CURRICULUM
FOR
ALGEBRA I
GRADE 9
This curriculum is part of the Educational Program of Studies of the Rahway Public Schools.
ACKNOWLEDGMENTS
Cary Fields, Program Supervisor of Math and Science
The Board acknowledges the following who contributed to the preparation of this curriculum.
Sara Long
Subject/Course Title:
Algebra I
Grade 9
Date of Board Adoptions:
August 30, 2011
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Equations
Target Course/Grade Level:
Algebra I/ Grade 9
Unit Summary: Students will solve equations by adding, subtracting, multiplying, and dividing. Students will
solving multistep equations. Students will use the distributive formula and solve literal equations.
Approximate Length of Unit: 3 weeks
Primary interdisciplinary connections: Solving scientific equations such as mass or converting from Celsius to
Fahrenheit. Students will need to solve multiple equations in chemistry and physics.
LEARNING TARGETS
Standards:
CPI#
Algebra: Creating equations and Reasoning with Equations and Inequalities
A-CED.4
A-REI.3
Create equations that describe numbers and relationships
Solve equations and inequalities in one variable
Unit Understandings
Students will understand that…
• You can solve equations using addition and subtraction
• You can solve equation using multiplication and division
• Equations can represent real-world situations
• You can use the distributive property to solve equations
• You can solve real world problems by using multi-step equations
Unit Essential Questions
•
•
How can real world situations be represented as equations?
How can you solve an equation for the variable of interest?
Knowledge and Skills
Students will know…
• Subtraction property of equality
• Addition property of equality
• Division property of equality
• Multiplication property of equality
• Distributive property
Students will be able to…
•
•
•
•
Solve one step equations using addition, subtraction, multiplication, and division
Write and solve multi-step equations
Write and solve real-world problems
Solve literal equations for a specific variable
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
Fundraising Project on pg. 154 in Algebra textbook. Students are given multiple information on different
pricing scenarios for fundraising for a track team. Students need to write equations to determine when the cost
of the fundraiser will equal the income and determine when they will “break even.”
Students can write word problems and switch papers with a partner. The partner will write an equation for the
partner’s word problem and solve the equation.
Students can research different literal equations that they will need to use in the real world. Then students can
solve the literal equations for a different variable than what is given.
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
Algebra Textbook chapter 3 pg. 114-159 practice problems. Equation Match game at
http://www.onlinemathlearning.com/algebra-math-games.html
Two step equation basketball game at http://www.math-videos-online.com/solving-equations-games.html
Multi-step equation games at http://www.shodor.org/interactivate/activities/AlgebraFour/
One, two, or multi-step free worksheets at www.kutasoftware.com
Video on solving equations at http://www.mathplayground.com/howto_solvevariable.html
PowerPoint on solving equations at ww.rbrhs.org/wt/valentino/.../solvingequationswithoneoperations.ppt
RESOURCES
Teacher Resources:
Online website that give literal equations
Algebra I textbook
Equipment Needed:
Projector for PowerPoint and video
Computer room access for equation games
Calculators
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Linear Functions
Target Course/Grade Level:
Algebra I/ Grade 9
Unit Summary: Students will be able to graph linear functions, and write linear functions in different forms.
Approximate Length of Unit: 6 weeks
Primary interdisciplinary connections: Students will need to know how to graph linear function in science
classes. For instance in science students will need to graph data and write a linear function of best fit for the data.
Students will need to understand how to describe slopes of linear functions in order to understand graphs in
science of motion, velocity and acceleration, and graphs of stock prices in history. Students in driver’s education
can investigate the relationship between stopping distance and speed of travel in a car. Gather data from the
driver’s education manual or online through the Motor Vehicle Commission, graph the values found, note that the
relationship is linear, and look for an equation that fits the data.
LEARNING TARGETS
Standards:
CPI#
Interpreting Functions
F-IF.1-2
F-IF.4-6
Understand the Concepts of a Function and Use Function Notation
Interpret Functions that Arise in Terms of the Context
Unit Understandings
Students will understand that…
•
•
•
Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing
patterns of change.
Functional relationships can be expressed in real contexts, graphs, algebraic equations, tables, and
words; each representation of a given function is simply a different way of expressing the same idea.
A variety of families of functions can be used to model and solve real world situations.
Unit Essential Questions
•
•
•
•
•
•
•
How can change be best represented mathematically?
