ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Simplifying Radicals
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
Covers basic terminology and demonstrates how to simplify terms containing square roots.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-CED
Create equations that describe numbers or relationships.
1. Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential
functions
Unit Essential Questions:
How to apply the rules for simplifying square roots of positive numbers?
Unit Enduring Understandings:
Students will be able to complete a mixed practice of simplifying radicals.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …



Recognize and simplify expressions in radical form
Apply rules for simplifying radicals
Explain applications for simplifying radicals
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Facilitated Individual or Group Discussion
Small Group Journal or Log
Creating a video or Power Point Presentation
Portfolio
Formative Assessments:
Journals
Project
Tests
Quarterly Assessment
Student Self-Assessment and Reflection:
Notebook
Class Discussion
Projects
Homework
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
ALGEBRA 2
Summative Assessment:
Facilitated Individual or Group Discussion
Small Group Journal or Log
Creating a video or Powerpoint Presentation
Portfolio
Formative Assessments:
Journals
Project
Tests
Quarterly Assessment
Student Self-Assessment and Reflection:
Notebook
Class Discussion
Projects
Homework
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Larson Hostetler
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
ALGEBRA 2
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Simplifying radicals as needed for applications of the Pythagorean Theorem will be reviewed.

Hook the learner with engaging work.
The students will begin by completing a Matching Game. The teacher will place an
index card on the back of each student with a perfect square or perfect root. The students
will then receive two more index cards with integers on them. They will then go around
the room and give the integer card to the corresponding square or root. Hold cards until
the end of the period for closure discussion.

Equip for understanding, experience and explore the big ideas.
Lesson on simplifying radicals.

Rethink opinions, revise ideas and work.
Have the students’ journal and discuss why they are holding the cards that the other students
gave to them.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in simplifying radicals? Discuss this with
your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign classwork/homework over a range of abilities, allowing the students to complete
various problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Applying the Pythagorean Theorem
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to determine missing lengths of sides of geometric figures using the
Pythagorean Theorem
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) (G-SRT 8)
Use the Pythagorean Theorem to solve right triangles in applied problems.
Unit Essential Questions:
How do you determine the missing side of a right triangle given the lengths of the other two
sides?
Unit Enduring Understandings:
State the Pythagorean theorem.
Evaluating the length of a side of a right triangle given the lengths of the other
two sides.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to describe and apply the Pythagorean theorem,
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
ALGEBRA 2
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Larson/Hostetler Houghton Mifflin
o
o
o
o
o
o
o
o
Overhead projector
White board
Graphing Calculators
TI Smartview computer calculator
Teacher Text Resources
Equation Editor
Geometer’s Sketchpad
EdHelper
ALGEBRA 2
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will have an understanding of the uses of the Pythagorean Theorem. The
students will be able to use skills learned in geometry for applications in Algebra 2 .

Hook the learner with engaging work.
The students will complete one of the following Webquests in the Media Center.
http://www.nobrassmusic.com/pythagorean.htm
http://www.besd61.k12.il.us/webquests/7th%20Grade/crabtree/theorems/webquest2001/PythW
Qbeginpg.htm
http://www.rblewis.net/technology/EDU506/WebQuests/pythagoras/pyththeorem2.htm

Equip for understanding, experience and explore the big ideas.
Have students complete a worksheet on the applications of the Pythagorean Theorem,
including HSPA problems, word applications, and visuals.

Rethink opinions, revise ideas and work.
Have the students create a PowerPoint Presentation or Webquest on the “Uses of the
Pythagorean Theorem”.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign classwork/homework over a range of abilities, allowing the students to complete
various problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Trigonometric Functions
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
The students will be able to find missing parts of right triangles using sine, cosine, and tangent
functions.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): G-SRT 6,7,8
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
Unit Essential Questions:
What information must be given in order to solve a triangle?
How do you evaluate a trigonometric function using sine, cosine and tangent?
Unit Enduring Understandings:
Angles exist in triangles and are the domain of the trigonometric functions.
The trigonometric functions enable you to find missing sides and angles of a right triangle.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to solve right triangles using the sine, cosine, and tangent trigonometric
functions.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
o
o
o
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Larson/Hostetler Houghton Mifflin
Overhead projector
White board
Graphing Calculators
TI Smartview computer calculator
Teacher Text Resources
Equation Editor
ALGEBRA 2
o
o
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to find missing parts of right triangles using sine, cosine, and
tangent functions. Given real world applications, the students will apply skills to solving these
applications.

Hook the learner with engaging work.
Have the students guess how far around the Earth is at the equator. (25,000 miles)
Discuss how it is different at different latitudes.
This can be found quite easily using the Cosine ratio!!!

Equip for understanding, experience and explore the big ideas.
Complete sample problems of using different cities of importance to the students.

Rethink opinions, revise ideas and work.
Compare and Contrast your finding with a peer and journal any concerns or
interesting findings.

Evaluate your work and adjust as needed.
Students will be given a problem to try individually. At this time, the student will be able to
assess his/her own progress. The student will be given time in class to ask any additional
questions to clarify their understanding.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete
various problems as they feel capable of completing.
ALGEBRA 2

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Applying Matrix Operations (+,-,x)
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
The students will be able to read, create and manipulate data in matrix form. In this unit we will
study the structure and many uses of matrices. A matrix is a rectangular array of elements that
are excellent tools of storing and organizing data represented in tables. We will study how to
perform operations with matrices: we will find the sum and the difference, and scalar multiples of
matrices. We will discuss what the entries of the newly formed matrices mean.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): N-VM 6,7,8
Perform operations on matrices and use matrices in applications.
6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network.
7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a
game are doubled.
8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
Unit Essential Questions:
How can I apply math principles to matrices?
What is the purpose of displaying data in matrix form?
Unit Enduring Understandings:
Students will understand that matrices are used to store and organize data more conveniently
than in tables and such it has important business applications like keeping inventory.
Students will understand that matrix operations are different from operations with real numbers.
(For example, you cannot add any two matrices but you can add any two real numbers, etc.)
ALGEBRA 2
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Rules of matrices
B. Find the sum, difference and apply scalar multiplication to matrices
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Facilitated Individual or Group Discussion
Small Group Journal or Log
Creating a video or Power Point Presentation
Portfolio
Formative Assessments:
Journals
Project
Tests
Quarterly Assessment
Student Self-Assessment and Reflection:
Notebook
Class Discussion
Projects
Homework
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
ALGEBRA 2
o
o
o
o
o
o
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to apply matrices to solving systems of equations and use
matrices for models of data

Hook the learner with engaging work.
Students will be introduced to another method of solving systems of equations.
Finding the inverse of a matrix, etc will be completed using graphing calculator.

Equip for understanding, experience and explore the big ideas.
Students will solve a finance problem simulating a company that borrows
$1,500,000 dollars . Some borrowed at 7%, 8%, or 10%. Students will work
with different amounts to determine interest paid.

Students will set up a matrix of data for the number of snow boarders over
given years and use data to predict number of snow boarders in the future.
(Text p 747)
Rethink opinions, revise ideas and work.
Can anyone explain how to solve a system of equations using matrices?

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete
various problems as they feel capable of completing.
ALGEBRA 2
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will see the many uses of matrices in real life. One application would be to use matrices to
represent a large amount of data in a concise manner so that we can process the data in various ways
more conveniently

Hook the learner with engaging work.
Navajo Code
Show the following video to students and discuss relevance to topic.
http://en.kendincos.net/video-lnpfftn-navajo-code-talker-tribute.html (video tribute)
Navajo code was used during World War II as a means of transmitting secure messages via
telephone and radio. Those persons trained in Navajo code were called Navajo Talkers. From 1942
to 1945, Navajo Talkers participated in all U.S. marine assaults in the Pacific. The Japanese never
broke the code.
Philip Johnston, born and raised on a Navajo reservation, came up with the idea of using the
Navajo language for secure communications. He was aware that the United States military was
searching for a code that would be nearly impossible to decipher. He also knew that earlier codes
had been based on Native American languages, most notably the Choctaw language. The Navajo
language proved to be an excellent candidate because of its complexity, lack of alphabet and
symbols, and restricted use only in the American Southwest. In fact, it is estimated that only 30
non-Navajos worldwide understood the language by the outbreak of World War II.
In 1942, Johnston demonstrated to Major General Clayton B. Vogel that a three-line message
could be transmitted and decoded in English in 20 seconds. This was a 10-second improvement
on current machine-deciphered codes. Convinced, Major Vogel sent 29 Navajos to Camp
Pendleton, where they created the Navajo code and trained in its use. They were required to
memorize the dictionary of code words that they developed. After a Navajo talker was trained, he
was sent to a Marine unit in the pacific region, where he transmitted tactical information over the
telephone and radio. At Iwo Jima, six Navajo Talkers sent over 800 error-free messages. Major
Howard Connor credited them as being critical in the Marine capture of Iwo Jima.
Navajo messages were transmitted as a string of seemingly unrelated words. Each Navajo word
was translated into its English equivalent. The first letter of each of these English words was used
to spell another English word, wherein the actual message lay. For example the message "tsah,
wol-la-chee, ah-keh-di-glini, tsah-as-zih" translates to "needle, ant, victor, yucca" whose first
letters spell "Navy." Any Navajo word whose English translation has the same first letter can be
used interchangeably. For example, the word "be-la-sana," which means "apple," can be used in
place of the Navajo word "wol-la-chee" meaning "ant." The Navajo talkers also assigned several
Navajo words to directly translate to military terms. The Navajo word "besh-lo," for example,
which means "iron fish," was used for "submarine."
You can learn more from the Navajo Code Talkers page and Navajo Code Dictionary page hosted
by the Naval Historical Center of the Department of the Navy.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
Matrices are relevant in many mathematical representations. For example, the sales of different
types of pre-packed food from 3 stalls during a given period of time could be shown in the form of
a table here:
Packs of noodles sold
Packs of rice sold
Stall A
36
27
Stall B
21
56
Stall C
43
35
This table can be represented as a matrix:
This matrix could then be added with another that represents the sales for a different period of
time to get the total for the two periods of time, etc
Have students apply this method to

Rethink opinions, revise ideas and work.
Have students discuss other methods of representing this material (graphs, systems, etc)
Have open discussion on which method is used at various points in mathematics .

