Algebra 1 Algebra 1 Honors Curriculum Map 2016-2017rev 9-30-16

2016 - 2017

Algebra 1
Algebra 1 Honors
Curriculum Map

1200310, 1200320

Volusia County Curriculum Maps are revised annually and updated throughout the year.
The learning goals are a work in progress and may be modified as needed.

Volusia County Curriculum Maps are revised annually and updated throughout the year.

ThCe luearrnriincgugolaulsmareMa waorpk in&proRgreesvsiaendwmeayrb’esmCoodifmiedmas inteteedeed.

Name School Name School
Dawn Bourdette NSB High School Melanie Ford Atlantic High School
Kim Sparger Creekside Middle School Elias Freidus Spruce Creek High School
Lisa Jones Pine Ridge High School Shatonya Knight Taylor Middle/High School
Kristen Dawson University High School Cathy Hardy DeLand High School
Valentin Sotomayor Galaxy Middle School

Florida Standards
Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (MAFS.K12.MP.1)

Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process

which sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (MAFS.K12.MP.2)

The concrete and the abstract can complement each other in the development of mathematical understanding:

representing a concrete situation with symbols can make the solution process more efficient, while reverting to a concrete

context can help make sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (MAFS.K12.MP.3)

A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and

supporting evidence.

4. Model with mathematics. (MAFS.K12.MP.4)

Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MAFS.K12.MP.5)

Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen

mathematical understanding.

6. Attend to precision. (MAFS.K12.MP.6)

AttendiNnagmtoeprecise detail increaseSs crehloiaoblility of mathematical rNesaumltse and minimizes miscomSmchuonioclation of mathematical

explanMateiollnisssa. Ciulla Ormond Beach Middle School Mary Mosher NSB High School
7. Look for and make use of structure. (MAFS.K12.MP.7)

RecognJoizhinnHgoallasntdructure or pattern cHaenritbaegethMeidkdeleyStcohosoollving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (MAFS.K12.MP.8)

Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results

more quickly and efficiently.

Algebra 1: Florida Standards

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, called units,
deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a
linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Mathematical Practice Standards apply throughout each
course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their
ability to make sense of problem situations.

Relationships Between Quantities and Reasoning with Equations/Inequalities: By the end of eighth grade students have learned to solve linear equations in
one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier
experiences by asking students to analyze and explain the process of solving an equation. Students analyze and explain the process of solving an equation.
Students develop fluency, writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems.
They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential
equations.

Linear/Exponential Relationships and Functions: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships
between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many examples of functions,
including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the
limitations of various representations. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They
compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students explore systems of equations and
inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
This unit also builds upon students’ prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use
regression techniques to describe and approximate linear relationships between quantities. They use graphical representations and knowledge of the context to
make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

Expressions and Equations: In this unit, students build on their knowledge from the unit of Linear and Exponential Relationships, where they extended the laws
of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and
exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions.

Quadratic Functions and Modeling: In this unit, students consider quadratic functions, comparing the key characteristics of quadratic functions to those of
linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by
interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeroes of a related quadratic
function. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise-defined.

Algebra 1: Florida Standards At A Glance

FSA End of Course Assessment: Reporting Catagories and Percentage of Test:

Algebra and Modeling= 41% Functions and Modeling = 40% Statistics and the Number System = 19%

First Quarter Second Quarter Third Quarter Fourth Quarter

The standards listed below apply throughout the year. Refer to the learning targets for specificity related to the standard.

