1
OVERVIEW
I.
CONTENT: (Why is this unit important? What are the essential concepts in this unit?)
II.
PROCESS: (How are the thinking skills developed?)
III.
PRODUCT: (What will kids do/know as a result of this unit?)
Unit Overview: Alignment with
National / State / District Pupil Performance Standards
Overarching Benchmarks / Standards / Goals for COMPLETE unit of study:
Benchmark 1:
Standard A:
Standard B:
Benchmark 2:
Standard A:
Standard B:
Benchmark 3:
Standard A:
Standard B:
Benchmark 4:
Standard A:
Standard B:
Go to www.rogertaylor.com to download the complete curriculum writing template; Look under Resources
for this template and for your state’s grade-by-grade content standards
2
OVERVIEW
I.
CONTENT:
This lesson presents quadratic equations and their graphs. Students will learn to represent quadratic
relationships with tables, equations and graphs and to relate changes in equations to transformations of the
corresponding graphs.
Students will recognize that problem situations can be modeled by quadratic equations and graphs, and how it
all fits into the scheme of our world.
II.
PROCESS:
Students will investigate a variety of situations modeled by equations. Participate in hands on activities in
groups and independently that involve calculating maximum and minimum values, graphing, using a graphing
calculator, making observations and having class discussions. These activities will develop critical and
creative thinking skills, problem solving skills, interpersonal skills and research skills.
III.
PRODUCT:
Students will attain techniques to solve and model quadratic equations. Understand how math and science are
tied together. Use tables of values to sketch a parabola, and use algebra to find the coordinates of the points
where a parabola crosses the axis. Make the connections to economics, language arts, sports and history
integration with this unit.
Unit Overview: Alignment with
National / State / District Pupil Performance Standards
Benchmark 1: #4.3.12B: Students will be able to explain how price, supply and demand of a product
relate to a parabola.
Benchmark 2: #4.3.12C: Students will be able to observe reflections of a quadratic function and graph
quadratic functions.
Benchmark 3: #4.3.12C: Students will be able to explore the equation of a Parabola.
Benchmark 4: #6.6B2, 6.6E1, 4.3.12B: Students will be able to examine two maps that illustrate the
tendency for people in the United States to settle near the coasts. They will research some
environmental impacts on coastal ecosystems and create a table.
Benchmark 5: #6.5.A.3, 4.4.4.A.2: Students will be able to identify the various measurements used to
analyze an economy, and describe the four phases of the business cycle.
Benchmark 6: # 4.3.12B: Students will be able to determine the difference and similarities of a
parabola and a catenary.
Benchmark 7: #4.3.12B: Students will be able to understand the concept of the vertex
(Maximum/Minimum).
Benchmark 8: # 4.3C, 5.7B: Students will be able to investigate the importance of electricity and
calculate the kWh of usage and graph data.
Benchmark 9: # 4.3.12B: Students will be able to design a house of worship using parabolic functions.
Benchmark 10: #4.3.12B: Students will be able to discover math in nature.
Benchmark 11: #4.3.12D: Students will be able to factor trinomials and sketch the graph of a
parabola.
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Benchmark 12: #4.5.3C: Students will be able to recognize that mathematics is used in a variety of
contexts outside of mathematics.
Benchmark 13: #4.1.8A: Students will be able to calculate percent increase and decrease.
Benchmark 14: #4.3.8C: Students will be able to recognize that many real life situations can be
modeled with a quadratic equation.
Benchmark 15: #4.3.12C: Students will be able to create and solve quadratic equations in two
dimensions of projectile motion.
Benchmark 16: #4.3.12B: Students will be able to graph a system of linear equations.
Benchmark 17: #4.3.12B: Students will be able to solve quadratic equations and functions as it relates
to business (word problems).
4
PRODUCTS
INDEPENDENT RESEARCH PROJECTS
FOR GIFTED AND TALENTED STUDENTS
State each research project with an investigative focus and a "hands–on"
product to show research outcome.
(If writing curriculum for inclusion, design one I-Search project for Gifted and
Talented learners and a concrete operational project for special learners or
Students on IEPs.)
1.
PARADOXES:
Common notion not necessarily true in fact.
Self-contradictory statement or observation.
2.
ATTRIBUTES:
Inherent properties.
Conventional symbols or identities.
Ascribing qualities
3.
ANALOGIES:
Situations of likeness.
Similarities between things.
Comparing one thing to another.
4.
DISCREPANCIES:
Gaps of limitations in knowledge.
Missing links in information.
What is not known.
5.
PROVOCATIVE QUESTIONS:
Inquiry to bring forth meaning.
Incite knowledge exploration.
Summons to discovering new knowledge.
6.
EXAMPLES OF CHANGE:
Demonstrate the dynamics of things.
Provide opportunities for making alterations, modifications, or
substitutions.
7-18 will be found in the writing template as per page 2.
5
A Dance/A Letter/ A
Lesson
Advertisement
Animated Movie
Annotated
Bibliography
Art Gallery
Block Picture Story
Bulletin Board
Bumper Sticker
Chart
Choral Reading
Clay Sculpture
Code
Collage
Collection
Comic Strip
Computer Program
Costumes
Crossword Puzzle
Database
Debate
Demonstration
Detailed Illustration
Diorama
Diary
Display
Edibles
Editorial Essay
Etching
Experiment
Fact Tile
Fairy Tale
Family Tree
Fiction Story
Film
Filmstrip
Flip Book
Game
Graph
Hidden Picture
Illustrated Story
Interview
Jingle
Joke Book
Journal
Labeled Diagram
Large Scale Drawing
Learning Center
Letter to the Editor
Map with Legend
Mazes
Mural
Museum Exhibit
Musical Instruments
Needlework
Newspaper Story
Non-Fiction
Oral Defense
Oral Report
Painting Pamphlet
Pantomime
Papier Mache
Petition
Photo Essay
Pictures
Picture Story for
Children
Plaster of Paris Model
Play
Poetry
Political Cartoon
Pop-Up Book
Postage Stamp,
Commemoratives
Press Conference
Project Cube
Prototype
Puppet
Puppet Show
Puzzle
Rap
Radio Program
Rebus Story
Recipe
Riddle
Role Play
Science Fiction Story
Sculpture
Skit
Slide Show
Slogan
Soliloquy
Song
Sound
Story Telling-Tall
Tales
Survey
Tapes–Audio–Video
Television Program
Timeline
Transparencies
Travel Brochure
Venn Diagram
Web Home Page
Working Hypothesis
Write a new law
Video Film
I-SEARCH INDEPENDENT RESEARCH PROJECTS
FOR GIFTED AND TALENTED STUDENTES
1.
PARADOXES:
Completing the square of a quadratic equation involves identifying and adding a constant to the equation.
Create two equations where factoring the equation is difficult or does not seem to be possible.
2.
ATTRIBUTES:
Create a poem or song describing the attributes of quadratic functions and how they can be applied in life.
3.
ANALOGIES:
List five similarities between the things you see/use in the world and compare them to quadratic
functions/parabolas. Create a power point presentation showing the similarities. For example: a thrown ball
looks like an upside down U. This curve has the same general shape as the graph of the squaring function y =
x².
4.
DISCREPANCIES:
The presidential election of 2004 George W. Bush and John Kerry denoted discrepancies in several states
where votes were counted first by machine then manually. Your task is to create a prototype voting machine
that would alleviate counting discrepancies for future elections with a written explanation as to how it will
operate.
5.
PROVOCATIVE QUESTIONS:
Hand is to glove as math is to science. What do you think would happen if there was no connection of math
to science? Write a persuasive paragraph justifying your answer.
6.
EXAMPLES OF CHANGE:
We live in a society where religion is taboo to discuss because of the various cultures residing in our country.
