PowerPoint Presentation - Unit 1 Module 1 Sets, elements, subsets

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					Part 3 Module 6
Units of Measure in Geometry
 Part 3 Module 6
 Units of Measure in Geometry

Next Tuesday all four parts of your finals week
    homework project will be posted. We will discuss
    the details at that time.
The first of the four parts will cover geometry (Part 3
    Modules 7 through 9), the topic that we will cover
    over the last two weeks of class.
As a preliminary to discussing geometry, we spend a
    moment in Part 3 Module 6, reviewing some basic
    facts about units of measure.
Part 3 Module 6 will be included on Test 3.
  Linear Measure

Linear measure is the measure of distance.

For instance, lengths, heights, and widths of geometric
    figures are distances, as are the radius, diameter and
    circumference of a circle. The perimeter of a figure is
    another example of distance.

Distance is measured in linear units, such as inches,
    feet, yards, miles, meters, centimeters, millimeters
    and kilometers.
   Converting Linear Units

In the United States, any educated person should be aware of the
     following relationships among basic units of linear measure in the
     English system (inches, feet, yards, miles), and among the basic
     units of linear measure in the metric system (meters, centimeters,
     millimeters, kilometers).

1 foot = 12 inches
1 yard = 3 feet
1 yard = 36 inches
1 mile = 5280 feet
1 meter = 1000 millimeters
1 meter = 100 centimeters
1 kilometer =1000 meters
  Multiply or divide

Referring to the conversion factors on the
   previous page, we convert from larger units
   to smaller units by multiplying (for instance,
   to convert from yards to inches we multiply by
   36); we convert from smaller units to larger
   units by dividing (for instance, to convert
   from centimeters to meters we divide by 100).
  Examples

1. How many meters are in 3 kilometers?

2. How many miles are in 20,000 feet?

Answers
1. To convert 3 kilometers to meters we multiply by 1000.
3 x 1000 = 3000 m in 3 km

2. To convert 20000 feet to miles we divide by 5280.
20000/5280 = 3.88 miles in 20000 ft.
  Square Measure

Square units (such as square inches or square
   centimeters) are used to describe the area of a
   two-dimensional figure.
Area is the amount of 2-dimensional space
   covered by a flat object.
To understand the difference between linear
   measure and square measure, and to correctly
   convert between square units, you must
   realize that one square unit is the area of a
   square that is 1 unit long and 1 unit wide.
  Exercise #1

(From The BIG UNIT-izer
www.math.fsu.edu/~wooland/unitizer.html )
How many square inches are in 9 square feet?

A. 0.75    B. 108     C. 0.063   D. 1296
  Solution #1

How many square inches are in 9 square feet?

A. 0.75      B. 108       C. 0.063      D. 1296
The answer is not B, because the question is not asking
   for the number of inches in 9 feet.
Square inches and square feet are different from inches
   and feet.
To answer correctly, we must first find the correct
    conversion factor when converting between square
    feet and square inches.
       Solution #, page 2
We must find the correct conversion factor when converting between square feet and
    square inches.

This will depend upon the fact that one foot equals 12 inches, and also upon the
     meaning on “square.”

“One square foot” means literally one foot times one foot.

1 sq. ft = 1 ft. x 1 ft.

= 12 in. x 12 in

= 144 sq. in.

We have figured out that to convert between square feet and square inches, the
    correct factor is 144, not 12.

So, to convert 9 sq. feet to sq. yards, we multiply by 144.

9 x 144 = 1296. The correct choice is D.
      Illustration
The figure below illustrates why 1 square foot = 144 square inches.

                                             One foot equals 12 inches
                          1 foot

                       1 square foot           1 square inch




                                                     One square foot
                                                     equals 144
                                            1 foot   square inches




                          1 foot
Cubic Units

Cubic units (such as cubic meters or cubic yards) are
used to describe the volume of a three-dimensional
figure.

Volume is the amount of 3-dimensional space occupied
by a solid object, for instance, or the amount of fluid that
can be contained in a hollow vessel.
Exercise #2

How many cubic yards are in 150 cubic feet?
A. 16.667
B. 450
C. 50
D. 5.556
Solution #2


How many cubic yards are in 150 cubic feet?
A. 16.667  B. 450 C. 50       D. 5.556

The answer is not C, because we are not converting feet
   to yards. We are converting cubic feet to cubic yards.

We must find the correct factor for converting between
   cubic yards and cubic feet.
This will depend upon the fact that one yard equals three
   feet, and the meaning of the word “cubic.”
Solution #2, page 2

“One cubic yard” means literally one yard times one yard
   times one yard.

1 cubic yard = 1 yard x 1 yard x 1 yard
= 3 feet x 3 feet x 3 feet
= 27 cubic feet

We have figured out that the correct conversion factor is
1 cubic yard = 27 cubic feet.
So, to convert 150 cubic feet to cubic yards, we divide by
   27.
150/27 = 5.556     The correct choice is D.
Illustration
The figure below illustrates why 1 cubic yard equals 27
   cubic feet.

				
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