Assess The Joshua And Leah Problem-Solving Strategies

Assess The Joshua And Leah problem Solving Strategies Given Below And

Assess the Joshua and Leah problem-solving strategies given below and respond to the following. What new information would complicate the answer in the initial post? What would change the dynamics of this problem? Joshua post For this week's discussion, I decided to choose option 1, hanging lights around a window for a party, as I am doing something similar myself and working out the math I think would be beneficial. The first thing that I need to do is measure the windows that I would be hanging lights around, let's say there are four windows of two different sizes.

As the windows are squares I just need to find the perimeter that the lights will be hanging around so I just have to measure the length and width of each window to figure that out. The first size has a length of 4 feet and a height of 4.5 feet. Multiplying those together each window has a perimeter of 18 feet so we will already need at least 2 strands of lights. The next set of windows has a length of 1.75 feet and a height of 6 feet. We then do the same thing to find out that these windows have a perimeter of 10.5 feet.

Adding all of these perimeters together we end up with 18+18+10.5+10.5= 57 feet. With just the perimeter in mind, it looks like I would want to only buy three strands of lights, however, as the windows are not directly next to each other I would want an extra strand overall so that each window will have a strand of lights around it. With this, I would want to buy 4 strands of lights (and maybe a fifth because I always worry that lights are going to go out). Leah post The problem I have chosen is the third option. I am updating my living room floor with a newer, more durable wood laminate.

The cost is $1.50 per square foot. To find the cost of my new floor, I must find the area of my living room, in feet, and multiply the area by the price of each square foot, $1.50. To find the area of my living room, I must multiply the length by the width. If the length of my living room is 23 feet and the width of my living room is 24 feet, the area of the living room is 552 square feet. Then I multiply the area, 552 square feet, by $1.50 for each square foot, the price of my new wood laminate flooring will be $828.

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The problem-solving strategies employed by Joshua and Leah demonstrate different approaches tailored to unique problems, each with its strengths and limitations. Analyzing these strategies offers insights into effective problem-solving techniques and highlights factors that could complicate their initial plans or influence the problem's dynamics.

Joshua's Strategy: Perimeter Calculation for Hanging Lights

Joshua's problem revolves around estimating the amount of lighting equipment required for decoration. His approach relies on geometric measurement—specifically, calculating the perimeter of windows to determine how much lighting string is needed. This is a practical application of perimeter calculation, where Joshua measures each window’s length and height, then sums these measurements. He divides the total perimeter by the length of a single strand to approximate the number of strands needed, adding an extra strand for safety and contingency.

One key aspect of Joshua's strategy is breaking down the problem into manageable steps: measuring each window, calculating individual perimeters, summing these, and then translating this total into the number of light strands. This systematic approach ensures a clear pathway from data gathering to decision-making, reflective of logical problem-solving principles.

However, several factors could complicate this strategy. For example, if the measurements are inaccurate or if the windows are irregularly shaped rather than square, the perimeter calculations might be flawed, leading to insufficient or excessive purchases. Additionally, the spacing between windows or the desire for aesthetic uniformity could influence the actual amount of lighting needed, diverging from straightforward perimeter calculations. External variables such as the presence of window trims or curtains that obstruct lighting could also affect the effective perimeter that requires lighting, complicating the initial calculations. Weather conditions or the need for additional safety margins, especially in outdoor settings, might necessitate purchasing more strands, further influencing the planning process.

Furthermore, the type of lighting used (e.g., LED vs. incandescent) and the length of each strand create logistical considerations. If the strands are not flexible or if they only come in fixed lengths, adjustments in the strategy may be necessary, such as cutting or connecting strands, which adds complexity. Overall, advancements in lighting technology, measurement inaccuracies, or aesthetic preferences could significantly alter the initial approach, requiring adaptive problem-solving.

Leah's Strategy: Calculating Cost Based on Area

Leah's problem involves estimating the expenditure for replacing her living room flooring with durable laminate. Her approach is grounded in basic area calculation—multiplying length by width to find total square footage—and then multiplying this by the cost per square foot to estimate total expenditure. This straightforward mathematical application exemplifies quantitative reasoning, common in budgeting and capacity planning.

Leah's method ensures simplicity and accuracy when room dimensions are clear and the flooring material is uniform across the space. Her calculation hinges on precise measurement of the living room's length and width, ensuring that the total square footage is accurate before multiplying by unit cost. Once the area is known, the total cost can be easily derived, making this approach efficient and reliable for straightforward projects.

However, multiple factors could complicate this approach. For instance, real-world spaces often contain irregularities such as alcoves, uneven walls, or built-in features that make measuring more complex. If the room isn't a perfect rectangle, Leah would need to subdivide the space into smaller sections, calculate each area separately, and then sum these to get an accurate total. Additionally, variations in the flooring material—such as irregular cuts, waste, or the need for additional pieces—could increase costs beyond the initial estimate, complicating the problem-solving process.

Similar to Joshua’s approach, external factors like installation costs, underlayment, or future maintenance might influence the overall budget, which the simple area calculation does not account for directly. These considerations highlight that while Leah's approach is effective for straightforward, rectangular spaces, more complex room layouts demand a more detailed analysis, potentially involving advanced measurement techniques or cost estimation models.

In conclusion, both Joshua and Leah utilize logical, quantitative problem-solving strategies suited to their specific problems. Joshua’s perimeter-based calculation simplifies planning for decorative lighting but can be complicated by measurement inaccuracies and aesthetic or environmental factors. Leah’s area-based estimate offers a clear, quick method for budgeting flooring costs, yet it can be challenged by irregular room shapes and additional installation considerations. Recognizing these potential complications enhances problem-solving flexibility and prepares individuals for real-world complexities that often extend beyond initial calculations.

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