There was a time when prayer was allowed in school and is now forbidden. If you could change the law,
weather for or against, write a newspaper article expressing why or why not the law should be modified to
allow or not allow prayer in public school.
Also take a survey in your community and include your
findings using a graph.
7.
EXAMPLES OF HABIT:
Most equation solving requires using a formula. Create an acronym that would help a classmate remember
what he/she needs to do to solve a problem. For example, SAFE – Standard form is Ax² +bx + c = c, Always
use an alternate method when on way doesn’t work, Factoring and completing the square finds the root,
Equation always equals zero.
8.
ORGANIZED RANDOM SEARCH:
The number balls in a lottery are selected at random. Create your own system to randomly select numbers
and explain what approach you would use.
9.
SKILLS OF SEARCH:
Write a program on a graphics calculator or a computer to solve a quadratic equation using the quadratic
formula. The input should be a, b, and c.
10.
TOLERANCE FOR AMBIGUITY:
Different cars and road conditions may produce different stopping distance formulas. Research stopping
distances for various vehicles under various conditions. For example, how quickly the driver begins to break
(reaction time), the condition of the road, the weight of the car, etc.
11.
INTUITIVE EXPRESSION:
NASA has selected you to try out the ejection seat of their YF-4J aircraft at the Dryden Flight Research
Center. Describe from head to toe how it felt and what went through your mind after landing on ground
safely. Sketch pictures to represent your feelings.
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12.
ADJUSTMENT TO DEVELOPMENT:
Often times in math students take short cuts to solve problems rather than demonstrate a step by step approach
to problem solving. Create a cartoon strip showing what you have learned from your mistakes and the
process you took to improve.
13.
STUDY CREATIVE PEOPLE AND PROCESS:
Select your favorite major league pitcher or tennis player and find out the speeds at which he/she pitches or
hits the ball. Research his/her past records and record the current status and explain how they are measured.
14.
EVALUATE SITUATIONS:
Your sibling is not as well rounded as you in math and has the same teacher you had in Algebra. Mr.
Unknown gives the same tests to each of his classes. Do you give your sibling the test to memorize so he can
do well or do you study with him so he knows it for himself? Prepare a skit with this story line and conclude
it with your decision.
15.
CREATIVE READING SKILL:
If a product of factors is zero, one or more of the factors must be zero. How does this statement help you
solve the equation (20 – x) (30 + 5x) = 0. Find the x and y intercepts.
16.
CREATIVE LISTENING SKILL:
Interview a marine biologist and a chemist, record the adjectives that describe their profession and create a
crossword puzzle. Use the words from the Marine biologist as the across and the chemist the down.
17.
CREATIVE WRITING SKILL:
Find a picture of a parabola. Sketch it on graph paper. Tell at least three things you know about it.
18.
VISUALIZATION SKILL:
Make a collage of architectural structures with quadratic images.
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ACADEMIC / CRITICAL THINKING SKILLS
ANALYZING HUMAN ACTIVITIES! (AHA!)
©Dr. T. Roger Taylor
STATE STANDARD #
STUDENTS WILL BE ABLE TO
.
ESSENTIAL QUESTION: How does the Universal Theme of Producing, Exchanging and Distributing
create mastery learning of essential concepts in this unit? State the essential concept(s) that this specific
lesson will teach. ESSENTIAL QUESTION:
1. PRODUCING, EXCHANGING, AND DISTRIBUTING [ECONOMICS]
Textbook or Database:
KNOWLEDGE:
Defines, describes, identifies, labels, lists, matches, names, outlines, reproduces, selects, states.
(Include ANCHORING ACTIVITY / ANTICIPATORY SET, at least 2 “for examples”)
Anchoring Activity / Anticipatory Set:
Students will:
Formative Assessment:
COMPREHENSION:
Converts, defends, distinguishes, estimates, explains, extends, generalizes, gives examples, infers, paraphrases, predicts,
rewrites, summarizes. (Include “for examples”)
Short-term / Cumulative Assessment:
APPLICATION:
Changes, computes, demonstrates, discovers, manipulates, modifies, operates, predicts, prepares, produces, relates,
shows, solves, uses. (Include ANCHORING ACTIVITY / ANTICIPATORY SET, and at least one IN-CLASS
TEAM PRODUCT)
Anchoring Activity / Anticipatory Set:
Students will create a (class / team product):
Formative Assessment / Rubric for Product:
Multicultural and/or ESL and/or Bilingual Link:
Mathematics/Science Link and/or Humanities Link:
School-to-Career/Tech Prep Link:
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Paradoxes, Attributes, Analogies, Discrepancies, Provocative Questions, Examples of Change, Examples of Habit,
Organized Random Search, Skills of Search, Tolerance for Ambiguity, Intuitive Expression, Adjustment to
Development, Study Creative People and Process, Evaluate Situations, Creative Reading Skill, Creative Listening Skill,
Creative Writing Skill, Visualization Skill. (Include ANCHORING ACTIVITY / ANTICIPATORY SET, and
at least one IN-CLASS TEAM PRODUCT)
Anchoring Activity / Anticipatory Set:
Students will:
Class/team/individual product:
Summative Assessment:
INDIVIDUAL JOURNAL ASSIGNMENT:
HOMELINK:
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CRITICAL THINKING SKILLS ACADEMIC
ANALYZING HUMAN ACTIVITIES! (AHA!)
STATE STANDARD #4.3.12B STUDENTS WILL BE ABLE TO explain how price, supply and
demand of a product relate to a parabola.
ESSENTIAL QUESTION: How does the Universal Theme of Producing, Exchanging and Distributing
create mastery learning of essential concepts in this unit?
PRODUCING, EXCHANGING, AND DISTRIBUTING [ECONOMICS]
Textbook or Database: Integrated Mathematics 1 by McDougal Littell
2.
KNOWLEDGE:
Anticipatory Set:
1) www.businessweek.com - Watch video clip of Business Week Interview with Netflix CEO Reed Hastings
“You’ve Got Movies” 5/15/03 (5mins). The clip discusses the supply and demand of movie rentals via mail
and the current competition.
2) Listen to a portion of the song “What Goes Up, Must Come Down” by Blood Sweat and Tears.
Students will: 1) Define the words Supply, Demand, Free Enterprise, Surplus, Shortage and Equilibrium. 2)
List two products that supply and demand affect.
COMPREHENSION:
1) In pairs, take turns with your partner and explain how your selected products are produced, exchanged for
money and distributed to others (via mail, catalog and/or supermarkets).
2) Entire class will discuss how these products have an effect on consumers.
APPLICATION:
Anticipatory Set: Power point presentation “Pricing the New Megatrend Laptop Computer”
1) In groups of 4, students will look at the equation and graph in Step 1 of Sara Ortiz’s presentation and
answer for the following questions. Y = -100x + 300,000. Y = number sold, x = price
a. Is this function an example of linear growth or linear decay?
b. Which is the control variable? Which is the dependent variable?
c. As the price goes up, what happens to the number sold? Why do you think this happens?
d. What is the x-intercept? What does it mean in terms of the situation?
e. When Sara Ortiz wrote the equation, she assumed that Megatrend will never sell more than 300,000 laptops
in any given year. How can you tell?
2) Look at the graph in Step 2 of the presentation. Y = (-100x + 300,000) x the graph is a parabola.
a. Which is the control variable in the equation? Which is the dependent variable?
b. What are the x-intercepts? What do they mean in terms of the situation?
c. What is the y-intercept? What does it mean in terms of the situation?
d. What price should Megatrend set for the laptop computer? Why?
Multicultural and/or ESL and/or Bilingual Link: Are laptops distributed internationally? If so, name three
countries.
Mathematics/Science Link and/or Humanities Link: How would the currency in another country have an
effect on international trade? Explain.