Evaluate your work and adjust as needed.
Would this method change the format that you may decide to use in solving the following
problems?
1.
In tracking the number of books sold at two locations of a bookstore, the store has
gathered the following information for the week of July 1-7. Downtown store: 83
paperbacks, 65 hardbound fiction, 98 hardbound nonfiction. Suburban mall store: 33
paperbacks, 20 hardbound fiction, 50 hardbound nonfiction. This can be written as a
matrix with the downtown store as column 1 and the mall store as column 2. Each type of
book would become a row in the matrix.
Explain how matrices might be more useful in some situations then others.

Tailor the work to reflect individual needs, interests, and styles.
Many students have difficulty seeing the connection of mathematics to their lives.
What better place to draw upon for ideas in this cluster than life itself!


Head to the newspaper.
Read through a current events article and craft at least 3 problems based on realworld situations that you could represented using a matrix. Be sure to find articles
ALGEBRA 2


that will be of some importance and interest to you. Work through at least 3
articles in this way, creating 3 different "scenarios" for each.
Ask students to present the articles and problems to students in your class.
Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o Begin with the hook.
o Introduce essential questions.
o Discuss uses of matrices and mathematical properties that apply.
o Direct Instruction.
o Homework – Practice skills and short writing task.
o Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Finding and working with Slope
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
In this unit students will find the slope of a line, classify parallel and perpendicular lines,
and use slope to solve real-life problems.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial
Literacy; Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): S-ID7; G-GPE 5
Use coordinates to prove simple geometric theorems algebraically.
5. Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
line that passes through a given point).
Unit Essential Questions:
What does slope measure?
How might slope help us to find a rate of change?
How does slope reflect properties of parallel and perpendicular lines?
What factors cause positive, negative, zero, or undefined slope?
Unit Enduring Understandings:
Understand the concept of slope and how it relates to real-life situations.
ALGEBRA 2
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to define slope of a line using points, graphs, and an equation.
Students will calculate and predict the slope of a line given a graph, equations, or
points and apply it to a variety of problems.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
Digital Collaboration/Blogs/Wiki
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Algebra and Trigonometry
Authors: Larson/Hostetler Published by Houghton Mifflin
Discovering Algebra: an Investigative Approach
Published by Key Curriculum Press
Teacher Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
o
Overhead projector
White board
Graph board
Graphing Calculators
TI Smartview computer calculator
LCD Projectors
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
o
o
o
Equation Editor
Geometer’s Sketchpad
EdHelper
o
o
o
E-workbook
Internet lessons
Power Point lessons
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
This unit is a review of slope from previous courses to prepare the students for the more
In depth study of slope as rate of change.

Hook the learner with engaging work.
Biking Activity
ALGEBRA 2
Pedal Power Activity Sheet
This lesson provides students with a graph of an authentic situation. Students can use any method
they like to determine the meaning of points and slope on the graph as it relates to the situation
of three people biking uphill.
Distribute the Pedal Power activity sheet, which shows the distance-time graph for three cyclists.
Pedal Power Activity Sheet
To begin the lesson, present students with the following situation:
Bicyclists claim that the longest steep hill in the world is in Haleakala National Park, and they
have the sore muscles to prove it! The hill leads up a volcano on the island of Maui, Hawaii.
Over the course of a 38-mile road, this hill rises from sea level at the coast to over 10,000 feet.
Three proficient cyclists—Laszlo, Cliantha, and Joseph—rode this entire hill to the top. They
started together at the bottom of the volcano, and they reached the top at the same time. The
graph shows the distance of each cyclist with respect to time.
To heighten interest in the problem, you may wish to show students pictures of the Haleakala
National Park or provide some background information. Some pictures and details can be found
at the following sites:

Haleakala National Park – Terra Galleria Photography
ALGEBRA 2


Haleakala National Park – National Park Service
Haleakala National Park – Answers.com
Students may want to use the Internet to find information on bicycles and speeds that can be
maintained when riding uphill.


BBC Sports Academy
Newton’s Apple
To get students thinking about the situation, ask the following warm-up questions:


Lance Armstrong’s average speed in his six Tour de France victories from 1999-2004
was about 24 miles per hour. Assuming that he pedals at his average speed and takes no
breaks, how long would it take him to get to the top of the volcano?
People who aren’t Lance Armstrong can travel at about 12 miles per hour on a bike. At
that speed, how long would it take to reach the top of the volcano?
[At 24 miles an hour, it would take 38/24 hours, or about 1 hour, 35 minutes, for Lance
Armstrong to climb the hill. At 12 miles an hour, it would take 38/12 hours, or about 3
hours, 10 minutes, for an average biker to climb it. However, both of these estimates are
probably too low, as all bikers travel slower going uphill.]
After a brief discussion, allow students to consider each question on the activity sheet
individually. Then, have students share their thoughts with a small group. Each group should
reach consensus and then present their results to the class. A whole-class discussion should
follow, focusing on the question groups below:





Estimate the vertical coordinate of B. Justify your guess.
Estimate the horizontal coordinate of B? Justify your guess.
What are the coordinates of B?
What are the coordinates of A? Explain your answer.
What are the coordinates of C? Explain your answer.
[A biker on flat ground can average about 12 miles per hour. Climbing Haleakala, an
average biker would likely go much slower, maybe 5-9 miles per hour. Therefore, it
would take about 4-7 hours to complete the ride up Haleakala, so a reasonable estimate
for the x-coordinate of B is about 5 hours. The distance to the top of Haleakala is
38 miles, so the y-coordinate of B is 38 miles. With B at (5,38), then students might
estimate the coordinates of A to be roughly (2,26) and the coordinates of C to be
approximately (3,13).]


Which cyclist had a steady speed all the way up the hill? How do you know?
Which cyclist was slow at first and then sped up? How do you know?
ALGEBRA 2

How would you describe Laszlo’s speed?
[Cliantha held a consistent pace up the hill, because the slope of her line never changed.
Joseph started slowly and then increased his speed, which is evident by an increase in
slope. On the other hand, Laszlo started very quickly but then slowed down, because the
slope of his line decreased.]

The three cyclists started together at the bottom, and they reached the top at the same
time. Is there any other time that Laszlo, Cliantha, and Joseph were at the same height at
the same time? How do you know?
[No, there are no other times when they were at the same height. If they were, their lines
would cross at locations other than O and B.]

Find the slope of each line segment on the graph. What does each slope mean in the
context of the problem?
[Assuming a time of 5 hours to travel the 38 miles up Haleakala, the slope of Cliantha’s
line is 38/5 = 7.6. This means that Cliantha’s speed was 7.6 miles per hour for the entire
trip. From the bottom to A, the slope is 26/2 = 13, meaning that Laszlo’s average speed
for the first portion of the ride was about 13 miles per hour. He then slowed down, and
his speed dropped to (38 - 26) / (5 - 2) = 4 miles per hour for the remainder. From the
bottom to C, the slope is 13/3 ≈ 4.3, and from C to the top, the slope is
(38 - 13) / (5 - 3) = 12.5. This indicates that Joseph’s speed increased from 4.3 miles per
hour to 12.5 miles per hour.]

Equip for understanding, experience and explore the big ideas.
The formula for slope is m = (y2 – y1)/(x2 – x1)
The slope of the graph of a linear equation is the coefficient of x when y is isolated.
Slope gives an average rate of change comparing the dependent variable to the
independent variable.

Rethink opinions, revise ideas and work.
Does the slope determined from the equation make sense with the graph?
Share with your peer what you have learned about slope.

Evaluate your work and adjust as needed.
Any questions left unanswered?
ALGEBRA 2
Is your homework accurate?

