Download Math for College Readiness

THE SCHOOL DISTRICT OF LEE COUNTY
Quarterly Content Guide 2014-2015
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Intermediate Algebra Graphs & Models
(Q1.A)
Number Sense
8 – 10 block days
(Q1.B)
Percent & Proportion
4 – 6 block days
(Q1.C & Q2.A)
Linear Expressions & Equations
10 – 12 block days
Quarter 1 – 21 Block Days
(Q1.C & Q2.A)
Linear Expressions & Equations
10 – 12 block days
(Q2.B)
Linear Functions
7 – 9 block days
(Q2.C)
Graphing Linear Functions
7 – 9 block days
Quarter 2 – 23 Block Days
Additional Course Information
This course is targeted for grade 12 students,
whose test scores on the Postsecondary
Educational Readiness Test (P.E.R.T.) are at or
below the established cut scores for mathematics,
indicating that they are not yet “college ready” in
mathematics or simply need some additional
instruction in content to prepare them for success
in college level mathematics. This course
incorporates the Florida Standards for
Mathematical Practices as well as the following
Florida Standards for Mathematical Content:
Expressions and Equations, The Number System,
Functions, Algebra, Geometry, Number and
Quantity, Statistics and Probability, and the Florida
Standards for High School Modeling. The standards
align with the Mathematics Postsecondary
Readiness Competencies deemed necessary for
entry-level college courses.
Page 1 of 28
(Q3.A)
Systems of Linear Equations & Inequalities
6 – 8 block days
(Q3.B)
Polynomials & Factoring
7 – 9 block days
(Q3.C & Q4.A)
Rational Expressions & Functions
7 – 9 block days
Quarter 3 – 23 Block Days
State Assessment Information
Florida Department of Education P.E.R.T.
PERT Study Guides:
P.E.R.T. Study Guide
Study Guide 2
Study Guide 3
Test Questions by Subject
(Q3.C & Q4.A)
Rational Expressions & Functions
7 – 9 block days
(Q4.B)
Radical Equations & Functions
5 – 7 block days
(Q4.C)
Quadratic Functions
8 – 10 block days
Quarter 4 – 21 Block Days
Helpful Websites
Shmoop: Math videos
http://www.shmoop.com/video/math-videos
Edgenuity: Access video lessons and examples
http://learn.education2020.com/educator/
Kuta Software: Free worksheets
https://www.kutasoftware.com/
Math Drills: Free worksheets
www.math-drills.com
Online practice problems
www.InteractMath.com
(Click Enter, go to Choose book, then select "Bittinger, Int Alg, Graphs
& Models, 3e for the white text or 4e for the green textbook)
www.Pertfreetestpractice.com
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 1.A
Mathematics for College Readiness (1200700)
Pacing Range: 8-10 block days
Adopted Instructional Materials: Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students revisit number sense concepts initially introduced in middle grades 7 and 8. Students are able to make sense of
and work with rational numbers and real numbers, including numbers written in scientific notation and square roots. Students understand and can make sense of
rational numbers that are both positive and negative. Students will understand and apply properties of exponents in order to simplify expressions.
Standards
Math Content Standards
MAFS.7.NS.1: Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers.
MAFS.7.NS.1.1: Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent addition and
subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For
example, a hydrogen atom has 0 charge because its two constituents
are oppositely charged.
b. Understand 𝑝 + 𝑞 as the number located a distance |𝑞| from 𝑝, in the
positive or negative direction depending on whether 𝑞 is positive or
negative. Show that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers by describing
real-world contexts.
c. Understand subtraction of rational numbers as adding the additive
inverse, 𝑝 − 𝑞 = 𝑝 + (−𝑞). Show that the distance between two
rational numbers on the number line is the absolute value of their
difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational
numbers.
MAFS.7.NS.1.2: Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational
numbers by requiring that operations continue to satisfy the properties
of operations, particularly the distributive property, leading to products
such as (−1)(−1) = 1 and the rules for multiplying signed numbers.
Page 2 of 28
Suggested Mathematical Practice Standards
MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.
 What is this problem asking?
 Could someone else understand how to solve the problem based on
your explanation?
MAFS.K12.MP.6.1: Attend to Precision.
 Using precise vocabulary, explain how to simplify the problem.
 Looking at the two ways we solved this problem, explain why one way
is more efficient than the other.
 Using precise vocabulary, explain how to simplify the problem.
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
 How could solving a simpler problem help with performing operations
with scientific notation?
 What generalizations can you make about negative exponents?
 Instead of using the expanded form for exponents to solve problems,
are there any shortcuts you’re taking to solve?
Updated: August 8, 2014
Interpret products of rational numbers by describing real-world
contexts.
b. Understand that integers can be divided, provided that the divisor is not
zero, and every quotient of integers (with non-zero divisor) is a rational
number. If 𝑝 and 𝑞 are integers, then (𝑝/𝑞) = (𝑝)/𝑞 = 𝑝/(𝑞).
Interpret quotients of rational numbers by describing real-world
contexts.
c. Apply properties of operations as strategies to multiply and divide
rational numbers.
d. Convert a rational number to a decimal using long division; know that
the decimal form of a rational number terminates in 0s or eventually
repeats.
