Angie Escamilla
Strategy Overview
Guess and Check is a method where you make a guess about the answer to a problem, check if it works, and then adjust your guess until you find the right solution. It’s like being a detective, trying different ideas to see which one solves the mystery. This strategy is great for problems where you have some information, but not enough to solve it directly. It works well with word problems, puzzles, or any situation where you can try different possibilities.
When is it NOT very useful?
Guess and Check might not be helpful for very complex problems with lots of numbers or when there’s a more straightforward formula or method to use. It can also be slow if there are too many possibilities A common mistake is not keeping track of your guesses, which can lead to repeating the same wrong guesses. Also, sometimes people don’t adjust their guesses enough, sticking too close to their first try even if it’s wrong.
How does this strategy help students become better mathematical thinkers?
Guess and Check helps students develop persistence and problem-solving skills. It teaches you to think creatively and not give up when the answer isn’t immediately clear. By trying different solutions, you learn to analyze and adjust your thinking—skills that are invaluable in math and in life! When you use Guess and Check, you become like a math detective, piecing together clues and learning from each attempt until you crack the case.
Example Problems
Problem 1:
Farmer Jones
Farmer Jones raises ducks and cows. She tries not to clutter her mind with too many details, but she does think it’s important to remember how many animals she has and how many feet those animals have. She thinks she remembers having 54 animals with 122 feet. How many of each type of animal does Farmer Jones have? (Johnson, Kerr, & Kysh, 2018, p. 164)
Problem 2:
Dan’s Nickels and Quarters
Dan has twice as much money in nickels as he does in quarters. He has 33 coins in all (all nickels and quarters). How much money does he have? (Johnson, Kerr, & Kysh, 2018, p. 169)
Worked Examples + Think-Alouds
Problem 1:
Farmer Jones has 54 animals in total, with a combined total of 122 feet. To solve this problem using Guess and Check, start by guessing a number of ducks and calculate the corresponding number of cows. Remember, ducks have 2 feet, and cows have 4 feet.
Why This Strategy Works:
- Start with a reasonable guess: We began with 30 ducks and 24 cows because that splits the 54 animals roughly in half. This gives us a starting point to see if we’re in the right ballpark.
- Check your math: For each guess, we multiply the number of ducks by 2 feet and the number of cows by 4 feet, then add them together. This tells us if our guess gives too many or too few feet.
- Adjust logically: When we got 156 feet (too high), we knew we needed more ducks (which have fewer feet) and fewer cows (which have more feet). Each adjustment moved us closer to 122 feet.
- Look for patterns: Notice how the total feet decreased as we increased ducks and decreased cows. This pattern helped us know which direction to adjust our guesses.
- Stay organized: The table keeps track of what we’ve tried so we don’t repeat guesses and can see our progress toward the solution.
Problem 2:
Dan has twice as much money in nickels as he does in quarters and a total of 33 coins. How much money does he have?
This problem has two conditions we need to satisfy: (1) the total number of coins is 33, and (2) the money from nickels is twice the money from quarters. Let’s use Guess and Check to find the right combination!
Hmm, none of our guesses worked! Let’s think about this differently. We need the money from nickels to be exactly twice the money from quarters. Let’s try some smaller numbers of quarters.
Success! Dan has 3 quarters and 30 nickels. Let’s verify: 3 + 30 = 33 coins ✓, and the money from nickels ($1.50) is exactly twice the money from quarters ($0.75). Dan has a total of $2.25.
Why This Strategy Works:
- Understand the constraints: We have two rules to follow—total coins must equal 33, and nickel money must be double quarter money. Both must be true at the same time.
- Calculate systematically: For each guess, we calculate the number of nickels (33 minus quarters), then find the money from each type of coin.
- Check both conditions: It’s not enough for the coins to add up to 33—we also need to check if the nickel money is exactly twice the quarter money.
- Adjust strategically: When our first guesses didn’t work, we realized we needed fewer quarters to make the ‘twice as much’ condition easier to satisfy.
- Verify your answer: Always check that your final answer satisfies all the conditions in the problem!
Student Self-Talk Questions
- Am I keeping track of my guesses and results effectively?
- How can I adjust my guesses based on the feedback from my previous attempts?
Teacher Notes and Instructional Tips
Lesson Launch Ideas
Introduce the concept of Guess and Check with a simple puzzle or riddle.
Teacher Questions & Anticipated Student Responses
- What information do we have?
- How can we adjust our guesses based on what we found?
- Students might struggle with organizing their guesses or understanding how to adjust them logically.
Differentiation Suggestions
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Support:
- Provide a structured table to record guesses and results.
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Extend:
- Challenge students with more complex problems or additional constraints.
Formative Assessment Tools
Use exit tickets where students explain one successful guess and one adjustment they made.
Student Reflection Prompts
- How did my strategy change as I worked through the problem?
- What did I learn about problem-solving from this exercise?
What prior knowledge do students need?
Basic arithmetic operations and understanding of word problems.
What classroom challenges commonly arise?
Students may initially struggle with organizing their work or understanding the iterative nature of Guess and Check.
Media Attributions
- Solving the Farmer Jones Problem © Angie Escamilla is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Solving Dan’s Nickels and Quarters Problem, Step 1 © Angie Escamilla is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Solving Dan’s Nickels and Quarters Problem, Step 2 © Angie Escamilla is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