Tailor the work to reflect individual needs, interests, and styles.
Students will be asked to demonstrate zero, positive, negative, and undefined slope with
lines on graph paper and modeling with their arms.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
Hook
Describe the slopes determined as positive, negative, zero, or undefined.
Find slope using definition.
Find slope using slope-intercept form.
Identify parallel and perpendicular lines based on slope.
Finding rates of change using slope formula in real life problems including aqueducts,
pitch of a roof, change in temperature, and oceanography.
Closure activity – have students write a description of a real life situation that has a
positive, zero, negative or undefined rate of change.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Solving 1-variable Equations and Inequalities (including absolute value)
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
This unit will review solving and graphing one variable equations on a number line. The students will also
be introduced to graphing the solutions to absolute value equations in one variable. The students will be
introduced to interval notation.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-REI 3
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Unit Essential Questions:

How do you show solutions on a number line?

How do you isolate the variable in this linear relationship?
Unit Enduring Understandings:
Students will be able to graph and interpret solutions on a number line.
Students will be able to give solutions in interval notation.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. To know how to use the different techniques of solving and graphing one variable equations and
inequalities.
ALGEBRA 2
B. To produce a graphical representation on a number line and describe with interval notation.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Facilitated Individual or Group Discussion
Small Group Journal or Log
Creating a video or Power Point Presentation
Portfolio
Formative Assessments:
Journals
Project
Tests
Quarterly Assessment
Student Self-Assessment and Reflection:
Notebook
Class Discussion
Projects
Homework
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Larson Hostetler
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
ALGEBRA 2
o
o
o
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Students will know how to:
o Solve linear equations using addition, subtraction, multiplication and division in
application to real-life problems.
o Use two or more transformations to solve a linear equation.
o Solve equations with variables on both sides and how to apply such equations to solve
real-life problems.

Hook the learner with engaging work.
Cricket chirping frequency correlates to outside temperature.
Tonight do the following activity:
Step 1
You will need to be in a place that you can hear crickets chirping.
Step 2
Count the number of chirps in 15 seconds and add 37. This is approximately the temperature
Outside.
Step 3
Test your answer with a thermometer. How accurate is your calculation?

Equip for understanding, experience and explore the big ideas.
Interestingly enough, linear correlations are found throughout real world applications.
Solve the following application and we will discuss the results as a class.
Write an equation representing the problem and solve with the information given.
Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per
month and charge $40 per hour per student. If they have 15 students each for one hour per
week how much profit do they make together in a month? (assume 4 weeks per month)

Rethink opinions, revise ideas and work.
Discuss your finding with a peer and journal any concerns or interesting findings.
ALGEBRA 2

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Students will be given a problem to try individually. At this time, the student will be able to assess
his/her own progress. The student will be given time in class to ask any additional questions to clarify
their understanding.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Solving Literal Equations and Problem Solving
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to solve literal equations for a given variable and students will apply this skill in
solving real life problems.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) (A-CED 2, 4)
Create equations that describe numbers or relationships.
2.Create equations in two or more variables to represent relationships between quantities.
4.Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Unit Essential Questions:
How do you rearrange formulas to solve for a given unknown?
How do you create equations in two or more variables to represent relationships between quantities?
Unit Enduring Understandings:
Solve literal equations for a given variable.
Solve real life problems based on formulas.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to solve literal equations.
ALGEBRA 2
Students will be able to solve real life problems rearranging formulas and solving the equations.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
Digital Collaboration/Blogs/Wiki
Homework, Projects, Notebook, Discussion
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
ALGEBRA 2
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to manipulate any equation, solving for a specific variable. This will make
using an application of formulas simpler.

Hook the learner with engaging work.
Say you want to use your calculator to find the solutions to an equation. You have to enter the
equation into the calculator first. Well, the calculator can only accept equations in y= form. What if
your equation is 3x + 8y = 22?
This is also an issue with some common formulas, like Distance = Rate * Time. This is great if you
have the distance and time, but what if you need rate?

Equip for understanding, experience and explore the big ideas.
Discuss the different formulas for perimeter of a rectangle, P = 2(l + w) and P = 2l + 2w .
Have the students manipulate both of these to solve for w. Discuss any problems that
The students may have encountered.
How might this format be more useful than the originals?
Show students the use of this form in the TI graphing calculator.
ALGEBRA 2

Rethink opinions, revise ideas and work.
Have the students’ journal and discuss the use of rewriting an equation or formula.
Discuss if the students had the option, whether they would solve for a specific unknown before or
after substituting data.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in rewriting formulas and equations?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Graphing Linear Functions
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
In this unit students will be able to use the slope-intercept form or the standard form of a linear equation
to graph the equation. The students will be able to identify the characteristics of linear functions (ie, slope,
intercepts)
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-REI 3
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Unit Essential Questions:
What are the methods for graphing a linear equation?
What are the advantages and disadvantages to each method of plotting a line?
What information is needed in order to graph a linear equation
How are linear equations used to make real-life decisions?
Unit Enduring Understandings:
Visualize a linear equation and function by creating and analyzing its graphical representation.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to know how to use the different techniques of graphing linear equations.
Students will be able to produce a graphical representation of a linear equation using data, two points,
point slope, and slope intercept form.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
BOOKS
o
Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead projector
White board
Graphing Calculators
TI Smartview computer calculator
ALGEBRA 2
o
o
o
o
o
o
o
o
o
Equation Editor
Geometer’s Sketchpad
EdHelper
Power Point lessons
Internet lessons
E-workbook
McDougal Littell internet site
NJPEP website
NJCCCS website
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to identify and apply the slope intercept method of graphing
equations.

Hook the learner with engaging work.
Many real life situations can be described in terms of pairs of numbers. Medical charts record both
the height and weight of the patient, while weather reports may include both temperature and
windspeed. One way to analyze the relationships between two quantities is to graph the pairs of data
on a coordinate axis. Such a graph is called a scatter plot.

Equip for understanding, experience and explore the big ideas.
Working in groups of 3-4, have students use the following application to create a chart and graph
using the girls in the class, all of their mothers, and grandmothers if possible.
The average lifespan of American women has been tracked, and the model for the data is
y = 0.2t + 73, where t = 0 corresponds to 1960.
Explain the meaning of the slope and y-intercept.

Rethink opinions, revise ideas and work.
Have students journal and discuss the use of data in a graph form as compared to a chart.
Also, reflect on the data found as it relates to each students individual experience.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in graphing simple algebraic linear equations?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.
ALGEBRA 2

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of linear equations and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Finding an Equation of a Line
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
In this unit students will find the equation of a line given point(s), slope, or the graph of a line.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) A-CED 1
Create equations that describe numbers or relationships.
1.Create equations in one variable and use them to solve problems.
Unit Essential Questions:
What is needed to determine the equation of a line?
What does the equation of a line represent?
Unit Enduring Understandings:
A point and the slope of a line or two points is sufficient to find the equation of a line.
The equation of a line represents relationships between quantities.
The equation of a line can be used to evaluate additional dependent values given
an independent value.
Key Knowledge and Skills students will acquire as a result of this unit:
Determine an equation of a line and use it to solve problems.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
Teacher’s Resource Kits
Test Ready Plus workbooks
ALGEBRA 2
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The student will be able to describe, analyze, and use key characteristics of linear functions and their
graphs.
The student will be able to recognize, express, and solve problems that can be modeled using linear
functions and interpret solutions in terms of the context of the problem.

Hook the learner with engaging work.
Problem: The velocity of sound in dry air increases as the temperature increases. At 40 degrees C
sound travels at a rate of about 355 meters per second. At 49 degrees C it travels at a rate of about
360 meters per second.
Assignment: Write a linear model for the velocity (in meters per second) of sound based on the
temperature T (in degrees Celsius). The estimate the velocity of sound at 60 degrees C. Gather
information online to find a town where this would apply and justify your solution. Present your
findings to the class.
Problem: When the length of a rectangle is fixed, the area A (in square inches) of the rectangle
varies directly with its width w (in inches). When the width of a particular rectangle is 12 inches, its
area is 36 square inches.
Assignment: Write an equation that gives A as a function of w. Then find A when w is 7.5 inches.
Create a rectangle that meets this criterion and present your findings to the class.
Problem: Investigate the relationship between stopping distance and speed of travel in a car.
Assignment: Gather data from the driver’s education manual or online through the Motor Vehicle
Commission (Technology Integration), graph the values found, note the relationship is linear, and look
for an equation that fits the data.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
Extend the hook and make find different values that work in the equations.
Have students discuss how this would be relevant in real-life situations.

Rethink opinions, revise ideas and work.
Have students identify and distinguish among parameters and the independent and dependent variables
in a linear relationship. Have open discussions on describing the effects of varying the parameters m and
b in linear functions of the form f(x) = mx + b. Have students think aloud and in pairs to compare their
results. Have students discuss parallel and perpendicular relationships.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have about writing and evaluating the information from the
equations? What follow-up work is needed?

