Solving Math Word Problem Crane Weight Lifting Capacity

In the realm of mathematics, word problems serve as a bridge connecting abstract numerical concepts to real-world scenarios. These problems challenge our ability to interpret language, identify relevant information, and apply appropriate mathematical operations to arrive at a solution. This article delves into a specific word problem involving weight lifting capacities of cranes, providing a step-by-step approach to deciphering the question and formulating the correct number sentence. Understanding word problems is essential for developing critical thinking and problem-solving skills, crucial not only in mathematics but also in various aspects of life.

The word problem presented poses a scenario involving Elliot Construction, a company with two cranes of differing lifting capacities. The large crane can lift up to 7 tons, while the small crane can lift up to 6 tons. The core question asks: "How much more weight can the large crane lift than the small crane?" To effectively address this problem, we need to break it down into manageable parts and identify the key pieces of information. Analyzing the word problem, we first recognize that the problem involves comparing two quantities: the lifting capacity of the large crane and the lifting capacity of the small crane. The phrase "how much more" signals that we are looking for the difference between these two quantities. This understanding is crucial in selecting the appropriate mathematical operation to solve the problem.

Identifying Key Information

To solve the problem, we need to extract the essential numerical data provided. The problem explicitly states that the large crane can lift 7 tons, and the small crane can lift 6 tons. These values are the foundation of our calculation. We must also recognize the relationship between these values as described by the question. The question is not asking for the total weight the cranes can lift combined, nor is it asking for a ratio or proportion. Instead, it is asking for the difference, which implies a subtraction operation. Extracting the key information is a critical step in solving any word problem. It involves identifying the numbers, the units, and the relationships between them. In this case, the numbers are 7 and 6, the unit is tons, and the relationship is a comparison of "how much more," leading us to subtraction.

Formulating the Number Sentence

With the key information identified, we can now formulate the number sentence that accurately represents the problem. A number sentence is a mathematical equation that uses numbers and symbols to express a relationship. In this case, we need to represent the difference between the lifting capacities of the two cranes. Since we are looking for how much more the large crane can lift, we subtract the small crane's capacity from the large crane's capacity. Therefore, the number sentence that matches this word problem is:

7 - 6 = ?

This equation succinctly captures the mathematical operation needed to solve the problem. The symbol "-" represents subtraction, and the "=" symbol indicates that we are looking for the result of this operation. The question mark "?" represents the unknown quantity we are trying to find. Creating the correct number sentence is a pivotal step in the problem-solving process. It translates the word problem into a mathematical format, making it easier to apply the necessary calculations.

Once the number sentence is correctly formulated, solving it becomes a straightforward task. In this case, the number sentence is 7 - 6 = ?. Performing the subtraction, we find that 7 minus 6 equals 1. Therefore, the solution to the number sentence is:

7 - 6 = 1

This result tells us that the large crane can lift 1 ton more than the small crane. It is important to include the unit of measurement (tons) in the final answer to provide a complete and meaningful solution. Solving the number sentence is the computational aspect of the problem. It requires applying the correct mathematical operations to the numbers involved. In this instance, simple subtraction provides the answer, but other problems may involve addition, multiplication, division, or more complex operations.

Interpreting the Solution

The final step in solving a word problem is to interpret the solution in the context of the original problem. We have found that the difference in lifting capacity between the large and small cranes is 1 ton. This means that the large crane can lift 1 ton more than the small crane. This interpretation provides a clear and concise answer to the original question. Interpreting the solution is crucial because it connects the mathematical result back to the real-world scenario described in the word problem. It ensures that the answer makes sense and addresses the question that was initially posed.

While the solution to this particular problem is relatively simple, word problems can often be more complex and require additional considerations. Some problems may involve multiple steps, different units of measurement, or extraneous information that needs to be filtered out. Therefore, it is important to develop a systematic approach to solving word problems, including:

1. Reading the problem carefully: Understanding the context and what is being asked.
2. Identifying key information: Extracting the relevant numbers, units, and relationships.
3. Formulating a plan: Deciding on the appropriate mathematical operations and steps.
4. Solving the problem: Performing the calculations accurately.
5. Checking the answer: Ensuring the solution makes sense in the context of the problem.

By following these steps, you can effectively tackle a wide range of word problems and improve your mathematical problem-solving skills. Adopting a systematic approach to solving word problems is essential for tackling more complex scenarios. This involves breaking down the problem into manageable steps, from reading and understanding the question to checking the final answer.

Word problems are an integral part of mathematics education, providing a practical application of numerical concepts and problem-solving skills. The word problem involving Elliot Construction's cranes demonstrates how to break down a question, identify key information, formulate a number sentence, and interpret the solution. By mastering these steps, one can confidently approach and solve a variety of mathematical challenges. The ability to solve word problems is not just a mathematical skill; it is a life skill that enhances critical thinking and decision-making abilities in various contexts. Mastering word problems is a crucial skill that extends beyond the classroom. It enhances critical thinking, analytical skills, and the ability to apply mathematical concepts to real-world situations. By understanding the steps involved in solving word problems, individuals can develop a systematic approach to tackling complex challenges.