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7 Ploya problems solving with answers

Sagot :

yankeriii

Here are 7 Pólya problem-solving steps with answers:

1. Understand the Problem:

Problem: Find the area of a rectangle with a length of 8 cm and a width of 5 cm.

Answer: The area of the rectangle is 8 cm x 5 cm = 40 square cm.

2. Devise a Plan:

Problem: How many ways can you arrange 4 different books on a shelf?

Answer: There are 4! = 4 x 3 x 2 x 1 = 24 ways to arrange the books.

3. Carry Out the Plan:

Problem: Solve the equation 2x + 5 = 11.

Answer: Subtract 5 from both sides to get 2x = 6, then divide by 2 to find x = 3.

4. Look Back:

Problem: A car travels at 60 km/h for 2 hours. How far did it travel?

Answer: Distance = speed x time = 60 km/h x 2 h = 120 km. Confirming the answer against the original problem ensures accuracy.

5. Generalize:

Problem: Find the 10th term of the sequence: 2, 4, 8, 16, ...

Answer: Each term doubles the previous one, so the 10th term is 2^10 = 1024.

6. Make an Extension:

Problem: If a triangle has sides of length 4 cm, 5 cm, and 6 cm, is it a right triangle?

Answer: Check if the Pythagorean theorem holds: 4^2 + 5^2 = 16 + 25 = 41 which is not equal to 6^2, so it is not a right triangle.

7. Solve a Similar Problem:

Problem: If a basketball player makes 70% of their free throws and attempts 20 free throws, how many can we expect them to make?

Answer: 70% of 20 is 0.7 x 20 = 14, so we can expect the player to make 14 free throws.

These 7 Pólya problem-solving steps illustrate a structured approach to solving a variety of mathematical problems, emphasizing understanding, planning, execution, reflection, generalization, extension, and tackling similar problems for improvement and mastery.

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