Math 10 3 Measurement Unit.notebook February 19, 2015

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1 What kinds of things can we measure? What tools What units of of measuremenmeasureme t n do we use? t do we use?

2 technology/measurement/forgood measure canada converts to metric/metric muddle.html Should Canada switch back to the Imperial System? Criteria: Guiding Questions: What are the main units used in each system? What are the relationships among units? Is it based on decimals or fractions? Why? /3 (1/2 mark for ech for each system) Conclusion: Use your criteria and research to answer the problem. Use 2 3 sentences and address all your criteria. /3 for answering the problem using the criteria and your research

3 Lesson 1: Measurement Systems Vocabulary: Base unit Volume SI measuring system or metric The base unit for measuring length is the (m), the base unit for measuring mass is the (g) and the base unit for measuring volume is the (L). This system is a system because it is based on. Any measurement stated in one SI unit can be converted to another SI unit by or by a multiple of 10. inches, feet etc. This system is used in many trades. The base unit for length is the, the base unit for measuring mass is the and the base unit for measuring volume is the. This system is NOT a system. This system was developed at a different time to meet different needs, so each group has a particular relationship. For example, there are, 3 feet in 1 yard. Some Common Imperial Units:

4 Estimating Linear Measurements When estimating the lengths of objects, it is important to have a. Examples: the length of your stride is pretty close to an (or ~30 cm) Your pinky is probably close to about the same as (or ~5 cm). The length from your finger tips of one arm to the should of the other arm is probably close to (or ~1 yard) How could we use these estimations to measure the length of objects in the room? Fraction Review Remember, fractions represent For example: If a pie is cut into 4 pieces, and you have 1 piece, what fraction do you have? How do we write this? Think: 4 parts make up the whole, 1 part is taken out Write: *Remember, the numerator is the number on top, and the denominator is the number on the bottom!* When fractions, you MUST make the of each fraction equal to the same number. by whole numbers until they are the same. You may remember this as the or LCD. Ex. 1) Find the LCD of these two fractions. 2) Multiply the numerator and denominator of the first fraction by to change it to the LCD of. 3) Since the second fraction already has the LCD of 4, it. 4) Add the numerators of the two fractions to get the answer:

5 Lesson 2: Converting Between Imperial Units The Imperial system was developed in ancient Rome based on referents from the human body and everyday activities. A referent is a known measure used for comparing and estimating. When measuring length with the imperial system, the following units are used: Inch (in. or ) Foot (ft or ) Yard (yd) Mile (mi) 12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile The following chart may be helpful when converting between Imperial units: 1) Ex. Taylor is buying fabric for her graduation dress. Her dress pattern is in inches, but the fabric store only sells in yards. How many inches are there in one yard? We HAVE yards we WANT inches Use the conversion chart to move from yards to inches: 2) Ex. Russell wants to determine how far away the cafeteria is from Mrs. Lin s classroom in miles. He counts 1584 feet from the classroom to the cafeteria doors. How far is it in miles? We HAVE feet we WANT miles Use the conversion chart to move from feet to miles Sometimes measurements will include feet and inches. If we want to convert to one unit only (either feet or inches) we must change one of the measurements to the desired unit. 3) Ex. Tristan is 5 11 tall. How tall is Tristan in inches? We know that 5 = 5 feet and 11 = 11 inches. We WANT inches so we must convert 5 feet into inches first. We can now add the 11 inches to determine Tristan s height in inches. We also have to consider that inches are divided into 16 parts. This means we will also have to add and subtract fractions when working with the Imperial system of measurement. 4) Ex. Janet wants to build steps up to her porch. There will be six steps, with each step measuring 7 1/4 inches high. What will the height of the staircase be in feet and inches? First we will consider the whole number inches. Next, we will consider the fraction of inches. *Remember, when MULTIPLYING fractions, we multiply the numerators together, and the denominators together. We then change the fraction to a decimal or a reduced fraction. Now, combine the two measurements: Next, we will convert to feet The very last step is to convert the remainder BACK to inches.