School-to-Career/Tech Prep Link: Interview a store owner in your community and ask him/her how supply
and demand has had an effect on their business. Record their answer and present to class.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Evaluate a company of your choice and create a table using x-intercept as supply/demand
and y-intercept as price.
Students will: Plot points on a coordinate plane demonstrating a demand curve, supply curve and an
equilibrium point. Use colored pencils to differentiate between the demand and supply curves.
INDIVIDUAL JOURNAL ASSIGNMENT:
Summarize what you learned from this lesson about supply and demand? Do you see a math connection?
9
HOMELINK:
Ask your parents if price, brand loyalty, or product features play a major role in the purchases they make.
STATE STANDARD # 4.3.12C STUDENTS WILL BE ABLE TO observe reflections of a quadratic
function and graph quadratic functions.
2. TRANSPORTATION
Textbook or Database: Algebra II Resource Book
KNOWLEDGE:
Anticipatory Set: Watch sports clips showing professional pool ball players, golfers, and basketball player.
Students will:
1) Discuss how reflections help operate and support many real world
situations as seen in the sports clip.
2) Contribute other real world examples of reflections and explain how they are useful. I.e. satellites use
reflections to focus and strengthen the signal of radio waves. 3) Find a, b and c so that the parabola whose
equation is y = ax²+ bx + c. 4) Find the vertex using x = (-b/2a), f(x). 5) Make a table of values.
COMPREHENSION:
An even function f(x), any function that holds the property f(-x) = f(x), an odd function f(x) any function that
holds the property f(-x) = -f(x).
1) In pairs, students will identify a series of functions and determine if they are even, odd, or neither. For
example,
f(x) = 5x² + 2
g(x) = -3x + 4
h(x) = -7x³ + 5x
2) Give students some problem solving situations relating the different transformations. For example: Under
what condition is the region bounded by f(x) and f(-x) symmetrical? If f(x) is an even function, what
transformation will also be an even function? Explain why.
APPLICATION:
Anticipatory Set: View portion of the movie October Sky and a portion of NASA’s Space Shuttle Launch
and Land. Students will: Use a quadratic equation to model the path of a rocket in flight.
A model rocket is launched vertically with a starting velocity of 100 feet per second. After how
many seconds will the rocket be 50 feet above the ground?
Step 1 – Use the vertical motion formula h = -16t² + vt + s to solve.
Step 2 – Use the quadratic formula to find t. x = -b + √¯b² - 4ac
2a
Multicultural and/or ESL and/or Bilingual Link: Research the words rocket and space shuttle in 6
different languages.
Mathematics/Science Link and/or Humanities Link: Quadratic equations from the discipline of physical
science.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Examine a model rocket.
Students will: Speculate what qualifications might be necessary to pilot or become a crew member on a
space shuttle. Use reference materials such as the internet or those found in a library to discover the
qualifications necessary to be a candidate to ride into space and share findings with classmates.
INDIVIDUAL JOURNAL ASSIGNMENT:
Reflect what it might feel like to be the first in your school to ride on a space shuttle.
10
HOMELINK:
Ask parents/guardians if they have ever traveled using any other means of transportation besides a car, bus or
train to travel out of the state. If so, what? If no, why?
STATE STANDARD #4.3.12C STUDENTS WILL BE ABLE TO explore the equation of a Parabola.
ESSENTIAL QUESTION: How does the Universal Theme of Communications create mastery
learning of essential concepts in this unit?
3. COMMUNICATIONS
Textbook or Database: IMP by Fendel, Resek, Alper and Fraser
KNOWLEDGE:
Anticipatory Set: Watch video clip from Contact that shows Radio Telescopes. Show clips from Apollo 13
discussing the “Vomit Comet.”
Students will:
1) discuss the shape of radio telescopes and satellite dishes.
2) use a graphing calculator to: A) find the x and y intercepts. B) Determine the vertex of the function. C)
Find the line of symmetry.
COMPREHENSION:
Students will be given sets of equations and graphs to match each equation with its graph.
APPLICATION:
Anticipatory Set: Show video clip from Real Genius showing satellites.
Students will: Work in small groups (3-4) to create a replica of a Satellite Dish.
Multicultural and/or ESL and/or Bilingual Link: In Arecibo, PR, a telescope with a 1000 foot wide
parabola shaped disk broadcast radio signals and has the capability of mapping the surfaces of the planets
Venus, Mercury, and Mars.
Mathematics/Science Link and/or Humanities Link: Research - TV Satellite antennas, reflectors for car
headlights, and mirrors in telescopes contain curved surfaces in the shape of a parabola. Find a diagram of
one of these. Use the diagram to describe how the surface focuses parallel rays.
School-to-Career/Tech Prep Link: Guest speaker from the television media/cable company to explain how
the parabola on the truck creates the signal that is received at the station.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Watch the Verizon Commercial “Can You Hear Me Know”.
Students will: Work in small groups and design a parabola to make their personal cell phones sound better.
INDIVIDUAL JOURNAL ASSIGNMENT: Which section of the lesson did you enjoy most? Explain
why?
HOMELINK: Continue working on cell phone project.
STATE STANDARD #6.6B2, 6.6E1, 4.3.12B STUDENTS WILL BE ABLE TO examine two maps that
illustrate the tendency for people in the United States to settle near the coasts. They will research some
environmental impacts on coastal ecosystems and create a table.
ESSENTIAL QUESTION: In a 2000 report, the World Resources Institute stated the following: "In 1995,
over 2.2 billion people - 39 percent of the world's population - lived within 100 km [62 miles] of a coast, an
increase from 2 billion people in 1990. The coastal area accounts for only 20 percent of all land area."
According to the National Oceanic and Atmospheric Administration, in 2002, over 50 percent of people in the
United States lived within 50 miles of the ocean or Great Lakes. It is clear that coastal areas tend to be some
11
of the most highly developed regions of the world and country. This development, unsurprisingly, has some
negative impacts on marine and lake ecosystems.
4. PROTECTING AND CONSERVING
Textbook or Database: http://www.census.gov/geo/www/mapGallery/2kpopden.html
KNOWLEDGE:
Anticipatory Set: Class discussion on environmental issues affecting the oceans.
Students will: 1) After discussion, list environmental issues affecting the oceans. 2) Ask them how many of
these problems they think are occurring close to the coast versus hundreds or thousands of miles offshore. 3)
Have students open up the picture file of the U.S. Census Bureau's Population Distribution Map, ask them to
examine this map and discuss the population distribution pattern it shows. 4) Have students look at a map of
residential housing construction in coastal areas.
COMPREHENSION:
After viewing Residential Housing Constructions in Coastal Areas, in small groups, students will answer the
following questions:
• Which metropolitan areas had the most residential construction in this time period? (Students should refer
to a United States map to make sure they can name specific cities and metropolitan areas).
• Why would people want to build houses in these areas?
• What factors might make one part of the coastline more favorable than other parts of the coastline as a
location for a primary or second home?
• Along which parts of the coastline might you expect to find the worst water pollution?
APPLICATION:
In same groups, students will brainstorm some of the environmental impacts associated with coastal
development. They should list as many impacts as they can think of. Discuss their lists as a class afterwards.
Anchoring Activity / Anticipatory Set: Pilot Analysis of Global Ecosystems (PAGE): Coastal Ecosystems
page. http://marine.wri.org/Pubs_description.cfm?PubID=3054
Students will: Under the heading "Executive Summary," they'll see a list of different aspects of coastal
ecosystems and their environmental status. Ask students to go to each of the sections in the "Executive
Summary" and write the answers to these questions:
• What is the overall conclusion presented in this part of the "Executive Summary"?
• What are three important points made to support this conclusion?
• How do you think the points made in this report relate to the population distribution patterns you've seen
on the maps?
Each group will answer one question and report back to the class on their findings.