MAFS.8.NS.1: Know that there are numbers that are not rational, and
approximate them by rational numbers.
MAFS.8.NS.1.1: Know that numbers that are not rational are called irrational.
Understand informally that every number has a decimal expansion; for rational
numbers show that the decimal expansion repeats eventually, and convert a
decimal expansion which repeats eventually into a rational number.
MAFS.8.NS.1.2: Use rational approximations of irrational numbers to compare
the size of irrational numbers, locate them approximately on a number line
diagram, and estimate the value of expressions (e.g. π², ). For example, by
truncating the decimal expansion of √2 , show that √2 is between 1 and 2,
then between 1.4 and 1.5, and explain how to continue on to get better
approximations.
MAFS.8.EE.1: Work with radicals and integer exponents.
MAFS.8.EE.1.1: Know and apply the properties of integer exponents to generate
1
equivalent numerical expressions. For example, 32 × 3−5 = 3−3 = 33 = 1/27
MAFS.8.EE.1.4: Perform operations with numbers expressed in scientific
notation, including problems where both decimal and scientific notation are
used. Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities (e.g., use millimeters per
year for seafloor spreading). Interpret scientific notation that has been
generated by technology.
MAFS.912.N-RN.2: Use properties of rational and irrational numbers.
MAFS.912.N-RN.2.3: Explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational number is
irrational; and that the product of a nonzero rational number and an irrational
number is irrational.
Page 3 of 28
Updated: August 8, 2014
Big Idea(s)
Number Sense for rational, irrational, radicals and scientific numbers.
Essential Outcome Question(s)


Why is it helpful to write numbers in different ways?
Why would we need to be able to write numbers in different ways?
Understand, write, compare, and solve problems involving real numbers in various
forms
Aligned Learning Goals
Page 4 of 28
Add, subtract, multiply, and divide fractions, mixed numbers, and
decimals
Apply order of operations when simplifying mathematical
expressions
Compare and order rational numbers on a number line,
understanding the difference between terminating and repeating
decimals
Understand vocabulary associated with rational number
operations, such as opposites, additive inverse, and absolute value,
to explain how to solve problems containing rational numbers
Perform operations with integers and evaluate algebraic
expressions containing rational numbers
Know and apply properties of integer exponents and evaluate
algebraic expressions containing real numbers and integer
exponents
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Intermediate Algebra
Graphs & Models
MAFS.7.NS.1.1: Video
Lesson idea Integers
Shmoop video
combining like terms
Chapter 1, Lessons 1.1,
1.2 and 1.4
MAFS.7.NS.1.2 &
8.NS.1.1 & 1.2: Lesson
exploration of fractions
and decimals
Shmoop video adding
and subtracting
fractions
MAFS.8.EE.1.1: Integer
Exponent SMART
Resources
MAFS.8.EE.1.4: Khan
Academy Videos on
Scientific Notation
MAFS.8.EE.1.4:
LearnZillion Video
Lessons on Scientific
Notation
LearnZillion Video series
Evaluating Algebraic
Expressions
Know when to use scientific notation and perform operations with
numbers written in scientific notation
Updated: August 8, 2014
Formative Assessment Options:
MFAS Tasks: 7.NS.1.1:
 Exploring Additive Inverse
 Adding Integers
Summative Assessment(s)
Page 5 of 28
MFAS Tasks: 7.NS.1.2:
 Understanding Products
 Negative Times
 Negatives Explained
 Quotients of Integers
 Integer Division
MFAS Tasks: 8.NS.1.1:
 Rational Numbers
 Fraction to Decimal
Conversion
 Decimal to Fraction
Conversion
MFAS Tasks: 8.EE.1.1:
 Exponents Tabled
 Multiplying and Dividing
Integer Exponents
 Negative Exponential
Expressions
 Equivalent Powers
Expressions
MFAS Tasks: EE.1.4:
 Mixed Form Operations
 Sums and Differences in
Scientific Notation
 Scientific Multiplication
and Division
 Scientific Calculator
Display
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Quarter: 1.B
Adopted Instructional Materials:
Academic Plan 2014-2015
Mathematics for College Readiness (1200700)
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students work with percents and proportions to solve mathematical and real-world problems. Students recall and
understand the meaning of a proportion and solve simple proportions in both mathematical and real-world contexts. Students apply what they know about
solving proportions to finding missing numbers in a set of numbers (e.g. a test grade needed for an A average). In addition, students will apply what they know
about proportions to identify and explain direct and inverse variation. Students revisit creating equations from previous courses or apply what they know about
proportions in order to find the percent of a number. Students will extend finding the percent of a number to also finding part of a number or a number given the
percent.
Teacher Note:
Textbook is not used, proportions must connect Algebra concepts with slope as a ratio and Geometric proportions for real world problems from
supplemental resources.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.8.EE.2: Understand the connections between proportional relationships,
lines, and linear equations.
MAFS.8.EE.2.5: Graph proportional relationships, interpreting the unit rate as
the slope of the graph. Compare two different proportional relationships
represented in different ways. For example, compare a distance-time graph to a
distance-time equation to determine which of two moving objects has greater
speed.
