Guess-and-check problems
Key Notes :
1. Understanding the Guess-and-Check Method:
- The guess-and-check method is a problem-solving strategy used to find solutions by making an initial guess, checking whether it is correct, and then adjusting the guess as needed.
- This method works well when the problem has multiple possible answers and requires testing different possibilities to find the correct one.
2. Steps Involved in Guess-and-Check:
- Step 1: Understand the Problem: Carefully read the problem and identify what is being asked.
- Step 2: Make a Guess: Based on the information given, make an educated guess or choose a starting point for your solution.
- Step 3: Check Your Guess: After making a guess, check if it satisfies the conditions of the problem. If it’s correct, you’re done!
- Step 4: Revise Your Guess: If the guess doesn’t work, adjust it. Try a higher or lower number, or modify the guess in another logical way.
- Step 5: Repeat: Continue adjusting the guess and checking it until the correct solution is found.
3. Examples:
- Example 1: If you are asked to find a number that, when doubled, gives 16:
- Guess: 5 → 5 × 2 = 10 (too small).
- Guess: 8 → 8 × 2 = 16 (correct).
- Answer: 8 is the correct number.
- Example 2: You need to figure out how many apples are in a basket if you know that each basket contains 4 apples, and you have a total of 20 apples:
- Guess: 3 baskets → 3 × 4 = 12 (too few).
- Guess: 5 baskets → 5 × 4 = 20 (correct).
- Answer: 5 baskets.
Learn with an example
1) Logan made fudge brownies and peanut butter brownies. Each batch of fudge brownies makes 6 pans. Each batch of peanut butter brownies makes 7 pans. Logan made 6 batches and ended up with 41 pans of brownies.
How many batches of each type of brownie did he make?
____ batches of fudge brownies
____ batches of peanut butter brownies
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 6.
Guess #1: 2 batches of fudge brownies and 4 batches of peanut butter brownies
Find the number of batches:
2 + 4 = 6
Find the total pans of brownies:
(6 × 2) + (7 × 4) = 12 + 28 = 40
The guess is incorrect. Try another guess.
Guess #2: 4 batches of fudge brownies and 2 batches of peanut butter brownies
Find the number of batches:
4 + 2 = 6
Find the total pans of brownies:
(6 × 4) + (7 × 2) = 24 + 14 = 38
The guess is incorrect. Try another guess.
Guess #3: 1 batch of fudge brownies and 5 batches of peanut butter brownies
Find the number of batches:
1 + 5 = 6
Find the total pans of brownies:
(6 × 1) + (7 × 5) = 6 + 35 = 41
The guess is correct. Logan made 1 batch of fudge brownies and 5 batches of peanut butter brownies.
2) Walter went on a quiz show. The questions in the first round were worth 4 points. The questions in the second round were worth 1 point. Walter answered a total of 6 questions and earned 9 points.
How many questions did he answer in each round?
_____first-round questions
_____second-round questions
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 6.
Guess #1: 2 first-round questions and 4 second-round questions
Find the number of questions:
2 + 4 = 6
Find the total number of points:
(4 × 2) + 4 = 8 + 4 = 12
The guess is incorrect. Try another guess.
Guess #2: 3 first-round questions and 3 second-round questions
Find the number of questions:
3 + 3 = 6
Find the total number of points:
(4 × 3) + 3 = 12 + 3 = 15
The guess is incorrect. Try another guess.
Guess #3: 1 first-round question and 5 second-round questions
Find the number of questions:
1 + 5 = 6
Find the total number of points:
(4 × 1) + 5 = 4 + 5 = 9
The guess is correct. Walter answered 1 first-round question and 5 second-round questions.
3) Mrs. Lane bought 4 spools of thread. Each spool of orange thread is 5 metres long and each spool of purple thread is 3 metres long. If Mrs Lane bought 14 metres of thread in total.
How many rolls of each colour did she buy?
_____spools of orange thread
_____spools of purple thread
Use guess-and-check to solve the problem. Guess pairs of numbers that add up to 4.
Guess #1: 2 spools of orange thread and 2 spools of purple thread
Find the number of spools of thread:
2 + 2 = 4
Find the total metres of thread:
(5 × 2) + (3 × 2) = 10 + 6 = 16
The guess is incorrect. Try another guess.
Guess #2: 3 spools of orange thread and 1 spool of purple thread
Find the number of spools of thread:
3 + 1 = 4
Find the total metres of thread:
(5 × 3) + (3 × 1) = 15 + 3 = 18
The guess is incorrect. Try another guess.
Guess #3: 1 spool of orange thread and 3 spools of purple thread
Find the number of spools of thread:
1 + 3 = 4
Find the total metres of thread:
(5 × 1) + (3 × 3) = 5 + 9 = 14
The guess is correct. Mrs. Lane bought 1 spool of orange thread and 3 spools of purple thread.
Let’s practice!🖊️