MAFS.912.A-CED.1.1 MAFS.912.F-IF.2.4 MAFS.912.A-REI.4.11 MAFS.912.A-SSE.1.1 MAFS.912.F-IF.3.7 MAFS.912.F-IF.3.9

MAFS.912.F-BF.2.3

Review Systems of Linear Equations & Polynomials Analyzing Univariate Data

SMT 1 Inequalities MAFS.912.A-APR.1.1 MAFS.912.S-ID.1.1

Linear Equations MAFS.912.A-CED.1.3 MAFS.912.A-APR.2.2 MAFS.912.S-ID.1.2

MAFS.912.A-CED.1.4 MAFS.912.A.-REI.3.5 MAFS.912.A-APR.2.3 MAFS.912.S-ID.1.3

MAFS.912.A-REI.1.1 MAFS.912.A.-REI.3.6 MAFS.912.A-APR.3.4 MAFS.912.S-ID.1.4

MAFS.912.A-REI.1.2 MAFS.912.A.-REI.4.12 MAFS.912.A-APR.4.6

MAFS.912.A-REI.2.3 DIA2 MAFS.912.A-REI.2.4 Analyzing Bivariate Data

Exponents & Exponential Functions MAFS.912.A-SSE.1.2 MAFS.912.S-ID.2.5

Linear Functions MAFS.912.F-BF.1.1 MAFS.912.A-SSE.2.3 MAFS.912.S-ID.2.6

MAFS.912.F-BF.1.2 MAFS.912.F-BF.1.2 MAFS.912.S-ID.3.7

MAFS.912.F-IF.1.1 MAFS.912.F-IF.1.3 MAFS.912.S-ID.3.8

MAFS.912.F-IF.2.5 MAFS.912.F-IF.3.8 MAFS.912.S-ID.3.9

MAFS.912.F-IF.2.6 MAFS.912.F-LE.1.1 Quadratic Functions & Equations

MAFS.912.F-LE.1.2 MAFS.912.F-LE.1.2 MAFS.912.F-IF.2.6

MAFS.912.A-REI.4.10 MAFS.912.F-LE.2.5 MAFS.912.F-IF.3.8 FSA EOC

MAFS.912.N-RN.1.1 MAFS.912.F-LE.1.3

DIA1 MAFS.912.N-RN.1.2 *MAFS.912.A-REI.2.4

Equations of Linear Functions MAFS.912.A-SSE.1.2 MAFS.912.A-SSE.2.3 Italic standards are repeated

MAFS.912.A-CED.1.2 MAFS.912.A-SSE.2.3

MAFS.912.F-BF.1.1 MAFS.912.A-SSE.2.4 Highlighted = Algebra 1 Honors

MAFS.912.F-BF.2.4 DIA3 ONLY.

MAFS.912.F-IF.1.2 SMT2 Radical Functions

MAFS.912.F-LE.2.5 MAFS.912.F-BF.2.4

MAFS.912.S-ID.2.6 MAFS.912.A-REI.1.2

MAFS.912.S-ID.3.7 MAFS.912.N-RN.1.2

MAFS.912.N-RN.2.3

Linear Inequalities

MAFS.912.A-CED.1.3

MAFS.912.A-REI.2.3

Major cluster – Standards requiring greater amounts of time to develop in students (apx. 65-85% of class time)

Supporting Cluster Additional *According to the Focus documents from SAP - http://achievethecore.org/page/774/focus-by-grade-level

RN: The Real Number System Domain Abbreviations BF: Building Functions
CED: Creating Equations SSE: Seeing Structure in Expressions IF: Interpreting Functions
LE: Linear, Quadratic And Exponential Models REI: Reasoning with Equations and Inequalities
ID: Interpreting Categorical and Quantitative Data APR: Arithmetic with Polynomials and Rational Expressions

Fluency Recommendations
A/G- Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the
equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as
well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables).
A-APR.1- Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in Algebra, as well as in their
symbolic work with functions. Manipulation can be more mindful when it is fluent.
A-SSE.1b- Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring,
completing the square, and other mindful algebraic calculations.

The following Mathematics and English Language Arts CCSS should be taught throughout the course:
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.

LACC.910.RST.1.3: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements or performing
tasks, attending to special cases or exceptions defined in the text.
LACC.910.RST.2.4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in context
and topics.
LACC.910.RST.3.7: Translate quantitative or technical information expressed in words in a text into visual form and translate information
expressed visually or mathematically into words.
LACC.910.SL.1.1: Initiate and participate effectively in a range of collaborative discussions with diverse partners.
LACC.910.SL.1.2: Integrate multiple sources of information presented in diverse media or formats evaluating the credibility and accuracy of
each source.
LACC.910.SL.1.3: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or
exaggerated or distorted evidence.
LACC.910.SL.2.4: Present information, findings and supporting evidence clearly, concisely, and logically such that listeners can follow the
line of reasoning.
LACC.910.WHST.1.1: Write arguments focused on discipline-specific content.
LACC.910.WHST.2.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose,
and audience.
LACC.910.WHST.3.9: Draw evidence from informational texts to support analysis, reflection, and research.
ELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the

ELD.K12.ELL.SI.1: content area of Mathematics.
English language learners communicate for social and instructional purposes within the school setting.

