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How to check your math homework without the answer key

Most wrong answers on homework aren't wrong ideas. They're a dropped minus sign or a slip in line three. You can catch nearly all of them yourself in under a minute, without anyone telling you the answer.

1. Plug it back in

If you solved for something, put your answer back into the original problem, not your last line. Solved 3x + 4 = 19 and got x = 5? Check: 3(5) + 4 = 19. It works, so it's right. This one check catches most algebra slips, and it works for systems of equations and factoring too (multiply your factors back out).

2. Estimate first

Before you start, guess roughly what the answer should be. A train going about 60 mph for about 2 hours goes about 120 miles. If you get 1,200 or 0.12, something went wrong, even if every step looked fine.

3. Ask if it makes sense

• A length, a price or a count can't be negative.
• A probability is between 0 and 1.
• An angle in a triangle is less than 180°.
• Half of something should be smaller than the whole.

4. Check the units

Area comes out in square units, volume in cubic units, speed in distance per time. If your area is in plain feet, a step got lost.

5. Find the first wrong line

If the check fails, don't start over. Read your working top to bottom and ask of each line: "does this follow from the one above?" Look hardest at signs when you move a term across the equals sign, at distributing a minus over brackets, and at squaring both sides. Fix the first wrong line and redo from there.

When you can't find it

That's the moment to ask for help, and the useful question is "which line is wrong?", not "what's the answer?" Finding the slip yourself, even with a nudge, is what stops you making it again on the test.