Math 11 Home

Book 5: Measurement Teacher Version – Assessments and Answers Included

Book 5: Math 11 Home - Measurement Edited April 2015 Year Overview:

Earning and Spending Money

Home Travel and Transportation

Recreation and Wellness

1. Earning Money 2. Pay Statements

and Deductions 3. Responsible

Spending Habits

4. Data in Your Life 5. Measurement 6. Angles and

Triangles

7. Let’s Travel Project

8. Personal Health and Wellness

9. Puzzles and Games

Topic Overview The intent of this theme is to develop a deeper understanding of the use of measurement that you would experience in everyday life. This includes measuring with the imperial and SI systems of measurement. In using measurement, you will explore perimeter and surface area. Suggested Timeframe: ___ Hours

Outcomes

Overlapping Outcomes M11.1 Extend understanding of arithmetic operations to rational numbers to solve problems within the home, money, recreation, and travel themes. M11.7 Demonstrate understanding of proportional reasoning within the home, money, recreation, and travel themes.

Theme Specific Outcomes M11.4 Demonstrate understanding of measurement in the Système International (metric) and Imperial System within the home and travel themes.

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Book 5: Math 11 Home - Measurement Edited April 2015 Contents Topic Overview.................................................................................................................. 1

Outcomes ....................................................................................................................... 1

Overlapping Outcomes ........................................................................................... 1

Theme Specific Outcomes ....................................................................................... 1

Glossary of Terms ........................................................................................................... 4

Measurement - History ...................................................................................................... 5

Check What You Know ................................................................................................ 7

Vocabulary Check-Up .............................................................................................. 7

Check Your Skills ......................................................................................................... 8

5.1 Systems of Measurement ......................................................................................... 10

5.2 Imperial Measurement ............................................................................................. 11

A. Exploring Imperial Measurement ......................................................................... 11

B. Imperial Conversion Table ..................................................................................... 13

C. Symbols and Abbreviations Used for Imperial Measurement ......................... 13

5.3 Conversions: Imperial and SI System International .............................................. 14

A. Linear Measurements: Conversion Chart ........................................................... 14

Additional Materials ........................................................................................................ 14

• Math Essential 10 Student Edition p.79-91 ............................................................ 14

• Math Essentials 10 BLM 9 ......................................................................................... 14

B. Imperial and SI Conversions .................................................................................. 15

5.3B Practice Your Skills - Conversions .................................................................. 16

C. Perimeter, Linear Measurement and Conversion ............................................ 18

5.3C Practice Your Skills .......................................................................................... 19

5.4 Perimeter .................................................................................................................... 21

A. What is Perimeter? .................................................................................................. 21

Discuss the Ideas ...................................................................................................... 21

B. Finding Perimeter .................................................................................................... 22

C. Circumference of a Circle .................................................................................... 23

Discovering Pi - Circumference ............................................................................. 25

Discovering Pi – Finding a Solution ........................................................................ 26

5.4C Practice Your Skills - Circles ........................................................................... 28

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Book 5: Math 11 Home - Measurement Edited April 2015 5.5 Area ............................................................................................................................ 30

A. What is Area? .......................................................................................................... 30

Discuss the Ideas ...................................................................................................... 30

B. Units of Measure for Perimeter and Area ............................................................ 31

C. Figuring Area: Squares and Rectangles ............................................................. 32

D. Formulas for Calculating Perimeter and Area ................................................... 32

E. Perimeter and Area of Quadrilaterals ................................................................. 34

5.5E Practice Your Skills - Quadrilaterals ............................................................... 36

F. Perimeter and Area of Triangles............................................................................ 38

5.5F Practice Your Skills - Triangles ......................................................................... 40

G. Area of Circles ........................................................................................................ 42

Discovering Pi – Area of a Circle ........................................................................... 42

Discovering Pi – Area of a Circle – Finding a Solution ........................................ 44

Area of Circle Videos .............................................................................................. 44

5.5G Practice Your Skills - Radius and Area ......................................................... 45

Formula Sheet .................................................................................................................. 47

Student Evaluation .......................................................................................................... 49

Learning Log .................................................................................................................... 51

Show What You Know - Area ........................................................................................ 52

Show What You Know – Project .................................................................................... 53

Show What You Know – At Home Activity .................................................................. 54

Answers ............................................................................................................................. 55

Check Your Skills Answers ....................................................................................... 55

5.3B Practice Your Skills - Conversions .................................................................. 55

5.3C Practice Your Skills .......................................................................................... 56

5.4C Practice Your Skills - Circles ........................................................................... 56

5.5E Practice Your Skills – Quadrilaterals .............................................................. 57

5.5F Practice Your Skills - Triangles ......................................................................... 57

5.5G Practice Your Skills - Radius and Area ......................................................... 58