Algebra 1 / Algebra 1 Honors Pacing Guide

Week Date Topic Modules Units/DIAs
1 Review/SMT - 0
2-6 August 15 - August 19
August 22 – September Linear Equations & Linear Functions 2 1
7-9
10 23 Equations of Linear Functions 3&4 2
September 26 – October 5 2
11-13 Linear Inequalities
14 End of 1st Grading Period 6 2
14-17
October 17- October 20 Systems of Linear Equations & Inequalities
18-19
TDD October 21 Exponents & Exponential Functions 7 3
20-23 October 24 – November
23-26 Review/SMT 2 - -
27-28 10
November 14 – December End of 2nd Grading Period – Winter Break 3&4
29 3
9 Polynomials 8 & 11 4
30 December 12 - December 5
31-32 Quadratic Functions & Equations 9
33-35 20 5
36-39 TDD December 21 Radical Functions 10
January 4 – January 24
39 January 25 – February 17 Analyzing Univariate Data 12 & Math
February 21 – March 3 Nation

March 6 - March 9 End of 3rd Grading Period - Spring Break

TDD March 10 Analyzing Univariate Data Math Nation
March 20 – March 24
Analyzing Bivariate Data
March 27 - April 7
April 10 – April 28 Review and FSA Administration

May1 – May 25 Geometry Prep
End of 4th Quarter Period – Last Day for Students
May 26

Key Shifts in Mathematics

The Mathematics Florida State Standards build on the best of existing standards and reflect the skills and
knowledge students will need to succeed in college, career, and life. Understanding how the standards differ
from previous standards—and the necessary shifts they call for—is essential to implementing them.

The following are the key shifts called for by the Standards:

1. Greater Focus on fewer topics
2. Coherence: Linking topics and thinking across grades
3. Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal

intensity

 Conceptual understanding: The Standards call for conceptual understanding of key concepts,
such as place value and ratios. Teachers support students ‘ability to access concepts from a
number of perspectives so that students are able to see math as more than a set of mnemonics
or discrete procedures.

 Procedural skill and fluency: The Standards call for accuracy in calculation, number sense
and deep understanding of numerical principles, not blind memorization or fast recall (Boaler,
2009). Teachers structure class time and/or homework time for students to practice core
functions such as single; digit multiplication so that students have access to more complex
concepts and procedures.

 Application: The Standards call for students to use math flexibly for applications. Teachers
provide opportunities for students to apply math in context. . Correctly applying mathematical
knowledge depends on students having a solid conceptual understanding and procedural
fluency.

 The rigor of each Mathematical Florida Standards on this curriculum map has an Icon to identify
the component of rigor for the purpose of lesson planning.

Linear Equations

Essential Question(s):

How do you create equations that describe relationships? How do you solve equations with one variable?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-CED.1.1  identify the variables and quantities  In items that require the student to write an equation,

represented in a real world problem. equations are limited to exponential functions with one
translation, linear functions, or quadratic functions.
Create equations and inequalities in one variable  write the equation that best models  Items may include equations or inequalities that contain
and use them to solve problems. variables on both sides.
 the problem.  In items that require the student to write an exponential
solve linear equations. function given ordered pairs, at least one pair of consecutive
values must be given.
MFAS: State Fair Music Club Follow Me  interpret the solution in the context  In items that require the student to write or solve an
of the problem.

ALGEBRA NATION: Section 2 (Videos 3-7)

SMP: # 4  solve a formula for a given variable. inequality, variables are restricted to an exponent of one.
MAFS.912.A-CED.1.4  Items that involve formulas should not include overused

contexts such as Fahrenheit/Celsius or three-dimensional

Rearrange formulas to highlight a quantity of  solve problems involving literal geometry formulas.
interest, using the same reasoning as in solving equations.  In items that require the student to solve literal equations and
equations.
MFAS: Solving Literal Equations  explain a process to solve formulas, a linear term should be the term of interest.
equations.  Items should not require more than four procedural steps to
Solve for X
 apply the distributive property when isolate the variable of interest.
ALGEBRA NATION: Section 2 (Video 9) necessary to solve equations.  Items may require the student to recognize equivalent

SMP: # 4, 5, 7  construct a viable argument to expressions but may not require a student to perform an
justify a solution method. algebraic operation outside the context of Algebra 1.

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.
NO CALCULATOR

MFAS: Does it Follow?