MAFS.912.A-CED.1: Create equations that describe numbers or relationships.
MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear and quadratic
functions, and simple rational, absolute, and exponential functions.
MAFS.912.N-Q.1: Reason quantitatively and use units to solve problems.
MAFS.912.N-Q.1.1: Use units as a way to understand problems and to guide the
solution of multi-step problems; choose and interpret units consistently in
formulas; choose and interpret the scale and the origin in graphs and data
displays.
MAFS.912.N-Q.1.2: Define appropriate quantities for the purpose of descriptive
modeling.
MAFS.912.N-Q.1.3: Choose a level of accuracy appropriate to limitations on
measurement when reporting quantities.
Page 6 of 28
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of
others.
 What do you think about _____’s work?
 Is your answer different than ____’s? If so, how?
MAFS.K12.MP.4.1: Model with mathematics.
 Does your solution make sense?
 What do you know about the situation already?
Updated: August 8, 2014
MAFS.912.S-ID.3: Interpret linear models.
MAFS.912.S-ID.3.7: Interpret the slope (rate of change) and the intercept
(constant term) of a linear model in the context of the data.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems
algebraically.
MAFS.912.G-GPE.2.6: Find the point on a directed line segment between two
given points that partitions the segment in a given ratio.
MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles, e.g., using the distance formula.
Big Idea(s)
Percent and Proportions
Essential Outcome Question(s)
Use proportions to solve a variety of problems in realworld and mathematical situations
•How can you use mathematics to describe change and model real-world situations?
•How can percent help you understand situations involving money?
Aligned Learning Goals
District Adopted
Materials
Intermediate Algebra
Use a variety of strategies, including models, percent proportions, Graphs & Models
and percent equations, to solve simple percent, part, and whole
Use supplemental
problems using proportions or percent equations
resources
Page 7 of 28
Supplemental
Resources
Strategies for
Differentiation
BetterLesson.com
Finding Missing data
point
Shmoop video word
problems with
percents
LearnZillion Solving
percent of a number
problems
Shmoop video percent
of change
Solve percent problems in real-world contexts
Rates and Proportional
relationships
Find the missing value in a data set to achieve a desired mean
Khan Academy videos
direct and inverse
variation
Khan Academy for ratios
and proportions
Use proportional relationships to solve problems, including direct
variation and inverse variation
Updated: August 8, 2014
Formative Assessment Options:
Khan Academy 8.EE.2.5
 Percent Word Problems
 Constructing Proportions
Summative Assessment(s)
Page 8 of 28
MAFS Tasks: 8.EE.2.5
 Interpreting Slope
 Lines and Linear Equations
 Compare Slopes
 Proportional Paint
MAFS Tasks: 912.A-CED.1.1:
 Quilts
MAFS Tasks: 912.N-Q.1.1:
 Fishy Formulas
 Notebooks To Trees
MAFS Tasks G-GP. 2.6 and 2.7
 Partitioning a Segment
 Perimeter and Area
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 1.C & 2.A
Mathematics for College Readiness (1200700)
Pacing Range: 9-11 block days
Adopted Instructional Materials: Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students learn to use equations to model and solve real-world problems. Students extend their knowledge of one-step
equations and inequalities to include multi-step equations and inequalities. Students use the property of equality to solve equations, building on their knowledge
of solving using concrete and visual models to solving algebraically. Students will extend their understanding of solving simple equations by using them to
understand, model, and solve real-world problems. Students will apply what they learn about equations to understand, write, and solve linear inequalities.
Students will understand how to solve absolute value equations and inequalities.
Standards
Math Content Standards
MAFS.7.EE.2: Solve real-life and mathematical problems using numerical and
algebraic expressions and equations.
MAFS.7.EE.2.4: Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and inequalities to solve
problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form 𝑝𝑥 + 𝑞 = 𝑟
and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic solution
to an arithmetic solution, identifying the sequence of the operations
used in each approach. For example, the perimeter of a rectangle is 54
cm. Its length is 6 cm. What is its width?
b. Solve word problems leading to inequalities of the form px + q > r or px
+ q < r, where p, q, and r are specific rational numbers. Graph the
solution set of the inequality and interpret it in the context of the
problem. For example: As a salesperson, you are paid $50 per week
plus $3 per sale. This week you want your pay to be at least $100.
Write an inequality for the number of sales you need to make, and
describe the solutions.
MAFS.912.A-CED.1: Create equations that describe numbers or relationships.
MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear and quadratic
functions, and simple rational, absolute, and exponential functions.
MAFS.912.A-CED.1.3: Represent constraints by equations or inequalities, and by
systems of equations and/or inequalities, and interpret solutions as viable or
Page 9 of 28
Suggested Mathematical Practice Standards
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
 What does the number ____ represent in the problem?
 How can you represent the problem with symbols and numbers?
MAFS.K12.MP.7.1: Look for and make use of structure.
 How is ____ related to ____?
 Why is this important to the problem?
Updated: August 8, 2014
non-viable options in a modeling context. For example, represent inequalities
describing nutritional and cost constraints on combinations of different foods.
MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations. For example, rearrange Ohm’s
law V = IR to highlight resistance R.