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Book 5: Math 11 Home - Measurement Edited April 2015 Glossary of Terms area

the total surface area of a two-dimensional shape circumference

perimeter or distance around a circle conversions

convert between various units of measurement diameter

a straight line segment that passes through the center of a circle with endpoints on the circle perimeter

imperial system

system of measurement originating in the British Empire (ex. inch, foot, mile) perimeter

the distance measured around a shape or figure Pi

the ratio of a cirlcle's circumference to its diameter quadrilateral

any four-sided shape radius

in a circle or sphere, the length of a line segment from its center to its perimeter

referent

an object that represents approximately one unit of measurement Système international d’unités (SI)

also known as the metric system

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Book 5: Math 11 Home - Measurement Edited April 2015 Measurement - History Throughout time, cultures have invented their own systems of measurement – using the cycles of the moon, knots in a string, the length of a hand or a foot, the observation of the night sky, or other clues in nature. Humans have always needed to use measurements to make comparisons and to perform tasks such as building shelters or trading goods. But for thousands of years, there was no universal system of measurement. Instead, measurements were based on customs and usage. Human body parts were used as the first measurement units. For example the Egyptians used:

• ‘cubit’ = distance from a person’s elbow to the tip of their middle finger.

• ‘digit’ = width of a finger • ‘palm’ = width of a hand

Figure 1 Egyptian measures 'palm' and 'cubit'.

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Book 5: Math 11 Home - Measurement Edited April 2015

To watch Numberphile’s humorous explanation of the Imperial Number System, go to https://www.youtube.com/watch?v=r7x-RGfd0Yk

The Imperial measurement system we use today was also created based on units related to human body parts. Original measurement units used in England in the Middle Ages included:

• Ynce (inch) = width of a thumb • Foot = length of a human foot • Ulna (yard) = tip of a person’s nose to the end of

their middle finger of an outstretched arm • Fathom = distance across a person’s outstretched

arms from fingertip to fingertip. (MathWorks 10, Pacific Educational Press, 2010)

Today’s metric system uses the kilogram (kg) as its unit of mass. All mass measures are compared to a cast iron weight called the International Prototype of the Kilogram. It was created in 1875 and is held in a secure vault at the International Bureau of Weights and Measures. In the picture of the prototype, the credit card is used to give us an idea of its size.

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Book 5: Math 11 Home - Measurement Edited April 2015 Check What You Know

Vocabulary Check-Up Do you know the meaning of the following words? Circle all of the words that you know. area circumference conversions diameter imperial system diameter imperial system

perimeter Pi quadrilateral radius referent Systeme international d’unites

Pick any 2 of the words that you know already and write down what they mean, in your own words. 1. 2. Write down all of the words that you don’t know already and find out what they mean. You might ask someone else to tell you, or look them up in the dictionary or on the internet. After doing so, write down what they mean below, in your own words.

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Book 5: Math 11 Home - Measurement Edited April 2015 Check Your Skills Ask your teacher how many of the following questions you should complete. 1. Measure the height and width of the items below in centimetres and then in inches. a) b)

Math skills are embedded into real life situations. In this unit, you will use the following skills:

• Measuring items using the SI and Imperial systems of measurement

• Rounding to two decimal places

• Adding and subtracting fractions

• Adding and subtracting decimal numbers

• Multiplying and dividing rational numbers

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Book 5: Math 11 Home - Measurement Edited April 2015 2. Round the following decimal numbers to two decimal places. a) 5.48973 b) 4.134 c) 0.15555 d) 1.921 3. Add or Subtract a) 1/4 + 3/4 b) 1 ¾ + 2 ½ c) 4 ½ - 3 ½ d) 7/8 – ¾ 4. Add or Subtract a) 7.7 + 12.5 b) 125.45 + 76.4 c) 100 – 12.5 d) 36.89 – 3.6 5. Multiply or Divide a) 12.4 x 5 b) 3.14 x 6 c) 65.2 ÷ 4 d) 0.0463 ÷ 3

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Book 5: Math 11 Home - Measurement Edited April 2015 5.1 Systems of Measurement

In Canada two systems of measurement are used: the Système international d’unités (SI) (also known as the metric system) and the Imperial System. Canadians typically discuss the weather in degrees Celsius, purchase gasoline in litres, and observe speed limits set in kilometres per hour (km/h), and read road signs and maps displaying distances in kilometres. Cars have metric speedometres and odometres, although many speedometres include smaller figures in miles per hour (mph). Fuel efficiency for new vehicles is published by litres per 100 kilometres and miles per gallon. Window stickers in dealer showrooms often include "miles per gallon" conversions. The railways of Canada continue to measure their track age in miles and speed limits in mph. Canadian railcars show weight figures in both imperial and metric.

