Math 11 Home. Book 5: Measurement. Name:

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2 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. 1

3 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 Systems of Measurement Imperial Measurement A. Exploring Imperial Measurement B. Imperial Conversion Table C. Symbols and Abbreviations Used for Imperial Measurement Conversions: Imperial and SI System International A. Linear Measurements: Conversion Chart Additional Materials Math Essential 10 Student Edition p Math Essentials 10 BLM B. Imperial and SI Conversions B Practice Your Skills - Conversions C. Perimeter, Linear Measurement and Conversion C Practice Your Skills Perimeter A. What is Perimeter? Discuss the Ideas B. Finding Perimeter C. Circumference of a Circle Discovering Pi - Circumference Discovering Pi Finding a Solution C Practice Your Skills - Circles

4 5.5 Area A. What is Area? Discuss the Ideas B. Units of Measure for Perimeter and Area C. Figuring Area: Squares and Rectangles D. Formulas for Calculating Perimeter and Area E. Perimeter and Area of Quadrilaterals E Practice Your Skills - Quadrilaterals F. Perimeter and Area of Triangles F Practice Your Skills - Triangles G. Area of Circles Discovering Pi Area of a Circle Discovering Pi Area of a Circle Finding a Solution Area of Circle Videos G Practice Your Skills - Radius and Area Formula Sheet Student Evaluation Learning Log

5 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 diametre 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 diametre 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 4

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

6 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'. 5

7 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. To watch Numberphile s humorous explanation of the Imperial Number System, go to 6

8 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 diametre imperial system diametre 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 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. 7

a) b) Math skills are embedded into real life situations.

9 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 8

10 2. Round the following decimal numbers to two decimal places. a) b) c) d) 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) b) c) d) Multiply or Divide a) 12.4 x 5 b) 3.14 x 6 c) d)

11 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. 10

12 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. 11

13 Imperial Measurements Item Estimation using referent Imperial measurement Difference 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? 12

14 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 = because there are 3 feet in each yard. 2.5 mi = ft 13

15 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 mm = 1 km Centimetres 0.1 cm = 1 mm 10 cm = 1 dm 100 cm = 1 m cm = 1 km Metres 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 = inches 1 cm = inches 1 m = feet 1 m = yards Conversion Factors Imperial to SI 1 inch = 2.54 cm (25.4 mm) 1 foot = m 1 yard = m 1 mile = km Additional Materials Math Essential 10 Student Edition p Math Essentials 10 BLM 9 14

16 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 inch 2.54 cm = 5 inches x 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 inch 2.54 cm = 5 inches x 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. Example: How many feet are in 4.9 meters? Step 1: Set up a ratio 1 m feet = 4.9 m x feet Step 2: Cross multiply to solve for x x = (4.9)(3.2808) x = Step 3: Round your answer to two decimal places and include the units of measure in your answer. x = feet There are feet in 4.9 meters Sometimes in science you may see: 5iiii 2.54 cccc 1 iiii = 12.7 cccc 15

17 5.3B Practice Your Skills - Conversions Convert the following measurements. Round your answers to two decimal places inches to feet inches to feet and inches centimetres to metres metres to centimetres inches to yards feet to yards 7. 5 miles to yards 16

18 8. 6 metres to feet centimetres to feet millimetres to inches feet 3 inches to yards to yards feet to metres centimetres to feet 17

19 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. 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 inch 2.54 cm = x inches 71.1cm Step 2: Cross Multiply 2.54x = 71.1 Step 3: Solve for x x = x = Step 4: Think about the most reasonable answer Ivan should buy the door that is 28 wide. 18

b) Will this one fit? 2. Jolie is renovating her living room and wants new baseboards. She needs 13.

20 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? 19

21 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? 20

22 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 21

23 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

The circumference of the circle is the distance around the circle and the diametre of the circle is the distance across the circle passing through the center point.

