Math Heuristics for Problem Solving
Primary 3 Guess-and-Check & Its Method
What is Guess-and-Check in Math?
The Guess-and-Check method is a problem-solving strategy used in math to find a solution by making an initial guess and checking whether it is correct or not. If the guess is incorrect, a new guess is made and checked until the correct answer is found. This method can be used when there is no obvious formula or method to solve the problem, and is particularly useful when dealing with word problems. It can be time-consuming, but can also be a useful way to develop problem-solving skills and intuition.
Guess-and-Check is useful when a word problem provides the values of both items, the total quantity, and the total value. In such cases, both the Assumption or Guess-and-Check method can help find the solution.
How to Solve Math Questions with Guess-and-Check Method?
Let's take a look at this Primary 3 word problem example:
Ronald bought 8 pens and rulers for $21. Each pen cost $3 and each ruler cost $2. How many pens did Ronald buy?
Identify the Concept
The question has 2 values and 2 totals, the total quantity and the total value. Both Guess-and-Check and Assumption methods can works for this scenario.
Workings Explained
- The Total Quantity → 8 pens and rulers
- The Total Value → $21 (The total amount Ronald paid for all the pens and rulers)
- 2 Values → 1 Pen cost $3, 1 Ruler cost $2.
For Guess and Check, we can actually start with any number as long as the total quantity adds up to the total quantity that was provided. Most teachers will advise their pupils to start with half-half (half of each item).
Note: For Guess & Check method, there must at least 3 guess.
1st Guess
- 4 rulers cost: 4 (rulers) × 2 (cost of 1 ruler) = 8
- 4 pens cost: 4 (pens) × 3 (cost of 1 pen) = 12.
- Total value: 8 + 12 = 20
✗ Wrong guess
2nd Guess
- 5 rulers cost: 5 (rulers) × 2 (cost of 1 ruler) = 10
- 3 pens cost: 3 (pens) × 3 (cost of 1 pen) = 9.
- Total value: 10 + 9 = 19
✗ Wrong guess
3rd Guess
- 3 rulers cost: 3 (rulers) × 2 (cost of 1 ruler) = 6
- 5 pens cost: 5 (pens) × 3 (cost of 1 pen) = 15.
- Total value: 6 + 15 = 21
✓ Correct guess