ALGEBRA NATION: Section 2 (Videos 2 & 3)

SMP: # 2, 3

Linear Equations (continued)

Essential Question(s):

How do you create equations that describe relationships? How do you solve equations with one variable?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-REI.1.2  define extraneous solutions.

Solve simple rational and radical equations in  solve rational equations in one variable.
one variable, and give examples showing how  determine which numbers cannot be
extraneous solutions may arise.
solutions of rational equation and explain
why they cannot be solution.

SMP: # 1,3  generate examples of rational equations
with extraneous solutions..

MAFS.9.12.A-REI.2.3  explain a process to solve equations.  Items will not require the student to recall names of

 apply the distributive property when properties from memory.
necessary to solve equations.
Solve linear equations and inequalities in one
variable, including equations with coefficients  construct a viable argument to justify a
represented by letters. solution method.

ALGEBRA NATION: Section 2 (Videos 1 & 3)

MAFS.912.A-SSE.1.1  define expression, term, factor, and co-  In items that require the student to transform a quadratic
efficient. equation to vertex form, the coefficient of the linear term
Interpret expressions that represent a quantity must be an even factor of the coefficient of the quadratic
in terms of its context.  group the parts of an expression differently term.
in order to better interpret their meaning.
a. Interpret parts of an expression, such as  For A-SSE.2.3b and A-SSE.1.1, exponential expressions
terms, factors and coefficients.  interpret the real-world meaning of the are limited to simple growth and decay. If the number e is
term, factors, and co-efficient of an used then its approximate value should be given in the
b. Interpret complicated expressions by expression in terms of their units. stem.
viewing one or more of their parts as a single
entity.  For A-SSE.2.3a and A-SSE.1.1, quadratic expressions
should be univariate.
MFAS: Interpreting Basic Tax
 For A-SSE.2.3b, items should only ask the student to
interpret the y value of the vertex within a real-world context.

ALGEBRA NATION: Section 1 (Videos 1-3)

SMP: # 7

Standard Linear Functions Assessment Limits/ Stimulus Attributes:
The students will:
Essential Question(s):  Items that require the student to
How do you identify linear equations, intercepts, and zeros? determine the domain using
equations within a context are
How do you graph and write linear equations? limited to exponential functions with
How do you use rate of change to solve problems? one translation, linear functions, or
quadratic functions.
Learning Targets
I can:  Items may present relations in a
variety of formats, including sets of
MAFS.912.F-BF.1.2  explain that recursive formula tells me how a ordered pairs, mapping diagrams,
graphs, and input/output models.
sequence starts and tells me how to use the
 Items may present relations in a
Write arithmetic and geometric sequences previous value(s) to generate the next element of the variety of formats, including sets of
ordered pairs, mapping diagrams,
both recursively and with an explicit formula, sequence. graphs, and input/output models.

use them to model situations, and translate  define an arithmetic sequence as a sequence of  In items requiring the student to find
domain from graphs, relationships
between the two forms. numbers that is formed so that the difference may be discontinuous.

between consecutive terms is always the same

known as a common difference.

SMP 4, 7  determine the common difference between two

terms in an arithmetic sequence.

 explain how to change a term of an arithmetic

sequence into the next term and write a recursive

formula for the sequence, = −1 + .
 write an explicit formula for an arithmetic sequence,

an = a1 + (n − 1)d..
 decide when a real world problem models an

arithmetic sequence and write an equation to model

the situation.

MAFS. 912.F-IF.1.1  define relation, domain and range.

 define a function as a relation in which each input

Understand that a function from one set (domain) has exactly one output (range).

(called the domain) to another set (called the  decide if a graph, table or set of ordered pairs

range) assigns to each element of the domain represent a function.

exactly one element of the range. If f is a  decide if stated rules (both numeric and non-

function and x is an element of its domain, the numeric) produce ordered pairs that form a function.

f(x) denotes the output of f corresponding to  explain that when ‘x’ is an element of the input of a
the input x. The graph of f is the graph of the
function f(x) represents the corresponding output.
equation y=f(x).
explain that the graph of ‘f’ is the graph of the

MFAS: Identifying Functions equation y=f(x).

ALGEBRA NATION: Section 3 (Video 1 & 2)

SMP: #6, 7

Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will:
I can:

MAFS. 912.F-IF.2.4  locate the information that explains what each  Functions represented algebraically are

quantity represents. limited to linear, quadratic, or exponential.