How can we use mathematical language to describe change?
How can we use mathematical models to describe change or change over time?
How can patterns, relations, and functions be used as tools to best describe and help explain
real-life situations?
How are functions and their graphs related?
How can technology be used to investigate properties of linear functions and their graphs?
How can systems of equations be used to solve real-life situations?
Knowledge and Skills
Students will know…
• Whether a relation is a function.
• The slope of a horizontal and vertical line.
• Equations for horizontal and vertical lines.
• How to identify parallel and perpendicular lines by comparing their slopes.
Students will be able to…
•
•
•
•
•
•
•
•
Describe the domain and range of a function.
Calculate the slope of a line from the ratio of the differences in y- and x- coordinates.
Solve for the rate of change from a graph.
Solve and graph direct variation equations.
Use the slope-intercept form of a linear equation.
Define and use the standard form for a linear equation.
Define and use the point-slope form for a linear equation.
Write equations of lines that are parallel or perpendicular to given lines.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
As you ride home from a football game, the number of kilometers you are away from home depends
(largely) on the number of minutes you have been riding. Suppose that you are 13 km from home when
you have been riding for 10 minutes, and 8 km from home when you have been riding for 15 minutes.
(Assume that the distance varies linearly with time.) Make a graph with the vertical axis representing
distance home and the horizontal axis representing time. Label your graph. Plot the data given as two
points on your graph. About how long did it take (on average) to travel 1 km? About how far was the
football game from your home? Explain your answer.
The Math Club needs to raise money for its annual neighborhood park beautification project. The club
members decide to have a one-day car wash to raise money for this project. After estimating the cost
of the activities, determine the total cost of sponges, rags, soap, buckets, and other materials, and investigate
the average local charge for washing one car. Write a general rule to determine how much money can be
raised for any number of cars. Realistically, can the car wash raise enough money to support this activity?
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
Algebra Textbook chapter 5 pg. 218-273 practice problems.
Linear function PowerPoint at teachers.henrico.k12.va.us/math/.../2-2/2_2%20presentation.ppt
Linear function video at http://www.khanacademy.org/video/basic-linear
-function?playlist=Algebra%20I%20Worked%20Examples
The following worksheets are available at: http://www.kutasoftware.com/free.html
Finding slope from a graph
Finding slope from two points
Finding slope from an equation
Graphing lines using slope-intercept form
Graphing lines using standard form
Writing linear equations
Graphing absolute value equations
Graphing linear inequalities
Linear function games at http://www.math10.com/en/math-games/games/linear-functions/gamesfunctions.html and http://www.shodor.org/interactivate/activities/LinearFunctMachine/
Algebra Textbook portfolio activity pg. 233, 243, 263 and project on pg. 264-265
Graph different absolute value functions and describe how they are alike and different.
Laying The Foundation Lesson: Interpreting Graphs
Laying The Foundation Lesson: Linear Functions
Laying The Foundation Lesson: Functions- Show the graph
RESOURCES
Teacher Resources:
Algebra I textbook
Online websites
Equipment Needed:
Projector for PowerPoint and video
Computer room access for equation games
Graph paper
Graphing Calculators
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Systems of equations and inequalities
Target Course/Grade Level:
Algebra I/ Grade 9
Unit Summary: Students will solve systems of equations and inequalities using three different methods:
graphing, substitution, and elimination.
Approximate Length of Unit: 6 weeks
Primary interdisciplinary connections: Many subjects require students to solve for many variables at once. In
science and economics students are often looking at the effects of multiple variables on a situation. Make a model
of the relationship between Celsius and Fahrenheit temperatures. Represent the relationship as an equation, and
check the equation against two known data points – 0 degrees C = 32 degrees F and 100 degrees C = 212 degrees
F. Use the equation to convert between Celsius and Fahrenheit temperatures.
LEARNING TARGETS
Standards: Creating Equations and Reasoning with Equations and Inequalities
CPI#
A-CED.3
A-REI.5-8
Create equations that describe numbers or relationships.
Solve systems of equations.
Unit Understandings
Students will understand that…
•
•
You can solve systems of equations and inequalities using multiple different methods.
Some systems will have infinite solutions and some will have no solutions.
Unit Essential Questions
•
•
•
•
Will you get the same solution set if you solve a system of equations or inequalities using different
methods?
When is it beneficial to use each method for solving systems?
How would the solutions differ if the systems of equations include intersecting, parallel, or coinciding
lines?
