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MEASUREMENT LESSON 1: REVIEW AND PREVIEW Rounding Number One Ten Hundred Tenth Hundredth First Second Decimal Decimal Place Place 538.5968 539 540 500 538.6 538.60 538.6 538.60 Look at the number after the one trying to round and see if it is 5 or greater, if it is that number will move up one. Using a graphing calculator to round off (page 2 of workbook) Rounding feature: Math: 2: round Example: round(0.95*0.83,2)=0.79 Use a graphing calculator to round off where indicated: a. 10.6297 to three places __________(pg. 3, Ex. 2a) b. 1.95 x 4.68 to 2 decimals __________ (pg. 3, Ex. 2d) Scientific Notation: (pg. 4) 150 000 000 = 1.5 10 8 Find the first number and place a decimal point after it. Count to the right starting with the first number after the decimal point, and that will become your exponent. Ex. 75 300 000 = _____________ (pg. 4, Ex. 3a) Measurement Look on page 4 on how to use your graphing calculator for Scientific Notation. Substitution: Find the value of each for the following if x = 2 and y = -3 a. y2 7x 3 (pg. 6, Ex. 5a) 3 7 2 3 8 2 b. v = 12, solve for t (pg. 7, Ex. 7a) 60 = vt Converting a Fraction to Decimal: (pg. 7, Ex. 8ab) 5 7 a. 8 b. 16 Converting a Decimal to a Fraction: (pg. 8) 124 31 45 5 0.124 0.45 1000 250 (terminating) 99 11 (repeating) Assignment: pg. 9-13 #1-13 2 Measurement LESSON 2: ACCURACY AND PRECISION IN MEASUREMENT Accuracy: indicates how close a measurement comes to it’s real value. Measurement Error: Difference between a measurement and its real value Precision: how close a set of measurements are to one another using the same measuring device. Uncertainty: acceptable range of the measuring device. The uncertainty is one-half of the smallest measuring scale on the measuring device. Class Ex. 2 ( pg. 16) A player throws four darts in a game where the goal of the game is to throw as many darts as possible in the centre. The first three attempts are shown in the workbook. a. Determine which diagram best represents the following phrases: i) accurate and precise ii) precise but not accurate iii) neither accurate nor precise 3 Measurement Class Ex. 3 (pg. 16) Rema has security bars installed in a door frame at her new home. The installer uses a tape measure to measure the door frame at 0.86 m by 2.32m. a. The precision of the measuring device is: b. The uncertainty of the measurements are between: Class Ex. 4 (pg. 17) Explain whether or not the following measuring instruments are appropriate for the given situation: a. a track coach uses a watch with a precision of 1 second to time runners in a 50m sprint b. a bathroom scale with a precision of 1 pound to measure a football players weight. Assignment: pg. 17-20 #1-10 4 Measurement LESSON 3: MEASURING DEVICES Units of Measure – Imperial and Metric **Look over and read pg. 21 – 23 Review Handout Class Ex. #1 (pg. 25) a. b. Class Ex. #2 (pg. 25) 63 3 1 3 inch 3 a. Metric: ________, Imperial: 128 inch. 8 128 b.Metric: __________, Imperial: _________ Homework: pg. 26-29 #1-3, 6, 7, 9 5 Measurement LESSON 4: PERIMETER, AREA, SURFACE AREA AND VOLUME Review and define the following: Perimeter: Distance around a closed figure Area: value expressed in units squared which is needed to cover a surface Surface Area: area needed to cover all surfaces of a solid. Volume: amount of space in a solid **Have students review pg. 31 of workbook Give students the formula sheet to look over. Class Example #1: (pg. 33) a. Perimeter is 144 b. Perimeter: need to find circumference of circle first: C 2 r C 2 35 219.8 219.8 + 95 +95 = 409.8 Class Example #3: (pg. 34) a. A long rectangular garden has an area of 48 m squared. If the length is 16m, then find the width of the garden: b. A square driveway has an area of 121 m squared. Find the lengths of its sides. 