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Math-in-CTE Lesson Plan Template Lesson Title: Calories: Burn ‘em up! Lesson # H06 Occupational Area: Health CTE Concept(s): Digestive System Math Concepts: Estimation, interpolation, graphs, charts Lesson Objective: Student will demonstrate a working knowledge of: Estimation from a graph Interpolation from a chart and/or graph Rounding Relate data to health care Use data to answer questions and draw conclusions Supplies Needed: Copies of student worksheets, pencils, paper Link to accompanying materials: Health Occupation H06 Downloads TEACHER NOTES THE "7 ELEMENTS" (and answer key) 1. Introduce the CTE lesson. Health Concept(s): Understanding of basal metabolic The teacher will explain the following: rate as it relates to gender, age We need food for energy daily. The and activity amount of food we need can depend on gender, age (growth periods) and activity. We can measure this with the basal Math Concept(s): metabolic rate (BMR), which is the rate Estimation from a graph food is catabolized (broken down) under Interpolation/Extrapolation from a basal conditions (when the individual is chart and/or graph resting, but awake, is not digesting food, Rounding numbers and is not adjusting to a cold external environment). We can also define BMR Teacher Attachment: See as the number of calories of heat that detailed explanation of health must be produced per hour by concept catabolism, just to keep the body alive, awake, and comfortably warm. This is important to maintaining homeostasis. We will be using estimation skills to interpolate the BMR of normal men and women from a graph. This information is used in weight management programs. 2. Assess students’ math Sample dialog for teacher: awareness as it relates to the Sample problems: CTE lesson. If your gas gauge is reading empty The teacher will ask the students can you tell how far you are able to the following questions. 1 We use estimation skills everyday in drive before you will need to call our lives. Can you cite examples of for help? how you use estimation in your life? If you are in the lunch line and you How did you solve these problems? want pizza, breadsticks and a small salad, how do you know if Did you have to round numbers? you have enough money to cover all of these items? If you are in a restaurant and your bill is $54.32, you may want to leave a 10% tip. You would probably move the decimal point one place to the left, giving you a tip of $5.432. Many people would round down and leave a tip of $5.00. Have students solve their own problems or the above problems. Did they use rounding? Use this opportunity to review the rules of rounding. Rules of rounding: Find the place value to which you are rounding. Look at the digit one place to the right. If it is equal to or greater than 5 round up, less than 5 round down. These examples show the value of estimation. By mastering this skill you can avoid potential disaster or embarrassment in your lives. In your math class or in the newspaper have you ever had to estimate a value Interpolation is defined as: from a chart or graph? A procedure for estimating For example: values between those found on a table or a process to find a value on a graph or chart that is not identified on a grid line. 2 Health Care Employment 100 90 Number of Employees 80 1995 ≈ 70 physicians employed 70 60 Physicians 50 Nurses 40 Aides 30 20 10 0 1980 1990 2000 Year ≈ means “is approximately equal to” Estimate how many physicians were employed in 1995. If this chart shows activity level throughout an average day, how much energy did teens expend at 1pm? Teens at 1pm ≈ 35% Daily Energy Expenditures Energy Expended in 100 80 Infants PErcent 60 Teens 40 Elderly 20 0 9am 12N 3pm 9pm Have you ever predicted future Extrapolation is defined as: results based on the data given on a The ability to predict values chart? beyond those given on a chart Do you know what the name for or graph. this process of future prediction is? Does it always work? What are some of its limitations? 3 Exercise-One Mile Walk Sue ≈ 15 min. Time in minutes 80 60 Jane It would depend on the extent of 40 Sue brain damage caused by the 20 stroke. 0 June July Aug. Sept. Jan and Sue are stroke rehab patients. How long do you think it will take Sue to walk one mile at the end of October? Will they continue to improve beyond October and November? 