Today, Canadians typically use a mix of metric and imperial measurements in their daily lives. However the use of the metric and imperial systems varies according to generations. The older generations mostly uses the imperial system, while the younger generations use the metric system more frequently. Newborns are measured in SI at hospitals, but the birth weight and length is also announced to family and friends in imperial units. In addition, Fahrenheit is often used for cooking, as are imperial cooking measurements, although some appliances in Canada are labeled with degrees Celsius or are convertible, and metric cooking measures are widely available; imperial temperatures are also often used outside of the kitchen, such as when measuring the water temperature in a pool. Stationery and photographic prints are also sold in sizes based on inches and the most popular paper sizes, letter and legal, are sized in imperial units. Canadian Football League games continue to be played on fields measured in yards; golfers also expect courses to be measured in yards.

http://en.wikipedia.org/wiki/Metrication_in_Canada

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Book 5: Math 11 Home - Measurement Edited April 2015 5.2 Imperial Measurement A. Exploring Imperial Measurement Although the metric system is most commonly used in daily life, the imperial system is used in many trades. To work in the trades you need to be familiar with both the metric and the imperial systems. In this activity, you will work with a partner to take imperial measurements and create an imperial conversion table. With your partner, select 6 objects and distances to measure. Write down:

• 3 objects that fit in your hand • 2 objects that are larger than your desk • 1 distance that is longer than and outside of the classroom

How could you estimate these measurements if you didn’t have a ruler, measuring tape, or other tool? 1. A referent is an object that represents approximately one unit of

measurement. For example, an object that is about one inch long could be used as a referent to estimate inches. Working independently from your partner, find referents that you could use to estimate one inch, one foot, and one yard. Record the referent you used and its approximate length. Compare your referents with your partner’s and share your reasons for choosing each referent.

Referents: 1 inch = _______________________

1 foot = _______________________

1 yard = _______________________

2. Use your referents to estimate the measurements of the objects and distances you selected in question 1. Take as many measurements of the objects as are necessary to give the object’s dimensions (i.e. length, width, height). Record your estimates in the table provided.

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Book 5: Math 11 Home - Measurement Edited April 2015

3. Next you’ll measure each object with the imperial measuring tools. Before

you start measuring, look at the division markers on your imperial measuring tools. Imperial rulers and tape measures are marked in fractions of an inch.

What is the smallest fraction indicated on each of your measuring tools?

4. Measure each of your objects and distances and record your answers. How did you decide on the appropriate measuring tool to use for each of your measurements? Record your measurements in the table.

5. Calculate and record the differences between your estimates and the actual imperial measurements. Record your answers in the table on the next page. Were your estimates close? How did your answers compare to your partner’s answers?

Imperial Measurements

Item Estimation using referent

Imperial measurement Difference

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Imperial Conversion Table

Fill in the missing information to create an imperial conversion table.

IMPERIAL CONVERSION TABLE

1 foot = _____ inches

1 yard = ______ feet = _______ inches

1 mile = 1760 yards = ______ feet

C. Symbols and Abbreviations Used for Imperial Measurement

• in or ″ (the double prime symbol) is used to show inches • ft. or ′ (the prime symbol) is used to show feet • mi is used to show miles • yd. is used to show yards

Example 1: Convert 6 feet to inches: Multiply 6 x 12 because there are 12 inches in each foot.

6’ = 72” Example 2: Convert 5 yards to inches. Multiply 5 x 3 = 15 because there are 3 feet in each yard. Multiply 15 x 12 = 180 because there are 12 inches in each foot.

5 yd = 180” Example 3: Convert 2.5 miles to feet. Multiply 2.5 x 1760 = 4400 because there are 1760 yards in each mile. Multiply 4400 x 3 = 13 200 because there are 3 feet in each yard.

2.5 mi = 13 200 ft

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Book 5: Math 11 Home - Measurement Edited April 2015

5.3 Conversions: Imperial and SI System International

A. Linear Measurements: Conversion Chart Millimetres 10 mm = 1 cm 100 mm = 1 dm 1000 mm = 1 m 1 000 000 mm = 1 km

s 0.1 cm = 1 mm 10 cm = 1 dm 100 cm = 1 m 100 000 cm = 1 km

Metres 0.001 m = 1 mm 0.01 m = 1 cm 0.1 m = 1 dm 1000 m = 1 km

Imperial Conversions Inches 12 in = 1 ft 36 in = 1 yd

Feet 12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi

Yards 36 in = 1 yd 1760 yd = 1 mi

Metric – Imperial Conversions Conversion Factors – SI to Imperial 1 mm = 0.0394 inches 1 cm = 0.3937 inches 1 m = 3.2808 feet 1 m = 1.0936 yards

Conversion Factors – Imperial to SI 1 inch = 2.54 cm (25.4 mm) 1 foot = 0.3048 m 1 yard = 0.9144 m 1 mile = 1.6093 km

Additional Materials • Math Essential 10 Student Edition p.79-91 • Math Essentials 10 BLM 9

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Imperial and SI Conversions It is often helpful to set up a ratio to figure out conversions. For example, if you were trying to figure out how many cm are in five inches, you could set up a ratio like this:

1 inch2.54 cm =

5 inchesx cm

You would then cross multiply to find the value of x.

x = (5) (2.54) x = 12.7 cm

There are 12.7 cm in 5 inches. In a similar way, you could set up and solve a ratio like this:

1 inch5 inches =

2.54 cmx cm

You would then cross multiply to find the value of x.

x = (5) (2.54) x = 12.7 cm

There are 12.7 cm in 5 inches.

