MATH 11 FOUNDATIONSName:
Acute Triangles in First Nations and Metis CulturesPartner:
Unit 1 and 2 Culminating Project
BACKGROUND INFORMATION
Structures made from polygons and acute triangles are used in many cultures. The first Nations and Metis peoples who live on the Prairies used tipis, structures supported by acute triangles, for shelter and ceremonial purposes. A tipi (also tepee or teepee) is a cone-shaped tent, traditionally made of animal skins upon wooden poles. A tipi is distinguished from other conical tents by the smoke flaps at the top of the structure. The number of poles used is indicative of geographic area and people, ranging from 13 to 21 poles. Tipis suit a life based on the migration of the buffalo because they are easily assembled and taken down.
PURPOSE
In this project, you and a partner will design, calculate the measurements of, and build a model tipi.
PROCEDURE:
PART ONE: DESIGN YOUR MODEL ( /4)a)Decide on the number of poles: ______
b)Decide on the interior height: ______cm
c)Decide on the diameter of the base: ______cm
d)Draw a diagram of your tipi to the right
- Use a ruler
- Include measurements decided on in Part 1b, and 1c
PART TWO: TIPI BASE ( /6)
a)Draw a diagram (with a ruler) of the base of your model tipi / b)What regular polygon forms the base of your tipi? ______
c)For the base of your model tipi, calculate (and show the work for) the following:
i)The sum of the interior angles / ii)The measure of each interior angle / iii)The measure of each exterior angle
d)Label your diagram in Part 2a with the measurements you calculated in Part 2c.
PART THREE: SUPPORTING POLES ( /5)
Knowing the diameter and height of your tipi (decided by you in Part 1):
a)What type of triangle is formed by the height of the tipi, the ground and the supporting poles?
______
b)Draw and label a diagram of the above triangle below
e)Label your diagram in Part 3b with measurements you calculated in Part 3c and 3d. / c)Calculate the length(to the nearest tenth of cm) of the supporting pole.
d)Calculate the angle(to the nearest degree) that each supporting pole makes with the ground.
PART FOUR: FRAME TRIANGLE ( /5)
In Part 3, you determined the length of each supporting pole.
a)Draw a diagram of one of your frame triangles and label the side lengths of the two supporting poles.
b)What type of triangle is your frame triangle?
______/ c)Calculate the missing angles (to the nearest degree) and side length (to the nearest tenth of a cm) of your frame triangle.
d)Label your diagram in Part 4a with the measurements you calculated in Part 3c
PART FIVE: BUILD YOUR MODEL TIPI ( /10)
Using the material of your choosing, build your model tipi.
Using masking tape, label the measurements you have calculated in the previous sections.
PART Six: CALCULATIONS VS MODEL ( /3)
Compare your calculated measurements (side lengths and angles) to the actual measurements of your model. If there are differences, how can you account for those differences?