For a function that models a relationship between  interpret the meaning of an ordered pair.  Functions may be represented using tables,
two quantities, interpret key features of graphs  determine if negative inputs and/or outputs make graphs or verbally. Functions represented
and tables in terms of the quantities, and sketch using these representations are not limited to
graphs showing key features given a verbal sense in the problem. linear, quadratic or exponential.
description of the relationship.  identify and explain the x and y intercept.
NO CALCULATOR  define intervals of increasing and decreasing of a  Functions may have closed domains.
 Functions may be discontinuous.
table or graph.

MFAS: Elevation Along a Trail  Items may not require the student to use or
know interval notation. Key features include x-

ALGEBRA NATION: Section 3 (Video 7) intercepts, y-intercepts; intervals where the
function is increasing, decreasing, positive, or

SMP: #1, 7, 8 negative; relative maximums and minimums;
symmetries; and end behavior.

MAFS. 912.F-IF.2.5  define a function as a relation in which each input  Items must be set in a real-world context.

(domain) has exactly one output (range).

Relate the domain of a function to its graph and,  determine if a graph, table or set of ordered pairs

where applicable, to the quantitative relationship it represent a function.

describes.  determine if stated rules (both numeric and non-
MFAS: Car Wash
numeric) produce ordered pairs that form a function.
 explain that when ‘x’ is an element of the input of a

function f(x) represents the corresponding output.

ALGEBRA NATION: Section 3 (Video 2)  explain that function notation is not limited to f(x).

SMP: #4

MAFS. 912.F-IF.2.6  define and explain interval, rate of change and  In items where a function is represented by a

average rate of change. graph or table, the function may be any

Calculate and interpret the average rate of change  calculate the average rate of change of a function, continuous function.

of a function (presented symbolically or as a table) represented either by function notation, a graph or a  Items should not require the student to find an

over a specified interval. Estimate the rate of table over a specific interval. equation of a line.

change from a graph.  compare the rates of change of two or more

MFAS: Pizza Palace functions
 interpret the meaning of the average rate of

ALGEBRA NATION: Section 3 (Videos 8) change in the context of the problem.
 construct an equation given the slope and a point.

SMP #4, 5  construct an equation given two points.

Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will:
I can:

MAFS.912.F-IF.3.7a  identify that the parent function for lines is the line  Items that require the student to transform a

f(x) = x. quadratic equation to vertex form, the

Graph function expressed symbolically and show  identify and graph a line in the point-slope form: y- coefficient of the linear term must be an even

key features of the graph, by hand in simple cases y1=m(x-x1). factor of the coefficient of the quadratic form.

and using technology for more complicated  identify and graph a line in slope-intercept form:

functions. f(x) =mx+b.

a. Graph linear and quadratic functions and  identify the standard form of a linear function as

show intercepts, maxima, and minima. Ax + By = C.

MFAS: Graphing a Linear Function  use the definitions of x and y intercepts to find the
intercepts of a line in standard form and then graph

ALGEBRA NATION: Section 3 (Videos 7 & 8) and the line.
relate the constants A, B, and C to the values of the

Section 4 (Video 2-4) x and y intercepts and slope.  Functions represented algebraically are

SMP: #7, 8  compare properties of two functions when limited to linear, quadratic, or exponential.
MAFS.912.F-IF.3.9 represented in different ways (algebraically,  Functions may be represented using tables,
graphically, numerically in tables, or by verbal
Compare properties of two functions each descriptions). graphs or verbally.
represented in a different way (algebraically,  Functions represented using these
graphically, numerically in tables, or by verbal
descriptions). representations are not limited to linear,
quadratic or exponential.
 Functions may have closed domains.
 Functions may be discontinuous. Items may

ALGEBRA NATION: Section 7 (bonus video) not require the student to use or know interval
notation.

MFAS: Comparing Linear Functions  Key features include x-intercepts, y-intercepts;
intervals where the function is increasing,

SMP: #7 decreasing, positive, or negative; relative
maximums and minimums; symmetries; and

end behavior.

Linear Functions (continued)

Standard Essential Question(s): Assessment Limits/ Stimulus Attributes:
The students will: How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?
How do you use rate of change to solve problems?