Sometimes in science you may see: 5𝑖𝑖𝑖𝑖 × 2.54 𝑐𝑐𝑐𝑐

1 𝑖𝑖𝑖𝑖= 12.7 𝑐𝑐𝑐𝑐

Example: How many feet are in 4.9 metres? Step 1: Set up a ratio 1 m

4.9 m=

3.2808 feetx feet

Step 2: Cross multiply to solve for x x = (4.9)(3.2808) x = 16.07592 Step 3: Round your answer to two decimal places and include the units of measure in your answer. x = 16.08 feet There are 16.08 feet in 4.9 metres

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Book 5: Math 11 Home - Measurement Edited April 2015 5.3B Practice Your Skills - Conversions Convert the following measurements. Round your answers to two decimal places.

1. 42 inches to feet

2. 16 inches to feet and inches

3. 209 centimetres to metres

4. 5.7 metres to centimetres

5. 96 inches to yards

6. 13 feet to yards

7. 5 miles to yards

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Book 5: Math 11 Home - Measurement Edited April 2015

8. 6 metres to feet

9. 153.2 centimetres to feet

10. 81 millimetres to inches

11. 9 feet 3 inches to yards

12. 16’4” to yards

13. 75 feet to metres

14. 315 centimetres to feet

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Book 5: Math 11 Home - Measurement Edited April 2015

Example: Ivan measured an interior door in his house that he wanted to replace and found that it was approximately 71 cm wide. When he got to the home improvement store, he realizes that the doors are sold in 28”, 30” or 32” width. Which door should he buy to fit his doorway? Ivan needs to convert 71.1 cm to inches. Step 1: Set up a ratio

1 inch2.54 cm

= x inches71.1cm

Step 2: Cross Multiply

2.54x = 71.1 Step 3: Solve for x

x = 71.1÷ 2.54 x = 27.9921259…

Step 4: Think about the most reasonable answer

Ivan should buy the door that is 28” wide.

C. Perimeter, Linear Measurement and Conversion Measurements cannot be added if they have different units of measure. Conversion is required. Decisions need to be made about which unit is being converted. There is choice depending on preference or context of the question. The important thing is that you are adding inches to inches or metres to metres etc. For example, if you are buying baseboards for your living room and they are sold in linear feet, you should measure your room in linear feet as opposed to centimetres or metres. It may happen that you measured a distance in Imperial and you go to the store and the item is being sold in SI (metric) measurements. In this case, you can use your conversion skills to figure out the amount of materials that you need.

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Book 5: Math 11 Home - Measurement Edited April 2015 5.3C Practice Your Skills 1. Neil is renovating his bathroom and he needs a new vanity. He measures the space where the vanity needs to fit and it is 80 cm long. a) Will this one fit? b) Will this one fit?

2. Jolie is renovating her living room and wants new baseboards. She needs 13.5 m of baseboards. The baseboards she wants are sold in 8 foot lengths. a) How many feet does she need? b) How many pieces of 8ft long baseboards should she buy?

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Book 5: Math 11 Home - Measurement Edited April 2015 3. Jan is buying a curtain rod a 7 foot long window in her bedroom. The curtain rod she found is 248 cm long. Will it be big enough to go across her whole window?

4. Robert is buying strings of Christmas lights for the outside of his house. He needs 15.2 metres of lights. He finds a string of lights that is 10 feet long. How many should he buy?

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Book 5: Math 11 Home - Measurement Edited April 2015 5.4 Perimeter

A. What is Perimeter? Brainstorm: “What do you know about perimeter?” With a partner, jot down all of your ideas. Share your ideas with another pair.

Discuss the Ideas

1. How is perimeter measured?

2. Does every shape have a perimeter?

3. How can you calculate perimeter?

4. Perimeter is…

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Finding Perimeter To find the perimeter of a shape, you must add together the measure of all sides of the shape. Find the perimeter of the following shapes in both centimetres and inches.

