Problem Solving – Guess and Check
Guess and Check sounds like cheating, but is really a good strategy to help you
understand and solve a problem quickly. You probably have guessed at the answer
to a math problem before. Maybe you guessed on some problems on the IOWA
tests. You may have also checked your work. Hopefully, your past teachers (not just
math!) got you in the habit of checking your work for accuracy. When you combine
the two – guessing and checking – in a________________________ way, it is a powerful tool.
Guess and check is also a __________________________builder. If you believe you can solve
a problem and use _____________________________ systematically, you can solve many
problems that you might not even understand when you start.
Example – Saturday at the “Five and Dime” Garage Sale
On Saturday, Zoe had a garage sale where she charged a dime for everything, but
accepted a nickel if the buyer bargained well. At the end of the day she had sold all 12
items and collected 95 cents. She had only dimes and nickels. How many of each did
she have? Use guess and check even if you know how to set it up algebraically.
Pause the video and work this on your own.
Here is one possible approach.
Guess 7 nickels. We know there must be an _______number of nickels for the
total to end in a “5” as in 95 cents.
With 7 nickels there must be 5 dimes, because a coin would be collected for
each of the___________ items.
5 x 10 + 7 x 5 = 85 cents. This is not the correct answer, but we are close but
________.
Try the next odd number of nickels, 9.
9 x 5 + 3 x 10 = 75 cents. This is not the correct answer AND it is going in
the______________ direction because the answer is too ______________
Try the next odd number of nickels going the other direction – 5 nickels.
5 x 5 + 7 x 10 = 95 cents. We know that she has 5 nickels and 7 dimes.
Key points to remember in working Guess and Check are as follows:
1. _______________Guessing. Don’t hesitate. As you guess and work through the
guess, you will learn more about the problem.
2. Keep your work ________________________. Use some sort of chart to keep track of
values tried and the result.
3. Be ready to start ______________.
4. _____________________ the range of your answer by guessing values that are
above and below the desired value.
Example Problem - Ducks and Cows
Farmer Renkins has a farm where she raises only ducks and cows. She is not
big on details. She remembers that she has 54 animals and that they have
122 feet all together. How many ducks and how many cows does Farmer
Renkins have? Here is one possible way to organize your data. Use it if you
like or try your own.
Ducks Duck
Feet
Cows
Cow
Feet
Total
Feet
Total
Animals
Check