating even and odd numbers. Is the sum of two even numbers always even? Write it as an equation: (2n) + (2m) = 2(n+m). The result is always even. Is the sum of two odd numbers always even? Yes: (2n+1) + (2m+1) = 2(n+m+1). Even. These investigations are algebraic reasoning using the structure of even and odd numbers.