Learning Targets
I can:

MAFS.912.F-LE.1.2  determine if a function is linear given a  In items where the student must write
a function using arithmetic operations
sequence, a graph, a verbal description or a or by composing functions, the student
should have to generate the new
Construct linear and exponential functions, table. function only.

including arithmetic and geometric sequences,  describe the algebraic process used to  In items where the student constructs
an exponential function, a geometric
given a graph, a description of a relationship, or construct the linear function and exponential sequence, or a recursive definition
from input-output pairs, at least two
two input-output pairs (include reading these from a function that passes through two points. sets of pairs must have consecutive
inputs.
table).  determine if a function is linear or
 In items that require the student to
MFAS: Writing a Function from Ordered Pairs exponential given a sequence, a graph, a construct arithmetic or geometric
verbal description or a table. sequences, the real-world context
should be discrete.
ALGEBRA NATION: Section 4 (Video 1)
 In items that require the student to
SMP: #2, 7 construct a linear or exponential
function, the real-world context should
MAFS.912.A-REI.4.10  explain that every ordered pair on the graph be continuous.
of an equation represents values that make
Understand that the graph of an equation in two the equation true.  In items where a function is
variables is the set of all its solutions plotted in the represented by a graph or table, the
coordinate plane, often forming a curve (which  verify that any point on a graph will result in function may be any continuous
could be a line). a true equation when their coordinates are function.
substituted into the equation.

MFAS: What Is the Point?

ALGEBRA NATION: Section 2 (Video 10), Section
4 (Videos 2 & 3)

SMP: #2

Equations of Linear Functions

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will: I can:

MAFS.912.A-CED.1.2  write equations of lines in  Items may include equations or inequalities that contain

Create equation in two or more variables to various forms that best models variables on both sides.
represent relationships between quantities;
graph equations on coordinate axes with the problem.  Items may include compound inequalities
labels and scales
MFAS: Model Rocket  graph equations on  In items that require the student to write or solve an inequality,

ALGEBRA NATION: Section 2 (Video 10) coordinate axes. variables are restricted to an exponent of one.
SMP #4
 determine appropriate labels  Items that involve formulas should not include overused
MAFS.912.F-BF.1.1
and scales. contexts such as Fahrenheit/Celsius or three-dimensional
Write a function that describes a
relationship between two quantities. geometry formulas.
a. Determine an explicit expression, a
recursive process, or steps for calculation  In items that require the student to solve literal equations and
from a context.
b. Combine standard function types using formulas, a linear term should be the term of interest.
arithmetic operations.
 Items should not require more than four procedural steps to
MFAS: Saving for a Car
isolate the variable of interest.
ALGEBRA NATION: Section 4 (Video 1)
 Items may require the student to recognize equivalent

expressions but may not require a student to perform an

algebraic operation outside the context of Algebra 1.

 define explicit and recursive  In items where the student must write a function using

expressions of a function. arithmetic operations or by composing functions, the student

 identity the quantities being should have to generate the new function only.

compared in a real-world  In items where the student constructs an exponential function,

problem. a geometric sequence, or a recursive definition from input-

 write an explicit and/or output pairs, at least two sets of pairs must have consecutive

recursive expressions of a inputs.

function to describe a real-  In items that require the student to construct arithmetic or

world problem. geometric sequences, the real-world context should be

 recall the parent function y=x. discrete.

 In items that require the student to construct a linear or

exponential function, the real-world context should be

continuous.

SMP: #4, 7

Equations of Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.F-BF.2.3  explain why f(x) + k translates the  Functions represented algebraically are limited to

original graph of f(x) up k units and why linear, quadratic, or exponential.

Identify the effect on the graph of replacing f(x) –k translates the original graph of  Functions represented using tables or graphs are not

f(x) by f(x) + k, k (f(x), f(kx),and f(x+k) for F(x) down k units. limited to linear, quadratic, or exponential.

specific values of k. ( positive and negative)  Functions may be represented using tables or
; find the value of k given the graphs. graphs.
Experiment with cases and illustrate an
explanation of the effects on the graph  Functions may have closed domains.
using technology.  Functions may be discontinuous. Items should have

a single transformation.

MFAS: Saving for a Car  Items may require the student to explain or justify a
transformation that has been applied to a function.

ALGEBRA NATION: SECTION 3 (Video 10)  Items may require the student to explain how a graph
is affected by a value of k.

SMP #5, 7  Items may require the student to find the value of k.
 Items may require the student to complete a table of

values.