3. Work through the math example embedded in the CTE lesson. As men and women age, the amount of energy used by the body when at rest, called the Basal Metabolic Rate, decreases. The graph below shows the normal rates. Normal Basal Metabolism for Men and Women 60 Basal Metabolism (calories/sq meter/hr) 55 50 45 Males Female 40 35 a. What is the unit of measurement 30 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 for the basal metabolic rate Age (in years) shown in the graph? (basal metabolism - calories/square meter/hour - calories/m2/hr) b. What is the unit of measurement for the basal metabolic rate shown b. How are the values for men and in the graph? women distinguished in the graph? c. How are the values for men and (two separate lines) women distinguished in the graph? 4 d. What would be the normal basal c. What would be the normal metabolic rate of a forty-seven basal metabolic rate of a forty- year old female patient? seven year old female patient? We need to interpolate the graph, which means to “read between the lines” Find the approximate place for 47 along the horizontal axis, which is the age of the patient. Run a vertical line upwards until it intersects with the female curve and trace horizontally to the left to read the approximate value on the vertical axis. (35 calories/m2/hr) e. A lab result indicated that a twelve- year old male patient has a rate of d. A lab result indicated that a 12 70 calories/m2/hr. A rate of twice year old male patient has a rate the normal rate is considered of 70 calories/m2/hr. A rate of hyperactivity. Would this patient twice the normal rate is be considered hyperactive? considered hyperactivity. Would this patient be considered hyperactive? Find the approximate place for 12 along the horizontal axis, which is the age of the patient. Run a vertical line upwards until it intersects with the male curve and trace horizontally to the left to read the approximate value on the vertical axis. (43 calories/m2/hr. How does twice this number compare to 70? Twice 43 is greater than 70 so our patient would not be considered hyperactive.) Optional: If students are interested in calculating their own BMR see Student Activity Sheet. Be aware the units are different than those on chart. 5 4. Work through related, contextual Teacher solution: math-in-CTE examples. Find the closest ideal weight A suggested calorie-intake guide for in pounds to George’s men at various ages is shown below. weight of 147 lbs. George I. Buprofen weighs 147 (145) pounds and is 45 years old. What Follow horizontally across to calorie allowance would you suggest the 45-year-old column. he use? (2365) The value below it would represent a 156 pound, 45 Ideal Daily calorie allowance for year old male weight men (2465) in 25 45 65 Estimate the difference of pounds years years years the two caloric values, 2525 90 1775 1665 1405 and 2375. 101 1925 1815 1505 (approx. 100 calories) 112 2075 1965 1605 Estimate the difference of 123 2225 2065 1755 the two weights, 145 and 130 2325 2215 1805 156. 134 2375 2290 1855 (10 lbs.) 145 2525 2365 2005 Divide the calories by the 156 2625 2465 2055 pounds. (100/10 = 10) This 167 2775 2615 2155 represents the number of additional calories needed per gain of one pound of body weight. These steps have allowed us to interpolate data from a chart versus the graph we used in the last problem. Since George is two pounds over the listed 145 pounds, we would need to add 20 calories to the caloric value of 2365. We should suggest that Robert takes in (2385) calories per day to maintain his body weight. 6 5. Work through traditional math ANSWERS: examples. 1. Jeff and Julie are the parents of newborn twins. They are trying to determine what the weekly need for diapers will be. On Monday they used 18 diapers, Tuesday 20, Wednesday 22, Thursday 16, Friday 20, Saturday 18, and Sunday 22. Disposable diapers come in a box 48. a. About how many diapers did they use each day? 1. a. ≈ 20 b. Estimate how many days a b. 2-3 days new box of diapers will last? c. Should an estimate like this c. too large, babies have be expected to be too large accidents or too small? Explain. 2. You currently earn about $60 a week from an after-school job. The management has announced a 4.5% raise for all employees. a. Estimate how much increase 2. a. $3.00 ( $60 · 0.05 ) you can expect in each week’s pay. b. About how much will this increase your annual pay? b. ≈ $150. ($3.00 · 50 weeks) (Hours will be the same all year). c. Use your calculator to obtain an exact answer to the c. $140. ($60 · 0.045 * 52) above questions. (Round your answer to the nearest dollar). 