Tailor the work to reflect individual needs, interests, and styles.
Have the students model real-life quantities that can be represented by a linear equation and describe the
effects on the outcome when changing the parameters.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
Hook.
Hook extension vocabulary.
Create a real-life situation that can be represented by a linear equation.
Identify independent and dependent variables.
Write the equation of a line.
Discuss how changing the parameters affects the outcome.
Share your findings with the class.
Closing activity.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Distance Formula
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
In this unit students will be able to apply the distance formula given two positions and apply formula to
classify polygons.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): G-GPE 4
Use coordinates to prove simple geometric theorems algebraically

4. Use coordinates to prove simple geometric theorems algebraically.
Unit Essential Questions:
Given two points, what is the distance between them?
How do you classify a polygon based on its vertices?
Unit Enduring Understandings:
Students will calculate the distance between two points.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to determine the distance formula given any two points.
Students will be able to calculate the distance between two vertices and apply
the distance formula to a variety of problems.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
Teacher’s Resource Kits
Test Ready Plus workbooks
ALGEBRA 2
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Students will be able to use the distance formula to find the distance between two positions
as previously studied. The concept will be extended by applying the distance formula to basic geometric
proofs.


Hook the learner with engaging work.
Say you want to find the distance a medical helicopter must travel.
Use the following information to find the distance a medical helicopter would have to travel to St. John’s
hospital from each highway intersection. The Highway Department of Sangamon County in Illinois uses a
map with coordinate plane whose origin represents downtown Springfield. Each unit represents one mile
and the letters N, S, E, W are used to indicate the direction. For example, 3E 5S corresponds to (3,-5), a
point 3 miles east and 5 miles south of downtown Springfield. St. John’s Hospital is located at 1 E 0, or
(1,0).

Equip for understanding, experience and explore the big ideas.
Determine the distance a medical helicopter must travel to reach a hospital from different highway
intersections.
a) Rt.1 –Rt.32 intersection at 19E 6N
b) Rt. 37 – Rt.40 intersection at 6E 9S
c) Rt. 18 – Rt.40 intersection at 6W 9S
d) Rt. 10 – Rt.47 intersection at 14W 1N.

Rethink opinions, revise ideas and work.
Consider how you would determine the distance a medical helicopter must travel if another hospital must
be used due to the extent of the injuries.
ALGEBRA 2

Evaluate your work and adjust as needed.
Consider what you happen if the paramedics had difficulty reaching the accident due to weather
conditions and traffic.

Tailor the work to reflect individual needs, interests, and styles.
Show answers visually using graphs and discuss written work.
Allow the individual students to display the information on the whiteboard using PowerPoint.
Students can also use the Easiteach board to discuss and display the information.
Students will work in pairs to solve the problem .

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
1.
2.
3.
4.
5.
6.
7.
Begin with the hook question.
Introduce essential questions.
Hook extension.
Homework- Practice skills and short writing task..
Discuss the accuracy of estimating one’s position and translating it into ordered pairs.
Direct Instruction.
Self assessment questions.
Summative assessment.
8.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Midpoint
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to find the midpoint of a segment and use coordinates to prove simple geometric
theorems algebraically.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): G-GPE 4, 6
4. Use coordinates to prove simple geometric theorems algebraically.
6. Find the point on a directed line segment between two given points that partitions the segment in a
given ratio.
Unit Essential Questions:
Given two endpoints, what is the formula for the midpoint of the segment?
How do you prove a geometric property of a figure using the midpoint formula?
Unit Enduring Understandings:
Students will calculate the midpoint of a line segment.
What is the other endpoint of a segment given the midpoint and one endpoint?
ALGEBRA 2
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to find the midpoint of a segment.
Students will be able to use coordinates to prove simple geometric theorems
algebraically.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
ALGEBRA 2
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to apply the midpoint formula to various geometric concepts. This is a
review of a concept covered in Geometry which will be applied to analytic geometry proofs.

Hook the learner with engaging work.
Midpoints are one of the most powerful tools in astrology but are often ignored because they are
difficult to calculate. Used correctly, they allow you to find the synthesis of two points or planets in
an astrological chart and can provide very powerful methods of interpretation.
In recent years, midpoint astrology has seen a resurgence and is particularly popular in England.
If you'd like to find out more about midpoint astrology you can visit the WWW.
There is a calculator created for determining astrological midpoints. It will calculate the "near" and
"far" midpoints between 2 locations in a chart since any two points in a 360 degree chart will have
2 midpoints, both of them exactly 180 degrees in opposition. In most cases you will want to use
the "near" midpoint in your astrological calculations.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
Map projections
Using the concept of Map projections, have the class perform the assignment discussed below.
A lot of distortion occurs when the earth is projected onto a flat surface, for instance, a map using the
Mercator Projection. Because of this distortion, if you plot two points on a flat map along with the
corresponding calculated midpoint, you will find that the midpoint is often far out of alignment with the
two points. This can be easily illustrated by an example. If you place a ruler on a flat wall map
between Phoenix, Arizona and Kabul, Afghanistan, the midpoint for the two cities will appear to be in
the Atlantic Ocean a few hundred miles off the tip of Portugal. However, the Geographic Midpoint
Calculator gives the true midpoint coordinates of latitude 88°57'N 172°57'W, which is 72 miles (116
km) from the North Pole. You can verify this by stretching a string between the two cities on a world
globe.
In general, a true midpoint in the Northern Hemisphere will be farther north than you might expect it to
be when viewed on a flat map, and conversely, a true midpoint in the Southern Hemisphere will be
farther south than you might expect it to be. For cities that are close together this apparent difference
between a spherical earth and a flat map is only slight, but the difference can be great for cities with a
lot of longitude separation, such as cities on different continents. Also, there tends to be More
distortion in the polar regions than near the equator. So if your calculated midpoint is farther north
than you expect it to be, this is the explanation. Usually, if you take a look at a world globe it will begin
to make sense.
Choose two cities on the same continent and find both the 2-dimensional midpoint and compare it to
the midpoint as found on a globe.
Do the same with two cities on either side of the world. Compare and contrast your findings in a chart.
Write a lab report describing your experience.

Rethink opinions, revise ideas and work.
You can find the midpoint of a line segment with the formula, but how do you answer this
question?
Find the coordinates of the point on line segment AB that is one-fourth the
distance from A to B for A(8,3) and B(10,-5).
Can anyone explain how to work this step by step?

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/ homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.
ALGEBRA 2

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Solving Quadratic Equations
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
This unit concentrates on how to solve quadratics.
The lesson also focuses on solving quadratic equations by factoring using zero product property,
completing the square, taking the square root, and the quadratic formula.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) (A – SSE 2, 3a, A – REI 4ab, N – CN 7)
Solve quadratic equations with real coefficients that have complex solutions.
2.Use the structure of an expression to identify ways to rewrite it.
3a.Factor a quadratic expression to reveal the zeros of the function it defines.
4a.Solve quadratic equations in one variable.
4b.Solve quadratic equations by inspection.
7.Solve quadratic equations with real coefficients that have complex solutions.
Unit Essential Questions:
What is a complex number?
What do the solutions of a quadratic equation represent on the graph of the equation?
When does a quadratic equation have two, one, or no solutions?
ALGEBRA 2
Unit Enduring Understandings:
Quadratic equations can be solved by finding the square root.
Quadratic equations can be solved by factoring, using the quadratic formula, completing the square, and
graphing.
Acknowledge that the solution to a quadratic equation can sometimes be irrational or imaginary.
Key Knowledge and Skills students will acquire as a result of this unit:
To be able to solve a quadratic equations with a radical solution.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
This unit concentrates on how to solve quadratics and equations requiring taking square roots. The
lessons also focus on solving quadratic equations by factoring using zero product property. The students
also learn the techniques that can be used to solve any quadratic equation, such as completing the
square and the quadratic formula.

Hook the learner with engaging work.
The students will complete this unit using various Webquests. They will complete one of the following in
the Media Center:
http://www.rblewis.net/technology/EDU506/WebQuests/quadratics/quadratics.html
http://poster.4teachers.org/worksheet/view.php?id=70100&page=2
http://www.scsk12.org/STT99_WQ/STT99/Collierville_HS/brashers/Webquest-Quadratics.htm
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
The students will organize their learning into a one page note sheet to share with the class.

Rethink opinions, revise ideas and work.
Compare and Contrast your finding with a peer and journal any concerns or interesting findings.

