Integrating Standards-Based Math and Science
into Engaging and Real-World Contexts
Leslie A. Texas
leslie@leslietexasconsulting.com
July 12, 2010
Philadelphia, PA
KEEPING IN TOUCH
Website:
http://leslietexasconsulting.com
Phone:
(502) 253-1844 office
(502) 777-5312 cell
What is the probability?
http://www.youtube.com/watch?v=fzKc_LbakuQ
Table Talk
What would be the purpose of sharing this video?
Integrated Content and Process Skills
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
Puzzling Problems
Cooperative Learning Activity
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!!!
Math in the Workplace
http://www.micron.com/k12/math/index
Possible Uses
•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
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?
ANSWER
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
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?
ANSWER
1000 x .005 (0.5% solution) = 5 ml (if full strength)
5 ml
.10 (10% concentration) = 50 ml
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?
ANSWER
Use Pythagorean Theorem: a² + b² = c²
Special case for 45° right triangles:
Since a=b, equation becomes 2a² = c²
Length C:
side a1 = b1 = 12 + 2 = 14"
2a² = c²
2 x 14² = C²
2 x 196 = C²
392 = C²
√ 392 = 19.8" = Length C
ANSWER
Length D:
side a2 = 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 a3 = 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
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 ft3.
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
Problem 5
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?
ANSWER
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)
Concentration of sample
= 15.81 wt %
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?
2.2 pounds = 1 kg
How many tablets need to be
dispensed for the 5 days?
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?
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?
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.
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.
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 ft
diameter of conduit = .5 ft
Formula: (area of base ft3) - 2 (area of conduit ft3)
yd3 = concrete needed
(p r2 · h) - 2 ( p r2 · h )
yd3 = cubic yards
(3.14 x 22 x 14) - 2 ( 3.14 x 0.252 x 14 )
3 ft x 3 ft x 3 ft = cubic yards
175.84 ft3 - 5.495 ft3
27 ft3 = 6.3 cubic yards
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?
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
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?
ANSWER
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
Problem-Solving Process
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
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.
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
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
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
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)
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