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Math 103 Measurement Unit.notebook
1
March 03, 2015
Converting Area MeasurementsWe already know how to convert between units of linear measurement.
Ex.
‐ To convert between units of area, we have to remember that area is
equal to__________________________________________, or length
X width. This means we have to convert BOTH the length AND the
WIDTH.
‐ This is easier than you might think: all you do is multiply or divide by
the conversion factor______________________! Once for the length
and once for the width.
Ex: 100cm2 = ____________________m2
1) Find how to convert between cm and m on your conversion chart.
2) To convert the area, we divide by 100 two times
Ex: How many square feet are there in a square yard?
1) We know that ___________________ make a yard, so the length
conversion is to multiply by 3
2) To find the area, we must multiply 3 two times
(or_______________)
3)
4) WE can see this in the following diagram (count the square feet):
Ex) Convert 30 square feet to square meters.
1) Converting between SI and imperial area units is the same process
as the above examples.
2) First, find the conversion factor you need.
3) So we must multiply 30ft2 by 0.3048 twice:
Remember, you need to check if your answer makes sense!
Think: “Will my answer be more or less”?
‐ If the unit you are converting to is smaller than the unit you are
given, your answer will be _______________________ than the
number you start with.
Ex: Convert 5 square metres into square feet
1) Will the answer be more or less than 5?
2) The conversion is 1 ft =
3) Try both dividing and multiplying 5 by the conversion factor:
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March 03, 2015
Whiteboard Practice:
Convert 50m2 to cm2
Convert 23yd2 to m2
Remember to check if your answer makes sense!
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March 03, 2015
Math 103: Feb 24th
Outline for the day:
1. Area word problems practice2. Review/catch up (QUIZ TOMORROW!)
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March 03, 2015
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March 03, 2015
Area Word Problems
Ms. Kierstead wants to lay grass on her acreage property. If her property is 250 m by 300 m how much land needs to be covered? Draw a picture.
Shelley is trying to decide whether to put hardwood flooring or carpet on her living room floor. The dimensions of the room are 22 ft by 16 ft. The hardwood flooring costs $18.99 / m2 with an installation cost of $1500.00. The carpet costs $21.95 / yd2 with an installation cost of $1350.00. Which type of flooring costs less?
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You try:
Irina purchased a farm in Saskatchewan. She wants to plant balsam fir seedlings, and she estimated the field measures 72 yards by 65 yards. The tree nursery manager told her that each seedling requires an area of 64 ft2 to grow properly. How many seedlings can Irina plant on her acre of land?
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March 03, 2015
Math 103: Day 15
Outline for the day:
1. Lesson on circumference and area of circles 2. Circles practice and assignment
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March 03, 2015
5 cm2 =
0.007 m2
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March 03, 2015
Circumference and Area of a Circle‐ All the points on a circle are equidistant (the samedistance) from the_______________________________________of thecircle.‐ A line that passes through the center of a circle andtouches the edge of the circle on both sides is called the___________________________________.
‐ A line that starts at the center of the circle and touches anoutside edge is called the_________________________________________.
ACTIVITY: Using the string, a ruler and the circular shapes
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Circle
Circumference Use a licorice
whip to
measure
Diameter (d)– use a ruler to
measure
Compare:C/d
123
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How can we calculate radius, diameter, and circumference?‐ The radius can be calculated by dividing the diameter by 2
‐ The diameter can be calculated by multiplying the radiusby 2 ‐ The ________________________________________ of acircle is the perimeter of the circle. It can be calculatedwith the formula : Where C = circumference (perimeter)
= “pi” a constant that is 3.14….d = diameter
Ex) What is the circumference of a circle with a diameter of 8cm?
Ex2. What is the circumference of a circle with a radius of 2.5mm?
How can we calculate the area of a circle?
‐ Use the formula A=πr2‐ This means we need to know the radius
Ex) What is the area of the following circle:
Ex) What is the area of the following circle:
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Practice:
1) What is the circumference of a circle with a radius of 2cm?
2) What is the area of the circle with a radius of 2cm?
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March 03, 2015
Journals:
One thing I need to practice before the quiz tomorrow is...
One thing I need help with is...
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March 03, 2015
Math 103: Day 16
Outline for the day:
1. Review for quiz: any last questions?2. Perimeter and area quiz3. Surface area of prisms
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March 03, 2015
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March 03, 2015
Math 103: Day 17
Outline for the day:
1. Review surface area of prisms2. Lesson on surface area of cylinders and cones and practice3. Surface area assignment
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Surface Area
Surface area is the total area of all the sides in a 3D object added together.
One of the easiest ways to get a simplified formula for surface area is to look at the net of the shape.
Rectangular Prism
‐ We need to find the area of each side (a total of 6 sides), and then add them all up
Ex) Find the surface area of the following rectangular prism.
Triangular Prism‐ Find the area of the triangular ends. Remember, the formula for the area of a triangle is ‐ Then find the area of the 3 rectangular sides‐ Add all the sides together
Ex) Find the surface area for the following triangular prism.
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March 03, 2015
Practice: Find the surface area of the following triangular prism
6ft
2ft
h= 1.6ft
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March 03, 2015
Whiteboard Review: find the surface area of the rectangular prism
7cm
2cm
1cm
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March 03, 2015
Surface Area of Cylinders and Cones
Cylinder: We need to find the area of the top, bottom, and sides.
1) The top and bottom are circles, so the formula for the area of both together is:
2) The side is a rectangle that is wrapped around. The base of the rectangle is the circumference of the circles and the height is the height of the cylinder. This means that the area of the side is:
3) To find the total surface area of the cylinder, add the area of the top and bottom to the area of the side.
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March 03, 2015
Ex) Find the surface area of the following cylinder
30cm
Diameter = 10cm
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March 03, 2015
Whiteboard Practice:
Radius =3cmHeight= 5cm
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March 03, 2015
Cones
‐ Find the area of the circle at the bottom of the cone:
‐ Find the area of the top. The formula is:
‐ Add the two areas together to find the total area
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March 03, 2015
Radius = 3cm
6cm
Ex) Find the surface area for the following cone.
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March 03, 2015
Whiteboard Practice:
Radius =3cmS= 5cm
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March 03, 2015
Complete the Surface Area Assignment
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March 03, 2015
Math 103: Day 18
Outline for the day:
1. Quick surface area review 2. Aluminum foil prank?
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March 03, 2015
Question: Can we cover everything in this room in aluminum foil for under $50?
Group 1: desks, chairs, floor
Group 2: my desk, computer, chair
Group 3: cabinets, filing cabinet, fridge
Group 4: tables, bins, bulletin boards
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March 03, 2015