C. Measurement Systems and Linear MeasurementMath 10: A and W

Key Terms:• Find the definitions of

each of the following terms:

• Base Unit• Systeme International• Imperial System• Conversion Factor• Referent

1. Linear Measurement

•Math on the Job p. 94

•Read through together and solve

•Why would animals need a correct amount of calories of food before and after surgery?

•To much food could interfere with the anesthetic while too few calories could slow the healing process or cause reactions when the animal is taking medications

•Animal health technologists use a Maintenance Energy Requirement (MER) formula to calculate the number of kilocalories an animal needs per day

•We will not be using this however and will simply set up proportions to solve these problems

•Fractions Review

•It is nearly impossible to use any form of measurement without having a way to express fractions

•A fraction may be expressed in 3 different ways without altering its value:

•As a fraction•As a decimal•As a percent

•The proper fraction and mixed fraction are the types most often used in measurement

•Proper Fraction – denominator > numerator

•Mixed Fraction – has a whole number in front of the fraction

•Remember that only fractions with common denominators can be added and subtracted

Examples

•Fractions like these are seen and used more in the Imperial System, which we will look at soon.

•Decimals are used and seen more in the SI System

•In Canada, we use two systems of measurement: the Systeme International d’unites (SI) also known as the metric system and the Imperial System

•Although we use the SI most often in our daily lives, imperial measurements are also used in many trades.

•For example, plumbers and carpenters typically take measurements in feet and inches, which are imperial units.

•To work in the trades you need to be familiar with both SI and imperial systems.

a) In the SI system, the base unit for measuring length is the meter (m). The base unit for measuring volume is the liter (L).

•The SI is a decimal system because it is based on multiples of 10. Any measurement stated in one SI unit can be converted to another SI unit by multiplying or dividing by a multiple of 10.

•Multiples of the base units (m) are indicated by SI prefixes

•For example, the prefix centi means one-hundredth, so 1 centimeter is one-hundredth of a meter (0.01). The prefix kilo means 1000 so 1 kilometer equals 1000m.

•SI Units of Measurement (length)

SI Prefix Symbol Combined Symbolkilohectodecameterdecicentimilli

b) In the Imperial System, the base unit for measuring length is the foot and the base unit for measuring volume is a pint.

•The imperial system is not a decimal system, and rather uses fractions.

•Because the imperial units were developed at different times to meet different needs, each group of units has a particular relationship.

•For example, there are 12 inches in a foot and there are 3 feet in a yard.

•Imperial Units of Measurement (length)

Unit Abbreviationinchfootyardmile

•In order to solve measurement problems, you may have to convert the given measurements into common units.

•To convert from unit to another is the SI system we mulitply or divide by multiplies of 10

•To convert from a smaller measurement to a larger measurement unit we divide by a multiple of 10 and move the decimal to the left.

•To convert from a larger measurement to a smaller measurement unit we multiply by a multiple of 10 and move the decimal to the right.

Converting to m Converting from m

Example

1. Andre is installing a chandelier is a house with a 2.4m ceiling. The chandelier hangs down 51cm. His client is 1.8m tall. Will Andre’s client be able to walk under the chandelier?

•To convert from one imperial unit to another imperial unit, you use a unit conversion factor

•A unit conversion factor is a fraction that is equal to 1. The numerator of the fraction contains the units to which you want to convert. The denominator of the fraction contains the original units in which the measurement was taken.

•Conversion factor:

•So what would the conversion factor be for converting feet to inches?

•Activity 3.1 – Exploring Imperial Units p. 96

•Grab some measuring tools for measuring both imperial and SI units

•Move through the activity doing each question for both imperial and SI units

Example1. Max is a finishing carpenter who is replacing the

case moulding around a double French door and the baseboards around the 4 walls of a living room. The dimensions of the room are 20’x15’. The French door is along one of the 20’ walls, and the door frame measures 72” wide and 84” high.

Case moulding costs $9.50 a linear foot and baseboard cost $4.50 a linear foot. These items must be purchased in whole feet. If Max’s labour charge is $8.50 a linear foot, what will be the total cost of this job?

Example2. Kiri needs to replace the wooden fence that

surrounds her yard. She measured her property, and it is 18 yards wide and 12 yards deep. There is no fence in front of her house, and the gap in the fence at the front of the property is 42 feet.

Kiri plans to replace the existing fence pickets with 5-foot-long cedar boards placed vertically. The boards are 5 ½ inches wide and will be spaced ¼ inch apart. She ordered 275 boards. Dis she order enough boards?

Example3. Julie, a baker, specializes in wedding cakes. She

would like to calculate the cost of decorating a 3-tiered circular cake with fresh flowers around the base of each level. The bottom cake has a 14” diameter, the middle layer has a 10” diameter, and the top layer has a 6” diameter.

All three layers are stacked on top of each other without spacers. If the cost of 1 ½” wide red roses is $0.99 each and the cost of 2 1/2” wide red roses is $1.49 each, which size of roses should Juilie decorate with to give her client the best price?

•Activity 3.3 – Designing a tin can layout p. 101

•We will read through this together and solve.

Mental Example

1. The Canadian Football League record for the longest field goal is held by Paul McCallum. In 2001, while playing for the Saskatchewan Roughriders, he kicked a 62-yard field goal. How many feet is that?

Building your Skills

•Ex. 3.1 (p. 102) #1-8

2. Converting Linear Measurements•Math on the Job p. 106

•Read through together and solve

•In many jobs you need to know how to convert from SI units into imperial units.

•For example, the US, which is Canada’s largest trading partner, uses imperial units, so doing business with a US company, you need to know the equivalent of SI unit.

•We will be using proportional reasoning and conversion factors to convert between SI and imperial units.

•Activity 3.4 – Converting between SI and Imperial Units p. 107

•We will read through and solve as a class.

•Discuss the Ideas – Installing a Chandelier p. 107

•Read through together and solve

Example1. The land speed record is the fastest speed

achieved on land by any wheeled vehicle. A turbofan-powered car holds the current record. The car reached a speed of 766.609 mph for one mile, breaking the sound barrier.

a) Express the statement about the car’s speed in kilometers per hour.

b) At 15°C, the speed of sound is 1116ft/s. This speed is given a measurement called Mach 1. How many miles per hour above Mach 1 was the car’s top speed? How many kilometers per hour above Mach 1 was that speed?

Example

2. In a triathlon, competitors swim for 1.5km, run a distance that is 6 times the length of the swim and ride a bike for a distance that is 4 times as long as the run.

a) Compute the length of each part of the triathlon to the nearest tenth of a km.

b) Compute the length of each part of the triathlon to the nearest tenth of a mile.

c) What is the total distance of the competition in km? in miles?

Building your Skills

•Handout