6 Lesson 2: Converting between SI measurements SI is a system because it is based on multiples of 10. This means that if you have one given unit you can convert to any other SI unit by multiplying or dividing by multiples of. Unit Referent Estimate A helpful way to remember the order of the SI units. K H D m d c m King Henry Danced down country meadows Kilo Hecto Deca [BASE UNIT *m, g or L*] deci centi mili The tells us what we are measuring. Examples Ex. Convert 250cm to m 1) Use the following chart to help you: 2) Place your finger on the unit you are starting with 3) Move your finger to the unit you want. Count how many times you have to multiply/divide by 10. 4) Multiply/divide your current unit by 10 until you reach your desired unit. Ex 2.) Matt is visiting his grandpa s farm. Matt wants to buy a 3.8 km x 4.6 km piece of land off of his grandpa to set up a paint ball course. Matt s grandpa only knows meters. What are the dimensions of this piece of land in meters? 1) We HAVE kilometers (km). We WANT meters (m) 2) Start at and move 3 spaces to the right to get to 3) Multiply by to change to the desired unit for each measurement.

7 1) White board practice: 2) Convert 6.54 m into cm. 3) How many mm are there in m? Complete assignment 3: Imperial Measurement Problems

8 Conversions Between SI and Imperial Take a look at a ruler. Approximately how many cm are there per inch? How many cm per foot? **To convert between metric and imperial units, we will use proportions** Conversions factors will be provided in a conversion chart! Follow these steps to convert between metric and imperial units: 1) Set up a fraction : Place an x and the units for what you WANT. 2) Find the appropriate conversion on the chart. 3) Set up a second fraction, with the units of what you WANT in the numerator and what you HAVE in the denominator 4) Cross multiply and divide to get the correct answer. Ex 1). Convert 14mm to inches. 1) WANT inches HAVE millimeters 2) We are converting from SI imperial, so we will use: 1 cm = in 3) 4) Ex 2). Convert 3.5 miles to km 1) WANT km HAVE mi 2) We are converting Imperial SI so we will use: 1 mi = km 3) 4) We may need to complete more than one conversion if what we want is not on the conversion factor chart. For example, you may need to change from Imperial SI first, then convert the SI units to the desired unit. Ex 3) Convert 0.8m to inches 1) We WANT inches we HAVE meters. BUT there is no conversion on the chart from meters to inches. We must first convert m feet then feet inches. 2) SI Imperial so we will use: 1 m = ft 3) 4)

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10 Math 10 3: Unit 1 Part 1 Review Package 1. For each of the following, indicate which METRIC and which IMPERIAL units of measurements you would use, and then estimate the length. a) Height of a desk b) Length of the text book c) Width of the classroom d) Distance form St. Joes to Costco e) Thickness of 1 sheet of paper 1. John rode 2 kilometers on his bike. His sister Sally rode 3000 meters on her bike. Who rode the farthest and how much farther did they ride (answer in km)? 2. A low bridge has a posted maximum vehicle height of 7 6. Your truck is 2.3 m high. Will it fit under the bridge? 3. Riley works for a company that develops a measurement device used by skydivers. The system uses SI measurements. He is presenting the device to an American company and must change the examples into feet. His primary example uses 4200 meters. How many feet is this? 4. Katie is applying for her driver s license. The application asks her what her height is in cm. Katie is 5 4 tall. What is her height in cm?

11 Perimeter of 2D Objects People who work in the trades, such as carpenters, plumbers and electricians often use measurements to solve problems. There are usually many 2 D and 3 D shapes involved in measurements. means two dimensional ; These shapes are flat, and you can draw them on a piece of paper. When we work with 2 D shapes we are usually considering and/or. 2 D drawings are used for floor plans of buildings, yards, parks, etc. means three dimensional ; These shapes have depth, and are difficult to draw on a piece of paper. A three dimensional shapes would include a box, soup can, ball, most of the objects that we use in our everyday lives. When we work with 3 D shapes we are usually considering and/or. Review shapes: Quadrilateral a shape with, such as a square, rectangle, parallelogram, or trapezoid. Square all sides are of an equal length Rectangle two sides are the same length, and the other two are the same length. We usually call this and. Parallelogram usually described as a slanted rectangle. means that two (or more) lines will never cross. Squares and rectangles are technically parallelograms. Trapezoid a four sided shape with only one set of parallel lines. Triangle Three sided figure. Perimeter the distance around the outside of an object. You can calculate the perimeter of a shape by the lengths of each side of the object. Imagine that you start at one corner of a football field. If you walk around the outside line, you will have found the perimeter of the field. Ex 4). What is the name and perimeter of the following shape? Ex 5). Marcel wants to put an ice rink in his back yard. He determines that the length of the rink will be 25 ft and the width will be 10 ft. What is the perimeter of his ice rink?