The next-to-last step of any problem solving should be checking your answer for reasonableness. (The last step, of course, is stating the answer clearly and completely.) Often when we’re working through a problem, especially a math problem, we can lose sight of the bigger picture of the problem we’re working on. We get down in the details of the math or other problem solving. When we come up out of these weeds and near the end of the problem, we’re so relieved we just want to get it done. At some point, we all will have a result that makes absolutely no sense in context. If we rush through in our relief, we may not notice this glaring problem. Even children know something about the world in which they live and can do this step.
Below are a few ways to approach this process of checking for reasonableness. Think of it as a choose-your-favorite ideas list. As with many of my posts, have fun with these. Use them to build your relationships through laughter and sharing jokes while still learning math. Or if you’re working by yourself, at least use them to give yourself a chuckle!
At the end of the movie Monsters Inc., the corporation discovers that children’s laughter generates even more power for the monsters’ world than children’s screams. Connection, laughter, and enjoyment — even little tiny moments of them — are similarly more powerful for learning than fear, boredom, and doubt.
This post was originally published on mathteacherbarbie.com. If you are viewing it somewhere else, you are viewing a stolen copy.
1. Start with three estimates: too big, too small, and best guess
This suggestion comes in at the beginning of the problem solving process. Before doing any math but after reading the problem, make three guesses about the answer. Make one guess that’s bigger than you think the answer could possibly be (I recommend making it hilariously big and having a good laugh trying to imagine it). Make one guess that’s smaller than you think the answer could possibly big (I also recommend trying to imagine this one for a chuckle). Then make one final guess that you suspect might be about right, or at least reasonable. At the end, you can compare your solution to these three guesses. Hopefully it’s closer to your middle “reasonable” guess than to the extremes.
2. Read the solution aloud
Put your answer into an answer sentence. Then read the sentence aloud to yourself. Does it sound right? Does it sound reasonable? If someone said that sentence to you, would you look at them funny because the number sounded so weird in that context?
3. Call your grandma (or relative, friend, etc)
They’ll love hearing from you! And you can tell them you need to read them an answer and ask whether it makes sense. Then, just like for number 2 above, read your solution in an answer sentence. If they laugh or act surprised at the number, then that’s good feedback that the answer might not be reasonable.
4. Look for clues in the problem
Is there anything in the problem statement that gives you clues about what types of answers might be reasonable? (If Jim and Jane each have 7 apples, it doesn’t make sense that they would have 2,783 apples together. The “correct” answer is probably a lot fewer digits than that.)
5. Do research
Maybe it’s a context you don’t know much about. Do a tiny bit of research. Whether this be actually performing jumping jacks yourself to find out what’s a reasonable number to do in a minute (if that’s the context of the problem, of course), looking something up on the internet, a simple brainstorm session, or asking someone, there are more ways than ever before of finding out information about what’s reasonable in a given scenario.
6. Take a break and come back later with fresh eyes
Sometimes we need a fresh perspective. That sense of “I’m almost done” relief can be a powerful thing. It can even overwhelm our sense of reality. Doing something else, whether just another problem, having a snack, or sleeping, can refresh our sense of reality and reasonableness. Reread your solution after this break. If it still makes sense, great! If not, you might need to check your work while you still can.
7. Make sure you answer the question asked
Sometimes we get sidetracked or misread the question that was actually asked in the problem. Go back and check that question. Does your answer make sense in response to that request? Do your processes and steps make sense in response to that request? We all do it. We all end up answering different questions other than the ones asked sometimes. It probably tells you something about the context of the problem, even if it doesn’t answer the question directly.
Use rounding and other estimation strategies to figure out an approximate answer quickly with simpler arithmetic. It’s often easier to keep our perspective when the arithmetic and other steps in the middle are easier to do. Is your final answer close to the estimate? If so, that’s a great sign! (Note: in a quick web search, this comes up as by far the most frequent suggestion for checking reasonableness. Those results lead me to believe this is likely the one your child is being directly taught in class. I wanted to give a few out-of-the-box ideas here as well for those times estimating fails you or is simply not quite enough.)
9. “Plug in” your solution to check for a true statement
Unlike most of the other strategies on this list, this one applies to very specific problems, not all of them. However, also unlike the other suggestions, it can give you a definitive “yes” or “no” answer for whether your solution is correct. If you were asked to “solve” an equation (or inequality) for an unknown number, then you can check by plugging your solution back into the original equation (or inequality) to make sure that it creates a true statement.
10. Try a similar problem
If you can, make up a similar problem — either similar context or different context but similar math structure. Hopefully it’s a problem that you find easier to solve. Solving that problem can give insights about the original problem and what might be right and what might be wrong in the original work and answer.
Whatever strategies you choose, establishing these habits of checking reasonableness serve us all well throughout life, not just math class. And if you’re a regular reader, you know that’s one of the themes I love!
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