Problem-Solving Blueprint

Pre-Algebra · Axiom Academy

LESSON Problem-Solving Blueprint A systematic four-step approach — Understand, Plan, Solve, Check — worked all the way through one real word problem. Before solving anything, pin down exactly what you're being asked. The most common mistake isn't bad arithmetic — it's confidently solving the wrong problem. So read the sentence and pull out two things: the knowns (the facts you're given) and the unknown (what you're trying to find). What facts am I given? (the knowns) What am I trying to find? (the unknown) Can I restate the problem in my own words? What relationship ties the knowns to the unknown? Knowns: Sarah's books Tom's books; total = 48 books. Unknown: the number of books Sarah has. Relationship: Sarah's books + Tom's books = 48 . Now decide how you'll solve it before touching any arithmetic. For a problem with one unknown quantity and a clear relationship, the natural plan is to name the unknown with a variable and translate the relationship into an equation . Let t stand for the number of books Tom has. Sarah has 3 times Tom's, so Sarah = 3t . "Together 48 " becomes t + 3t = 48 . Combine like terms, then divide to isolate t . Tom's books plus Sarah's books equals the total Execute the plan one line at a time, showing every move so a mistake has nowhere to hide. We combine the like terms on the left, then undo the multiplication to get t by itself.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.