Equations of Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus

The students will: I can: Attributes:

MAFS.912.F-BF.2.4  define inverse of a function.  items that require the student to
find a value given a function, the
 write the inverse of a function by solving f(x) = c; for x. following function types are
allowed: quadratic, polynomials
Find inverse functions.  explain that after f(x) = c; for x, c can be considered the input whose degrees are no higher than
6, square root, cube root, absolute
a. Solve an equation of the form f(x) = c for and x the output. value, exponential except for base
e, and simple rational.
a simple function f that has an inverse  write the inverse of a function in standard notation by replacing
and write an expression for the inverse.  Items may present relations in a
the x in my inverse equation with y and replacing the c in my variety of formats, including sets of
For example, () = 2 3 () = ordered pairs, mapping diagrams,
inverse equation with x. graphs, and input/output models.
(+1) ≠ 1.
(−1)  use the composition of functions to verify that g(x) and f(x) are  In items requiring the student to
find the domain from graphs,
b. Verify by composition that one function inverses by showing that g(f(x))=f(g(x)) = 1. relationships may be on a closed or
open interval.
is the inverse of another.  decide if a function has an inverse using the horizontal line
 In items requiring the student to
c. Read values of an inverse function from test. find domain from graphs,
relationships may be discontinuous.
a graph or a table, given that the  use the definitions of functions, inverse functions, and 1:1 Items may not require the student
to use or know interval notation.
function has an inverse. functions to explain why the horizontal line test works.

d. Produce an invertible function from a  list values of an inverse given a table or graph of a function

non-invertible function by restricting the that has an inverse.

domain.  identify and eliminate the part of the graph that caused it to fail

the vertical line test.

 state the domain of a relation that has been altered in order to

pass the horizontal line test.

 write the inverse of the invertible function in function notation.

MAFS.912.F-IF.1.2  convert a table, graph, set of ordered pairs or description

Use function notation, evaluate functions for into function notation by identifying the rule used to turn

inputs in their domains, and interpret statements inputs into outputs and writing the rule.
that use function notation in terms of a context.
 use order of operations to evaluate a function for a given
domain value.

MFAS: Evaluating a Function  identify the numbers that are not in the domain of a
function.

ALGEBRA NATION: SECTION 3 (Video 1 & 2)  choose and analyze inputs (and outputs) that make

sense based on the problem.

SMP: #7

Equations of Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/

The students will: I can: Stimulus Attributes:

MAFS.912.F-IF.3.7a  identify that the parent function for lines is the line f(x) = x.

Graph function expressed symbolically and show  identify and graph a line in the point-slope form: y-y1=m(x-
key features of the graph, by hand in simple cases x1).
and using technology for more complicated
functions.  identify and graph a line in slope-intercept form: f(x) =mx+b.
MFAS: Graphing a Linear Function  identify the standard form of a linear function as Ax + By =

C.
 use the definitions of x and y intercepts to find the intercepts

ALGEBRA NATION: Section 3 (Videos 7 & 8) and of a line in standard form and then graph the line.
Section 4 (Video 3)  relate the constants A, B, and C to the values of the x and y

intercepts and slope.

SMP: #7, 8

MAFS.912.F-LE.2.5  identify the names and definitions of the parameters m and  Items should be set in a
real-world context.
b in the linear function () = + .
 Items may use function
Interpret the parameters in a linear or exponential  explain the meaning of the slope of a line when the line notation.

function in terms of a context. models a real-world relationship.  Items should use real-
NO CALCULATOR  explain the meaning of the y-intercept and other points on world data and be set in
a real-world context.
MFAS: Computer Repair the line when the line models a real-world relationship.
 compose an original problem situation and construct a

SMP: #2, 4 linear function to model it.

MAFS.912.S-ID.2.6  identify the independent and dependent variable and

describe the relationship of the variables.

Represent data on two quantitative variables on a  construct a scatter plot with an appropriate scale.

scatter plot, and describe how the variables are  identify any outliers on the scatter plot.

related.  sketch the line of best fit on a scatter plot that appears

a. Fit a function to the data; use functions fitted linear.

to data to solve problems in the context of the data.

c. Fit a linear function for a scatter plot that

suggests a linear association.

MFAS: Swimming Predictions

ALGEBRA NATION: Section 10 (Video 3-5)

SMP: #2,4

Equations of Linear Functions (continued)

Essential Question(s):

How do you identify linear equations, intercepts, and zeros?