MAFS.912.A-SSE.1: Interpret the structure of expressions.
MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of
its context.
c. Interpret parts of an expression, such as terms, factors, and coefficients.
d. Interpret complicated expressions by viewing one or more of their parts
as a single entity. For example, interpret
as the product of P and
a factor not depending on P.
MAFS.912.A-REI.1: Understand solving equations as a process of reasoning
and explain the reasoning.
MAFS.912.A-REI.1.1: Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable
argument to justify a solution method.
MAFS.912.A-REI.2: Solve equations and inequalities in one variable.
MAFS.912.A-REI.2.3: Solve linear equations and inequalities in one variable,
including equations with coefficients represented by letters.
Big Idea(s)
Writing and solving Linear Expressions, Equations, and Inequalities.
Essential Outcome Question(s)


What does it mean to say two quantities are equal?
Why would it be helpful to model real-world problems with equations or inequalities?
Page 10 of 28
Updated: August 8, 2014
Aligned Learning Goals
Simplify algebraic expressions and Solve linear equations and
inequalities
Simplify algebraic expressions, including combining like terms
District Adopted
Materials
Supplemental
Resources
Strategies for
Differentiation
Intermediate Algebra
Graphs & Models
MAFS.912.A-SSE.1.1:
Manipulating
Polynomials Lesson
Shmoop multi-step
equations
Chapter 1, 1.6, and 1.7
Translate real-world situations into algebraic expressions
Chapter 4, Lessons 4.1
and 4.4
Evaluate equations and inequalities to determine solutions
Shmoop video
graphing absolute
value equations
Khan Academy Video
Lessons area and
perimeter word
problems
Khan Academy videos
absolute value equations
Solve linear equations and solve and graph linear inequalities
Khan Academy videos
absolute value
inequalities
Solve literal equations
Absolute value equation
and inequality problems
with worked out
solutions attached
Solve absolute value equations and inequalities
Solve real-world problems, including perimeter problems
Formative Assessment Options:
MFAS Tasks: A-CED.1.1:
 County Fair
 Music Club
 Quilts
 Follow Me
Summative Assessment(s)
Page 11 of 28
MFAS Tasks: A-CED.1.3:
 Sugar and Protein
 The New School
 Constraints on Equations
MFAS Tasks: A-CED.1.4:
 Solving Literal Equations
 Literal Equations
 Solving Formulas for a
Variable
 Surface Area of a Cube
 Rewriting Equations
MFAS Tasks: A-REI.1.1:
 Justify the Process - 1
 Does it Follow?
 Justify the Process - 2
 Equation Logic
MFAS Tasks: A-CED.1.1:
 County Fair
 Music Club
 Quilts
 Follow Me
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 2.B
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students will continue their work with functions--describing characteristics of functions and understanding functions in a
variety of mathematical and real-world contexts. Students will use multiple methods to model and compare linear functions, including comparing the properties
of two functions represented in different ways. Students will identify and give examples of both linear and non-linear functions and will describe the functional
relationship between two quantities by analyzing the graph of the function. Students will describe equations in the form 𝑦 = 𝑚𝑥 + 𝑏 as linear functions and will
be able to identify intercepts, rate of change, and initial values of functions. By the end of this unit, students will be using appropriate vocabulary to describe
functions and will have a clear understanding of what a function is. Students will work with various representations of functions, manipulating them to model a
situation, including those involving compositions of functions.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.8.F.2: Use functions to model relationships between quantities.
MAFS.8.F.2.4: Construct a function to model a linear relationship between two
quantities. Determine the rate of change and initial value of the function from a
description of a relationship or from two (𝑥, 𝑦) values, including reading these
from a table or from a graph. Interpret the rate of change and initial value of a
linear function in terms of the situation it models, and in terms of its graph or a
table of values.
MAFS.912.F-IF.1: Understand the concept of a function and use function
notation.
MAFS.912.F-IF.1.1: Understand that a function from one set (called the domain)
to another set (called the range) assigns to each element of the domain exactly
one element of the range. If 𝑓 is a function and x is an element of its domain,
then 𝑓(𝑥) denotes the output of 𝑓 corresponding to the input x. The graph of 𝑓
is the graph of the equation 𝑦 = 𝑓(𝑥).
MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the
context.
MAFS.912.F-IF.2.5: Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes. For example, if the
function h(n) gives the number of person-hours it takes to assemble n engines in
a factory, then the positive integers would be an appropriate domain for the
function.
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of
others.
 Do you agree with that answer? Explain.
 Repeat what he/she said in your own words.
 How do you know what you are saying is true?
MAFS.K12.MP.4.1: Model with mathematics.
 What other ways could you use to model the situation mathematically?
 What connections can you make between different representations of
the situation?
MAFS.K12.MP.7.1: Look for and make use of structure.
 How can you use what you know to explain why this works?
What patterns do you see
Page 12 of 28
Updated: August 8, 2014
MAFS.912.S-ID.2: Summarize, represent, and interpret data on two categorical
and quantitative variables.
MAFS.912.S-ID.2.5: Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies). Recognize
possible associations and trends in the data.
MAFS.912.S-ID.2.6: Represent data on two quantitative variables on a scatter
plot, and describe how the variables are related.
Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. Use given functions or choose a function suggested by the
context. Emphasize linear, and exponential models.
Informally assess the fit of a function by plotting and analyzing residuals.
Fit a linear function for a scatter plot that suggests a linear association.
Big Idea(s)
Linear Functions and their graphs.
Essential Outcome Question(s)


How can you find and use patterns to model real-world situations?
How can we model relationships between quantities?
Aligned Learning Goals
Understand and manipulate functions
Understand and identify domain and range for a function
Page 13 of 28
District Adopted
Materials
Supplemental
Resources
Intermediate Algebra
Graphs & Models
LearnZillion video
lessons function
notation, evaluating
functions
Chapter 2, Lesson 2.1
and Lesson 2.5
Evaluate functions for a specific value
Add, subtract, multiply, and divide functions
Khan Academy video
lessons function
composition
Strategies for
Differentiation
Shmoop video
introduction to
functions
SMART Intro to
Functions Resources
Khan Academy video
lessons domain and
range of a function
Find the composition of two functions
Updated: August 8, 2014
Formative Assessment Options:
MFAS Tasks: F.1.1
 What is a Function?
 Identifying Algebraic
Functions
 Recognizing Functions
 Tabulating Functions
Summative Assessment(s)
Page 14 of 28
MFAS Tasks: F.1.2
 Innovative Functions
 Speed Reading
 Competing Functions
 This House is Mine!
MFAS Tasks: F.1.3
 What Am I?
 Explaining Linear Functions
 Nonlinear Functions
 Linear or Nonlinear?
MFAS Tasks: F.2.4
 Construction Function
 Profitable Functions
 Trekking Functions
 Smart TV
 Drain the Pool
MFAS Tasks: F-IF.2.5:
 Height vs. Shoe Size
 Car Wash
 Describe the Domain
 Airport Parking
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 2.C
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students work with two-variable linear equations and inequalities to solve problems. Students will write and graph
equations in slope-intercept form, identifying key features of the graph. Students will identify parallel and perpendicular lines on the coordinate plane and will
understand how to graph parallel and perpendicular lines. To round out graphs of linear functions, students will write and graph linear inequalities, understanding
constraints when graphing inequalities.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.8.EE.2: Understand the connections between proportional relationships,
lines, and linear equations.
MAFS.8.EE.2.5: Graph proportional relationships, interpreting the unit rate as
the slope of the graph. Compare two different proportional relationships
represented in different ways. For example, compare a distance-time graph to a
distance-time equation to determine which of two moving objects has greater
speed.
MAFS.8.F.2: Use functions to model relationships between quantities.
MAFS.8.F.2.4: Construct a function to model a linear relationship between two
quantities. Determine the rate of change and initial value of the function from a
description of a relationship or from two (x, y) values, including reading these
from a table or from a graph. Interpret the rate of change and initial value of a
linear function in terms of the situation it models, and in terms of its graph or a
table of values.
MAFS.912.F-IF.1: Understand the concept of a function and use function
notation.
MAFS.912.F-IF.1.1: Understand that a function from one set (called the domain)
to another set (called the range) assigns to each element of the domain exactly
one element of the range. If 𝑓 is a function and x is an element of its domain,
then 𝑓(𝑥) denotes the output of 𝑓 corresponding to the input x. The graph of 𝑓
is the graph of the equation 𝑦 = 𝑓(𝑥).
MAFS.912.F-BF.1: Build a function that models a relationship between two
quantities.
MAFS.912.F-BF.1.1: Write a function that describes a relationship between two
quantities.
MAFS.K12.MP.2.1: Reason abstractly and quantitatively
 What do each of the numbers in the equation represent?
 How can you show or prove that the equation and the table are
related?
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of
others.
 How do you know the graph of the line is represented by that equation?
 How do you know if a graph represents a proportional relationship?
 Compare the graph of a function to the table of another function. What
comparisons can you make?
Page 15 of 28
Updated: August 8, 2014
a. Determine an explicit expression, a recursive process, or steps for
calculation from a context.
b. Combine standard function types using arithmetic operations. For
example, build a function that models the temperature of a cooling body
by adding a constant function to a decaying exponential, and relate
these functions to the model.
c. Compose functions. For example, if 𝑇(𝑦) is the temperature in the
atmosphere as a function of height, and ℎ(𝑡) is the height of a weather
balloon as a function of time, then 𝑇(ℎ(𝑡)) is the temperature at the
location of the weather balloon as a function of time.
MAFS.912.A-CED.1: Create equations that describe numbers or relationships.
MAFS.912.A-CED.1.2: Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate axes with
labels and scales.
MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.
MAFS.912.A-REI.4.10: 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).
MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the
context.
MAFS.912.F-IF.2.5: Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes. For example, if the
function h(n) gives the number of person-hours it takes to assemble n engines in
a factory, then the positive integers would be an appropriate domain for the
function.
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems
algebraically.
MAFS.912.G-GPE.2.5: 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).
Big Idea(s)
Graphing Linear Functions
Essential Outcome Question(s)


How can you communicate mathematical ideas effectively?
In what ways are graphs useful for modeling real-world situations?
