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Building a Survival Shelter - ppt video online download

Building a Survival Shelter - ppt video online download

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REI is offering a Wilderness Survival class and wants to provide instruction in building a survival shelter that is elevated but is built without access to measurement tools such as protractors and rulers. Students will create a Guide for Building a Survival Shelter that is based on Pythagorean Theorem. Optionally, the shelter construction will be validated with a three-dimensional scale model.
A Project Based Learning Unit. For 8th Grade Mathematics. June,
REI is offering a Wilderness Survival class and wants to provide instruction in building a survival shelter that is elevated but is built without access to measurement tools such as protractors and rulers. Students will create a Guide for Building a Survival Shelter that is based on Pythagorean Theorem. Optionally, the shelter construction will be validated with a three-dimensional scale model.
How can the Pythagorean Theorem be represented through models and pictures
8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: 8.7B use geometric concepts and properties to solve problems in fields such as art and architecture. 8.7C use pictures and models to demonstrate the Pythagorean Theorem. 8.9 Measurement. The student uses indirect measurement to solve problems. The student is expected to: 8.9A use the Pythagorean Theorem to solve real-life problems.
You and your companions have just survived a small plane crash Your group of survivors managed to salvage the following twelve items. List in order of importance for your survival. A ball of steel wool. A small ax. A loaded .45 caliber pistol. Newspapers. Cigarette lighter (without fluid) Extra shirt & pants for each survivor. 20 x 20 ft piece of canvas. A small ax. An air map made of plastic. 1 quart 100-proof whiskey. A compass. Chocolate bar for each survivor.
Today, REI wants to add a Wilderness Survival class to its Outdoor School offerings. As part of that class, they want to provide instruction for building an elevated survival shelter that is built without access to measurement tools. You will create a Guide for Building a Survival Shelter that is based on the Pythagorean Theorem.
Why and what is REI requesting What mathematical concepts are required in building the structure Why might this be a challenging task What are some of the requirements of the survival guide
It’s all about the process.
Using chart paper, each group will sketch their idea for a survival shelter. This will be the starting point for your project and will be refined over the next two weeks as you gain more information.
INVESTIGATION: Group Activity What is the role of right angles in construction
Discover the formula for Pythagorean Theorem using a geometric proof.
The Pythagorean Theorem is a relationship among the lengths of the sides of a right triangle. What do you notice about the hypotenuse and the legs of a right triangle Leg. hypotenuse. c. a. Longest side of the triangle. The legs form the right angle. Across from the right angle. b. Leg.
Leg. hypotenuse. c. a. b. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (See Warm-up) In any right triangle with legs a and b and hypotenuse c, Leg. a2 + b2 = c2 .
Leg. hypotenuse. a2 + b2 = c2.
3 sides: 5 feet, 12 feet, 13 feet. 13 feet. 5 feet. Longest side. 12 feet. a2 + b2 = c2. (5)2 + (12)2 = (13) = 169. TRUE.
Work with a partner. Determine which of the following drawings represent the Pythagorean Theorem.
Using the sticks provided, form as many triangles as you can. Measure the length of the sides of the triangle and fill in the table. Remember, c must always be the longest side. Using your protractor determine if the triangle is a right triangle. Complete the table with the triangles you formed.
Do the Right Thing. Finding Missing Measurements. Using. Pythagorean Theorem.
A spider is crawling on a 18 x 18 square window. The path of the spider is shown below. Calculate the distance traveled by the spider.
A spider is crawling on a 18 x 18 square window. The path of the spider is shown below. Calculate the distance traveled by the spider. We know that each leg is 18 and we are looking for the length of the diagonal or the hypotenuse. c
The Pythagorean Theorem can be used to find unknown side lengths in right triangles.
Television sizes are described by the diagonal measurement across the screen. The rectangular screen of John’s television set measures 12 inches by 16 inches. What is the size of his television to the nearest inch a2 + b2 = c2. (12)2 + (16)2 = (c) = c2. c. 400 = c2. To solve for c, do the opposite of squaring a number which is to find the square root = c2. = c. 20. John has a 20-inch set.
A 10-foot long piece of lumber is leaning against a wall. The bottom of the piece of lumber is 8 feet from the base of a wall. How high up the wall does the piece of lumber reach a2 + b2 = c2. b. (8)2 + (b)2 = (10)2. Form a ZERO PAIR to get b2 by itself! 64 + b2 = b2 = 36. To solve for b, do the opposite of squaring a number which is to find the square root. = 36. b2. b = 6. The piece of lumber reaches 6 feet up the wall.
Practice finding missing measurements using Pythagorean Theorem.
Work in Pairs. Materials: tape measure or meter stick, calculator. Part One – Calculate the hypotenuse. Find a rectangle in the room. Measure the length and width (a and b) in inches. Draw a sketch. Calculate the diagonal ( c ) and show work. Check your answer by measuring the diagonal. Part Two – Calculate the side. Find another rectangle in the room. Measure the width and the diagonal ( a and c) Draw a sketch. Calculate the length of rectangle (b) and show work. Check you answer by measuring the length of the rectangle.
Model Geometric Proof. Examples of Solving Real-World Problems with Pythagorean Theorem. Pythagorean Spiral.
Identify Pythagorean Theorem Triples. Find missing measurements using triples.
When the three side lengths of a right triangle are all whole numbers, such as 3, 4, 5 or 5, 12, 13, the set of three side lengths is known as Pythagorean Triples.
What do you notice that’s similar between these sets of triples a2 + b2 = c2. (3)2 +(4)2 = (5) = a2 + b2 = c2. (5)2 +(12)2 = (13) = 169. If you multiply 3, 4, and 5 by 3, you will get 9, 12, and 15. If you multiply 5, 12, and 13 by 2, you will get 10, 24, and a2 + b2 = c2. (9)2 +(12)2 = (15) = a2 + b2 = c2. (10)2 +(24)2 = (26) = 676. Any Multiple of A Pythagorean Triple is also a Pythagorean Triple!
There are an infinite number of Pythagorean Triples. Greek philosopher Plato discovered a way to generate some of them. For any number, n, the legs of a right triangle are 2n and n2 - 1 and the hypotenuse is n For example, for n = 5, the Pythagorean Triple is 10 or 2 x 5, 24 or 52-1 and 26 or So the Pythagorean triple is 10, 24, 26. Proof: = = 676.
In ancient Egypt there were men called rope-stretchers. They discovered that if a rope was tied in a circle with 12 evenly spaced knots that it could be used to form a right triangle. This technique enabled them to ensure that the foundations of their buildings were square (90 degree angles at each corner). Work with your team to come up with an explanation of their method.
Develop a blueprint of your survival shelter.
Description of wilderness environment. Blueprint of the design. Instructions for Assembly. Suggested Material. Model of Pythagorean. Explanation of geometric concepts used in design.