How can real world problems be modeled as systems of equations or inequalities?
Knowledge and Skills
Students will know…
•
•
How to find an exact solution to a system of linear equations by using the substitution method.
How to find an exact solution to a system of linear equations by using the elimination method.
•
•
What qualifies as a consistent and inconsistent system of equations.
What qualifies as a dependent and independent system of equations.
Students will be able to…
•
•
•
•
•
Graph systems of equations
Solve a system of equations by inspecting a graph.
Choose an appropriate method to solve a system of equations.
Graph the solution to a linear inequality.
Graph the solution to a system of linear inequalities.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
Project 1: pg. 360-361- Minimum cost and maximum profit
Project 2:
Choice A: The Cape May-Lewes Ferry has space for cars and buses. Using the internet, investigate how
many of each can be transported on a single trip. Use variables to represent the unknowns (e.g. x for cars
and y for buses) and develop the graph of the inequality, using either paper-and-pencil or a graphing
calculator. Recognizing that the solutions have to be whole numbers, students should identify the points
whose coefficients are non-negative integers and in the first quadrant on or below the line.
Choice B: Jim spent $200 on gifts for his family. He spent the money on toys, clothes, and a $15 DVD.
He spent 4 times as much on clothes as he did on toys. Write an equation in one variable that can be used
to determine how much money Jim spent on toys. Solve the equation to determine how much Jim spent
on toys.
Choice C: Cell phone plan A charges a fixed cost of $45.00 per month, which includes 200 minutes.
Each additional minute, or part of a minute, for Plan A costs $0.30. Cell phone Plan B charges a fixed
cost of $65.00 per month, which includes 300 minutes. Each additional minute, or part of a minute, for
Plan B costs $0.15. How many minutes need to be used for the plans to have the same cost? Show or
explain your work.
Choice D: A landscaping contractor uses a combination of two brands of fertilizers, each containing a
different amount of phosphates and nitrates. In a package, brand A has 4 lb. of phosphates and 2 lb. of
nitrates. Brand B contains 6 lb. of phosphates and 5 lb. of nitrates. On her current job, the lawn requires
at least 24 lb. of phosphates and at least 16 lb. of nitrates. How much of each fertilizer does the contractor
need? (Students represent the given conditions as inequalities and use the intersection of their regions as
the set of feasible answers.)
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
Algebra Textbook chapter 7 pg. 318-367 practice problems.
Portfolio activity pg. 325, 337
Solve the linear system by the method that you think is best. Show or explain your work. Explain why
you chose that method.
7x – 8y = 6
4x + y = 9
Solving systems of equations video at http://www.algebra.com/algebra/homework/Systems-ofequations/Solving-Systems-of-Equations-2.lesson
Solving systems of inequalities video at http://www.mathvids.com/lesson/mathhelp/77-solvingsystems-of-linear-inequalities-by-graphing
Solving systems of inequalities PowerPoint at http://teachers.henrico.k12.va.us/math/hcpsalgebra2/34.htm
Solving system of equations PowerPoint at
teachers.henrico.k12.va.us/math/hcpsalgebra2/.../3.../2006_3_1.ppt
Solving systems worksheets at www.kutasoftware.com has the following worksheets:
Solving systems of equations by graphing
Solving systems of equations by elimination
Solving systems of equations by substitution
Systems of equations word problems
Graphing systems of inequalities
Solving system of equation games at http://www.math-play.com/System-of--Equations-Game.html
RESOURCES
Teacher Resources:
Algebra I textbook
Online websites
Equipment Needed:
Projector for PowerPoint and video
Computer room access for equation games
Graph paper
Graphing Calculators
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Exponents and Exponential Functions
Target Course/Grade Level:
Algebra I/ Grade 9
Unit Summary: Students will learn about the laws of exponents. Students will also learn how to graph
exponential function and how to apply them to real world situations.
Approximate Length of Unit: 4 weeks
Primary interdisciplinary connections: Exponential growth and decay can be related to how things evolve
over time in economics, history, and science. Biology students can learn how to date biological material by
how much it has decayed over time. History students can discuss why populations have grown or declined overtime.