Page 16 of 28
Updated: August 8, 2014
Understand and graph linear
functions in slope-intercept form,
identifying key features of the graph
Aligned Learning Goals
District Adopted
Materials
Graph and write linear equations and functions in slope-intercept
form
Identify key features of linear graphs, including slope, x-intercepts,
and y-intercept
Supplemental
Resources
Intermediate Algebra
Graphs & Models
Lesson connecting unit
rate and slope
Chapter 2, Lessons 2.2
and 2.3
LearnZillion graphing in
slope-intercept form
Khan Academy video
lessons parallel and
perpendicular lines
Find slope from a variety of mathematical representations,
including graphs and tables
Strategies for
Differentiation
Lesson Designing a
Skateboard Kicker
Ramp
Shmoop Slope
Intercept form
SMART Linear
Functions Resources
MAFS.912.G-GPE.2.5:
Parallel and
Perpendicular Lines
Find the slope of vertical and horizontal lines and apply to graph
parallel and perpendicular lines
Formative Assessment Options:
MFAS Tasks: F-BF.1.1:
 Giveaway
 Saving for a Car
 How much Bacteria?
 Furniture Purchase
Summative Assessment(s)
Page 17 of 28
MAFS Tasks: A-REI.4.10:
 Finding Solutions
 What is the Point?
 Case in Point
MAFS Tasks: A.CED.1.2:
 Tech Repairs
 Tech Repairs Graph
 Trees In Trouble
 Hotel Swimming Pool
 Model Rocket
MAFS Tasks: G-GPE.2.5:
 Finding Equations of Parallel and Perpendicular Lines
 Writing Equations for Parallel Lines
 Writing Equations for Perpendicular Lines
 Proving Slope Criterion for Parallel Lines - One
 Proving Slope Criterion for Parallel Lines – Two
 Proving Slope Criterion for Perpendicular Lines – One
 Proving Slope Criterion for Perpendicular Lines - Two
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 3.A
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students will apply what they know about linear relationships to write, solve, and graph systems of linear equations and
inequalities. Students will apply previous knowledge about graphing and solving to choose appropriate solution methods and will be able to justify solutions and
estimate solutions from visual representations. Students will also deepen their understanding of constraints on the domain and range, if any, based on the
solution of a problem.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.912.A-REI.3: Solve systems of equations.
MAFS.912.A-REI.3.5: 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.
MAFS.912.A-REI.3.6: Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear equations in two
variables.
MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically.
MAFS.912.A-REI.4.11: 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.
MAFS.912.F-IF.3: Analyze functions using different representations.
MAFS.912.F-IF.3.7: 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.
MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.
 What is this problem asking?
 Could someone else understand how to solve the problem based on
your explanation?
MAFS.K12.MP.5.1: Use appropriate tools strategically.
 What math tools are available for finding the solution to a system of
equations or inequalities?
Big Idea(s)
Systems of Equations and Inequalities
Page 18 of 28
Updated: August 8, 2014
Essential Outcome Question(s)


How are the different representations of systems related?
What are similarities and differences between the solution of a system of equations and the solution(s) of a single linear equation?
Understand the connections between
graphs, real-world contexts, and solutions of
systems of linear equations and inequalities
Aligned Learning Goals
Use multiple methods for solving and justifying systems of linear
equations and inequalities
District Adopted
Materials
Supplemental
Resources
Intermediate Algebra
Graphs & Models
MAFS.912.A-REI.3.6:
Lesson Graphing vs.
Substitution
Chapter 3, Lessons 3.1
and 3.2
Understand and interpret graphs of systems of linear equations
and inequalities
MAFS.912.A.REI.3:
Lesson Solving Systems
Chapter 4, Lesson 4.5
Create systems of linear equations and inequalities from a variety
of contexts
Strategies for
Differentiation
Shmoop video Solving
by Elimination
Shmoop video Solving
by Substitution
Shmoop video Solving
by Graphing
SMART Systems
Resources
Represent and interpret constraints for systems of linear equations
and inequalities
Formative Assessment Options:
MFAS Tasks: A-REI.3.5:
 Solutions Sets of Systems
 Adding Linear Equations
Summative Assessment(s)
Page 19 of 28
MFAS Tasks: A-REI.3.6:
 Apples and Peaches
 Solving a System of Equations 1
 Solving a System of Equations 2
 Solving a System of Equations 3
MFAS Tasks: A-REI.4.11:
 Graphs and Solutions
 Graphs and Solutions 2
 Using Tables
 Using Technology
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 3.B
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students will expand their knowledge of expressions and equations to include polynomial expressions and equations. They
will use structure and knowledge of arithmetic properties to simplify polynomials and to perform addition, subtraction, and multiplication on polynomials. This
work will lead to factoring and using factoring to simplify quadratic expressions and solve quadratic equations. In addition to factoring quadratic expressions,
students will also factor sums and differences of cubes.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.912.A-APR.1: Perform arithmetic operations on polynomials.
MAFS.912.A-APR.1.1: Understand that polynomials form a system analogous to
the integers, namely, they are closed under the operations of addition,
subtraction, and multiplication; add, subtract, and multiply polynomials.
MAFS.912.A-APR.2: Understand the relationship between zeros and factors of
polynomials.
