Word Problems - Cubes Strategy

Conquer Word Problems: Mastering the CUBES Strategy

Word problems can be the bane of many students' existence. Even so, with the right approach, even the most challenging word problems become manageable. This article introduces the CUBES strategy, a powerful tool to systematically tackle word problems and improve your mathematical problem-solving skills. These seemingly simple problems, cloaked in everyday language, often hide complex mathematical concepts that require careful analysis and strategic problem-solving. We'll explore each step of the CUBES strategy in detail, providing examples and tips to enhance your understanding and confidence in tackling any word problem you encounter.

Understanding the CUBES Strategy

The CUBES strategy provides a structured approach to solving word problems. It's an acronym that stands for:

• Circle the numbers.
• Underline the question.
• Box the keywords.
• Eliminate unnecessary information.
• Solve and check.

This systematic approach ensures you don't miss crucial details and helps you break down complex problems into smaller, more manageable steps. Let's dive deeper into each step.

1. Circle the Numbers: Identifying the Numerical Data

The first step, "Circle the numbers," is straightforward. Simply identify all the numerical values mentioned in the word problem and circle them. On the flip side, this seemingly simple action helps you quickly locate the essential data needed to solve the problem. Don't just circle single digits; circle entire numbers, including decimals and fractions. This initial step helps you visually isolate the quantitative information from the descriptive text.

Example:

Problem: John bought 3 apples for $1.50 each and 2 oranges for $0.75 each. How much did he spend in total?

In this problem, you would circle: 3, $1.Even so, 50, 2, and $0. 75.

2. Underline the Question: Clarifying the Goal

The second step, "Underline the question," is crucial for focusing your efforts. Because of that, by underlining the question, you ensure you understand the ultimate goal of the problem and avoid unnecessary calculations. Many students struggle with word problems because they lose sight of what the problem is asking them to find. That's why the question often contains keywords like "how many," "what is," "how much," or "find the. " Make sure you clearly identify the specific quantity or value the problem is seeking.

Example:

Using the same problem above, you would underline: "How much did he spend in total?"

3. Box the Keywords: Identifying the Operations

"Box the keywords" is where you begin to decipher the mathematical operations needed to solve the problem. Keywords indicate the type of calculation required, such as addition, subtraction, multiplication, or division. Common keywords include:

• Addition: total, sum, in all, altogether, more than, increased by
• Subtraction: difference, less than, decreased by, minus, remaining
• Multiplication: product, times, of, multiplied by
• Division: quotient, divided by, shared equally, per

Identifying these keywords helps you translate the word problem into a mathematical equation.

Example:

In the apple and orange problem, "in total" indicates addition.

4. Eliminate Unnecessary Information: Focusing on Relevance

"Eliminate unnecessary information" is a vital step that often separates successful problem-solvers from those who struggle. Word problems frequently include extraneous information designed to distract you. By carefully reading the problem and identifying information that is irrelevant to the question, you simplify the problem and focus on the essential details.

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Example:

Consider a problem about calculating the area of a rectangle. Here's the thing — the problem might include details about the color of the rectangle or the material it's made of. This information is irrelevant to calculating the area and should be ignored.

5. Solve and Check: Executing and Verifying the Solution

The final step, "Solve and check," involves performing the calculations and verifying the accuracy of your answer. This ensures that you can identify any errors and learn from them. And after you find a solution, check your answer to make sure it is reasonable and makes sense within the context of the problem. Write out your calculations clearly and logically, showing each step of your work. Consider estimation or using alternative methods to verify your result.

Example:

For the apple and orange problem:

• Cost of apples: 3 apples * $1.50/apple = $4.50
• Cost of oranges: 2 oranges * $0.75/orange = $1.50
• Total cost: $4.50 + $1.50 = $6.00

Because of this, John spent a total of $6.00.

Advanced Applications of the CUBES Strategy: Tackling Complex Problems

The CUBES strategy is versatile and adaptable to a wide range of word problems, including those involving:

• Fractions and Decimals: The CUBES strategy remains effective when dealing with problems involving fractions and decimals. Simply circle the numerical values, including fractions and decimals, and proceed with the other steps as usual.

• Multi-step Problems: Many word problems require multiple steps to solve. The CUBES strategy helps you break down these problems into smaller, more manageable parts. Address each step sequentially, using the CUBES approach for each part.

• Geometry Problems: Geometry problems often involve several pieces of information. The CUBES strategy helps you identify the relevant numerical data (lengths, angles, areas, volumes), the question being asked, and the necessary formulas. That alone is useful.

• Rate, Time, and Distance Problems: These problems often involve multiple variables. Use the CUBES strategy to identify the known variables (rate, time, or distance) and the unknown variable you need to solve for. Then, apply the appropriate formula (e.g., distance = rate × time).

Frequently Asked Questions (FAQ)

Q: What if the word problem doesn't have any numbers?

A: While unlikely, if a word problem lacks explicit numbers, you need to infer the numerical values from the descriptive text. Focus on identifying the relationships and quantities implied in the problem statement.

Q: What if I'm still struggling after applying CUBES?

A: If you're still struggling, try drawing a diagram or picture to visually represent the problem. This can help clarify the relationships between the different elements in the problem. Consider reviewing the basic mathematical concepts involved. Seek assistance from a teacher, tutor, or classmate.

Q: Can CUBES be used for all types of math problems?

A: While CUBES is highly effective for word problems, it might not be directly applicable to all types of math problems, such as pure equation solving or abstract algebraic manipulations. Still, the underlying principles of careful reading, identifying key information, and systematic problem-solving are valuable in all areas of mathematics.

Conclusion: Empowering You to Solve Word Problems

The CUBES strategy is a powerful tool that provides a systematic and effective approach to solving word problems. Plus, by following the five steps – Circle the numbers, Underline the question, Box the keywords, Eliminate unnecessary information, and Solve and check – you can significantly improve your ability to tackle even the most challenging word problems. And remember that practice is key. The more you use the CUBES strategy, the more confident and proficient you will become in solving word problems and mastering mathematical problem-solving skills. Embrace the challenge, break down complex problems, and celebrate your successes as you conquer the world of word problems!