Teach students the same technique research mathematicians use! (Seriously.)
"Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem.Need more tips and tricks for teaching math? You can find them in our math resources center.
Solve the Problem
Now, solve the problem. You may want to set up a table to record the guesses.
| Guess Number | Blue Jays | Diamondbacks | Red Sox | Total |
| First Guess | 10 | 20 | 10 | 40 |
Guess a greater number of Blue Jays.
| Guess Number | Blue Jays | Diamondbacks | Red Sox | Total |
| First Guess | 10 | 20 | 10 | 40 |
| Second Guess | 20 | 40 | 10 | 70 |
Now guess a greater number of Blue Jays.
| Guess Number | Blue Jays | Diamondbacks | Red Sox | Total |
| First Guess | 10 | 20 | 10 | 40 |
| Second Guess | 20 | 40 | 10 | 70 |
| Third Guess | 40 | 80 | 10 | 130 |
Now guess a number lesser than 40 and greater than 20.
| Guess Number | Blue Jays | Diamondbacks | Red Sox | Total |
| First Guess | 10 | 20 | 10 | 40 |
| Second Guess | 20 | 40 | 10 | 70 |
| Third Guess | 40 | 80 | 10 | 130 |
| Fourth Guess | 30 | 60 | 10 | 100 |
That is the answer.
Check
Read the problem again to be sure the question was answered.
Yes, I found the number of Blue Jays.
Check the math to be sure it is correct.
30 doubled is 60. 30 + 60 + 10 = 100
Determine if the best strategy was chosen for this problem, or if there was another way to solve the problem.
Guess and check was a good way to solve this problem.
Explain
The last step is explaining how the student found the answer. Demonstrate how to write a paragraph describing the steps and how decisions were made throughout the process. Have students justify their answers.
Guided Practice
Have students try solving this problem using the strategy of Guess and Check.
Of 25 rounds at the regional spelling contest, the Mighty Brains tied 3 rounds and won 2 more than they lost. How many rounds did the Mighty Brains win?
Have students work in pairs, groups, or individually to solve this problem. They should be able to tell or write about how they found the answer and justify their reasoning.
How Can You Stretch Students' Thinking?
Guess and check can be made more sophisticated by improving each guess based on the last guess. Encourage students to analyze their guesses to determine what the next guess should be. Students can use patterns in the problem or in their guesses to determine the correct guess.
Students may not want to use any other strategy once they have learned guess and check, because it is so easy to use. When children are completely stuck, guessing and checking provides a useful place to start, but may not be the most efficient strategy. As problems get more difficult, other strategies become more important and more effective, but by starting with guess and check, the students may find a more efficient strategy that leads to a solution.
