Guess-and-check problems
Key Notes :
⭐ What is Guess-and-Check?
It is a problem-solving strategy where you
👉 make a guess,
👉 check if it works, and
👉 change your guess if needed.
🎯 Helps find answers when the solution is not obvious.
🔍 Steps to Use Guess-and-Check
1️⃣ Read the problem carefully 👀
2️⃣ Make a reasonable guess 🤔
3️⃣ Check if your guess fits the conditions ✔️❌
4️⃣ If it doesn’t work, adjust your guess 🔄
5️⃣ Keep trying until you get the correct answer 🎉
🎨 Why Use Guess-and-Check?
✔️ Useful for word problems
✔️ Helps when equations are difficult
✔️ Encourages logical thinking 🧠
✔️ Makes problem-solving more fun and interactive 🎲
🧩 Example
Problem: Two numbers add up to 30. One number is 5 more than the other. What are the numbers?
👉 Guess 10 and 20 ❌ (difference is too big)
👉 Guess 12 and 18 ❌
👉 Guess 12.5 and 17.5 ❌
👉 Guess 12 and 18 → Check difference = 6 ❌
👉 Guess 12.5 and 17.5 → difference = 5 ✔️
🎉 Answer: 12.5 and 17.5
(Simpler examples can also be used in class!)
🎈 Tips for Guess-and-Check
🌟 Start with easy guesses
🌟 Keep guesses organized in a table 📝
🌟 Use pattern clues from the problem
🌟 Don’t repeat wrong guesses
🌟 Think: “⏳ Try → Check → Improve → Solve!”
🧮 Guess-and-Check Table Example
| Guess 🤔 | Check ✔️❌ | Correct? 🎯 |
|---|---|---|
| 5, 10 | ❌ | No |
| 8, 13 | ❌ | No |
| 10, 15 | ✔️ | Yes 🎉 |
🎉 When to Use Guess-and-Check
➡️ Age puzzles 🧓🧒
➡️ Number puzzles 🔢
➡️ Price and cost problems 💰
➡️ Measurement and time problems ⏰
➡️ Missing value questions ❓
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!🖊️