Multicultural and/or ESL and/or Bilingual Link: 1) each student, pair, or group will choose one metropolitan
area or beach resort that is on the coast. Some ideas might include: Los Angeles, CA; San Francisco, CA;
Long Island, NY; Ocean City, MD; or Ft. Lauderdale, FL. 2) Ask students to research the area to learn about
current efforts to protect the ocean ecosystem from the effects of high population density in that area. 3) They
should then examine their search results to find sites that list conservation organizations working in those
areas. 4) Have students address these questions in a report about the area that they've chosen to study:
• Describe at least one environmental impact that people are working to curtail in this area.
• What causes this environmental problem? Is it related to high population density along this part of the
coast?
• What are people trying to do about it?
• Is anyone opposed to the conservationists' efforts? If so, why?
• What do you think should be done? Why?
Mathematics/Science Link and/or Humanities Link: Create a table documenting the current costal versus
non-coastal constructions.
School-toCareer/Tech Prep Link: Take a field trip to
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Watch a clip of a presidential/political debate.
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Students will: Stage a series of class debates regarding the coastal environmental issues that students have
learned about in this lesson. Each debate should focus on one issue and should allow students to take turns
playing specific roles and being part of the audience.
INDIVIDUAL JOURNAL ASSIGNMENT:
Hurricane Katrina confirmed that homes need to be built higher to avoid flood damages. What happens if
many of the foundations historically used are not adequate for higher flood elevations?
HOMELINK:
Ask your parents if the had an opportunity to live in a coastal area, where would it be and why?
STATE STANDARD #6.5.A.3, 4.4.4.A.2 STUDENTS WILL BE ABLE TO identify the various
measurements used to analyze an economy, and describe the four phases of the business cycle.
ESSENTIAL QUESTION: How does the Universal Theme of Providing Education create mastery
learning of essential concepts in this unit? State the essential concept(s) that this specific lesson will
teach.
5. PROVIDING EDUCATION
Textbook or Database: Marketing Essentials 2nd edition (Farese, Kimbrell, Woloszyk)
KNOWLEDGE:
Students will define Business cycle, Inflation, Standard of living, Gross National Product, Gross Domestic
Product and Productivity.
Anticipatory Set: Watch clip of a professor talking about the business cycle.
http://www.video.google.com/videoplay?docid=8415267688491832655
Students will: Share what they know about the terms defined and how they fit into our economy.
COMPREHENSION:
Each student will work with a partner making sure that their partner understands the difference between GNP
and GDP by explaining in their own words what it means. This will be done in a timed pair share each
student will have the same amount of time to do this.
APPLICATION:
Anticipatory Set: Review short clip on the GNP. http://www.aeispeakers.com/videophp?SpeakersID=465
Students will: Research the current US GDP and inflation, interest, and unemployment rates. Use the
figures you gather to determine the business cycle phase of the US economy at the present time. Summarize
your findings in a one-page report and include a coordinate plane with a graph depicting economic activity on
the y-axis and time on the x-axis.
Multicultural and/or ESL and/or Bilingual Link: How is it possible for a place like Hong Kong, with few
natural resources, to develop a strong economy?
Mathematics/Science Link and/or Humanities Link: Why is double digit inflation bad for an economy?
School-to-Career/Tech Prep Link: Ask your employer about labor costs above and beyond wages paid to
employees. What government taxes and employee benefits cost your employer additional money? Ask you
employer what can be done to cut down on labor costs? Share your findings with the class.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Role Play.
Students will act out this situation: Assume you are an employee in a local family restaurant. A few
homeless people come to the back of the restaurant every evening to see if there re any scraps of food that you
can give them. A few regular patrons of the restaurant have commented on their presence. The owner, who is
from Sweden, is fearful that the homeless people will chase away customers. He approaches you about the
situation, noting that where he came from the homeless were taken care of by the state. Why, he asks with
exasperation, does this situation exist in a prosperous capitalist country? How would you respond?
13
Class/team/individual product: You will be evaluated on how well you do the following:
• Identify the three basic economic questions that must be answered by all economies.
• Explain how command and market economies answer those questions.
• Compare capitalist, socialist, and communist economies.
• Describe the goals of any economy.
INDIVIDUAL JOURNAL ASSIGNMENT: Would you like to live in a country where the government
guaranteed employment, housing, food, and medical care for all its people? Why or why not?
HOMELINK: Pose you journal assignment to your parents and record their answer.
STATE STANDARD # 4.3.12B STUDENTS WILL BE ABLE TO determine the difference and
similarities of a parabola and a catenary.
ESSENTIAL QUESTION: How does the Universal Theme of Making and Using Tools and/or
Technology create mastery learning of essential concepts in this unit?
6. MAKING AND USING TOOLS AND/OR TECHNOLOGY
Textbook or Database: http://www.du.edu/~jcalvert/math/parabola.htm and
http://www.du.edu/~jcalvert/math/catenary.htm
KNOWLEDGE:
Anticipatory Set: Identify the difference and similarities of parabolas and catenaries.
Students will: Define the word Parabola and Catenary and write the definitions in notebook.
COMPREHENSION:
With a face partner, students will drill each other to make sure they both know the difference and similarity of
parabola and catenary.
APPLICATION:
Anticipatory Set: Show class pictures of the Gateway Arch St. Louis Missouri, several bridges and TV
dishes.
Students will: Create their version of the parabola using blocks or marshmallows.
Multicultural and/or ESL and/or Bilingual Link: Research international locations for shapes of parabolas
and catenaries. Record what it is, the state or country it is located, and the source used to find it.
Mathematics/Science Link and/or Humanities Link: The Parabola is used for focusing waves, studying
motion, describing orbits, surveying and making bridges. Parabolas are functions that have the form f(x) =
ax² + bx + c.
School-to-Career/Tech Prep Link: Invite an Engineer from a local company to speak about architecture
structures and how quadratic functions relate to designs.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Create a replica of catenary a curve using string and 2 straws.
Students will: Suspend string from the two straws, creating a catenary curve. (This can be done with a rope
or a chain suspended from two points.)
INDIVIDUAL JOURNAL ASSIGNMENT:
If you were an engineer, what would the bridge you design look like? Sketch the picture.
HOMELINK:
Look in any form of media (magazine, internet, etc.) and bring in a picture of something that has a
parabola/catenary curve.
14
STATE STANDARD #4.3.12B STUDENTS WILL BE ABLE TO understand the concept of the vertex
(Maximum/Minimum).
ESSENTIAL QUESTION: How does the Universal Theme of Moral, Ethical and Spiritual Behavior
creates mastery learning of essential concepts in this unit?
7. PROVIDING RECREATION
Textbook or Database: Algebra II Textbook by McDougal/Littel
KNOWLEDGE:
Anticipatory Set: Watch a clip on Fireworks – families gathered at Liberty State Park.
Students will: discuss the Ups and Downs of Fireworks. Up represents the positive (+) and Down represents
the negative (-)
COMPREHENSION:
Students will work with a partner to solve a few problems that will 1) introduce the term vertex and 2)
establish the sign of the coefficient determines the direction of the graph (up/down).
APPLICATION:
Anticipatory Set: Given a set of functions and graphs.
Students will: Work with a partner to determine if the function opens up or faces down, or write the function
if the picture is a graph. (When “A” is positive it opens up and when “A” is negative it faces down.
Multicultural and/or ESL and/or Bilingual Link:
Mathematics/Science Link and/or Humanities Link:
School-to-Career/Tech Prep Link:
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Watch a video clip of a school that won a championship football game. To celebrate the
triumph, the school put on a firework display.
Students will: Create a list of questions determining if the graph opens p or down.
INDIVIDUAL JOURNAL ASSIGNMENT:
Summarize what you have learned from this lesson.
HOMELINK:
How long will it take for the rocket to come down to the ground using the data collected from the video?
