Mathematics Unit 2 - Measuring Length

Transcription

1 Mathematics 1202 Unit 2 - Measuring Length Section Imperial Length Measurements The imperial units of length are: inch (in.) - the smallest unit foot (ft) - there 12 in. in a foot yard (yd) - there are 3 feet in a yard mile (mi) - there 1760 yd in a mile The imperial units are based on personal features, or reference. An inch is half of your thumb, a foot is the length of your foot or the length of your forearm, a yard is a stride length or the distance from the tip of your fingers to your nose and a mile is how far a person can walk in 20 mins. Do you see a problem with this? 1

2 Even though personal referents are not exact they are still very helpful in a pinch or when you only need an estimate. *Activity (BLM 2-4) Textbook page #1, 2, 3, 4, 8, 10 Measuring in Imperial Units Measuring in imperial units involves fractions. On most rulers/measuring tapes, an inch is divided into 16 parts. So when you are measuring something in inches and you need a part of an inch you count how many lines you have and write that number over 16. Remember to reduce the fraction if need be. 2

3 When measuring in feet, we use inches for part of a foot. For example, when we talk about our height we say 5 ft 6 in. Most measuring tapes have feet marked on them so you only have to read it off the tape. Activity: Measure the length of the window, the length of a desk and height of the door. When adding feet and inches, remember to add like with like. In other words, you add the feet together and then add the inches together. One small catch, if you have more than 12 inches, then have to change it into feet. 3

4 Textbook page 62 63#4, 5, 6; portfolio entry 2.1 Section SI Length Measurements The SI units is the formal term for the metric system. SI stands for Systeme Internationale. There are many SI units for length but the only ones we will be dealing with, from smallest to largest are: millimetre centimetre metre kilometre The metric system is based on the powers of 10, which means that you only have to move the decimal either to the left or to the right to change from one metric unit to another. 4

5 Textbook page #3, 6, 8, 5

6 Just like with imperial units, you can use personal referants to help estimate the length of something in SI units. Activity (BLM 2 6) Portfolio entry 2.2 Section Length Conversions Sometimes we may need to convert from Imperial Units to SI units and from SI Units to Imperial units. One way to do this is to use your measuring tape. Since most measuring tapes have both inches/feet and centimeters on them, you simply have to look for the length in the given units and then take the number on the opposite side of the tape. Ex. Convert 8 in. into centimeters using your measuring tape. Ex. Convert 25 cm into inches using your measuring tape. 6

7 Sometimes using your measuring tape is impractical, like convert miles into kilometers. For these we have to use conversions. These are done like before: set up fractions and cross multiply. For converting from Imperial Units to SI Units we use the following conversions: 1 in. = 2.54 cm 1 ft = 30 cm 1 ft = 0.3 m 1 yd = 90 cm 1 yd = 0.9 m 1 mi. = 1.6 km To convert from SI units to Imperial units we us the following conversions (Note: Imperial units are usually written with fractions and not decimals but to make things a little easier we will use decimals): 1 mm = 0.04 in. 1 cm = 0.4 in 1 m = 39 in 1 m = 3.25 ft 1 km = 0.6 mi Note: Even though I am using equal signs in all of these conversions, they are actually, for the most part, approximations. 7

8 Ex. Convert 4 km into miles. Ex. Convert 12 mi into kilometers. Ex. Convert 16 in. into centimeters. Ex. Convert 5 m into feet. 8

9 Ex. Carrie works in a St. John's home decor store that sells products from all over the world. A rectangular mirror imported from the US has dimensions 30" by 48". How can she convert the dimensions to the nearest centimetre? Ex. A circular area rug imported from India has a diameter of 150 cm. How can she convert 150 cm to feet and the nearest inch? Textbook page #2, 6, 8, 11a 9

10 Ex. Speed limits in the US are in miles per hour (mph). What 70 mph be in km/h? Ex. The speed limit on a private road is 50 km/h. Calculate the speed in mph. 10

11 Ex. Gander is 330 km from St. John's. What is the distance in miles? Ex. Boston is 207 miles from New York City. What is the distance in kilometers? Textbook page #4, 5, 6; portfolio entry

12 Section Working with Length First we need to review a couple of terms and formulas. Perimeter is the total of all of the sides in a figure. To find the perimeter of an object we have to add all the side lengths. Circumference is the distance around a circle. Since a circle has no sides we have to use a special formula to calculate the circumference of a circle. We use this formula if we are given the diameter We use this formula is we are given the radius. Since we are using π, we will always have long decimals, so round each one to 2 decimal places. Ex. A tire has a radius 12 inches. What is its circumference? 12

13 Ex. The circumference of a CD is cm. What is its diameter? Ex. A rectangular window frame measures 24 in. by 36 in. If trim for the window costs $2.75 per linear foot, how much will it cost to put trim around the window? 13

14 Ex. Most items are imported into NL on planes and ships. Sometimes, the cost to ship these items is based on its weight and other times its based on its size. The size is the length of the package plus the girth (the distance around the package, i.e. two times the width plus the length for rectangular boxes or πd for cylinders). a. A package has a length of 2.5 m, width of 1.5 m, and a height of 1 m. What is the length + girth measurement? b. A shipping tube has a diameter 1.5 m and length 4.5 m. What is the length + girth measurement, to the nearest tenth of a metre? Textbook page #1, 2, 6, 8 14

15 Sometimes it is necessary to find the midpoint of a measured length. For example, when hanging a picture you need to find the middle of the picture so that it will hang straight. There are a few ways to determine the midpoint: dividing the total length by 2 using a piece of string to cover the full distance and then folding it in half will give you the halfway point construct diagonals, where the lines intersect is the middle Ex. Determine the midpoint of the your desk, the bulletin board and the whiteboard. Textbook page #1, 7; portfolio entry

16 Attachments Math 1202 Chapter 2 Text.pdf