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Integrating Standards-Based Math and Science into Engaging and Real-World Contexts Leslie A. Texas leslie@leslietexasconsulting.com July 12, 2010 Philadelphia, PA

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KEEPING IN TOUCH Website: http://leslietexasconsulting.com Phone: (502) 253-1844 office (502) 777-5312 cell

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What is the probability? http://www.youtube.com/watch?v=fzKc_LbakuQ

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Table Talk What would be the purpose of sharing this video?

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1. Developing tables, charts and graphs often. 2. Using a scientific calculator. 3. Solving problems other than those in textbook. 1. Problem Solving 2. Reading and Communicating 3. Estimating and Verifying Answers and Solutions 4. Logical Reasoning 5. Using Technology Integrated Content and Process Skills

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Puzzling Problems

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1.Match your puzzle-piece with other similar pieces to form a problem to solve. 2.As a learning group team, select a strategy to solve the problem. 3.Solve the problem as a team then submit a solution to the class. Your team must be able to justify the solution!!! Cooperative Learning Activity

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Math in the Workplace http://www.micron.com/k12/math/index

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Pre-Assessment Exercise Introduce classroom procedures such as cooperative learning, solving word problems, and no “I don’t knows” accepted Hook for new unit Review Exit Slip Possible Uses

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Problem 1 1.Assuming a reaction time of.75 seconds, how fast was car A traveling at the beginning of its skid? The coefficient of friction (f) on the road is.80. The coefficient of friction is given for different circumstances, such as dry pavement, snow floor, or black ice. 2. What was the total stopping distance of car A? 3. How long did it take car B to turn if driver A reacted immediately when car B began its turn?

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1. S = √ 30 x f x d S = √ 30 x.80 x 50 S = √ 1200 S = 34.63 Speed = 35 mph at the start of the skid 2. fps = 35 x 1.467 = 51.345 Total stopping distance =.75 x 51.345 ft + 50 foot skid Total stopping distance = 88.5 ft Car A was about 88–89 feet from point of impact when car B started the left turn. 3. Time = d ÷ v Time = 90 ft ÷ 51.345 Time = 1.75 seconds for car B to begin turning and get hit ANSWER

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Problem 2 Health Services uses a 0.5% solution of calcium gluconate as a 20-minute eye flush when an employee in the manufacturing area accidentally splashes hydrofluoric acid in his or her eyes. The calcium gluconate comes in vials of 10% concentration and can be diluted with sterile saline water. How many milliliters (ml) of 10% calcium gluconate must be mixed with sterile saline water to make a 1L solution of 0.5% calcium gluconate?

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1000 x.005 (0.5% solution) = 5 ml (if full strength) 5 ml.10 (10% concentration) = 50 ml ANSWER

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Problem 3 A plumber needs to run three 2-inch lines around the mechanical room. He must offset the pipe around the air handlers in the corners. The outside line is to be 8 inches from the wall and 5 inches from the corner. The spreads between the lines are to be 9 inches and the angle is 45°. Pieces A and B are 3.75 inches and 7.5 inches respectively. What should be the length of pieces C, D, and E?

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Use Pythagorean Theorem: a² + b² = c² Special case for 45° right triangles: Since a=b, equation becomes 2a² = c² Length C: side a 1 = b 1 = 12 + 2 = 14" 2a² = c² 2 x 14² = C² 2 x 19 6 = C² 392 = C² √ 392 = 19.8" = Length C ANSWER

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Length D: side a 2 = 9 + 2 + 12 + 2 - 3.75 (piece A) = 21.25"" 2a² = D² 2 x 21.25² = D² 903 = D² √ 903.125 = 30.05" = Length D Length E: side a 3 = 9 + 2 + 9 + 2 + 12 + 2 - 7.5 (piece B) = 28.5" 2a² = E² 2 x 28.5² = E² 1624.5 = E² √ 1624.5 = 40.31" = Side E ANSWER

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Problem 4 The Ada County Highway District Pavement Management Technician needs to know how many tons of asphalt will be needed on a section of road. The section of road measures 5,280 feet (1 mile) in length and 26 feet wide. The asphalt needs to be 3 inches in depth. Asphalt weighs 144 tons per 2,000 ft 3.

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ANSWER 3 inches · (1 foot/12") =.25 ft 144 tons/2000 ft^3 =.072 tons of asphalt per cubic foot length · width · depth · weight per f^t3 = tons of asphalt 5,280 ft x 26 ft x.25 ft x.072 tons = 2,471 tons of asphalt

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The government requires that companies analyze and report the amount of ethyl Lactate present in waste sent to a waste disposal company. The ethyl lactate sample area is 6,821,193 counts. An ethyl lactate standard has a "concentration" of 10.16 wt% and a peak area of 10,617,862 counts. What is the concentration (amount) of ethyl lactate in a solvent sample from gas chromatography data? Problem 5

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Since the relationship is linear, use a ratio: Concentrate of standard (X1) is to counts of standard (c1) as concentrate of sample (X2) is to counts of sample (c2) ANSWER Concentration of sample = 15.81 wt %

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Problem 6 A horse weighs 1,200 pounds. He is sick and has been diagnosed with a certain disease. This disease is treated with Drug X. Instructions are to give 3 mg/kg orally twice a day for 5 days. The medicine is provided in 200 mg tablets. How many tablets need to be dispensed each day? How many tablets need to be dispensed for the 5 days? 2.2 pounds = 1 kg

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ANSWER 1,200 lbs/2.2 lbs/kg= 545 kgs (weight of horse) 545 kgs x 3 mg/kg = 1,635 mg 1,635 mg x 2 times/day = 3,270 mg per day (3,270 mg/day) /(200 mg/pill) = 16.35 or 16 pills per day 16.35 pills/day x 5 days = 81.75 pills to be dispensed *Open-ended discussion: What would you do about the partial pill?

