Guess and Check
Guess and check is a problem-solving strategy where you make a reasonable guess, test whether it satisfies the problem conditions, and revise until you find the correct answer. For example, if two numbers add to 20 and their difference is 6, you might guess 10 and 10, check, then revise to 13 and 7 — which works because 13 + 7 = 20 and 13 - 7 = 6. This strategy appears in Chapter 2 of Saxon Math Intermediate 4 and is a core 4th grade math skill that teaches logical reasoning and systematic problem-solving, preparing students for algebraic thinking in later grades.
Key Concepts
Property A problem solving strategy where you make a reasonable guess, check if it fits the problem's conditions, and revise your guess if it is wrong. Repeat the process until you find the correct answer.
Examples Problem: Two numbers add to 20 and their difference is 6. Guess: 10 and 10. Check: $10 10=0$. Revise: 13 and 7. Check: $13+7=20$ and $13 7=6$. Correct! Problem: A toy costs 45 cents. You pay with 10 coins (nickels and dimes). Guess: 5 nickels, 5 dimes = 75 cents. Revise: 7 nickels, 3 dimes = 65 cents. Revise again: 9 nickels, 1 dime = 55 cents.
Explanation Think of yourself as a super sleuth! Make a smart guess to crack the case, check your clues, and if you're wrong, just try another angle. Every guess gets you closer to the solution, detective!
Common Questions
What is the guess and check strategy in math?
Guess and check is a problem-solving method where you make an educated guess at the answer, test it against the problem conditions, and adjust your guess until it works. It is one of the fundamental strategies taught in elementary math to build logical thinking skills.
How do I use guess and check to solve a math problem?
Start by reading the problem carefully and making a reasonable first guess. Check if your guess satisfies all conditions. If not, use the result to make a better guess — if your answer was too high, guess lower, and vice versa. Repeat until you find the correct answer.
When should students use guess and check?
Guess and check works well when a problem has specific conditions that are easy to test, such as finding two numbers with a given sum and difference. It is especially useful in 4th grade math when students have not yet learned algebraic equations.
What are common mistakes with guess and check?
The most common mistake is making random guesses instead of using each result to guide the next guess. Students should also remember to check ALL conditions in the problem, not just one. Writing down each guess and its result in an organized table helps avoid repeating guesses.
How does guess and check relate to algebra?
Guess and check builds the foundation for algebraic thinking. When students systematically adjust guesses based on results, they are essentially doing what algebra does with variables and equations. This strategy helps students understand why algebra is useful — it provides a more efficient way to solve the same types of problems.
Which textbook covers the guess and check strategy?
Saxon Math Intermediate 4 covers guess and check in Chapter 2 (Lessons 11-20, Investigation 2). This strategy is also found in many other 4th grade math curricula as a core problem-solving approach.