LEARNING TARGETS
Standards:
CPI#
Interpreting Function, Exponential Models, and Real Number System
F-IF.7-8
N-RN.1-2
F-LE.1-5
Analyze functions using different representations
Extend the Properties of Exponents to Rational Exponents
Construct and compare linear, quadratic, and exponential models and solve
problems
Unit Understandings
Students will understand that…
•
•
Exponential growth and decay can represent real world problems
Scientific notation helps to make calculations easier for very large or small numbers
Unit Essential Questions
•
•
•
How do different exponents affect the base?
Why should we write numbers in scientific notation?
How can we apply exponential functions to real world situations?
Knowledge and Skills
Students will know…
•
•
•
•
How to define exponents can powers
The powers of negative and positive 1
The concepts of negative and zero exponents
The need for special notation in scientific calculations
•
•
Exponential functions and how they are used
The difference between graphs of exponential functions with different bases
Students will be able to…
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•
•
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Find products of powers, the power of a power, and the power of a product
Simplify products of monomials
Simplify quotients of powers and powers of fractions
Simplify expression containing negative and zero exponents
Perform computations involving scientific notation
Use exponential function to model applications that include growth and decay in different contexts
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
Project 1: In 1995 it was reported that there were 60,000 centenarians (people 100 or more
years old) in the United States. The researcher predicted a 7% annual growth rate for this
age group and claimed that the number of centenarians would reach 232,000 by year 2015.
Verify the predication numerically. Write a function to model this problem. Use your
calculator to determine when the number of centenarians will reach 1,000,000.
Project 2: The table below shows the growth of $5000 earning a fixed rate of interest
compounded annually. Find the rate by looking at successive quotients. Write a function
for the relationship. Calculate the amount through year 10. When will the amount meet
or exceed $10,000? $15,000?
Year
0
1
2
3
…
x
Amount
5000
5375
5778.13
6211.48
…
y
Quotients
5375/5000=?
?
?
…
?
Project 3: The wolves den pg. 416 in Algebra 1 textbook.
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired
results?
Algebra Textbook chapter 8 pg. 368-423 practice problems.
Exponent worksheets at www.kutasoftware.com has the following worksheets:
Exponential functions and graphs
Properties of exponents (easy, hard)
Writing numbers in scientific notation
Operations with scientific notation
Exponential Function video at http://tulyn.com/exponential_functions.htm
PowerPoints on exponents, scientific notation, and exponent functions at:
http://math.pppst.com/exponents.html
Working with exponents activity- Working with exponents becomes easier with practice.
Check out this fun activity using household supplies to learn more about working with exponents.
Exponent games at http://www.ezschool.com/Games/Exponents.html
Laying the Foundation: Negative Exponents
Laying the Foundation: Alien Invasion
Laying the Foundation: Discovery of patterns with positive and negative exponents
RESOURCES
Teacher Resources:
Algebra I textbook
Online websites
Equipment Needed:
Projector for PowerPoint and video
Computer room access for equation games
Graph paper
Graphing Calculators
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Polynomials and Factoring
Target Course/Grade Level:
Algebra I/ 9th Grade
Unit Summary: Students will perform basic operations on polynomials and solve equations by factoring
polynomials.
Approximate Length of Unit: 4 weeks
Primary interdisciplinary connections: Polynomials are useful for representing area and volume functions,
problems involving gravity, and consumer problems.
LEARNING TARGETS
Standards:
CPI#:
Seeing Structure in Equations
A-SSE.3.A-B Write Equations in Equivalent Forms to Solve Problems
Unit Understandings
Students will understand that…
•
•
•
Polynomials can be added, subtracted, and multiplied
Factoring requires an understanding of common factors
That you can solve equations by factoring
Unit Essential Questions
•
•
What are the different ways to factor polynomials?
How can you use factoring to help solve an equation?
Knowledge and Skills
Students will know…
•
•
•
•
Products of binomials by using the distributive property.
Products of binomials by using the FOIL method.
The definition of polynomial function.
How to find the zeros of a function.
Students will be able to…
•
•
Add and subtract polynomials.
Mentally simplify special products of binomials.
•
•
•
•
•
•
•
Solve problems involving polynomial function.
Factor a polynomial by using the greatest common factor.
Factor a polynomial by using a binomial factor.
Factor perfect-square trinomials.
Factor the difference of two squares.
Factor quadratic trinomials by using a grouping process.
Solve equations by factoring.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
Assessment 1- Students can write polynomials on index cards with the factored version on the back.
Then students will trade index cards with another student next to them and solve the partner’s
problems.