7 3. Ms. Savage, a lawyer for the local 3. hospital, charges a flat fee plus an hourly rate for consultations. The ≈ $1375 Find the amount for graph below shows the total each day of consultation, charges given the number of hours then add the fees. of consultation. Ms. Savage consulted on three separate days 7.5 hr ≈ $650, 3 hr ≈ $250, with Mr. Beast, Administrator, on a 5.5 hr ≈ $475 potential law suit by a patient. OR … add the total hours. Monday – 7.5 hours 16 hours is not on the chart, but 8 hours is. Double the value for 8 Wednesday – 3 hours hours… ≈ $680 doubled = $1360. Thursday – 5.5 hours From the graph, estimate the total consulting cost Ms. Savage will bill the hospital. 1000 900 800 700 Total Fee ($) 600 500 400 300 200 100 0 1 2 3 4 5 6 7 8 9 1011 Hours 8 4. You’ve worked so hard, you’ve earned a vacation. We are off to Cedar Point! You will solve a problem that requires estimation without interpolation. The weight capacity of the Blaster is posted at 500 pounds. Out of the following, which would probably be a safe load? Give justification for your answers. 4 elementary students 4 adults 12 college students 9 high school students An average weight of an elementary school child is about 50 pounds. So 4 200 lbs. Safe elementary students would weigh about ___________. (4 · 50 lbs. = 200 lbs.) An average adult woman could weigh about 150 pounds, while an adult 175 lbs. male weighs 200 pounds. Since the problem does not designate male or female, you could estimate the average weight to be ________. 700 lbs. Unsafe Four adults would weigh about (4 · 175lbs. = 700) ____________. 1800 lbs. Unsafe Using the female and male reasoning from above, an average college (150 lbs · 12= 1800 lbs.) student might weigh 150 pounds. Twelve college students would weigh about ___________. 1350 lbs. Unsafe Nine high school students would be of similar weights to the college students (150 · 9 = 1350 lbs.) and would also be ____________. 9 6. Students demonstrate their The worksheets contain 5 understanding. problems. The first four contain multiple questions ranging from See attached worksheets and basic to higher level. The fifth answer key. problem is higher level. 7. Formal assessment. Answers: 1. Your prescription calls for two 1. a. Yes tablets each day. Sunday morning, b. 23 ÷2 = 11 1/2 days before taking any tablets, you count the remaining tablets. You find that there are 23 tablets left. a. Estimate to find if you have enough medication left for the rest of the week. b. Exactly how many full days of medication do you have left? 2. Susie owns her own craft shop and attends a national craft show to 2. a. $22,800 purchase unique items for her shop. At a (5400+ 6200 + 3900 + recent show in Florida she ordered items 7300) in the following categories: kitchen crafts b. No $5425; yard ornaments $6230; general household items $3940; and holiday items $7260. Her total budget is $25000. a. Estimate the total cost of the orders to the nearest $100 b. Have these orders exceeded her budget for the year? 3. a. $3.75 Round 2 ¾ lbs to 3. Chocolate candy is on sale at 4 3 lbs. pounds for $5.00 dollars. The chocolate 4 lbs = 3 lbs candy you chose weighs 2 3/4 pounds. $5 X a. Estimate what the chocolate X= $3.75 will cost. b. Use your calculator to find b. $ 3.44 out how much the cashier will charge you? 2 3/4 lbs = 2.75 lbs 10 4lbs = 2.75 lbs $5.00 X (the calculator gives an answer of $3.4375 which would round UP to $3.44 because it involves money) 4. The graph below shows the first quarter test scores of Rita and Jane in the four classes they have together. Who has the higher total score? 100 90 4. Answer: Jane. 80 Jane’s scores are 70 approximately 85, 80, 80, 95 or 60 340 total. Percents Jane 50 Rita Rita’s scores are approximately 75, 85, 90, 75 or 325 total. 40 30 20 10 0 h lth e ic at nc us ea M ie M H Sc 11 References The Dawn Report (June 2003). Office of Applied Studies, Substance Abuse and Mental Health Services Administration (SAMHSA). MI CLIMB: Clarifying language in Michigan benchmarks, (2002). Lansing, MI : Michigan Department of Education. Thibodeau, G. A. & Patton, K. T. (1997). The human body in health and disease (2nd ed.). Carlsbad, CA: Mobsy Inc. Williams, S.R. (1995). Basic nutrition and diet therapy. (10th ed.) Carlsbad, CA: Mobsy Inc. 12