P2PU | Buy an HDTV | Formulating an Argument using Pythagoras' Theorem

Formulating an Argument using Pythagoras' Theorem

Make a proposal for purchasing what you think would be the best-sized HDTV for your classroom.

Skills needed

Work on this task to develop your ability to:

construct arguments using verbal or written explanations accompanied by mathematical expressions, equations, inequalities, models, and drawings, graphs, tables, and other data displays;
refine your mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning;
use the Pythagorean Theorem to solve real world problems through the application of both algebraic and geometric concepts;
determine the distance between two points by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse;
use both the Pythagorean Theorem and the distance formula to find missing side lengths in a coordinate plane and real-world situations;
find the square and cube roots of numbers and use the inverse operations of squaring and cubing numbers.

Keep it Real

Select an HDTV that is currently available, and design an optimum viewing space in your classroom to provide an immersive experience for at least 15 students at a time. Do measurements in your classroom (or another room chosen by you and your teacher), choose the best-sized widescreen HDTV (16:9), and determine how far away your viewing area will be. Your screen and viewing area needs to be as big as possible so that each of the students' field of vision is occupied by the full width of the television display. Yet, the screen should not dominate the room. The screen should be small enough to allow other activities to occur at the same time.

Make Digital Drawings

Provide drawings (that are digital or scanned, and that you link to online and/or embed in your proposal) with the following specifications:

Screen Size: Lable the diagonal size of the screen as well as the lengths of the vertical and horizontal sides of the screen. Use the Pythagorean Theorem to determine these lengths.
Location: Specify where the screen will be in the room, including height above the floor and distance from five positions in the viewing area--the four corners of the audience space and the middle viewer.
Angles of Vision: Show the degrees of the horizontal and vertical angles of vision for each of the five positions in the room, when measured from each of these viewers to the two sides of the screen. Use the Pythagorean Theorem to determine your measurements.
Pedagogical Considerations: What are the biggest and the smallest possible screen sizes and viewing areas for this room? What makes most sense for this room? Do you want this viewing area to dominate the room? If possible design a space that allows for other activities to continue while students are using the new HDTV viewing area.

Publish a Proposal

Write a proposal (that is published on Youth Voices and/or that you can link to online) for the purchasing committee at your school in which you make an argument that is supported by:

the measurements of the room you are designing,
your mathematical analysis and drawings using the Pythagorean Theorem,
how much you want the screen to dominate the room,
the recommendations made in consumer reports for HDTV's that you quote and cite.