_______cm _______in _______cm _______in

_______cm _______in Find the perimeter of 3 different shapes in the classroom. Choose appropriate units of measure in either Imperial or SI units of measure. 1. _______________________________________ 2. _______________________________________ 3. _______________________________________

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Book 5: Math 11 Home - Measurement Edited April 2015 C. Circumference of a Circle The “perimeter” or distance around a circle is called the circumference. You could measure the circumference of a circle with a string and they lay it out on a measuring tape but this is not always practical. The circumference of the circle is the distance around the circle and the diameter of the circle is the distance across the circle passing through the center point.

The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula:

d = 2 x r where d is the diameter and r is the radius.

If you know the diameter of a circle and you want to find the radius, you can use the formula:

r = d ÷ 2 where d is the diameter and r is the radius.

Example 1: If the diameter of a circle is 24 inches, what is the radius?

Solution: r = d ÷ 2

r = 24 ÷ 2

r = 12 inches

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Book 5: Math 11 Home - Measurement Edited April 2015 Example 2 :

The radius of a circle is 2 inches. What is the diameter?

Solution: d = 2 x r d = 2 x (2in) d = 4 in

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Book 5: Math 11 Home - Measurement Edited April 2015 Discovering Pi - Circumference Complete the following activity to discover the formula for calculating the circumference of a circle. Find as many examples of circles in our school as possible. Measure their circumference and diameter and fill in the spaces below.

Circular Object Found

Circumference Diameter Circumference ÷ Diameter

1. What relationship appears to exist between the circumference and diameter of circular objects? (Do you see anything interesting in the last column? 2. What relationship appears to exist between the circumference and radius of circular objects?

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Book 5: Math 11 Home - Measurement Edited April 2015

Discovering Pi – Finding a Solution If you measure the circumference of a circle as you did in the activity above and divide it by the diameter, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter π (pronounced Pi) to represent this value. The number π goes on forever. However, using computers, π has been calculated to over 1 trillion digits past the decimal point. π is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to π. This relationship is expressed in the following formula: 𝜋𝜋 =

𝑐𝑐𝑑𝑑

Another way to write this formula is:

C = π × d where C is the circumference and d is the diameter. This second formula is commonly used in problems where the diameter is given and the circumference is not known.

Example1: The diameter of a circle is 3 centimetres. What is the circumference?

Solution: C = π d

C = 3.14 · (3 cm)

C = 9.42 cm

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Book 5: Math 11 Home - Measurement Edited April 2015

Example 2: The radius of a circle is 2 inches. What is the circumference?

Solution: d = 2 r

d = 2 · (2 in)

d = 4 in

C = 3.14 · (4 in)

C = 12.56 in

Example 3: The circumference of a circle is 15.7 centimetres. What is the diameter?

Solution: C = π d 15.7 cm = 3.14 · d

15.7 cm ÷ 3.14 = d

d = 15.7 cm ÷ 3.14

d = 5 cm

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Book 5: Math 11 Home - Measurement Edited April 2015 5.4C Practice Your Skills - Circles Ask Your Teacher how many of these questions to do. Solve the problems below using your knowledge of circumference and area concepts. Use 3.14 for Pi. Round your answers to 2 decimal places if necessary. Show your work. 1. What is the diameter of a circle with radius of 7 inches? 2. What is the radius of a circle with a diameter of 9 centimetres? 3. If the diameter of a circle is 3.4 inches, then what is the radius? 4. If the circumference of a circle is 28.26 inches, then what is its diameter? 5. What is the circumference of a circle with diameter of 5 centimetres? 6. What is the circumference of a circle if its radius is 4 metres?

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Book 5: Math 11 Home - Measurement Edited April 2015 7. The distance around a bicycle wheel is 21.98 feet. What is its diameter? 8. The circumference of a dinner plate is 15.7 inches. What is its radius? 9. Greg needs to put a rubber edging around his circular hot tub so that it doesn’t leak. How much rubber edging will he need if his hot tub has a diameter of 3.2 metres?

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Book 5: Math 11 Home - Measurement Edited April 2015 5.5 Area

A. What is Area? Brainstorm: “What do you know about area?” By yourself or with a partner, jot down all of your ideas. Share your ideas with another pair.

Discuss the Ideas 1. What is area?

2. What is the difference between perimeter and area?

3. What do you need to know to measure area?

4. How is area measured?

5. How can you calculate area?

6. Why are the units for area always square units or units squared?

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Units of Measure for Perimeter and Area How are these expressions the same? How are they different? 2 + 2 + 2 2 × 2 × 2 How are these expressions the same? How are they different? feet + feet feet × feet How do you know if you should use exponents in your units?

• When you are calculating perimeter you are measuring different lengths in centimetres and then adding them together. The units remain the same.

Perimeter cm + cm = cm

• When you are calculating area, you are measuring the dimensions and multiplying to derive the number of units squared. The units will also be squared.