Evaluate your work and adjust as needed.
Students will be given a problem to try individually. At this time, the student will be able to assess
his/her own progress. The student will be given time in class to ask any additional questions to clarify
their understanding.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign classwork/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Solve quadratic equations by factoring
Solve quadratic equations by completing the square
Solve quadratic equations by the even-root property
Solve quadratic equations by the quadratic formula.
http://www.youtube.com/watch?v=fE0jbYVpekE (Quad formula)
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Graphing Quadratic Equations
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
The students will be able to graph quadratic functions using intercepts and manipulation of parent graphs.
Understand relations and functions and select, convert flexibly among, and use various representations
for them, including equations or inequalities, tables, and graphs.
Analyze and explain the general properties and behavior of functions of one variable, using appropriate
graphing technologies.
Understand and perform transformations on commonly-used functions.
Use functions to model real-world phenomena and solve problems that involve varying quantities.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): F-IF 7a A-SSE 3b
Analyze functions using different representations.
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima
Write expressions in equivalent forms to solve problems.
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the
function it defines.
Unit Essential Questions:
What are the connections among the solutions (roots) of quadratic equations, the zeros of
their related functions, and the horizontal intercepts of the graph of the function?
How can you solve quadratic equations using concrete models, tables, graphs, and
algebraic methods?
ALGEBRA 2
Unit Enduring Understandings:
All students will use mathematical processes of problem solving, communication, connections, reasoning,
representations, and technology to solve problems and communicate mathematical ideas involving
graphing quadratic functions.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
Graph quadratic functions using intercepts and manipulation of parent graphs.
Understand relations and functions and select, convert flexibly among, and use various representations
for them, including equations or inequalities, tables, and graphs.
Analyze and explain the general properties and behavior of functions of one variable, using appropriate
graphing technologies.
Understand and perform transformations on commonly-used functions.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
This unit headed towards introducing the transformations of functions with quadratics as an
example. This unit also reinforces completing the square which will be used in other topics.

Hook the learner with engaging work.
Students will examine the path of an egg thrown.
ALGEBRA 2
Egg Launch Activity Sheet

Have students read the first two paragraphs on the activity sheet. Ask the class what they notice
about the height of the egg as the distance from the starting line increases. If the data points are
plotted on a coordinate plane and connected, what shape do students think the graph makes?
[Students should notice that the height increases, then decreases. The shape is a parabola.]

Have students read the third paragraph. Ask the class to describe the shape described by the
equation.
[Students should recognize that this is a quadratic equation, whose graph is a parabola. The
negative coefficient before the x2 term means that the parabola opens down and has a maximum value.

Equip for understanding, experience and explore the big ideas.
Extend the hook discussion and introduce vocabulary including
parabola, vertex, axis of symmetry, maximum, minimum, and
concavity.
Introduce that the points where the parabola hits the graph would be
the roots of the equation.
Explain that this unit will explore the path of the parabola as well as
the equation that results in a given path.
Solving the quadratic equation (once set equal to zero) will give the
roots (x-intercepts) of the graph.

Rethink opinions, revise ideas and work.
Have students “think aloud” in pairs as to what they have learned.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have?
What follow-up work is needed?

Tailor the work to reflect individual needs, interests, and styles.
Have students create a projectile motion problem (sports, etc) and
exchange problems with a partner to solve.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Hook
Hook extension vocabulary
Graphing with vertex form
Rewriting quadratic equations in vertex form and graphing
Sketch the graph of quadratic functions in vertex form (y = a (x – h ) 2 + k) by hand using
concavity, vertex, and symmetry.
Closure – review methods of graphing quadratic equations.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Parent Functions
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to graph parent functions from memory: y = x^2, y = x^3,
y=
x , y = x , y = x, y =
3
x
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) F – IF 7 b
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and
using technology for more complicated cases.
Graph square root, cube root including step functions and absolute value
functions.
Unit Essential Questions:
What do the graphs of the parent functions look like?
How is the equation changed to transform the graphs to shift vertically or horizontally, reflect about the xaxis, condense or stretch?
Unit Enduring Understandings:
Graph the parent functions.
Describe how to change the equation to produce transformations of the graph.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to graph the parent functions and change their graphs with rigid transformations
vertically, horizontally, and reflecting about x-axis.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
Teacher’s Resource Kits
Test Ready Plus workbooks
ALGEBRA 2
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The unit is bridging the work done previously with quadratics to
generalized parent functions which will be used in graphing piecewise defined functions.

Hook the learner with engaging work.
Have the students sketch the following using the graphing calculator.
Have them take note of the transformation that takes place.
y = abs(x)
y = - abs(x)
y = 5 abs (x)
y = ½ abs (x)
y = abs (x+3)
y = abs (x – 3)
y = abs (x ) – 3
y = abs (x) + 3

Equip for understanding, experience and explore the big ideas.
Students will see that the graphs of functions are transformed
similarly.
Students will recognize manipulations of parent graphs caused by changes in
the equations.
ALGEBRA 2

Rethink opinions, revise ideas and work.
Practice transformations given a graph of a function f(x)
Sketch f(x) + 5; f(x + 8); etc
Have students sketch the parent functions.

Evaluate your work and adjust as needed.
Do I know the graphs of the parent functions?
What transformations do I need to revisit?

Tailor the work to reflect individual needs, interests, and styles.
Supply graph paper.
Use the TI – Smartview projection
Use class pad to highlight transformations in color.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Hook
Show graphs of parent functions
Demonstrate transformations
Have students generalize results using function notation
Pair-wise completion of practice exercises (different sheet for each pair).
Students will exchange papers and given the graphs of the original pair determine the
equations. Solutions will be checked and solutions discussed.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Piecewise Functions
Target Course/Grade Level: Algebra II
School: Hammonton High School
UNIT SUMMARY
This unit will help develop the ability to graph, evaluate, and write piecewise functions.
This unit will focus on the recognition and creation of real-world situations that model piecewise functions.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration; Creativity and
Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy; Global
Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): (F – IF 7b)
Analyze functions using different representations.

7. Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.★
b. Graph square root, cube root, and piecewise-defined functions, including step functions
and absolute value functions.
Unit Essential Questions:
What is a piecewise function?
How is a piecewise function evaluated or graphed?
How are piecewise functions used to display real-life situations?
Unit Enduring Understandings:
Functions in the form of a rule, an equation, a graph, table or a diagram can be used to transform
numbers into other numbers to solve problems.
ALGEBRA 2
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Use and recognize functional notation
B. Represent functions with tables, graphs, rules, and diagrams, including absolute value and piecewise defined functions.
C. Make predictions given data from a function.
D. Evaluate, write, and graph functions.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests
Exams
Papers
Journals
Lab Write-Ups
Project
Formative Assessments:
Minute Paper
Demonstration
Classroom Discussion by Students
Homework Exercises
Student Survey
Journal Entries
Pretests
Student Self-Assessment and Reflection:
Facilitated Individual or Group Discussion
Interview Activity
An Opinion Article
Small Group Journal or Log
Creating a Video or PowerPoint Presentation
Designing a Website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will learn that in many real-life problems, functions are represented by a combination of
equations. Such functions are called piecewise functions.

Hook the learner with engaging work.
A Real-Life Application
Why study piecewise functions? Well, there are some real-life practical examples for studying
piecewise linear functions. For example, we can talk about "flat" income tax versus a "graduated"
income tax.
ALGEBRA 2
A flat income tax would tax people at the same rate regardless of their income.
For instance, let's say that the flat tax is 30% of your income. Some people think that flat tax is unfair
for those in or near the poverty level because they are getting taxed at the same rate as those in a
higher income bracket.
Our income tax is based on a graduated tax calculation.
Let's say that the first $15,000 you earn is taxed at a rate of 20%, the next $45,000 you make is
This would be an example of a piecewise continuous linear function.

Equip for understanding, experience and explore the big ideas.
Have students review parent functions.
Have the students complete class work with discussion on board if needed.

Rethink opinions, revise ideas and work.
Have the students brainstorm different functions that may or may not be piecewise
Functions (renting a car, electric bill, etc.). Explore on the WWW as a homework
assignment. Bring finding back to class for discussion.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Properties of Exponents
Target Course/Grade Level: Algebra II
School: Hammonton High School
UNIT SUMMARY
This unit will reinforce and utilize properties of exponents and use scientific notation to represent
real numbers.
This unit will use exponents and scientific notation to solve real-life problems.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-SSE 3a,b,c N-RN 1,2
Write expressions in equivalent forms to solve problems.
3. Choose and produce an equivalent form of an expression to reveal and explain properties
of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value
of the function it defines
c. Use the properties of exponents to transform expressions for exponential functions.
Extend the properties of exponents to rational exponents.
1. Explain how the definition of the meaning of rational exponents follows from extending
the properties of integer exponents to those values.
2. Rewrite expressions involving radicals and rational exponents sing the properties of
exponents.
ALGEBRA 2
Unit Essential Questions:
What are the properties of exponents and how are they used?
Rewrite exponential expressions in radical form and rewrite radical expressions in exponential form.
How do you simplify an exponential expression?
How can you use the properties of exponents to solve real world applications?
Unit Enduring Understandings:
Rewrite exponential expressions in radical form and rewrite radical expressions in exponential form.
Utilize the properties of exponents when solving real world applications.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Use the properties of exponents.
B. Apply the properties of exponents including multiplying, dividing, raising to a power, and zero/negative
powers to simplify expressions and solve problems.
C. Rewrite exponential expressions in radical form and rewrite radical expressions in exponential form.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests
Exams
Papers
Journals
Lab Write-Ups
Project
Formative Assessments:
Minute Paper
Demonstration
Classroom Discussion by Students
Homework Exercises
Student Survey
Journal Entries
Pretests
ALGEBRA 2
Student Self-Assessment and Reflection:
Facilitated Individual or Group Discussion
Interview Activity
An Opinion Article
Small Group Journal or Log
Creating a Video or PowerPoint Presentation
Designing a Website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO
Where is the unit headed?
Students will review rules for integer exponents and apply them to expressions with
rational exponents. The students will also determine the relationship between rational
exponents and radicals.
ALGEBRA 2
Hook the learner with engaging work.
What do you find?
o Using your calculator, evaluate the square root of 81.
o Using your calculator, evaluate 81 ^ (1/2)
o Using your calculator, evaluate the cube root of 8.
o Using your calculator, evaluate 8 ^ (1/3)
o Using your calculator, evaluate the fourth root of 64.
o Using your calculator, evaluate 64 ^ (1/4)
o Using your calculator, evaluate 25 ^ (3/2)
o Using your calculator, evaluate the square root of 25^3.
o Using your calculator, evaluate the cube of the square root of 25.
o Investigate additional examples.