STATE STANDARD # 4.3C, 5.7B STUDENTS WILL BE ABLE TO investigate the importance of
electricity and calculate the kWh of usage and graph data.
ESSENTIAL QUESTION: How does the Universal Theme of Organizing and Governing create
mastery learning of essential concepts in this unit?
8. ORGANIZING AND GOVERNING
Textbook or Database: Mathematics across the curriculum.
KNOWLEDGE:
Anticipatory Set: Watch a clip from Ocean 11 when the machines in Vegas are shut down.
Students will: Discuss the effects of electrical black outs and what affect it has on us.
COMPREHENSION:
Ask students to list/name cultures who don’t depend on the use of electric historically and today.
APPLICATION:
15
Anticipatory Set: Problem: How can you use your home’s electric meter to measure the total power of all
the electric devices operating at any given time?
Your electric meter has a circular flat metal plate that rotates. There s a black mark on the plate so that you
can count or time the rotations. The rate of rotation, usually measured in rotations per minute (r/min.), relates
directly to the power being used at the time. On the face of the meter, look for a marking such as Kh6. This
is known as the meter constant. The meter constant allows you to calculate the power in watts being used at
any time in your home. Mathematically the power is found by:
• P(watts) = (r/min.) x 60 x Kh
• r/min. = the number of rotations of the plate in one minute
• 60 = the number of minutes in one hour
• Kh = the meter constant
• P(watts) = (the number of rotations of the plate in on minute) x (minutes in one hour) x (meter constant)
• I.e. – if you counted 3 revolutions of the plate in one minute, and the meter constant was 6, then the
power reading would be - P(watts) = 3 x 60 x 6 = 1080 W
Practice Problem – Your meter constant (Kh) is 2.5 and your plate rotates seven times per minute, what is the
power used per hour?
Multicultural and/or ESL and/or Bilingual Link: Research availability and use of energy in other cultures,
for example, East Africa and Mexico.
Mathematics/Science Link and/or Humanities Link: Locate Kisii, Kenya on the map of Africa. What is
its latitude? What is its Longitude? What is its elevation? What does this information tell you about
insolation (incoming solar radiation) in that part of Africa?
School-to-Career/Tech Prep Link: Invite an Electrician from PSE&G to speak to the class about planning
and wiring electricity for homes.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Show clip from Die Hard I police had power shut down and thieves were able to break
code to get into vault of gold. Die Hard II Lights went out at the airport.
Students will: 1) Hear the story of “A Dark Tuesday” in 1965 when the northeastern US was out of power
for 13 hours because of human error. 2) use an atlas or almanac to locate the areas in the US that were
affected by the blackout. Calculate the population that would be affected if a blackout occurred there today.
Graph your findings.
INDIVIDUAL JOURNAL ASSIGNMENT:
Explain the importance of energy in our technological world.
HOMELINK:
Talk with your parents and together decide upon an item that uses electricity and eliminate it from you life for
one day (a Saturday or Sunday). Keep a log (hourly) describing your feeling/thoughts about not having
access to this item.
STATE STANDARD # 4.3.12B STUDENTS WILL BE ABLE TO Design a house of worship using
parabolic functions.
ESSENTIAL QUESTION: How does the Universal Theme of Moral, Ethical and Spiritual Behaviors
create mastery learning of essential concepts in this unit?
ESSENTIAL QUESTION: How do Architects use parabolas in their designs?
9. MORAL, ETHICAL AND SPIRITUAL BEHAVIOR
Textbook or Database: Teaching secondary Mathematics through Applications by Herbert Fremont.
KNOWLEDGE:
Anticipatory Set: Watch a clip on Historical Religion Building.
Students will: Identify which parts of the building have parabolic shapes.
16
COMPREHENSION:
Teacher will show different pictures of parabolic shapes and write the equations with each shape in the form
of y = a(x-h)² + k and y = ax² + bx + c. Students will match the equation with the shape.
APPLICATION:
Anticipatory Set: Search the internet/magazines for parabolas shapes.
Students will: Create a Poster of religious buildings in their neighborhood that have parabolic shapes.
Multicultural and/or ESL and/or Bilingual Link:
Mathematics/Science Link and/or Humanities Link:
School-to-Career/Tech Prep Link: Invite Architect/Civil Engineer to school to speak with students.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Watch film “Building Big” by David Macaulay. Features major bridges from stone arch
bridges of the Roman Empire to Japan's giant, all-steel Akashi Kaikyo suspension bridge, the longest in the
world.
Students will: 1) Work in teams of 4(depending upon the class size) to estimate the distance between the two
towers of the Golden Bridge. 2) Tell what is the height above the road of the cable at its lowest point? 3)
Research the types of bridges that can be constructed. 4) Look at the archway of the Holland or Lincoln
Tunnel and approximate the height in feet of the ceiling from the ground of the tunnel. 5) Construct a bridge.
INDIVIDUAL JOURNAL ASSIGNMENT:
How do you view your house of worship now that you have more knowledge about the construction of the
building?
HOMELINK:
Ask your parents to look at the construction of your church, moss, temple appearance on their next visit to see
how many arch, parabola or catenary shapes they see.
STATE STANDARD #4.3.12B STUDENTS WILL BE ABLE TO discover math in nature.
ESSENTIAL QUESTION: How does the Universal Theme of Aesthetic Needs create mastery learning
of essential concepts in this unit?
10. AESTHETIC NEEDS
Textbook or Database: Math In Nature by John A. Adams
KNOWLEDGE:
Anticipatory Set: Listen to song The Rainbow Connection, written by Paul Williams and used by Kermit the
Frog of the Muppets.
Students will: 1) list the colors of the rainbow in order. 2) identify the shape of a rainbow (parabola).
List/name as many things as they can in art, science or nature that have line of symmetry
COMPREHENSION:
How does water separate light?
APPLICATION:
Anticipatory Set: Listen to song “I’m always Chasing Rainbows” by Alice Cooper.
Student will: create a rainbow and name the colors related to the rainbow in order and the number of
vertices.
Multicultural and/or ESL and/or Bilingual Link: Why did the Irish come up with the idea that there is a
pot of gold at the end of the rainbow?
Mathematics/Science Link and/or Humanities Link: Give a geometric explanation why the rainbow looks
like part of a circle.
17
School-to-Career/Tech Prep Link: Ask a meteorologist; are there any parabolic rainbows that form a
different shape? If not, why not?
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Nature has a correlation to math (line of symmetry) we see it in plants, butterfly wings,
angular shapes of crystals and many others.
Students will: Walk around school neighborhood and look for Fibonacci patterns in architecture and
buildings. 2) Identify an artist that uses geometric shapes to create art.
INDIVIDUAL JOURNAL ASSIGNMENT:
Explain what usually happens in the atmosphere when a parabolic rainbow falls?
HOMELINK:
Look through junk mail and advertising ads, company logos and analize the symmetries.
STATE STANDARD #4.3.12D STUDENTS WILL BE ABLE TO factor trinomials and sketch the
graph of a parabola.
ESSENTIAL QUESTION: How does the discipline/sub-discipline of factoring trinomials
mastery learning of using factors to sketch y = x² + bx + c?
relate to
11. Using factors to sketch y = x² + bx + c
Textbook or Database: Integrated Mathematics 1, McDougal Littell
KNOWLEDGE:
Anticipatory Set: The polynomial dance words by Dane R. Camp (sing to the tune “hokey pokey”
Students will:
1) Expand each product for the following 3 problems:
a) (x + 5) (x + 3)
b) (x – 2) (x + 6)
c) (x-3) (x – 8)
2) Build a rectangle to model the trinomial.
3) Look at the numbers in your expanded form and the numbers in the factored form. How are these
numbers related?
COMPREHENSION:
Make a conjecture about the relationship between the integers b and c in any trinomial of the form x² + bx + c
and the numbers in the factored form.
