Problem Solving Strategies

Key Concepts

Problem solving strategies are methods used to approach and solve mathematical problems. The key concepts include:

• Draw a Picture
• Make a List
• Guess and Check
• Work Backwards
• Use a Model
• Eliminate Possibilities
• Simplify the Problem
• Look for a Pattern
• Use Logical Reasoning
• Use a Formula

1. Draw a Picture

Drawing a picture can help visualize the problem and make it easier to understand. This strategy is particularly useful for geometry problems.

Example: If you need to find the area of a triangle, draw the triangle and label its base and height to help visualize the problem.

2. Make a List

Making a list organizes information and helps identify patterns or missing information. This strategy is useful for problems with multiple steps or options.

Example: If you need to find all the factors of a number, list out pairs of numbers that multiply to give the original number.

3. Guess and Check

Guess and check involves making an educated guess, checking the result, and adjusting the guess based on the outcome. This strategy is useful for problems with multiple variables.

Example: If you need to find two numbers that add up to 10 and multiply to 21, guess a pair of numbers, check if they meet both conditions, and adjust if necessary.

4. Work Backwards

Working backwards starts from the end of the problem and moves towards the beginning. This strategy is useful for problems with a clear final outcome.

Example: If you know the final amount after a series of discounts, work backwards to find the original price before any discounts.

5. Use a Model

Using a model involves creating a physical or visual representation of the problem. This strategy is useful for abstract or complex problems.

Example: If you need to understand the concept of fractions, use a pizza model to represent parts of a whole.

6. Eliminate Possibilities

Eliminating possibilities involves systematically ruling out options until only one remains. This strategy is useful for problems with multiple choices.

Example: If you need to find the correct answer from multiple-choice options, eliminate answers that are clearly wrong based on the problem's conditions.

7. Simplify the Problem

Simplifying the problem involves breaking it down into smaller, more manageable parts. This strategy is useful for complex or multi-step problems.

Example: If you need to solve a long division problem, break it down into smaller division problems and solve each part separately.

8. Look for a Pattern

Looking for a pattern involves identifying repeated elements or sequences in the problem. This strategy is useful for problems involving sequences or series.

Example: If you need to find the next number in a sequence, identify the pattern in the existing numbers and apply it to find the next number.

9. Use Logical Reasoning

Using logical reasoning involves applying rules and principles to deduce the solution. This strategy is useful for problems requiring step-by-step reasoning.

Example: If you need to solve a logic puzzle, use logical reasoning to follow the rules and deduce the correct answer step by step.

10. Use a Formula

Using a formula involves applying a known mathematical formula to solve the problem. This strategy is useful for problems with a clear formulaic solution.

Example: If you need to find the area of a circle, use the formula A = πr², where A is the area and r is the radius.

Examples and Analogies

Imagine you are a detective solving a mystery. Drawing a picture is like sketching the crime scene, making a list is like noting down clues, guess and check is like testing different suspects, working backwards is like tracing the crime from the end to the beginning, using a model is like creating a scale model of the crime scene, eliminating possibilities is like ruling out innocent suspects, simplifying the problem is like breaking down the case into smaller parts, looking for a pattern is like identifying a repeated method of operation, using logical reasoning is like deducing the culprit step by step, and using a formula is like applying the law to solve the case.

Another analogy is a chef preparing a meal. Drawing a picture is like designing a menu, making a list is like gathering ingredients, guess and check is like tasting and adjusting the recipe, working backwards is like planning the meal from dessert to appetizer, using a model is like creating a mock-up of the dish, eliminating possibilities is like discarding unsuitable ingredients, simplifying the problem is like breaking down the recipe into steps, looking for a pattern is like identifying common cooking techniques, using logical reasoning is like following the recipe step by step, and using a formula is like applying a standard cooking method.

Insightful Content

Understanding and applying problem-solving strategies is crucial for effectively tackling mathematical problems. By mastering these strategies, you can approach problems with confidence, break down complex tasks, and find solutions more efficiently. These skills are not only essential for mathematics but also valuable in everyday problem-solving and decision-making.