Equip for understanding, experience and explore the big ideas.
Hook extension: Have students discuss their findings and
derive a formula for a ^(b/n).
Problems completed at board.
Practice problems for students with guided practice

Rethink opinions, revise ideas and work.
Write an explanation of two ways to evaluate a ^(b/n).
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning and then pair and share.

Evaluate your work and adjust as needed.
How difficult were the exercises?
How do these problems relate to problems that you have done before?

Tailor the work to reflect individual needs, interests, and styles.
Have students demonstrate to a partner how to evaluate expressions with rational exponents.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
o
o
o
Begin with hook
Have students share what they found to be true.
Extend findings to determine formula for evaluating rational exponents.
Relate the rules for integer exponents to rational exponents.
Discuss use of scientific notation in sciences and real life applications.
Direct Instruction.
Guided practice.
Pair-wise completion of problems.
Self assessment questions.
Closure.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Systems of Linear Inequalities and Equations
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
The students will graph a system of linear equations and inequalities to find the solutions of the
system. They will be able to use systems to solve real-life applications.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-REI 3,5,6,7,11,12
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Solve systems of equations.
5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that
equation and a multiple of the other produces a system with the same solutions.
6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables.
7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables
algebraically and graphically. For example, find the points of intersection between the line y = –3x and the
circle x2 + y2 = 3. .
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations. Include
cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.★
12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in
the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables
as the intersection of the corresponding half-planes.
ALGEBRA 2
Unit Essential Questions:
What does the graph of two or more linear equations and inequalities represent?
Unit Enduring Understandings:
Real life situations can be represented graphically using systems of equations and inequalities.
Key Knowledge and Skills students will acquire as a result of this unit:
A. Key factors affecting the graphs of linear equations and inequalities.
B. Graph systems of equations and inequalities.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will extend knowledge of linear graph and inequalities to systems.

Hook the learner with engaging work.
The first task will be to review slope-intercept form. Next, students will be given a "notes worksheet" which
they will use to fill out sample problems. As a class, we will graph the examples by hand and on the
graphing calculator. They will then be given problems to try on their own. Students will be assessed for
understanding throughout the lesson with verbal questions and by the teacher walking around the room.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
Many problems lend themselves to being solved with systems of linear equations. In "real life", these
problems can be incredibly complex. This is one reason why linear algebra (the study of linear systems
and related concepts) is its own branch of mathematics. In your studies, however, you should generally
be faced with much simpler problems. What follows are some typical examples.
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people
enter the fair and $5050 is collected. How many children and how many adults attended?
In the past I would have set this up by picking a variable for one of the groups (say, "c" for "children") and
then use "(total) less (what I've already accounted for)" (in this case, "2200 – c") for the other group.
Using a system of equations, however, allows me to use two different variables for the two different
unknowns.
Solve this word problem using a system of equations.

Rethink opinions, revise ideas and work.
Discuss your finding with a peer and journal any concerns or interesting findings.
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning activity and then pair and share.

Evaluate your work and adjust as needed.
Students will be given a problem to try individually. At this time, the student will be able to assess
his/her own progress. The student will be given time in class to ask any additional questions to clarify
their understanding.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Probability
Target Course/Grade Level: Algebra II
School: Hammonton High School
UNIT SUMMARY
This unit will help develop the ability to count the number of ways an event can happen and to
calculate and use probabilities. This unit will also focus on problems in life that can be solved
using these concepts.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress Indicator
(CPI): S-CP 1,2,3,5,7,9 S-IC 3
Understand independence and conditional probability and use them to interpret data
1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,”
“not”).
2. Understand that two events A and B are independent if the probability of A and B occurring together is
the product of their probabilities, and use this characterization to determine if they are independent.
of A, and the conditional probability of B given A is the same as the probability of B.
4. Construct and interpret two-way frequency tables of data when two categories are associated with
each object being classified. Use the two-way table as a sample space to decide if events are
independent and to approximate conditional probabilities. For example, collect data from a random
sample of students in your school on their favorite subject among math, science, and English. Estimate
the probability that a randomly selected student from your school will favor science given that the student
is in tenth grade. Do the same for other subjects and compare the results.
5. Recognize and explain the concepts of conditional probability and independence in everyday language
and everyday situations. For example, compare the chance of having lung cancer if you are a smoker
with the chance of being a smoker if you have lung cancer.
Use the rules of probability to compute probabilities of compound events in a uniform probability model
7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the
model.
9. (+) Use permutations and combinations to compute probabilities of compound events and solve
problems.
ALGEBRA 2
Make inferences and justify conclusions from sample surveys, experiments, and observational studies
3. Recognize the purposes of and differences among sample surveys, experiments, and observational
studies; explain how randomization relates to each.
Unit Essential Questions:
How do you count the number of ways an event can happen?
How do you calculate and use probabilities?
Unit Enduring Understandings:
Calculate and use probabilities.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Determine the number of ways an event can occur using the fundamental counting principle,
permutations, and combinations.
B. Calculate and use probabilities.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests
Exams
Papers
Journals
Lab Write-Ups
Project
Formative Assessments:
Minute Paper
Demonstration
Classroom Discussion by Students
Homework Exercises
Student Survey
Journal Entries
Pretests
Student Self-Assessment and Reflection:
Facilitated Individual or Group Discussion
Interview Activity
An Opinion Article
Small Group Journal or Log
Creating a Video or PowerPoint Presentation
Designing a Website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Students will review the fundamental counting principle and basic probability concepts.
The students will also find combinations and permutations.

Hook the learner with engaging work.
Have a student complete a birth month distribution of students
in the class on the board. Discuss the results.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
When is probability used?
(games of chance, insurance, sports, etc)
What is the difference between theoretical and experimental probability?
What is the sample space for choosing a card from a standard deck of cards?

Rethink opinions, revise ideas and work.
Students will write out sample spaces for given events.
Have students think of times that probability has played a role in their lives.
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning activity and then pair and share.

Evaluate your work and adjust as needed.
What questions do you still have concerning probability?

Tailor the work to reflect individual needs, interests, and styles.
Have students perform experiments, log results and determine probabilities based on their findings.
Have students write a paragraph describing the difference between probabilities with and without
replacement.
Have students make a video and/or song about what they have learned about probability.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
o
Hook
Introduce definition of probability.
Have students practice with birthday months on board finding probabilities.
Have students write out sample space for tossing a coin and rolling a die.
Have students write out sample space for choosing a card.
Practice exercises finding probabilities without replacement.
Practice exercises finding probabilities with replacement.
Closure- have students summarize learning in song.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Statistics
Target Course/Grade Level: Algebra II
School: Hammonton High School
UNIT SUMMARY
In this unit measures of central tendency and measures of dispersion will be used to describe
sets of data.
This unit will focus on using statistics and statistical graphs to analyze real-world situations.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): (S – ID 1-3)
Summarize, represent, and interpret data on a single count or measurement variable

1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and
spread (interquartile range, standard deviation) of two or more different data sets.

3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
Unit Essential Questions:
How do find the measures of central tendency and measures of dispersion to describe data and draw
statistical graphs?
How do you interpret data information from graphs?
Unit Enduring Understandings:
Calculate and use statistics and statistical graphs to describe data and to make predictions based on the
data.
ALGEBRA 2
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A.
B.
C.
Use measures of central tendency and measures of dispersion to describe data.
Represent data graphically.
Use statistics and statistical graphs to analyze real-life data sets.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests
Exams
Papers
Journals
Lab Write-Ups
Project
Formative Assessments:
Minute Paper
Demonstration
Classroom Discussion by Students
Homework Exercises
Student Survey
Journal Entries
Pretests
Student Self-Assessment and Reflection:
Facilitated Individual or Group Discussion
Interview Activity
An Opinion Article
Small Group Journal or Log
Creating a Video or PowerPoint Presentation
Designing a Website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
Algebra 2 Published by AGS
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Algebra 2 Published by McDougal Littell
ALGEBRA 2
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The student will be able to use measures of central tendency and measures of dispersion to describe sets
of data.
The student will be able to use statistics and statistical graphs to analyze real-world situations.

