Math in CTE Lesson Plan Template - Download as DOC by rottentees

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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

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                                                             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

								
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