APPLICATION:
Anticipatory Set: Switch on a flashlight and hold it sideways against a wall in a darkened room. The light
from the flashlight forms a parabola.
Students will: Use the line of symmetry, the vertex, and the intercepts to sketch the graph of y = x² + 4x –
12. Step 1 – Find the line of symmetry and the vertex. Step 2 - Find the y-intercept. Step 3 – Find the xintercept. Step 4 – Sketch the graph.
Multicultural and/or ESL and/or Bilingual Link: Research the history of mathematics in an international
country.
Mathematics/Science Link and/or Humanities Link: Create a table listing “factored form” and “expanded
form”, then describe at least tow patterns that you see in your table, finally, use the patterns in the table to
help you write this product in expanded from:
(x – a) (x + a) =?
School-to-Career/Tech Prep Link: Invite an investment adviser to talk to the class about the use of
polynomials to figure returns on investments and to demonstrate other uses of polynomial expressions and
factoring in the world of finance.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
18
Anticipatory Set: Situation – An equation for the path of a baseball hit at a 45º angle with an initial speed of
about 103 ft/s is y = -0.003x² + x + 4. In factored form, this equation can be approximated by y = -0.003(x +
4) (x – 337).
Students will: A) at what height off the ground is the ball hit? Which form of the equation helps you answer
this question most easily? B) How far from home plate will the ball hit the ground? Which form of the
equation helps you answer this question most easily?
INDIVIDUAL JOURNAL ASSIGNMENT:
Explain how to use algebra to find the x-intercepts of the graph of y = x² + 3x + 2.
HOMELINK:
Teach a sibling or an adult how to factor trinomials.
STATE STANDARD #4.5.3CSTUDENTS WILL BE ABLE TO recognize that mathematics is used in a
variety of contexts outside of mathematics.
ESSENTIAL QUESTION:
How does the discipline/sub-discipline of mathematical principals relate to mastery learning of art and
architecture?
12. Mathematical principals influence art and architecture.
Textbook or Database: www.mathbits.com
KNOWLEDGE:
Anticipatory Set: View clip of Donald in Math magic Land (animated 1959 Buena Vista Home Video)
Students will: Discuss where golden rectangles may be found in everyday items.
COMPREHENSION:
Take class outside to find examples of the golden rectangle.
APPLICATION:
Anticipatory Set: View a variety of pictures that have golden rectangles.
Students will: Sketch three Golden Rectangles of different sizes.
Multicultural and/or ESL and/or Bilingual Link: Research artwork from other cultures and look for
Golden Rectangles.
Mathematics/Science Link and/or Humanities Link: Greek and Renaissance artisans used the Golden
Rectangle in designing many works of art and architecture, why do you think they chose this form of art?
School-to-Career/Tech Prep Link:
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Lab assignment.
Students will: Create a Golden Rectangle. Steps to constructing one can be found at
http://www.jwilson.coe.uga.edu/EMT669/student.Folders/May.Leanne/Leanne’s%20Page/Golden.Ratio/Gold
en.Ratio.html
INDIVIDUAL JOURNAL ASSIGNMENT:
It is said that beauty is in the eye of the beholder, how has beauty changed over the years in comparison to the
Renaissance period and today?
HOMELINK:
Pose your journal assignment question to your parents.
STATE STANDARD # 4.1.8A STUDENTS WILL BE ABLE TO calculate percent increase and
decrease.
19
ESSENTIAL QUESTION:
How does the discipline/sub-discipline of Increase and Decrease relate to mastery learning of
Proportions?
ESSENTIAL QUESTION: How do you calculate percent increase and decrease and using the arearatio principle?
13. Calculating percent increase and decrease using the area-ratio principle.
Textbook or Database: Discovering Algebra
KNOWLEDGE:
Anticipatory Set: Review food prices from various circulars for a given week.
Students will: 1) work in pairs to find the discount amount of 10 products, 2) find the percent of the price
retained, and 3) set up a proportion to determine the final cost of the item.
COMPREHENSION:
Students will: Summarize the final cost of items including sale tax by making a table for each supermarket
using the sales tax of 3%. 2) set up and solve proportions, organize data and convert percents and decimals.
APPLICATION:
Anticipatory Set: Trip to local supermarket/current week circular.
Students will: 1) Investigate which products have increased or decreased in price from prior list of products.
2) By using different pictures size to measure its dimensions (length, width and diagonal), explore how the
dimensions change when a picture is enlarged or reduced, and calculate the area and perimeter of each size.
Explain how to find the enlarge and reduce percents of area and perimeter.
Multicultural and/or ESL and/or Bilingual Link: Write about the relation between the percent of
population growth and culture in United States and China.
Mathematics/Science Link and/or Humanities Link: MUST COMPLETE THIS LINK
School-to-Career/Tech Prep Link: Graphic artists and designers. YOU MIGHT WANT TO MAKE A
CONNECTION TO LIFE SKILLS OR THE LIKE.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Trip to Merrill Lynch, downtown Jersey City.
Students will: 1) Write an application problem about Merrill Lynch showing the percent change in the stock
market. 2) Solve the application problems by switching problems with a partner.
INDIVIDUAL JOURNAL ASSIGNMENT:
Summarize the ideas about calculating percent increase and decrease and the area- ratio principle.
HOMELINK:
Ask parents what purchasing strategy they use. For example, do they wait for certain items to go on sale
before they purchase or do they just purchase whatever is on sale at the time?
STATE STANDARD #4.3.8C STUDENTS WILL BE ABLE TO recognize that many real life situations
can be modeled with a quadratic equation.
ESSENTIAL QUESTION:
How does the discipline/sub-discipline of modeling quadratic equations relate to mastery learning of
real life situations?
14. Real life situations
Textbook or Database: Algebra 1 Explorations and Applications by McDougal/Littell
20
KNOWLEDGE:
Anticipatory Set: Show clip of The Fast and the Furious.
Students will: 1) Discuss the various modes of transportation (walking, driving, flying, etc.) 2) Discuss all
factors that affect the stopping distance of a moving object.
COMPREHENSION:
1) Make sure class understands how to compute Distance, Time, Rate and Speed. 2) Students will work in
small groups to estimate how long it takes to travel to school in the morning and the distance that is traveled
to get to school. 3) Have group work cooperatively and determine the average speed in miles per hour for
each student’s morning commute.
APPLICATION:
Anticipatory Set: Investigating Speed Lab (page 360-361)
Students will: Create a ramp with a 10º angle using two meter sticks taped together. Use a stopwatch to
measure the time it takes the ball to reach the end of the ramp and record the time and distance. Complete 5
trials.
Multicultural and/or ESL and/or Bilingual Link: Create a bumper sticker promoting speed safety.
Mathematics/Science Link and/or Humanities Link: Research how their community uses traffic signals to
manage the movement of motor vehicles.
School-to-Career/Tech Prep Link: Field trip to the police prescient to collect data on accidents within the
past 5 years in the school zone.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Model Standing Long Jump in class.
Students will: Model the path of movement with a quadratic function. 1) we need 3 points (x,y) to model
the curve, and will use the following points: the starting point, mid-point of jump (the apex) assume the
highest point is halfway through the forward movement and an ending point.
Things to be measured are 1) the length of the jump and 2) the height of the jump.
• The length – use tape to make a starting line and more tape where the jumper’s feet come down.
• The height may be trickier, but one suggestion is to measure the jumper’s height by making a mark on the
whiteboard. Have someone tall or stand on a chair with a line of sight approximate the highest point the
jumper’s head reaches with another mark on the board. The difference between the two marks will
approximate the height of the jump.
• Record two data points: 1) length of jump = x1 inches 2) height of jump = y1 inches.