Hook the learner with engaging work.
The student can use a graphing calculator to find statistics and draw statistical graphs.
EXAMPLE.
The fat content and number of calories in several different sandwiches available at a restaurant are
shown in the tables below. Use a graphing calculator to:
(a) find the mean , median, mode, and range of the fat content in the sandwiches,
(b) draw a box-and-whisker plot of the fat content in the sandwiches, and
(c) draw a histogram of the number of calories in the sandwiches.
Sandwich
Hamburger
Cheeseburger
Quarter-pound hamburger
Quarter-pound cheeseburger
Double cheeseburger
Bacon cheeseburger
Fried chicken
Grilled chicken
Breaded fish on deluxe roll
Breaded fish on plain bun
Fat (g)
9
13
21
30
31
34
25
20
28
25
Calories
260
320
420
530
560
590
500
440
560
450
ALGEBRA 2
SOLUTION.
a) Use the Stat Edit feature to enter the data in a list. Then use the Stat Calc menu to choose 1variable statistics. The mean is x-bar and by scrolling you can find the median (Med). The range
is the difference of max X and min X .
b) Use the Stat Plot menu to choose the type of plot (box-and-whisker), the list of data, and the
frequency for the data. Then set an appropriate viewing window. Draw the box-and-whisker.
Use the Trace feature to view the minimum (9), the lower quartile (Q1/20), the median (25), the
upper or third quartile (Q3/30), and the maximum (34).

Equip for understanding, experience and explore the big ideas.
Extend the hook and use statistics and statistical graphs to analyze real-life data sets, such as the freethrow percentages for the players in the NBA.
Have students graph and discuss the results using their graphing calculators.

Rethink opinions, revise ideas and work.
Have open discussions on putting the information in the graphing calculator and interpreting the results
using the mean, mode, median, and range.
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning activity and then pair and share.

Evaluate your work and adjust as needed.
What questions and uncertainties do the students still have about using the graphing calculator to input
information and draw a box-and-whisker graph.

Tailor the work to reflect individual needs, interests, and styles.
Have the students model real-life problems that use measures of central tendency and dispersion. Have
students use standard deviation as another measure of dispersion.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
Hook.
Hook extension vocabulary. (standard deviation)
Working in pairs, find a real-life situation that can be represented by measures of central
tendency and measures of dispersion.
Graph the information and identify
Discuss your findings with the class using the measures of central tendency and measures of
dispersion.
Closing activity.
o
o
o
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Composition of Functions and Inverse Functions
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to compose and decompose given functions.
Students will be able to apply properties of inverses including their graphs are symmetric about y = x.
Students will be able to apply the horizontal line test to determine if the inverse will be a function.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) (F- BF 1c, 4a-c)
1.Write a function that models a relationship between two quantities.
1c. Compose functions.
4. Find inverse functions.
a) Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an
expression for the inverse.
b) Verify by composition that one function is the inverse of another.
c) Read values of an inverse function from a graph or a table, given that the function has an inverse.
Unit Essential Questions:
What is the composition of functions?
What is an inverse?
Unit Enduring Understandings:
Students will be able to compose and decompose functions.
ALGEBRA 2
Students will be able to find an inverse and determine if functions are inverses.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will recognize if f(g(x)) = g(f(x)) = x if and only if g are inverses.
Students will be able to find the inverse of a given function.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
ALGEBRA 2
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Students will understand and perform transformations such as arithmetically combining, composing, and
inverting commonly used functions, using technology to perform such operations on more-complicated
symbolic expressions.

Hook the learner with engaging work.
Finding inverses will help you to solve real-life problems like finding your bowling average. In bowling a
handicap is a change in score to adjust for differences in players’ abilities. You belong to a bowling
league in which each bowlers’ handicap h is determined by his or her average a using this formula:
h = 0.9 (200 – a ) *
*A bowler’s handicap is zero if his or her average is greater than 200.
ALGEBRA 2

Equip for understanding, experience and explore the big ideas.
Determine your average if your handicap is 27. What is the relationship between a and h?
Discuss inverses from the perspective how would you input handicap and get average as
compared to when you input average and get handicap.
Perform composition functions.

Rethink opinions, revise ideas and work.
Consider how you would revise your handicap equation and solve for the average since you
knew your handicap.
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning activity and then pair and share.

Evaluate your work and adjust as needed.
How difficult was this topic for you?
What follow up is needed?

Tailor the work to reflect individual needs, interests, and styles.
The problems will be demonstrated through power point presentation, described orally,
and a worksheet with corresponding problems will be distributed. Selected students
will complete problems with class pad.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
o
o
o
o
Begin with hook question.
Have students substitute h value and find a.
Discuss essential question of inverses.
Ask students for examples of inverses.
Introduce composition as a part of inverses.
Guided practice.
Pair wise completion of sample problems composing, decomposing, and finding
inverses.
Using TI students will sketch inverses and determine symmetry property.
Using graphs students will investigate inverses of functions that do not pass the
horizontal line test and respond to written prompts asking for a conclusion about the
graphs of inverses and the inverse of functions that do not pass the horizontal line
test.
Self assessment questions.
Oral review.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Simplifying Radicals
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
Covers basic terminology and demonstrates how to simplify terms containing square roots.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-CED.1
Create equations that describe numbers or relationships.
1. Create equations and inequalities in one variable and use them to solve problems. Include equations
arising from linear and quadratic functions, and simple rational and exponential functions
Unit Essential Questions:
How to apply the rules for simplifying square roots of positive numbers?
Unit Enduring Understandings:
Students will be able to complete a mixed practice of simplifying radicals.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …



Recognize and simplify expressions in radical form
Apply rules for simplifying radicals
Explain applications for simplifying radicals
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
Books -
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
ALGEBRA 2
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
Simplifying radicals as needed for applications of the Pythagorean Theorem will be reviewed.

Hook the learner with engaging work.
The students will begin by completing a Matching Game. The teacher will place an
index card on the back of each student with a perfect square or perfect root. The students
will then receive two more index cards with integers on them. They will then go around
the room and give the integer card to the corresponding square or root. Hold cards until
the end of the period for closure discussion.

Equip for understanding, experience and explore the big ideas.
Lesson on simplifying radicals.

Rethink opinions, revise ideas and work.
Have the students’ write and discuss why they are holding the cards that the other students gave to
them.
Have the students reflect on homework problems and determine areas of concern.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in simplifying radicals? Discuss this with your
group.
ALGEBRA 2

Tailor the work to reflect individual needs, interests, and styles.
Assign classwork/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Solving Radical Equations
Target Course/Grade Level: Algebra 2
School: Hammonton High School
UNIT SUMMARY
Students will be able to solve equations involving radicals and check for extraneous solutions.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI) (A – REI 2)
Understand solving equations as a process of reasoning and explain the reasoning.
2.Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
Unit Essential Questions:
How would radical equations produce extraneous roots?
What is the inverse of the square root function?
Unit Enduring Understandings:
Students will be able to solve equations with radicals and check for extraneous solutions.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to solve radical equations.
ALGEBRA 2
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
o
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
Teacher’s Resource Kits
Test Ready Plus workbooks
ALGEBRA 2
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
o
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The students will be able to solve and discuss the solutions to problems involving radical equations.

Hook the learner with engaging work.
Even after applying all of your math knowledge correctly to problem, your answers
may still not be correct! Why?

Equip for understanding, experience and explore the big ideas.
Using the WWW (http://www.regentsprep.org/regents/mathb/mathb-topic.cfm?TopicCode=7D3 )
or a PowerPoint lesson, the students will engage in various learning techniques.

Rethink opinions, revise ideas and work.
The students will write their thoughts on this learning activity and then pair and share.
The students will reflect on homework problems and determine areas of concern.

Evaluate your work and adjust as needed.
What questions and uncertainties do you still have in this lesson?
Discuss this with your group.

