1307.11 – Consecutive Integers Sum

The four numbers will each be about $\dfrac{1}{4} \times 17798$, which is 4449.5. Take two numbers on each side of 4449.5 and you'll have 4448, 4449, 4450, and 4451.

Or, Algebraically, let the numbers be $x$, $x + 1$, $x + 2$, and $x + 3$. Then we can write the equation $x + (x + 1) + (x + 2) + (x + 3) = 4x + 6 = 17798$, and go from there.

This is one of those problems where Algebra students might balk at making an equation if they can find the numbers without it. I think it best to honor this balking but also to say "here's what you can do if you're stuck." And then show them the equation.