• Discuss how to use this data to come up with three points on the graph: 1) (0,0) starting point, 2)
(x1/2,y1) apex of jump/vertex of parabola, 3) (x1,0) ending point.
• Finally, the modeling porting. Fit the data to the quadratic equation by substituting in the know points
from above: y = ax² + bx + c. Students should discover that c = 0, and that they are left with a system of two
equations that thy can solve for a and b.
INDIVIDUAL JOURNAL ASSIGNMENT:
What other models would you like to try?
HOMELINK:
Try recreating this model on a sibling.
STATE STANDARD #4.3.12C STUDENTS WILL BE ABLE TO create and solve quadratic equations
in two dimensions of projectile motion.
ESSENTIAL QUESTION: How does the discipline/sub-discipline of Projectile Motion
mastery learning of quadratic?
15. Horizontal and Vertical Projectile Motion
21
relate to
Textbook or Database: Integrated Mathematics 1 by McDougal/Littell
KNOWLEDGE:
Anticipatory Set: The flight of baseballs and basketballs are some examples of projectile motions. Let’s
analyze the projectile motion by breaking down the forces acting on the object.
Students will: Assume a ball was thrown horizontally at the velocity of 5 m/s.
Let's think about forces acting on x-direction, or horizontal direction, only. We know that the ball was thrown
at the velocity of 5 m/s. Because no other force acts on the ball in the air, we know the velocity will stay
constant (because the net force is zero). Therefore, after 5 seconds, the ball is d = vt = 5 m/s * 5s = 25 m, 25
m away. After 10 seconds, 5 m/s * 10 s = 50 m. The ball is 50 m away.
COMPREHENSION:
How far will the ball travel in 3 seconds in horizontal direction?
APPLICATION:
Anticipatory Set: Let’s now think about the forces in y-direction, or vertical direction. Since gravity is the
only force acting on it, the ball will accelerate at the rate of -9.8 m/s2, i.e. 9.8 m/s2 downward. After 2
seconds, the ball has traveled 19.6 m because
d = Vit + ½ at² = 0 + 4.9 * 2² = 19.6 m
Students will: Determine how far has the ball traveled after 4 seconds in vertical direction?
Multicultural and/or ESL and/or Bilingual Link: Role play three famous scientists Aristotle, Galileo and
Newton to discuss the contribution of each scientist to the Laws of Motion
Mathematics/Science Link and/or Humanities Link: List other objects/activities that use projectile
motion.
School-to-Career/Tech Prep Link: Invite upper classmen/ a physics teacher to come speak with math
students further on projectile motion.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Combine horizontal and vertical directions of the projectile motion.
Students will: Now, let's combine two forces at x and y directions and see its displacement. When t = 0, i.e.
right after the ball was thrown, the displacement on x and y direction are both 0. When t = 1, after 1 second,
the displacement on x direction is 5 m and on y direction is -4.9 m. When t = 2, the ball traveled 10 m on x
direction and -19.6 m on y direction. To summarize,
Time vs. Displacement
Time
Displacement on X
Displacement on Y
0s
0m
0m
1s
5m
-9.8 m
2s
10 m
-19.6 m
QUESTION: 1) what is the displacement of the ball in x direction after 3 seconds? 2) What is the
displacement of the ball in y direction after 3 seconds?
INDIVIDUAL JOURNAL ASSIGNMENT:
What experiment would you like to conduct?
HOMELINK:
Discuss your experience with your parents.
STATE STANDARD # 4.3,12/B STUDENTS WILL BE ABLE TO graph a system of linear equations.
ESSENTIAL QUESTION:
22
How does the discipline/sub-discipline of graphing systems of linear equations relate to mastery
learning of where the two lines intersect?
16. Graphing Systems Of Linear Equations
Textbook or Database: Algebra1 by McDougal/Littell
KNOWLEDGE:
Anticipatory Set: View clip from U-571 (war movie).
Students will: receive two linear equations to graphically determine their point of intersection.
COMPREHENSION:
Students will be given pairs of equations and graphs to determine which pairs of equations match, which
graphs.
APPLICATION:
Anticipatory Set: Cable commercial advertisement.
Students will: A friend is trying to choose between cable TV and renting videos. Here is the information
your friend gives you. “Cable TV costs $40.00 to install and then $20.00 each month. Adding a movie
channel costs an extra $11.00 each. On the other hand, the cost of a video cassette player is $170. Renting a
video costs $3.00, and I think I will rent 6 videos a month.”
a) Write an equation for the cost of installing cable TV with a movie channel. Write an equation for the cot
of buying a video cassette player and renting movies.
b) Graph the two equations on the same axis. Estimate the point of intersection of the graphs.
c) Solve the system of equations by substitution.
d) What advice would you give to your friend?
Multicultural and/or ESL and/or Bilingual Link: Habitat for Humanity International help needy families
in over 40 countries build houses, if you had an opportunity to be a part of the crew would you? Why or why
not?
Mathematics/Science Link and/or Humanities Link: Sandy and Rita are practicing for a 100 m dash
competition. Sandy gives Rita a 10 m head start. Write a graph of system of equations to model this
situation.
School-to-Career/Tech Prep Link: Visit a local shelter and reflect on the many things that you have
probably taken for granted.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Situation – Suppose three people can be housed in each available low income housing
unit. Then the number of available spaces would be 4,821,000 in 1977 and 3,384,000 in 1983.
Students will: a) draw a graph and plot the numbers. b) Write a system of equation and solve it by
substitution to check your estimate.
INDIVIDUAL JOURNAL ASSIGNMENT:
Do you enjoy putting your solutions in a graphing calculator or making your graphs by hand?
HOMELINK:
There seems to be a large number of homeless people in the community, discuss with your family what
impact that has on the city?
STATE STANDARD #4.3.12B STUDENTS WILL BE ABLE TO solve quadratic equations and
functions as it relates to business (word problems).
ESSENTIAL QUESTION: How does the discipline/sub-discipline of solving quadratic equations relate
to mastery learning of Business related questions (word problems)?
17. Quadratic Equations and Functions
23
Textbook or Database: Algebra 1 McDougal/Littell
KNOWLEDGE:
Anticipatory Set: Power point presentation modeling quadratic equation/function as it is related to business
concepts. – Cost, Revenue, and Profit,
Revenue Function: R(x) = (unit price) · x
Cost Function: C(x) = (variable cost) · x + (fixed cost)
Profit Function: P(x) = R(x) – C(x)
Common types of questions relating to cost/revenue/profit include: Find the Break Even point. At BreakEven (there is no profit, the costs equal the revenue). R(x) = C(x)
Example: If the total costs are C(x) = 500 + 90x, and total revenues are R(x) = 150x – x². Find the break-even
point(s).
R(x) = C(x)
150x - x² = 500 + 90x
x² - 60x + 500 = 0
x = 50, x = 10
(can bring this x value to either C(x) or R(x))
y = 500 + 90 · 50 = 5000
y = 500 + 90 · 10 = 1400
the break-even points are: (50, 5000), (10,1400
Generate Profit Function and find Maximum Profit
Profit Function: P(x) = R(x) – C(x)
Example: Using the above example, write the profit function, and find 1) what level production maximizes
the profit? 2) What is the maximum profit?
P(x) = R(x) – C(x)
= (150x – x²) – (500 + 90x)
= 150x – x² - 500 – 90x
= -x² + 60x -500
(At vertex, function reaches maximum point)
V = -b/2a = -60/(2· (-1)) = 30
(x)
1) Producing 30 units maximizes the profit.
V = -30² + 60 · 30 –500 = 2200
(y)
2) The maximum profit is $2,200.
Students will: Graph two quadratic functions: a) y = x² - 3x +1 b) y = -2x² + 4x + 7 (the standard way) 1)
decide the opening direction of the parabola. 2) Find the vertex of the function. 3) Decide two other points.