MAFS.912.A-APR.2.3: Identify zeros of polynomials when suitable factorizations
are available, and use the zeros to construct a rough graph of the function
defined by the polynomial.
MAFS.912.A-SSE.1: Interpret the structure of expressions.
MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to
rewrite it. For example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a
difference of squares that can be factored as (x² – y²)(x² + y²).
MAFS.912.A-SSE.2: Write expressions in equivalent forms to solve problems.
MAFS.912.A-SSE.2.3: 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.
MAFS.K12.MP.7.1: Look for and make use of structure.
 What patterns do you see?
 Can you look at the individual parts/terms of the polynomials to help
solve the problem?
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
 Are there generalizations you can make about multiplying binomials?
 Why are some products of binomials referred to as special cases?
Big Idea(s)
Page 20 of 28
Updated: August 8, 2014
Polynomials and Factoring
Essential Outcome Question(s)
When can a polynomial function be used to model and solve a real-world problem?
Make connections between the structure of polynomials and
using factoring to solve
Understand the structure
of and fluently perform
operations on
polynomials
Aligned Learning Goals
Page 21 of 28
Identify parts of polynomial expressions
District Adopted
Materials
Intermediate Algebra
Graphs & Models
Chapter 5, Lessons 5.1
through 5.7
Perform operations on polynomial expressions
Factor polynomials using a variety of strategies, including factoring
out a GCF and factoring by grouping
Supplemental
Resources
Khan Academy video
lessons factoring
quadratic expressions
Strategies for
Differentiation
SMART Polynomial
Resources
Lesson Plan: Solving
Quadratic Equations
MAFS.912.A-APR.2.3:
Zeros and Factorization
of a Quadratic
Polynomial I
LearnZillion: factoring
quadratics
Factor quadratic expressions with a leading coefficient of 1
Factor quadratic expressions with a leading coefficient other than 1
Factor special cases, including perfect square trinomials and
difference of squares
Factor sums and differences of cubes
Updated: August 8, 2014
Formative Assessment Options:
MFAS Tasks A-APR.1.1:
 Adding Polynomials
 Subtracting Polynomials
 Multiplying Polynomials 1
 Multiplying Polynomials 2
Summative Assessment(s)
Page 22 of 28
MFAS Tasks A-APR.2.3:
 Zeros of a Quadratic
 Use Zeros to Graph
MAFS Tasks A-SSE.2.3:
 Rocket Town
 Jumping Dolphin
 College Costs
MAFS Tasks .A-SSE.1.2:
 Find Missing Values
 Quadratic Expressions
 Rewriting Numerical
Expressions
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 3.C & 4.A
Mathematics for College Readiness (1200700)
Pacing Range: 6-8 block days
Adopted Instructional Materials: Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students will extend their knowledge of constraints to rational functions as they solve and graph. Students will apply their
knowledge of polynomials to perform operations on and simplify rational expressions. This unit brings together many of the concepts students have been building
upon all year. With a solid foundation in conceptual knowledge of key algebraic concepts, students apply what they know to more complex situations.
Teacher Note:
Students will graph linear, quadratic, and polynomial functions describing the important features of each type of graph. This can be done in connection with the
use of graphing technology.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.912.A-APR.4: Rewrite rational expressions.
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of
MAFS.912.A-APR.4.6: Rewrite simple rational expressions in different forms;
others.
write 𝑎(𝑥)/𝑏(𝑥) in the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and
 How can you use precise language to explain how to graph a rational
𝑟(𝑥) are polynomials with the degree of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using
function?
inspection, long division, or, for the more complicated examples, a computer
 Do you agree with ______’s answer?
algebra system.
 Can you re-explain ______’s solution method?
MAFS.912.A-APR.4.7: Understand that rational expressions form a system
analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add, subtract,
multiply, and divide rational expressions.
MAFS.912.F-IF.3: Analyze functions using different representations.
MAFS.912.F-IF.3.7: 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.
c. Graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
Big Idea(s)
Rational Expressions and Functions
Page 23 of 28
Updated: August 8, 2014
Essential Outcome Question(s)
How does analyzing the structure of an expression or equation help you simplify and solve more complex problems?
Identify key features
of the graphs of
polynomials
Perform operations on
rational expressions
Aligned Learning Goals
Use knowledge of factoring and factors to multiply and divide
rational expressions
District Adopted
Materials
Intermediate Algebra
Graphs & Models
Chapter 6, Lessons 6.1
and 6.2
Apply knowledge of fraction operations to add and subtract
rational expressions
Graph polynomial functions, identifying key features
Supplemental
Resources
Strategies for
Differentiation
MAFS.912.A-APR.4.7:
Lesson connecting
fraction addition to
adding rational
expressions
Khan Academy: add and
subtract rational
expressions
CPALMS: similarities and
differences of rational
expressions
Compare linear, quadratic, and polynomial functions
Formative Assessment Options:
MAFS F-IF.3.7:
 Graphing a Linear Function
 Graphing Root Functions
 Graphing a Quadratic Function
 Graphing a Rational Function
Summative Assessment(s)
Page 24 of 28
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 4.B
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students will extend their knowledge of exponents and general number sense in working with radicals. Students will be
able to simplify radical expressions and perform operations with radicals. Students will apply what they learn about radical operations to solve radical functions in
mathematical and real-world contexts..