Assessment 2- Students are given different three-dimensional shapes that have monomials as lengths
of sides, and will need to find the surface area and volume.
Assessment 3- Algebra Textbook pg. 456 #53-38 application on construction.
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
Use algebra tiles to model polynomials to understand how to add, subtract, and multiply polynomials.
Polynomial worksheets at kutasoftware.com has the following worksheets:
Naming polynomials
Adding and subtracting polynomials
Multiplying polynomials
Multiplying special case polynomials
Factoring quadratic polynomials
Factoring special case polynomials
Factoring by grouping
Dividing polynomials
Algebra Textbook chapter 9 pg. 426-477 practice problems.
Polynomials games at coolmath.com
Polynomials PowerPoint at http://math.pppst.com/polynomials.html
Polynomials video at http://hotmath.com/help/videos/algebra1_beginningalgebra/polynomials/
RESOURCES
Teacher Resources:
Algebra I textbook
Online websites
Equipment Needed:
Projector for PowerPoint and video
Computer room access for games
Graph paper
Graphing Calculators
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Content Area:
Algebra I
Unit Title:
Quadratic Function
Target Course/Grade Level:
Algebra I/ Grade 9
Unit Summary: Students will learn different methods for analyzing quadratic functions and quadratic equations.
Approximate Length of Unit: 4 weeks
Primary interdisciplinary connections: Often the height versus time of the flight of a projectile will resemble
a parabola, the graph of a quadratic function. Stopping distances for various vehicles can also be modeled by
quadratic functions.
LEARNING TARGETS
Standards:
CPI#:
Seeing Structures in Expressions and Reasoning with Equations and Inequalities
A-SSE.3.A-B
A-REI.4
Write Equations in Equivalent Forms to Solve Problems
Solve Equations and Inequalities in One Variable
Unit Understandings
Students will understand that…
•
•
•
There are multiple ways to solve a quadratic equation.
How quadratic equations can be used in real world situations.
You can find the number of solutions to a quadratic equation from the discriminant.
Unit Essential Questions
•
•
•
What are the different ways to solve a quadratic equation?
How can you determine how a quadratic has been transformed from the parent function?
How can you find the zeros of a quadratic function?
Knowledge and Skills
Students will know…
•
•
How adding a constant to the parent function y=x² affects the graph of the function.
The quadratic formula.
Students will be able to…
• Use the zeros of a quadratic function to find the vertex of the graph of the function.
• Solve equations of the form ax²=k.
• Solve equations of the form ax²=k where x is replaced by an algebraic expression.
• Solve quadratic equations by factoring.
• Use the quadratic formula to find solutions to quadratic equations.
• Use the quadratic formula to find the zeros of a quadratic function.
• Evaluate the discriminant to determine how many real roots a quadratic equation has and whether
it can be factored.
EVIDENCE OF LEARNING
Assessment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
Project 1- “Rescue at 2000 feet”- read the article and answer the questions in the Algebra I
textbook on pg. 504-505.
Project 2- Form a group. The leader begins by choosing a quadratic function with integer
coefficients and generating a sequence of five numbers. The leader then shows only the sequence
to the other students in the group. The group then tries to find the quadratic function that generated
the sequence.
Project 3- Use a motion detector to investigate a falling object. Drop an object from 10 feet. Use
the motion detector to find the object’s height above the ground over time. Use the time and height
data to compute second differences in the height values. What are the second differences? Make a
scatter plot of the data. Write an equation of the form y=-16x²+h where h is the initial height to fit
the data.
Learning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
Algebra Textbook chapter 10 pg. 478-523 practice problems.
Activity about Galileo discovering that objects fall with the same acceleration regardless
of the mass on pg. 486-487 in Algebra I textbook.
Quadratic functions worksheets at www.kutasoftware.com has the following worksheets:
Graphing quadratic functions
Graphing quadratic inequalities
Completing the square
Solving quadratic equations
-by taking square roots
-by factoring
-with the quadratic formula
Quadratic function PowerPoint at boston.k12.ma.us/teach/technology
Quadratic function video at http://www.yourteacher.com/algebra2/quadraticfunction.php
Jeopardy quiz quadratic function at http://www.quia.com/cb/24731.html
RESOURCES
Teacher Resources:
Algebra I textbook
Online websites
Equipment Needed:
Projector for PowerPoint and video
Computer room access for equation games
Graph paper
Graphing Calculators
Motion detector