Area cm × cm = cm2 (derived measure in units squared)

The perimeter of the rectangle below is 3 ft + 2ft + 3ft + 2ft = 10ft The area of the rectangle below is 3ft x 2ft = 6ft2

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Book 5: Math 11 Home - Measurement Edited April 2015 C. Figuring Area: Squares and Rectangles

Imagine you're planning to buy new carpeting for your home. You're going to put down carpeting in the living room, bedroom, and hallway, but not in the bathroom. You could try to guess at how much carpet you might need to cover these rooms, but you're better off figuring out exactly what you need. To determine how much carpet you'll need, you'll use this simple formula:

A = L x W

Or in other words, "area equals length times width." This formula is used to determine the area of a rectangle or square. In the floor plan below, all of the floor space (as well as the walls and ceilings) is made up of squares or rectangles, so this formula will work for figuring the area you need to carpet.

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Book 5: Math 11 Home - Measurement Edited April 2015 D. Formulas for Calculating Perimeter and Area Here are some other common formulas that are used to figure out perimeter and area.

a

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Book 5: Math 11 Home - Measurement Edited April 2015

E. Perimeter and Area of Quadrilaterals Example 1. Calculate the perimeter and area of the square. Perimeter P= 2 + 2+ 2+ 2 P = 8in OR P= 2a P = 2 (4) P = 8 in Area A = 2 x 2 A = 4 in2

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Book 5: Math 11 Home - Measurement Edited April 2015 Example 2. Calculate the perimeter and area of the rectangle. Perimeter P= 2 (a+b) P = 2(8+3) P = 2(11) P = 22 in Area A = l x w A = 8cm x 3 cm A = 24 cm2

Example 3. Calculate the perimeter and area of the parallelogram.

Perimeter P = 2(a+b) P = 2(12+6) P = 2(18) P = 36cm Area A = base x height A = 12 cm x 5 cm A = 60 cm2

6cm

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Book 5: Math 11 Home - Measurement Edited April 2015 5.5E Practice Your Skills - Quadrilaterals Ask your teacher how many of the following questions to do. A. Find the perimeter and area of each of the quadrilaterals

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Find the area of the following parallelgrams.

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Book 5: Math 11 Home - Measurement Edited April 2015

F. Perimeter and Area of Triangles Example 1. Find the perimeter. P = 4 ft + 5 ft + 2 ft P = 11 ft Example 2. Find the area.

𝐴𝐴 =𝑎𝑎 × 𝑏𝑏

2

𝐴𝐴 =7 × 10

2

𝐴𝐴 =702

𝐴𝐴 = 35 𝑐𝑐²

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Book 5: Math 11 Home - Measurement Edited April 2015 Example 3. Find the perimeter and area: 29m Perimeter P = 29 +29 + 25 P = 83m Area

𝐴𝐴 =𝑎𝑎 × 𝑏𝑏

2

𝐴𝐴 =25 × 26

2

𝐴𝐴 =650

2

𝐴𝐴 = 325 𝑐𝑐²

29m

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Book 5: Math 11 Home - Measurement Edited April 2015 5.5F Practice Your Skills - Triangles Ask Your Teacher how many of the following questions to do. A. Find the perimeter of each triangle.

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Book 5: Math 11 Home - Measurement Edited April 2015 B. Find the area of each triangle

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Book 5: Math 11 Home - Measurement Edited April 2015 G. Area of Circles Do the following activity and/or watch Area of Circle Videos.

Discovering Pi – Area of a Circle

On the following page you will see a circle and a square. The sides of the square are the same length as the radius of the circle (r).

Therefore, the area of the each square is r x r or r2.

Figure out how many r2 squares it takes to cover all of the area of the circle. Trace and cut out as many squares as you want or use any method to figure out how many squares it takes to fill up the circle.

When you have completed this activity, compare with a partner to see if you got the same results.

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Book 5: Math 11 Home - Measurement Edited April 2015

r r r

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Book 5: Math 11 Home - Measurement Edited April 2015 Discovering Pi – Area of a Circle – Finding a Solution You should have found that it took 3 squares and a little bit to cover the whole circle. This 3 and a little bit is Pi (π) which you will remember we used to find the circumference of a circle as well. Therefore, to find the area of a circle we can use the formula: A = π x r x r OR Area of a circle = π x r2

Example:

Find the area of a circle with a radius of 5 cm. Use 3.14 as the value for π.

A = π x r2

We know that the radius is 5 so we can just substitute 5 in for r in the formula. A = 3.14 x 52

A = 3.14 x 25 A = 78.5 cm2

The area of a circle with a radius of 5 cm is 78.5 cm2

Area of Circle Videos Here are some other ways that the area of a circle formula can be figured out. Watch: Area of a Circle, How to Get the Formula http://www.youtube.com/watch?v=YokKp3pwVFc Proof Without Words: The Circle http://www.youtube.com/watch?v=whYqhpc6S6g

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Book 5: Math 11 Home - Measurement Edited April 2015 5.5G Practice Your Skills - Radius and Area Ask Your Teacher how many of these questions to do. Round your answers to two decimal places

1a.

r = 8.1 mm Calculate the area of the circle.

