Download Math-in-CTE Lesson Plan Template

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
(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.
THE "7 ELEMENTS"
2. Assess students’ math
awareness as it relates to the
CTE lesson.
Sample dialog for teacher:
Sample problems:
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
values
between those found on a
For example:
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
Number of Employees
90
80
1995 ≈ 70 physicians employed
70
60
Physicians
50
Nurses
40
Aides
30
20
10
0
1980
1990
2000
≈ means “is approximately equal
to”
Year
Estimate how many physicians were
employed in 1995.
If this chart shows activity level
throughout an average day, how much
Teens at 1pm ≈ 35%
energy did teens expend at 1pm?
Energy Expended in
PErcent
Daily Energy Expenditures
100
80
60
40
20
0
Infants
Teens
Elderly
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
or graph.
Do you know what the name for
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
40
Sue
20
It would depend on the extent of
brain damage caused by the
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.
Basal Metabolism (calories/sq meter/hr)
Normal Basal Metabolism for Men and Women
60
55
50
Males
45
Female
40
35
a. What is the unit of measurement
for the basal metabolic rate
shown in the graph? (basal
metabolism - calories/square
meter/hour - calories/m2/hr)
30
0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age (in years)
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
basal metabolic rate of a fortymetabolic rate of a forty-seven
seven year old female patient?
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 twelveyear 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.

A suggested calorie-intake guide for
men at various ages is shown below.
George I. Buprofen weighs 147
pounds and is 45 years old. What
calorie allowance would you suggest
he use?


Ideal
weight
in
pounds
90
101
112
123
130
134
145
156
167
Daily calorie allowance for
men
25
45
65
years
years
years
1775
1665
1405
1925
1815
1505
2075
1965
1605
2225
2065
1755
2325
2215
1805
2375
2290
1855
2525
2365
2005
2625
2465
2055
2775
2615
2155




6
Find the closest ideal weight
in pounds to George’s
weight of 147 lbs.
(145)
Follow horizontally across to
the 45-year-old column.
(2365)
The value below it would
represent a 156 pound, 45
year old male
(2465)
Estimate the difference of
the two caloric values, 2525
and 2375.
(approx. 100 calories)
Estimate the difference of
the two weights, 145 and
156.
(10 lbs.)
Divide the calories by the
pounds. (100/10 = 10) This
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.
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?
b. Estimate how many days a
new box of diapers will last?
c. Should an estimate like this
be expected to be too large
or too small? Explain.
1. a. ≈ 20
b. 2-3 days
c. too large, babies have
accidents
2. You currently earn about $60 a
week from an after-school job. The
management has announced a
4.5% raise for all employees.
( $60 · 0.05 )
a. Estimate how much increase 2. a. $3.00
you can expect in each
week’s pay.
b. About how much will this
b. ≈ $150. ($3.00 · 50 weeks)
increase your annual pay?
(Hours will be the same all
year).
c. Use your calculator to obtain
an exact answer to the
above questions.
(Round
your answer to the nearest
dollar).
7
c. $140.
($60 · 0.045 * 52)
3. Ms. Savage, a lawyer for the local
hospital, charges a flat fee plus an
hourly rate for consultations. The
graph below shows the total
charges given the number of hours
of consultation. Ms. Savage
consulted on three separate days
with Mr. Beast, Administrator, on a
potential law suit by a patient.
≈ $1375
Find the amount for
each
day
of
consultation,
then add the fees.
7.5 hr ≈ $650,
5.5 hr ≈ $475
3 hr ≈ $250,
OR … add the total hours.
16 hours is not on the chart, but 8
hours is. Double the value for 8
hours… ≈ $680 doubled = $1360.
Monday – 7.5 hours
Wednesday – 3 hours
Thursday – 5.5 hours
From the graph, estimate the total
consulting cost Ms. Savage will bill the
hospital.
Total Fee ($)
3.
1000
900
800
700
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
elementary students would weigh
about ___________.
An average adult woman could weigh
about 150 pounds, while an adult
male weighs 200 pounds. Since the
problem does not designate male or
female, you could estimate the
average weight to be ________.
Safe
(4 · 50 lbs. = 200 lbs.)
175 lbs.
700 lbs. Unsafe
(4 · 175lbs. = 700)

Four adults would weigh about
____________.

Using the female and male reasoning
from above, an average college
student might weigh 150 pounds.
Twelve college students would weigh
about ___________.

200 lbs.
Nine high school students would be of
similar weights to the college students
and would also be ____________.
9
1800 lbs. Unsafe
(150 lbs · 12= 1800 lbs.)
1350 lbs. Unsafe
(150 · 9 = 1350 lbs.)
6. Students demonstrate their
understanding.
The
worksheets
contain
5
problems. The first four contain
multiple questions ranging from
basic to higher level. The fifth
problem is higher level.
See attached worksheets and
answer key.
7. Formal assessment.
Answers:
1. Your prescription calls for two
tablets each day. Sunday morning,
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.
1.
b. Exactly how many full days
of medication do you have
left?
2.
Susie owns her own craft shop
2.
and attends a national craft show to
purchase unique items for her shop. At a
recent show in Florida she ordered items
in the following categories: kitchen crafts
$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. Chocolate candy is on sale at 4
pounds for $5.00 dollars. The chocolate
candy you chose weighs 2 3/4 pounds.
a. Estimate what the chocolate
will cost.
b. Use your calculator to find
out how much the cashier
will charge you?
10
3.
a. Yes
b. 23 ÷2 = 11 1/2 days
a. $22,800
(5400+ 6200 + 3900 +
7300)
b. No
a. $3.75 Round 2 ¾ lbs to
3 lbs.
4 lbs = 3 lbs
$5
X
X= $3.75
b. $ 3.44
2 3/4 lbs = 2.75 lbs
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
approximately 85, 80, 80, 95 or
340 total.
60
Jane
50
Rita
40
30
20
10
us
ic
M
nc
e
Sc
ie
ea
lth
H
at
h
0
M
Percents
70
11
Rita’s scores are approximately
75, 85, 90, 75 or 325 total.
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