4) Decide scales. 5) Graph. Example a parabola opens upward, example b parabola opens downward.
COMPREHENSION:
Define term: Break-Even. (No profit, the costs equal the revenue)
APPLICATION:
Anticipatory Set: Power point presentation modeling (business concepts) Demand and Supply.
Demand and Supply
Common types of questions relating to demand/supply include:
Find Market Equilibrium Point
At Market Equilibrium, Demand = Supply.
Example: if the demand function for a product is given by p²+2q = 1600, and the supply function is given by
200 – p² + 2q = 0, find the equilibrium quantity and equilibrium price.
First of all, rewrite the demand and supply functions.
Demand Function: q = -(½)p² + 800
Supply Function: q = (½)p² - 100
(p represents price, q represents quantity)
At Market Equilibrium, Demand = Supply
-(½)p² + 800 = (½)p² -100
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p² - 900 = 0
p = 30 (p = -30 is not a valid answer)
the equilibrium price is $30.
(can bring this price to either supply or demand function)
q = (½)(30)² -100 = 350
the equilibrium quantity is 350 units.
Students will: Solve the following: A) For producing a certain product, if total costs can be represented by
C(x) = 1600 + 1500x, and the total revenues can be represented by R(x) = 1600x - x², find the break-even
point(s) and the maximum possible profit.
B) If the demand function for a commodity is given by the equation p² + 4q = 1600, and the supply function
is given by the equation 550 - p² + 2q = 0, find the equilibrium quantity and equilibrium price.
Multicultural and/or ESL and/or Bilingual Link: Use a graphing calculator to graph the equations.
Mathematics/Science Link and/or Humanities Link: Research an International company of your choice
and provide data on costs, profit and revenue.
School-to-Career/Tech Prep Link: Visit a large local and inquire about the operation of its business.
HIGHER ORDER THINKING SKILLS (H.O.T.S.):
Anticipatory Set: Describe the business you would like to own and the product/service your company will
offer its consumers.
Students will: Create and design a slogan for your company.
INDIVIDUAL JOURNAL ASSIGNMENT:
Would you hire family to work in your business? Why or why not?
HOMELINK:
Ask family members if they ever thought about starting their on business and discuss why they have or have
not done so.
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MORAL / ETHICAL / SPIRITUAL
REASONING AND DILEMMAS
FOR CHARACTER EDUCATION
TEN ETHICAL DILEMMAS
(Must be set in context of unit, but must also relate to the lives of today's students)
STATE STANDARD #
.
ESSENTIAL QUESTION: How does the content of this unit reflect character education through Moral and
Ethical dilemmas?
1.
Producing, Exchanging, and Distributing [Economics]
ESSENTIAL QUESTION: How does the Human Activity of Producing, Exchanging and Distributing
create moral/ethical dilemmas?
DILEMMA:
2.
Transportation
ESSENTIAL QUESTION: How does the Human Activity of Transportation create moral/ethical
dilemmas?
DILEMMA:
3.
Communications
ESSENTIAL QUESTION: How does the Human Activity of Communications create moral/ethical
dilemmas?
DILEMMA:
4.
Protecting and Conserving
ESSENTIAL QUESTION: How does the Human Activity of Protecting and Conserving create
moral/ethical dilemmas?
DILEMMA:
5.
Providing Education
ESSENTIAL QUESTION: How does the Human Activity of Providing Education create moral/ethical
dilemmas?
DILEMMA:
6-10 will be found in the writing template as per page 2.
26
MORAL / ETHICAL / SPIRITUAL
REASONING AND DILEMMAS
FOR CHARACTER EDUCATION
TEN ETHICAL DILEMMAS
(Must be set in context of unit, but must also relate to the lives of today's students)
STATE STANDARD # 4 3 12 .
ESSENTIAL QUESTION: How does the content of this unit reflect character education through Moral and
Ethical dilemmas?
1.
Producing, Exchanging, and Distributing [Economics]
ESSENTIAL QUESTION: How does the Human Activity of Producing, Exchanging and Distributing
create moral/ethical dilemmas?
DILEMMA: You own a Laundromat business, your business is bad, you cannot meet the expenses, will you
sell the business or you will buy new machines and fix up the place to meet up with the expense.
2.
Transportation
ESSENTIAL QUESTION: How does the Human Activity of Transportation create moral/ethical
dilemmas?
DILEMMA: you are on the turnpike, you and you have a car accident, what would you do to get to your job
on time?
3.
Communications
ESSENTIAL QUESTION: How does the Human Activity of Communications create moral/ethical
dilemmas?
DILEMMA: your second floor tenant stole electricity from your meter, what would you do about it?
Would you confront him or would you call an inspector?
4.
Protecting and Conserving
ESSENTIAL QUESTION: How does the Human Activity of Protecting and Conserving create
moral/ethical dilemmas?
DILEMMA: you write an English paper and you have to return it the next day, you have it in your laptop.
Then, you let it on your father’s car that morning somebody steel his car; what would you do about it? Do you
have a back up?
5. Providing Education
ESSENTIAL QUESTION: How does the Human Activity of Providing Education create moral/ethical
dilemmas?
DILEMMA: you won a full scholarship to New Jersey City University and you only received $4000 a year
to Colombia University, which college would you choose?
6.
Making and Using Tools and/or Technology
ESSENTIAL QUESTION: How does the Human Activity of Making and Using Tools and/or Technology
create moral/ethical dilemmas?
DILEMMA: you are a basketball super start in your school. Your school will offer you a scholarship to a
community college; would you would you take this offer or would you go a college of your choice and pay
for it?
7.
Providing Recreation
ESSENTIAL QUESTION: How does the Human Activity of Providing Recreation create moral/ethical
dilemmas?
DILEMMA: you are in a parachute and you have the chance to fall on a lake full of crocodile or a camp on
fire . Which one would you choose?
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8.
Organizing and Governing
ESSENTIAL QUESTION: How does the Human Activity of Organizing and Governing create
moral/ethical dilemmas?
DILEMMA: you don’t work on Saturday because of your religion belief. Now your boss tell you that you
have to work on Saturday that you will get a better salary or he would have to hire somebody else to your job;
what would you do?
9.
Moral, Ethical and Spiritual Behavior
ESSENTIAL QUESTION: How does the Human Activity of Moral, Ethical and Spiritual Behavior
create moral/ethical dilemmas?
DILEMMA: if you find a bag full of money and it has $60,000.Inside the bag there are a paper with the
person name and address; would return the money?
10.
Aesthetic Needs
ESSENTIAL QUESTION: How does the Human Activity of Aesthetic Needs create moral/ethical
dilemmas?
DILEMMA: You are selling your BMW car to your friend it is a 2005. It looks as new, but it has a mechanic
problem since new. Would you tell your friend about it?
CULTURAL LITERACY
Students must meaningfully use these terms to: (1) spell correctly, (2) use correctly in a sentence, and
(3) use a metaphor. Use E.D. Hirsch’s, The Core Knowledge Series (i.e. What Your Third Grader Needs
to Know), your textbooks and especially Hirsch’s New Dictionary of Cultural Literacy.
Axis of Symmetry
Catenary
Common Denominator
Constants
Curve
Direction
Distance
Factor
Linear equation
Order of Operation
Parabola
Perfect Square
Plane
Points
Quadratic equation
Quadratic formula
Root
Simplify
Square
Standard Form
Substitute
Substitution
Symmetry
Table of Values
Variables
Vertex
Create
Algebra
Arch
Undefined
Maximum
Variable
Positive Slope
X-axis
Physics
Velocity
Ordered Pairs
Up
Minimum
Acute Angle
Coordinates
Function
Obtuse Angle
Parallel
Y-axis
Focus
Design
Break-even
Polynomial
Satellite
Down
Negative Slope
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