1b.

r = 3.8 cm Calculate the area of the circle.

2a.

r = 3 ft Calculate the area of the circle.

2b.

r = 7.7 m Calculate the area of the circle.

3a.

r = 4.3 m Calculate the area of the circle.

3b.

r = 1.4 mm Calculate the area of the circle.

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Book 5: Math 11 Home - Measurement Edited April 2015 4. d = 6.9 m

Calculate the area of the circle.

5.

Calculate the area of the circle. | | d = 2.7 ft

6. You are designing a circular concrete pad for a park. You need to know the area of the circle so that you know how much concrete to order. You want the radius of the circle to be 6 feet. What is the area of the circle?

46

Book 5: Math 11 Home - Measurement Edited April 2015

Formula Sheet

a

47

Book 5: Math 11 Home - Measurement Edited April 2015

Circles

d = 2 x r where d is the diameter and r is the radius. r = d ÷ 2 where d is the diameter and r is the radius. C = π d where d is the diameter and C is the circumference 𝑑𝑑 = 𝐶𝐶

𝜋𝜋 where d is the diameter and C is the circumference

Area of a circle A = π x r2

48

Book 5: Math 11 Home - Measurement Edited April 2015 Student Evaluation

Insufficient Evidence (IE)

Developing (D) Growing (G) Proficient (P) Exceptional (E)

Student has not demonstrated the criteria below.

Student has rarely demonstrated the criteria below.

Student has inconsistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below. In addition they have shown their understanding in novel situations or at a higher level of thinking than what is expected by the criteria.

Proficient Level Criteria IE D G P E

M11.1 Extend understanding of arithmetic operations to rational numbers to solve problems within the home, money, recreation, and travel themes.

a. I can compare and order positive and negative numbers, using appropriate tools (e.g., change in temperature using a thermometer).

b. I can use whole numbers, integers, fractions, decimals, and percents.

c. I can compare and convert among fractions, decimals and percents.

d. I can round decimals.

e. I can determine if my answer is reasonable.

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Book 5: Math 11 Home - Measurement Edited April 2015

Proficient Level Criteria IE D G P E

M11.4 (WA10.4)Demonstrate understanding of measurement in the Système International (metric) and Imperial System within the home and travel themes.

It is intended that students explore, analyze for patterns, and develop understanding of many units in the systems of measurements. The units used should be those that are appropriate to the context being considered. These units include: • metres, grams, litres, and seconds along with appropriate prefixes

such as kilo, centi, and milli, and degrees Celsius (SI system). inch, foot, mile, teaspoon, tablespoon, cup, pint, quart, gallon, and degrees Fahrenheit (Imperial system).

a. I can determine and explain the lengths of common objects in the metric and imperial systems, using a variety of tools (e.g., measuring tape, metre or yard stick, measuring cups, graduated cylinders, trundle wheel).

b. I can use estimation techniques for lengths and distances in metric units and in imperial units by applying personal referents (e.g., the width of a finger is approximately 1 cm; the length of a piece of standard loose-leaf paper is about 1 ft; the capacity of a pop bottle is 2 L).

c. I can develop, explain, and apply strategies to estimate quantities (e.g., books in a shelving unit, time to complete a job, people in a crowd).

d. I can convert measures within and between systems (e.g., centimeters and metres, feet and inches, pounds and kilograms, degrees Celsius and degrees Fahrenheit) using a variety of tools (e.g., tables, calculators, online conversion tools).

e. Discuss and approximate measures between systems (e.g., 1 inch is approximately 2.5 cm, 1 kg is a little more than 2 lbs, 1 litre is approximately 1

4 US gallon).

M11.7 [WA 10.10] Demonstrate understanding of proportional reasoning within the home, money, recreation, and travel themes.

a. I can explain and apply strategies to solve ratio and rate problems.

b. I can recognize and represent equivalent rates and ratios.

c. I can calculate and compare the unit rate of items and the unit cost of items (e.g., cost per linear foot).

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Book 5: Math 11 Home - Measurement Edited April 2015 Learning Log Date Starting Point Ending Point

51

Book 5: Math 11 Home - Measurement Edited April 2015

3m

5m

Show What You Know - Area 1. Which room in your house requires the most, and which requires the least,

amount of carpet? What is the difference in the two amounts? 2. Calculate the area needed to paint your classroom walls or your bedroom

walls. 3. Calculate the area needed to tile the classroom floor. 4. Heith wants to create a concrete patio pad in the corner of his backyard. He

wants it to be in the shape of a right triangle with the dimensions in the diagram below. Calculate the area he will need to cover with concrete.

