The guess and check strategy is a commonly used strategy in mathematics in which you form a hypothesis about a probable answer to a problem and then check the answer by employing various mathematical techniques. The guess and check strategy encourages students to think logically, make predictions and follow up with mathematical operations. It also helps students to gain a deeper understanding of a problem rather than merely following a formula.
Make a Guess

Consider the following problem:
Susan has 50 marbles. Ten of her marbles are blue. The rest are green and red. She has three times as many red marbles as green ones. How many red and green marbles does Susan have?Students should be able to determine that they should guess more red marbles than green. An appropriate guess might be 25 red marbles and 15 green marbles.
Keep a Record

Instruct the students to keep a record of their guesses. An appropriate record might read:
Guess 1: 25 red marbles, 15 green marbles.
Guess 2:
Guess 3:
Guess 4:
Guess 5:Label future guesses to be filled in as needed.
Compute the Figures

If the students hypothesized that Susan had 15 green marbles, they should multiply this guess by three since the number of red marbles is three times as much as the number of green marbles.
15 x 3 = 45.Obviously the guess is wrong. In order for it to be right, the lesser number (15 green marbles) multiplied by three should equal the greater number (25 red marbles). When the number of green marbles (15) is added to the number of green marbles multiplied by three (15 x 3) the answer should equal 40.
Refigure

Since the first guess was too high, it makes sense for the students to move the number of green marbles to 10 and the number of red marbles to 30. The students should record the guess and recalculate the problem:
10 x 3 = 30; 10 + 30 = 40.Therefore, after checking once again, the students will find that there are 10 green marbles and 30 red marbles.