6 Measurement Class Example#4 (pg. 34) a. V = l x w x h = 6 x 3 x 9 = 162/2= 81 SA = 117cm² (2 triangles + 2 rectangles + 1 rectangle) Class Example #5: a. The volume of a cone is determined to be 95 m cubed. If the height of the cone is 5m, then find the radius to the nearest tenth. Homework: pg. 35-42 #1-16 7 Measurement LESSON 5: SURFACE AREA AND VOLUME OF SPHERES AND OTHER SOLIDS Recall Formula sheet: Need: Volume of a Sphere, Surface area of a cylinder and sphere Class Example #1 (pg. 47) The Shape of the planet Mars is approximately that of a sphere with a diameter of about 6786km. a. Calculate the surface area. SA 4 r 2 1.46 108 b. Calculate the volume. 4 V r3 3 1.6 1011 Class Example #2: (pg. 48) Germain uses a rope to wrap the outer edge of a beach ball exactly once. She then measured the distance the rope wrapped around the ball by stretching it out straight and using a ruler to measure its length. She determined the length to be 88.2cm. What is the volume of the beach ball? 8 Measurement Class Example #4: (pg. 48) The surface area of a sphere is 452.4 mm squared. Find the radius to the nearest mm of the sphere. Class Example #5: (pg. 48) The volume of a basketball is 14 137 cm cubed. Find the radius of the basketball. Homework: pg. 49-52 #1-11 9 Measurement LESSON 6: CONVERSION Read page 53 Look over conversion chart on page 54 Class Example#1: (pg. 55) Use the charts to convert the following: a. 60 in = 5ft (60/12) b. 60ml = 2 US fl. Oz c. 1 lb = ________ grains d. 1 stone = ________ g e. 5 yd = ______ in. f. 2.5L = ________Tsp 10 Measurement g. 2.0573 m = ______ft. _______in Homework: pg. 56-59 #1-11 11 Measurement LESSON 7: CONVERSION METRIC TO METRIC Look over chart on page 61 Class Example#1: (pg. 61) a. 75cm = _______m b. 35g = ________ mg Class Example #2: (pg. 61) a. 12 megametres = _________cm 12 megametres = 12 000 000 m 1 m = 100 cm 12 000 000 x 100 = 1 200 000 000 To convert measurements in area with the chart, multiply the number of places moved on the chart by two to determine the number of decimal places moved in the conversion Prefix Kilo Hecta- Deca- Metre Deci- Centi- Milli 2 2 2 2 2 2 2 Symbol km hm dam m dm cm mm Class Example #3: (pg. 62) a. 12m 2 = _____________mm 2 Move 3 places on the chart 3x2 = 6 place values to the right 12 000 000 b. 0.775km 2 = ____________________cm 2 12 Measurement To convert measurements in volume with the chart, multiply the number of places moved on the chart by three to determine the number of decimal places moved in the conversion Class Example #4: (pg. 63) a. 26m 3 = ____________mm 3 3 places on the chart (9 place values) 26 000 000 000 b. 389 275 cm 3 = ________________hm 3 Other common conversion in the metric system involve units of litres to units of cubes: 1mL = 1 cm 3 1L = 1000cm 3 1L = 0.001m 3 1kL = 1m 3 Class Example #5: a. 85 765cm 3 = __________ L 85765/1000= 85.765L Homework: pg. 66-69 #1-5, 7,8,10-13 13 Measurement LESSON 8: LINEAR SCALE FACTORS AND PERIMETER A linear scale factor describes the enlargement or reduction of length and width of objects as a ratio. A scale factor value greater than 1 describes an enlargement A scale factor value between 0 and 1 describes a reduction Class Example #1: (pg. 73) Jordan increased the length and width of a rectangular 8’’ x 10’’ picture by a scale factor of 5:2 a. What is the linear scale factor value? 2.5 b. Is this an enlargement or reduction? Enlargement c. Calculate the new dimensions of the picture. 20’’ x 25’’ d. Show how the original perimeter and linear scale factor value can be used to calculate the new perimeter. Original perimeter = 36 New perimeter = 36 x 2.5 = 90 e. Verify this by calculating the perimeter using the new dimensions. 