Week 7 Presentation By Instructor Name With Object Picture

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Analyze and present a real-world object that contains a right angle, measure its sides, calculate the hypotenuse using the Pythagorean theorem, and compare the measured and calculated hypotenuse. Include diagrams with measurements, and answer reflective questions about the process and results.

Paper For Above instruction

The purpose of this assignment is to engage students in applying the Pythagorean theorem to tangible objects in their environment by creating a visual presentation. This activity fosters understanding of geometric principles through real-world measurement, calculation, and critical reflection. The student is required to select an object that contains a right angle, measure its sides, draw a diagram with measurements, compute the hypotenuse theoretically, and then compare it with the actual measurement taken. Additionally, reflection questions prompt analysis of discrepancies and insights gained during the process.

In executing this assignment, the initial step involves selecting an object that clearly exhibits a right angle. This might include everyday items such as a picture frame, a wedge-shaped object, or a corner of a piece of furniture, or natural formations like a tree branch or a rock formation with clear right angles. Once selected, the student should take a photograph of the object ensuring the right angle is visible for clarity and proper presentation. The photograph should be clear and centered, demonstrating the right angle distinctly.

Following this, precise measurements of the two legs forming the right angle (the perpendicular sides) should be taken using a reliable measuring tool such as a ruler or measuring tape. It is essential to record these measurements in standard units (inches, centimeters, etc.), documenting each side carefully. Subsequently, measure the hypotenuse directly by drawing a diagram of the object and including the measured sides. The diagram must be annotated with the measured lengths and include units for clarity.

Using the measurements of the two legs, the student should then employ the Pythagorean theorem (a^2 + b^2 = c^2) to compute the theoretical hypotenuse. This involves squaring each leg's measurement, summing these squares, and taking the square root of the sum to find the hypotenuse length. Showing all work step-by-step is essential for transparency and understanding.

Next, the student will compare the measured hypotenuse with the calculated one to analyze the accuracy of their measurements and calculations. This comparison can reveal important insights about measurement reliability, possible errors, and the applicability of the Pythagorean theorem to real-world objects.

The reflection segment of the presentation involves answering three critical questions: (1) whether the measured and calculated hypotenuse are approximately equal, (2) the reasons for any discrepancies, considering factors like measurement error, visual perspective, or object deformation, and (3) personal lessons learned from undertaking the activity, including improved understanding of geometric concepts and measurement techniques.

The presentation must be created in PowerPoint with a voiceover narration, lasting approximately 2-3 minutes. It should include visual aids such as the photograph of the object, the annotated diagram with measurements, and clear verbal explanations. This exercise not only demonstrates knowledge of the Pythagorean theorem but also enhances skills in measurement, diagramming, and critical thinking regarding real-world applications of mathematical principles.

References

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  • Hofstetter, M. (2012). The Pythagorean Theorem: History, Methods, and Applications. Mathematics in Schools, 41(4), 16-21.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2018). Elementary and Middle School Mathematics: Teaching Developmentally. Pearson.
  • Murray, T., & Bressan, P. (2017). Measurement and Geometry in Grade 6: Teaching Strategies. Journal of Mathematics Education, 10(2), 105-119.
  • Smith, J., & Jones, L. (2015). Applying Pythagoras in Everyday Life. Journal of Mathematical Behavior, 39, 117-125.
  • Swinyard, C., & Stofflet, V. (2011). Geometric Measurement and Applications. The Mathematics Teacher, 104(9), 677-683.
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  • Williams, M. (2013). Visual Mathematics: Using Diagrams and Drawings to Enhance Learning. Math Education Review, 26(3), 35-42.

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