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.912.A-REI.1: Understand solving equations as a process of reasoning
and explain the reasoning.
MAFS.912.A-REI.1.2: Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
MAFS.912.F-BF.2: Build new functions from existing functions.
MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing 𝑓(𝑥) by
𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive
and negative); find the value of 𝑘 given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic expressions
for them.
MAFS.912.N-RN.1: Extend the properties of exponents to rational exponents.
MAFS.912.N-RN.1.1: Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer exponents to those
values, allowing for a notation for radicals in terms of rational exponents. For
example, we define
to be the cube root of 5 because we
want
=
to hold, so
must equal 5.
MAFS.912.N-RN.1.2: Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
MAFS.K12.MP.6.1: Attend to precision.
 Why are some solutions left in radical form and others simplified?
 What degree of accuracy is needed for the solution?
Big Idea(s)
Solving and Graphing Radical Equations
Essential Outcome Question(s)
What connections can be made between simplifying expressions and polynomials and simplifying radical expressions?
Page 25 of 28
Updated: August 8, 2014
Simplify algebraic expressions
containing radicals
Aligned Learning Goals
Simplify radicals and radical expressions
Multiply and divide rational expressions in mathematical contexts
Supplemental
Resources
Intermediate Algebra
Graphs & Models
Khan Academy: Radical
equations
Chapter 7, Lessons 7.1,
7.3 through 7.5, and 7.8
Khan Academy video
series fractional
exponents
Strategies for
Differentiation
Shmoop: Fractional
exponents
Perform multiple operations on radical expressions, including
rationalizing the denominator
Apply properties of complex numbers when performing operations
on rational expressions
Formative Assessment Options:
MAFS Tasks F-BF.2.3:
 Comparing Functions – Linear
 Comparing Functions - Quadratic
 Writing The Equations
 Comparing Functions - Exponential
Summative Assessment(s)
Page 26 of 28
District Adopted
Materials
MAFS Tasks N-RN.1.1 and 1.2
 Rational Exponents -1
 Rational Exponents -2
 Rational Exponents -3
 Rational Exponents -4
Progress Monitoring Assessment
Updated: August 8, 2014
THE SCHOOL DISTRICT OF LEE COUNTY
Academic Plan 2014-2015
Quarter: 4.C
Mathematics for College Readiness (1200700)
Adopted Instructional Materials:
Pacing Range: 6-8 block days
Intermediate Algebra Graphs & Models
Description of this Unit: In this unit, students make connections between visual representations of quadratic functions and their algebraic representations.
Students will learn a variety of additional methods to solve quadratic equations. Learning all types of solution methods will help students make associations to
structure, seeing when one solution type is more favorable than another. Students will be able to identify key features of quadratic functions, making connections
to similar key features with linear functions and paving the way for future transformations on various functions.
Standards
Math Content Standards
Suggested Mathematical Practice Standards
MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the
context.
MAFS.912.F-IF.2.4: For a function that models a relationship between two
quantities, interpret key features of graphs and tables in terms of the quantities,
and sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
MAFS.912.F-IF.2.6: Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a specified interval. Estimate
the rate of change from a graph.
MAFS.912.F-IF.3: Analyze functions using different representations.
MAFS.912.F-IF.3.8: Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph,
and interpret these in terms of a context.
MAFS.K12.MP.4.1: Model with mathematics.
 How does the graph of a quadratic function provide useful information for
solving real-life problems?
MAFS.K12.MP.5.1: Use appropriate tools strategically.
 What is another way to find the zeros of a quadratic? Is one way more
useful than another? Why or why not?
Big Idea(s)
Solving equations and graph of quadratics, connecting to transformational changes.
Essential Outcome Question(s)


What information does the solution(s) of a quadratic equation give you?
What does changing values in a quadratic equation tell you about its transformation and graph?
Page 27 of 28
Updated: August 8, 2014
Aligned Learning Goals
Solve and graph quadratic
equations
Use the quadratic formula to solve quadratic equations
Understand and identify key features of quadratic functions
District Adopted
Materials
Supplemental
Resources
Intermediate Algebra
Graphs & Models
MAFS.912.A-REI.3.7:
Problem solving task
Chapter 8 Lessons:
8.1 through 8.4,
8.6 through 8.8
MAFS.912.A-REI.2.4:
Khan Academy video
quadratic formula proof
Strategies for
Differentiation
MAFS.912.F-BF.2.3:
Video using
transformations to
graph quadratic
functions
Use various methods to solve quadratic equations
Formative Assessment Options:
MFAS Tasks A-REI.2.4:
 Complete the Square - 1
 Complete the Square - 2
 Complete the Square - 3
 Quadratic Formula Part 1
 Quadratic Formula Part 2
 Which Strategy?
 Complex Solutions?
Summative Assessment(s)
Page 28 of 28
MFAS Tasks F-IF.2.6:
 Pizza Palace
 Identifying Rate of Change
 Estimating the Average Rate of Change
Progress Monitoring Assessment
Updated: August 8, 2014