14 Measurement Class Example #2 (pg. 73) Kylie from Abstract Renovations designs a plan for a candy store to be renovated. The scale drawing on the plan of the candy store is 1cm: 50cm. a. What are the actual dimensions of the storage room if the scale drawing dimensions are 8cm x 12cm. b. What are the dimensions on the plan if the dimensions of the chocolate section of the store are to be expanded to be 3.5m x 4.75m? Homework: pg. 74-76 #1-11 15 Measurement LESSON 9: LINEAR SCALE FACTORS AND AREA Complete the chart: Original Original Linear New New Area Area Area Scale Dimensions Scale Factor Factor A 3x5 2 2:1 6x10 2 4:1 15cm 60cm B 2x6 2 3:1 6x18 2 9:1 12 cm 108cm C 8x2 2 1:2 4x1 2 1:4 16cm 4cm 2 D 9x6 54cm 1:3 3x2 6 1:9 Class Example #1: (pg. 80) Maggie has scanned an 8’’ x 10’’ photograph to her computer to enlarge and reduce. a. Maggie would like to increase the size by 40%. Determine the linear scale factor and the area scale factor. Scale factor of 1.4 is 7:5 or 1:1.4 Area scale factor is 49:25 or 1:1.96 b. Explain why these scale factors are different. One is the linear scale and the other is the area scale (squared) c. Determine the new dimensions of the photograph. d. Calculate the area the printer must cover by the following two methods. 16 Measurement i) Using the dimensions of the enlargement: ii) Using the original area and the area scale factor value: e. Maggie must also produce a print which will be reduced by 25% . What will the new dimensions and area of the photograph be? Leave 75% of the original. 3:4 8 x 0.75 = 6 10 x 0.75 = 7.5 New Area is 6 x 7.5 = 45 (9:16 = 0.5625 x 80 = 45) Homework: pg. 81 #1-7 17 Measurement LESSON 10: LINEAR SCALE FACTORS, SURFACE ARE AND VOLUME Complete page 85 of workbook Linear Scale Factor is a ratio in the form a:b which describes an enlargement or reduction of 1 dimensional figures. Linear Scale Factor Value is a number which describes how many times to enlarge or reduce a 1-D figure. To calculate the linear scale factor value (new dimension / original dimension) Area Scale Factor is a ratio in the form c:d which describes the area of an enlargement or reduction of a 2-D figure. Area Scale Factor Value is a number which describes how many times to enlarge or reduce the area of a 2-D figure. To calculate the scale factor value use (new area / original area) The area scale factor value = (linear scale factor value) 2 Surface Area scale factor is a ratio in the form c:d which describes the surface area of an enlargement or reduction of a 3-D figure. When c is greater than d, it is an enlargement Surface Area Scale Factor Value is a number which describes how many times to enlarge or reduce the surface area of a 3-D figure. To calculate the area scale factor value use (new area / original area). The area scale factor value = (linear scale factor value) 2 Volume Scale Factor is a ratio in the form e:f which describes the surface area of an enlargement or reduction of a 3-D figure. 18 Measurement Volume Scale Factor Value is a number which describes how many times to enlarge or reduce the surface are of a 3-D figure. To calculate the area scale factor value use (new volume / original volume). The volume scale factor value = (linear scale factor value) 3 Complete the chart on pg. 86 and 87 of the workbook Class Example #2: (pg. 89) Sllab Ltd. Produces beach balls with a diameter of 30cm. To increase the profile of the company in the market place the company hires Jen from Word of Mouth Advertising. She suggests to produce large beach balls with a diameter of 1.5m. a. The surface area and volume of the beach balls with a diameter of 30cm have been calculated below. Calculate the surface area and volume of the beach ball with a diameter of 1.5m to the nearest tenth. SA of 30 cm ball = 2827.4cm 2 V of 30 cm ball = 14 137.2cm 3 SA of 150cm ball = ____________ V of 150 cm ball = _____________ b. Determine the following: i) linear scale factor: 30:150 = 1: 5 ii) Surface Area Scale Factor: 1:25 iii) Volume Scale Factor: 1:125 19 Measurement c. Show how to use the volume scale factor to determine the linear scale factor value. d. Show how to use the volume scale factor value to determine the area scale factor value. e. Sllab. Ltd decides to produce a beach ball with a volume scale factor of 216:64 from the original. Determine the new surface area of the ball to the nearest tenth. 3 216 : 64 6 : 4 3 : 2 = linear scale factor Surface area scale factor = 3: 2 9 : 4 2 9 SAnew 2827.4 6361.7cm 2 4 Homework: pg. 90-92 #1-7 Lesson 11: Quiz Lesson 12: Review Lesson 13: Exam Lesson 14: Project (2-3 days) 20