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Problem 7 John and Joan are planning a new home. They want as much window area as possible. The local energy code permits a maximum window area of 17% of the house floor area. The windows John and Joan will use are each 3 ft. x 5 ft. and the floor area of the house is 1,720 square feet. How many windows can they put into their new house?

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ANSWER 17% of 1,720 sq. ft. = 292.4 sq. ft. Each window is 3' x 5' or 15 sq. ft. 292.4 15 = 19.49 Therefore, John and Joan can have at most 19 windows.

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Problem 8 An electrician has to pour a concrete signal base 4' in diameter, 14' deep with two 6" conduits coming up from the bottom and centered in the base. How much concrete does he need to order? Concrete is ordered by the cubic yard.

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ANSWER Subtract the area in cubic feet of the two conduits from the area in cubic feet of the base and translate to cubic yards. diameter of base = 4 ftdiameter of conduit =.5 ft Formula: (area of base ft 3 ) - 2 (area of conduit ft 3 ) yd 3 = concrete needed (p r 2 · h) - 2 ( p r 2 · h ) yd 3 = cubic yards (3.14 x 2 2 x 14) - 2 ( 3.14 x 0.25 2 x 14 ) 3 ft x 3 ft x 3 ft = cubic yards 175.84 ft 3 - 5.495 ft 3 27 ft 3 = 6.3 cubic yards

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Problem 9 Cattle graze on the Boise National Forest. To determine how many cattle graze on a pasture, it is necessary to determine how much feed is available and the quantity consumed by cattle. The pasture produces 1200 pounds of forage per acre. Cattle are only allowed to use 40% of this forage. The pasture contains 1,500 acres suitable for grazing. If a cow and her calf eat 33 pounds of food a day, how long can 500 pairs of cows and calves stay in the pasture?

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ANSWER (1200 lbs. forage/acre)(40%) = 480 lbs. usable feed/acre (480 lbs./acre)(1500 acres) = 720,000 lbs. usable feed 720,000 lbs. feed 33 lbs. cow-calf days = 21,818 cow-calf days 21.818 cow-calf days 500 cow-calf pairs = 43.6 days Rounded to the lowest whole day = 43 days

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Problem 10 A 220 pound male patient needs an intravenous infusion of dopamine. Dosage range of 2 – 20 mg/kg/minute is titrated. If you begin at a rate of 5 mg/kg/minute with a concentration of 3200mg/CC (mL), what is the rate of infusion at cc/hour for this patient?

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220 lbs ÷ 2.2 lbs = x ÷ 1 2.2 x = 220 x = 100 kg 5 mg / kg / min 5 mg x 100 kg x 60 minutes = 30,000 mg / hour Concentration is 3,200 mg / cc 3200 mg ÷ 30,000 mg = 1 cc ÷ x 3200 x = 30,000 x = 30,000 / 3200 x = 9.375 or ~9 cc/hr ANSWER

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1.Read the entire problem. 2.Cover everything but the last sentence. Read and determine what is being asked. Write the question on your paper. 3.Cover everything but the first sentence. Read and determine if there is any relevant information. Record on your paper. 4.Repeat step three for the remaining sentences. Problem-Solving Process

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5. Translate any verbal statements into mathematical statements. 6. Estimate what might be a logical answer or range of answers. 7. Solve and state the answer with appropriate units. 8. Check your answer for reasonableness. NOTE: If questions, identify which step is confusing and why. Problem-Solving Process

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Resources www.bced.gov.bc.ca/careers/aa/lessons/math.htm Lessons developed by teachers of Applied Mathematics in British Columbia. Firefighter, Lifeguard, Electrical Engineer, Event Planner, Vulcanologist, Roller Coaster Designer, Mechanical Drafter Designer, House Painter, Market Analyst, Computer Game Designer, Audiologist, Sportscaster, Animal Health Technologist, Golf Pro, Aerospace Engineer, and Piano Repair Technician

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Resources http://math.dartmouth.edu/~mqed/K-12eBookshelf.html The Little Bookshelf in the Big Woods-K-12 resources from Dartmouth that are also part of the Math Across the Curriculum project

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Resources http://www.ams.org/mathmoments The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Downloadable pdf resources

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Resources http://www.siam.org/careers/matters.php Matters, Apply It! (Topics include the math behind the following: CD’s and anti-skip technology, digital animation, using DNA, digital face recognition, stopping and preventing fires, cardiology and heart attacks, speeding up the Internet, and supercomputing)

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Resources http://voc.ed.psu.edu/projects/Institute/2004/sampleUnits_2004.html Sample CTE units (that incorporate math/science) developed by teachers in Pennsylvania http://www.iowa.gov/educate/index.php?option=com_content&task=view&id =1132&Itemid=1427 Math/Science in CTE Iowa

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