Tailor the work to reflect individual needs, interests, and styles.
Assign class work/homework over a range of abilities, allowing the students to complete various
problems as they feel capable of completing.
ALGEBRA 2

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
Begin with the hook.
Introduce essential questions.
Discuss uses of lesson and mathematical properties that apply.
Direct Instruction.
Homework – Practice skills and short writing task.
Self assessment questions.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Rational Expressions and Equations
Target Course/Grade Level: Algebra 2
School: Hammonton HS
UNIT SUMMARY
The students will learn to simplify and perform operations with rational expressions and equations.
The students will be able to solve and graph rational equations.
The students will learn how to use variation models and rational models in real-life applications.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): A-APR 2,6 A-REI 11 F-IF.7d
Understand the relationship between zeros and factors of polynomials.
A-APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder
on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
Rewrite rational expressions.
A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more complicated examples, a computer algebra system
Represent and solve equations and inequalities graphically.
A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations. Include
cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.
Analyze functions using different representations.
F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.★
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are
available, and showing end behavior
ALGEBRA 2
Unit Essential Questions:
What is a rational expression?
What are the methods used to solve rational expressions?
What are the common misconceptions when solving rational equations?
What is the domain of a rational equation?
Unit Enduring Understandings:
Simplifying rational expressions.
Solving rational equations that appear in real world situations.
Graphing rational equations.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Rules for simplifying rational expressions.
B. Simplify rational expression and solve rational equations.
C. Graphing rational equations, using asymptotes.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests, Quizzes
Exams
Papers
Journals
Lab write-ups
Projects
Formative Assessments:
Minute paper (warm up)
Demonstration
Classroom discussion by students
Homework exercises
Student survey
Journal entries
Pretests
ALGEBRA 2
Student Self-Assessment and Reflection:
Homework, Projects, Notebook
Facilitated Individual or Group Discussion
Interview Activity
An opinion article
Small group journal or log
Creating video or power point presentation
Designing a website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books -
o
o
Algebra 2
Published by AGS
Algebra 2
Published by McDougal Littell
Discovering Algebra: An Investigative Approach
Published by Key Curriculum Press
Algebra and Trigonometry
Published by Houghton Mifflin
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO
ALGEBRA 2

Where is the unit headed?
Students need to be able to factor. Students will be able to simplify rational expressions including
complex fractions. This will lead to solving rational equations and extraneous roots which will ultimately
lead to the concept of asymptotes and/or deleted points.

Hook the learner with engaging work.
Have students write out the steps to multiply the following problem: (4/11)(33/5)
Have students generalize and write instructions for multiplying any two arithmetic fractions.
Have students write out steps to add the following problem:
3/5 + 2/9
Have students generalize and write instructions for adding any two arithmetic fractions.

Equip for understanding, experience and explore the big ideas.
All fractions need common denominators to be added or subtracted.
Factoring is a basic technique when reducing fractions.
Students will be able to perform long and synthetic division.

Rethink opinions, revise ideas and work.
Reflect on homework problems and determine areas of concern.
The students will write their thoughts on this learning activity and then pair and share.

Evaluate your work and adjust as needed.
Am I proficient at factoring?
Can I determine the common denominator when adding and/or
subtracting?
Can I determine asymptotes?

Tailor the work to reflect individual needs, interests, and styles.
Provide an open-ended question that students may solve orally or in written form.
ALGEBRA 2

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
o
o
o
o
o
o
Hook
Simplifying rational expressions by factoring.
Multiplying rational expressions.
Dividing rational expressions.
Adding and subtracting rational expressions.
Simplify complex fractions involving addition and/or subtraction in numerator and
denominator.
Solving rational equations including checking for extraneous roots.
Graphing with asymptotes and deleted points.
Cumulative activity on all operations.
ALGEBRA 2
HAMMONTON PUBLIC SCHOOLS
CURRICULUM PROJECT
Creating a Student-Centered Classroom
Content Area: Mathematics
Unit Title: Logarithmic and Exponential Expressions and Equations
Target Course/Grade Level: Algebra II
School: Hammonton High School
UNIT SUMMARY
This unit will focus on evaluating, rewriting, and solving exponential and logarithmic expressions and
equations including base e.
This unit will focus on using exponential and logarithmic functions that model real-life situations.
21st Century Skills: Critical thinking and problem solving; Communication; Collaboration;
Creativity and Innovation
21st Century Themes: Civic Literacy; Financial, Economic, Business and Entrepreneurial Literacy;
Global Awareness; Health Literacy; Environmental Literacy
STAGE ONE: LEARNING TARGETS
2009 New Jersey Core Curriculum Standards including Cumulative Progress
Indicator (CPI): (F-IF 7e, F-BF 4,5)
Analyze functions using different representations.
F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.★
F-IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
Build new functions from existing functions.
F-BF.4 Find inverse functions.
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression
for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
(+) Verify by composition that one function is the inverse of another.
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
(+) Produce an invertible function from a non-invertible function by restricting the domain.
F-BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this
relationship to solve problems involving logarithms and exponents
ALGEBRA 2
o
Unit Essential Questions:
What is a logarithm?
How do you rewrite, condense, expand, solve, and graph a logarithmic equation?
How do logarithmic and exponential functions model situations that increase by the same percent over
equal periods of time?
Unit Enduring Understandings:
Logarithms provide another way to express exponential relationships.
Exponential and logarithmic functions model real-life situations.
Key Knowledge and Skills students will acquire as a result of this unit:
Students will be able to …
A. Evaluate, rewrite, and simplify exponential and logarithmic expressions including base e.
B. Graph logarithmic and exponential functions.
C. Solve exponential and logarithmic equations including exponential growth and decay functions.
D. Model data with exponential functions.
STAGE TWO: EVIDENCE OF LEARNING
Summative Assessment:
Tests
Exams
Papers
Journals
Lab Write-Ups
Project
Formative Assessments:
Minute Paper
Demonstration
Classroom Discussion by Students
Homework Exercises
Student Survey
Journal Entries
Pretests
ALGEBRA 2
Student Self-Assessment and Reflection:
Facilitated Individual or Group Discussion
Interview Activity
An Opinion Article
Small Group Journal or Log
Creating a Video or PowerPoint Presentation
Designing a Website
Portfolio
Reflective paper
Role play
STAGE THREE: THE LEARNING PLAN
Sequence of teaching and learning experiences
Unit Resources:
o
Books - Algebra 2 Published by AGS
Algebra 2 Published by McDougal Littell
Algebra and Trigonometry Authors: Larson/Hostetler
Published by Houghton Mifflin
Discovering Algebra Published by Key Curriculum Press
o
o
Teacher’s Resource Kits
Test Ready Plus workbooks
o
o
o
o
o
LCD Projector
Overhead Projector
White Board
Graphing Calculators
TI Smartview Graphing Calculator
o
o
o
o
o
o
o
o
o
McDougal Littell internet site
NJPEP website
NJCCCS website
E-workbook
Internet lessons
Power Point lessons
Equation Editor
Geometer’s Sketchpad
EdHelper
Instructional Guidelines: Aligning Learning Activities
WHERETO

Where is the unit headed?
The student will be able to evaluate, rewrite, and solve exponential and logarithmic expressions and
equations including base e.
The student will be able to use exponential and logarithmic functions that model real-life situations.
ALGEBRA 2

Hook the learner with engaging work.
EXPONENTIAL GROWTH AND DECAY.
Question: What relationships exist between exponential growth and exponential decay when a piece of
paper is folded repeatedly?
EXPLORING THE CONCEPT:
1. Fold a rectangular piece of paper in half. The fold divides the paper into two regions, each of
which has half the area of the paper.
2. Fold the paper in half again. In how many regions has the original piece of paper been folded?
What fraction of the paper’s area does each region have?
3. Continue to fold the paper until it is no longer possible to make another fold. After each fold,
record in a table like the one shown the fold number, the number of regions into which the paper
has been folded, and the fraction of the paper’s area that each region has.
Fold number
Number of regions
Fractional area of each region
0
1
1
1
2
1/2
2
3
3
5
4. Make two scatter plots of the data in the table. The first scatter plot
will have ordered pairs of
the form (fold number, number of regions) and the second will have ordered pairs of the form (fold
number, fractional area of each region).
DRAWING CONCLUSIONS:
1. The first scatter plot is an example of exponential growth. Write an equation for the graph.
2. Use the equation from Exercise 1 to determine the number of regions there would be after 8
folds.
3. The second scatter plot is an example of exponential decay. Write an equation for the graph.
4. Use the equation from Exercise 3 to determine the fractional area of each region after 8 folds.
5. Multiply the exponential expressions from Exercise 2 and Exercise 4. Explain why the product
should be 1.

Equip for understanding, experience and explore the big ideas.
Extend the hook and continue folding the paper and finding the number of regions and fractional area of
each region. Have students graph the results and discuss how the information from this activity can be
applied to real-life situations such as determining how altitude affects the air.
ALGEBRA 2

Rethink opinions, revise ideas and work.
Have students graph the variation between different parameters such as atmospheric pressure with
altitude and describe what happens to the atmospheric pressure as the altitude increases. (Estimate the
atmospheric pressure at the peak of a mountain.) Have open discussions on describing what would
happen to the amount of oxygen you have to breathe based on the changes in atmospheric pressure.
Have students think aloud and in pairs to compare their results.

Evaluate your work and adjust as needed.
What questions and uncertainties do the students still have about the relationship that exists between
exponential growth and decay? How do students determine whether the situation represents exponential
growth and decay?

Tailor the work to reflect individual needs, interests, and styles.
Have the students model real-life problems that can describe relationships that exist between exponential
growth and exponential decay. Have students make a video showing the situation and the results.

Organize the work flow to maximize in-depth understanding and success at
the summative tasks.
o
o
o
Hook.
Hook extension vocabulary.
Working in pairs, find a real-life situation that represents the relationship between exponential
growth and decay.
Graph the information and identify which scatter plot represents exponential growth or
exponential decay.
Discuss your findings with the class.
Closing activity.
o
o
o