24 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 diametre 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 diametre. Thus, the diametre 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 diametre and r is the radius. If you know the diametre of a circle and you want to find the radius, you can use the formula: r = d 2 where d is the diametre and r is the radius. Example 1: If the diametre of a circle is 24 inches, what is the radius? Solution: r = d 2 r = 24 2 r = 12 inches 23

25 Example 2 : The radius of a circle is 2 inches. What is the diametre? Solution: d = 2 x r d = 2 x (2in) d = 4 in 24

26 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 diametre and fill in the spaces below. Circular Object Found Circumference Diametre Circumference Diametre 1. What relationship appears to exist between the circumference and diametre 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? 25

27 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 diametre, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 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 diametre. Thus, for any circle, if you divide the circumference by the diametre, you get a value close to π. This relationship is expressed in the following formula: ππ = cc dd Another way to write this formula is: C = π d where C is the circumference and d is the diametre. This second formula is commonly used in problems where the diametre is given and the circumference is not known. Example1: The diametre of a circle is 3 centimetres. What is the circumference? Solution: C = π d C = 3.14 (3 cm) C = 9.42 cm 26

28 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 = in Example 3: The circumference of a circle is 15.7 centimetres. What is the diametre? 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 27

29 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 diametre of a circle with radius of 7 inches? 2. What is the radius of a circle with a diametre of 9 centimetres? 3. If the diametre of a circle is 3.4 inches, then what is the radius? 4. If the circumference of a circle is inches, then what is its diametre? 5. What is the circumference of a circle with diametre of 5 centimetres? 6. What is the circumference of a circle if its radius is 4 metres? 28

7. The distance around a bicycle wheel is 21.98 feet. What is its diametre? 8. The circumference of a dinner plate is 15.7 inches. What is its radius? 9.

30 7. The distance around a bicycle wheel is feet. What is its diametre? 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 diametre of 3.2 metres? 29

31 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? 30

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?

32 B. Units of Measure for Perimeter and Area How are these expressions the same? How are they different? 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 = cm 2 (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 = 6ft 2 31

33 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. 32

34 D. Formulas for Calculating Perimeter and Area Here are some other common formulas that are used to figure out perimeter and area. a 33

35 E. Perimeter and Area of Quadrilaterals Example 1. Calculate the perimeter and area of the square. Perimeter P= P = 8in OR P= 2a P = 2 (4) P = 8 in Area A = 2 x 2 A = 4 in 2 34

36 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 cm 2 Example 3. Calculate the perimeter and area of the parallelogram. 6cm 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 cm 2 35

37 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 36

38 B. Find the area of the following parallelgrams. 37

39 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 = AA = 70 2 AA = 35 mm² 38

40 Example 3. Find the perimeter and area: 29m 29m Perimeter P = P = 83m Area AA = AA = aa bb 2 AA = AA = 325 mm² 39

41 5.5F Practice Your Skills - Triangles Ask Your Teacher how many of the following questions to do. A. Find the perimeter of each triangle. 40

42 B. Find the area of each triangle 41

43 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 r 2. Figure out how many r 2 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. 42

44 r r r 43

45 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 r 2 Example: Find the area of a circle with a radius of 5 cm. Use 3.14 as the value for π. A = π x r 2 We know that the radius is 5 so we can just substitute 5 in for r in the formula. A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 The area of a circle with a radius of 5 cm is 78.5 cm 2 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 Proof Without Words: The Circle 44

46 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. 1b. r = 8.1 mm Calculate the area of the circle. r = 3.8 cm Calculate the area of the circle. 2a. 2b. r = 3 ft Calculate the area of the circle. r = 7.7 m Calculate the area of the circle. 3a. 3b. r = 4.3 m Calculate the area of the circle. r = 1.4 mm Calculate the area of the circle. 45

47 4. d = 6.9 m Calculate the area of the circle. 5. d = 2.7 ft Calculate the area of the circle. 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

48 Formula Sheet a 47

49 Circles d = 2 x r where d is the diametre and r is the radius. r = d 2 where d is the diametre and r is the radius. C = π d where d is the diametre and C is the circumference dd = CC where d is the diametre and C is the circumference ππ Area of a circle A = π x r 2 48

50 Student Evaluation Insufficient Evidence (IE) Student has not demonstrated the criteria below. Developing (D) Growing (G) Proficient (P) Exceptional (E) 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. 49

51 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 US gallon). 4 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). 50

52 Learning Log Date Starting Point Ending Point 51

2 Standards of Measurement

What You ll Learn the SI units and symbols for length, volume, mass, density, time, and temperature how to convert related SI units 2 Standards of Measurement (A), 2(D), 2(C), 2(E) Before You Read If someone