One class period
The study of projectile motion is called
ballistics. The equation h = -16t2 + vt + s is
used to model the path of a projectile. In this equation, h
represents the height of the object in feet, t represents
the time in seconds, v represents the initial velocity
in feet per second, and s represents the initial height
of the object. In this lesson, students will explore projectile
motion and make predictions regarding the path of a projectile,
such as firecrackers.
:
Algebra Two (Quadratic Functions, Coordinate Graphing)
The learner will:
• Model projectile motion algebraically and graphically.
• Make predictions based on the quadratic algebraic model.
National:
Principles and Standards for School Mathematics
http://Standards.nctm.org/document
• Represent and analyze mathematical situations and structures
using algebraic symbols.
• Use mathematical models to represent and understand quantitative
relationships.
• Formulate questions that can be addressed with data and
collect, organize, and display relevant data to answer them.
• Select and use appropriate statistical methods to analyze
data.
• Develop and evaluate inferences and predictions that
are based on data.
State:
Louisiana Mathematics Framework Bulletin
http://www.lcet.doe.state.la.us/doe/assessment/standards/MATH.pdf
In problem-solving investigations students demonstrate an understanding
of concepts and processes that allow them to analyze, represent,
and describe relationships among variable quantities and to
apply algebraic methods to real-world situations.
A-1-H: Demonstrating the ability to
translate real-world situations (e.g., distance versus time
relationships, population growth, growth functions for diseases,
growth of minimum wage, auto insurance tables) into algebraic
expressions, equations, and inequalities and vice versa.
A-3-H: Using tables and graphs as tools to interpret
algebraic expressions, equations, and inequalities In problem-solving
investigations, students discover trends, formulate conjectures
regarding cause-and-effect relationships, and demonstrate critical
thinking skills in order to make informed decisions.
D-1-H: Designing and conducting statistical experiments
that involve the collection, representation, and analysis of
data in various forms (Analysis should reflect an understanding
of factors such as: sampling, bias, accuracy, and reasonableness
of data.);
D-2-H: Recognizing data that relate two variables as
linear, exponential, or otherwise in nature (e.g., match a data
set, linear or non-linear, to a graph and vice versa).
The Power of Algebra Video Program Eight: Factoring
II
Per Student:
• Grid Paper
• Graphing Calculator
Students should be familiar with quadratic functions and graphing
calculator keystrokes.
CUE video to the opening.
1. a. Prepare students for viewing the Power of
Algebra (PoA) segments by asking, “Why do we use
formulas?”
Open class discussion to establish operational definitions of:
constant, variables, factors, and a quadratic equation. Ask
them to listen while watching for terms that are introduced
and appear to be related to the challenge that opens the show.
b. Show students the opening of Power of Algebra
Factoring II. Begin with
the animation of Homes and Watson at 00:00 and show through.2:50
with Watson looking out the window following Sherlock’s
words “All I can say is it was a common mistake.”
PAUSE TAPE.
2. a. Ask students for some terms that were introduced
and to draw from other classes to share an understanding of
those words. They should respond with acceleration and velocity.
Direct the discussion to have students reveal careers and fields
of research that are associated with these and related terms.
b. Before showing the next segment of the video ask students
to note how algebra is related to the pilot’s work. FORWARD
PoA to the “People and Numbers” segment that opens
with Capt. Bob Coffman at 6:37 and run through 7:59 when Capt.
Coffman ends with “standard algebra equations.” PAUSE
TAPE. What formula does Capt. Coffman refer to during his
presentation?
1. Arrange students in small groups (2-3 students).
2. Provide students with a copy of the problem scenario.
Discuss what each value in the problem scenario represents.
3. Have each group write the appropriate quadratic equation
that represents this scenario. Check each group’s equation.
4. Build a properly labeled table of values for this
scenario. Make sure the table has at least 12 values.
5. Draw a graph based on the table. Make sure each axis
is labeled and scaled. What is the shape of the graph?
6. Identify the maximum point on the graph. What does
this represent?
7. What are the zeros of the graph? What do these values
represent?
8. Using the STAT function on the graphing calculator,
enter the table values in Lists 1 and 2.
9. Draw a scatter plot of the values in the lists. How
does the scatter plot compare to the graph?
10. Compute the appropriate regression equation for the
scatter plot? How does this equation compare to the initial
equation?
11. Using the CALC function, calculate the maximum
and zeros of the graph. How do these values compare with the
answers in numbers 3 and 4?
12. Complete the activity sheet based on your findings.
1. Using factoring and the quadratic formula, find the
zeros of the function. How do these results compare with earlier
results?
2. What limitations exist in this problem? Cite specific
examples.
3. FORWARD TAPE. PLAY the conclusion to the PoA program
beginning at 10:55 with the clock showing 8 through the END
at 14:40.
Social Studies/World History: Discuss the major events
where fireworks displays are part of the celebration. What is
the historical basis for the celebration? Why do fireworks?
Have students investigate the development of fireworks and the
industry. Facilitate student discovery of the risks involved
with the use of fireworks by individuals and by professionals.
Social Studies/Current Events: Review the current mission
status and planned launches for the Space Shuttle program.
English/Language Arts: Students may write about their
participation in a community celebration, sporting event, family
vacation or other function where fireworks were used as a component
of the festivities and describe the effect viewing the display
had on them, their family and/or friends.
• Invite a representative of the Parks and Recreation Division
or whatever agency is responsible for any community fireworks
displays to speak to the class either at school or during a
field trip.
• Ask a critical care health worker, Emergency Medical
Technician or firefighter to discuss the problems of unsupervised
use play with fireworks.
Student handout: Celebrating the Fourth
HTML PDF
(Answers HTML PDF )