5. Charlotte wants to cover the surface of her coffee table with a glass protector. Calculate the amount of glass she will need.

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Book 5: Math 11 Home - Measurement Edited April 2015 Show What You Know – Project 1. Draw plans for a landscape design. Include one of the following design

elements, which will be in the shape of a rectangle: swimming pool, concrete patio, hockey rink, or beach volleyball pit. Also include a design element that is in the shape of a triangle and one that is in the shape of a circle.

2. Include the dimensions and areas of each of the required components.

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Book 5: Math 11 Home - Measurement Edited April 2015

Show What You Know – At Home Activity

1. Which room in your house requires the most, and which requires the least, amount of baseboard? Record the measures and units of each. Once you have measured in either Imperial or SI units, convert the measurement to the other system. Show your work.

2. What is the difference between the two rooms? Show your work. 3. Find the following:

• Remember that dimensions that are not in the same units must first be converted prior to adding

• Only measure once and then show your work to find the perimeter in metres.

a) How many linear feet of fencing are required to go around your yard? What is the measure in metres?

b) How many linear feet of garden edging are required to build a garden/flower garden? What is the measure in metres?

c) How many linear feet of baseboard/ are needed to complete a renovation of your bedroom? What is the measure in metres?

4. Find a circular object in your home. Draw a diagram and label the length of the radius and diameter. Calculate the circumference.

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Book 5: Math 11 Home - Measurement Edited April 2015

Answers Check Your Skills Answers 1. a) Height: 4 cm and 1.5 in Width: 2 cm and ¾ in b) Height: 7.6 cm and 3 in Width: 3.7 cm and 1 ½ in 2. a) 5.49 b) 4.13 c) 0.16 d) 1.92 3. a) 4/4 or 1 b) 4 ¼ c) 1 d) 1/8 4. a) 20.2 b) 201.85 c) 87.5 d) 33.29 5. a) 62 b)18.84 c)16.3 d)0.015

5.3B Practice Your Skills - Conversions Answers may vary slightly depending on rounding.

1. 3.5 ft

2. 1 ft 6 in

3. 2.09 m

4. 570 cm

5. 2.67 yd

6. 4.33 yd

55

Book 5: Math 11 Home - Measurement Edited April 2015

7. 8800 yd

8. 19.68 ft

9. 5.03 ft

10. 3.19 in

11. 3.08 yd

12. 5.44 yd

13. 22.86 m

14. 10.33 ft

5.3C Practice Your Skills 1. a) 80 cm = 31.5 in so this vanity would not fit b) 80 cm = 31.5 in so this vanity would fit 2. a) 44.29 ft b) She should buy at least 6 pieces. She might need more depending on the cuts she has to make 3. Yes, it is about 8.14 ft long 4. 15.2 m = 49.87 ft. He should buy 5 strings of lights.

5.4C Practice Your Skills - Circles 1. d = 14 in 2. r = 4.5 cm 3. r = 1.7 in 4. d = 9 in 5. C = 15.7 cm 6. C = 25.12 m 7. d = 7 ft 8. r = 2.5 in 9. 10.05 m (Source: http://www.mathgoodies.com/lessons/vol2/circumference.html)

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Book 5: Math 11 Home - Measurement Edited April 2015

5.5E Practice Your Skills – Quadrilaterals A. 1. A = 7.29 ft2

P = 10.8 ft 2. A = 28.09 cm² P = 21.2 cm 3. A = 50.41 yd² P = 28.4 yd 4. A = 17.64 m² P = 16.8 m 5. A = 110.25 in² P = 42 in 6. A = 73.21 mm² P = 35.6 mm 7. A = 87.63 in² P = 39.2 in 8. A= 329.6 mm² P = 73.2 mm 9. A = 42.75 m² P = 28 m B. 1. 201.6 ft² 2. 36.52 m² 3.190.71 in² 4. 288.6 yd² 5. 170.1 cm² 6. 44.02 ft²

5.5F Practice Your Skills - Triangles A. 1. 23 in 2. 27 in 3. 13 ft 4. 15 m 5. 19 ft 6. 16m B. 1. 10.56 m² 2. 55.18 in² 3. 42.78 mm² 4. 10.54 ft²

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Book 5: Math 11 Home - Measurement Edited April 2015

5. 12.96 cm² 6. 47.08 m² 7. 66.66 in² 8. 25.2 ft² 9. 55.68 mm²

5.5G Practice Your Skills - Radius and Area 1a. 206.02 mm2

1b. 45.34 cm2

2a. 28.26 ft2

2b. 186.17 m2

3a. 58.06 m2

3b. 6.15 mm2

4. 37.37 m2 5. 5.72 ft2

(Source: Homeschoolmath.net)

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