How do you graph and write linear equations?

How do you use rate of change to solve problems?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.S-ID.3.7  interpret the meaning of the slope in terms  Items should include data sets. Data sets

of the unit stated in the data. must contain at least six data pairs. The

Interpret the slope (rate of change) and the  interpret the meaning of the y-intercept in linear function given in the item should be

intercept (constant term) of a linear model in the terms of the units stated in the data. the regression equation.

context of the data.  The rate of change and the y-intercept

should have a value with at least a

MFAS: Slope for the Foot Length Model hundredths place value.

ALGEBRA NATION: Section 3 (Videos 7 & 8)

SMP: #2, 4, 5

Linear Inequalities

Essential Question(s):

How do you solve inequalities?

How do you solve compound inequalities?

How do you solve inequalities involving absolute value?

How can you graph inequalities?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will:
I can:
MAFS.912.A-CED.1.1
 identify the variables and quantities  In items that require the student to write an
Create equations and inequalities in one
variable and use them to solve problems. represented in a real world problem. equation for linear functions.
MFAS: State Fair
 write the inequality that best models the  Items may include equations or inequalities that
ALGEBRA NATION: Section 2
(Video 3, 5-7) problem. contain variables on both sides.
SMP #4
MAFS.912.A-CED.1.3  solve linear inequalities.  In items that require the student to write or

Represent constraints by equations or  interpret the solution in the context of the solve an inequality, variables are restricted to
inequalities, and by systems of equations
and/or inequalities, and interpret solutions problem and decide if they are reasonable. an exponent of one.
as viable or non-viable options in a
modeling context.  identify the variable and quantities  In items that require the student to write an
MFAS: The New School
represented in a real-world problem. equation as a constraint, the equation may be a
Constraints on Equations
 decide the best models for a real-world linear function.

problem and support choice.  Items must be set in a real-world context and

 write inequalities that best models a problem. may use function notation.

 interpret solutions in the context of the

situation modeled and decide if they are

reasonable.

ALGEBRA NATION; Section 2 (Video 7)  solve inequalities in one variable.  Items may include equations or inequalities that
SMP #4  construct an argument to justify my solution contain variables on both sides.
MAFS.912.A-REI.2.3
process.  In items that require the student to write or
Solve linear equations and inequalities in solve an inequality, variables are restricted to
one variable, including equations with an exponent of one.
coefficients represented by letters.

MFAS: Solve for X Solve for N
Solving Multistep Inequality

ALGEBRA NATION: Section 2 (Video 3, 5-
7)
SMP #5

Linear Inequalities

Essential Question(s):

How do you solve inequalities?

How do you solve compound inequalities?

How do you solve inequalities involving absolute value?

How can you graph inequalities?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will:
I can:
MAFS. 912.F-IF.2.4
 locate the information that explains what  Functions represented algebraically are limited to
For a function that models a relationship
between two quantities, interpret key each quantity represents. linear, quadratic, or exponential.
features of graphs and tables in terms of
the quantities, and sketch graphs showing  interpret the meaning of an ordered pair.  Functions may be represented using tables, graphs
key features given a verbal description of
the relationship.  determine if negative inputs and/or or verbally. Functions represented using these

NO CALCULATOR outputs make sense in the problem. representations are not limited to linear, quadratic

MFAS: Elevation Along a Trail  identify and explain the x and y intercept. or exponential.

ALGEBRA NATION: Section 3 (Video 7)  define intervals of increasing and  Functions may have closed domains.

SMP: #1, 7, 8 decreasing of a table or graph.  Functions may be discontinuous.

 Items may not require the student to use or know

interval notation. Key features include x-intercepts,

y-intercepts; intervals where the function is

increasing, decreasing, positive, or negative; relative

maximums and minimums; symmetries; and end

behavior.

Systems of Linear Equations & Inequalities

Essential Question(s):

How do you solve systems of equations using various methods?

How do solve systems of inequalities by graphing?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-CED.1.3  solve systems of linear equations by  In items that require the student to write an equation as

graphing. a constraint, the equation may be a linear function.

Represent constraints by equations or  write system of equations that best  In items that require the student to write a system of
inequalities, and by systems of equations models the problem. equations to represent a constraint, the system is
and/or inequalities, and interpret solutions as limited to a 2 x 2 with integral coefficients.
viable or non-viable options in a modeling  apply systems of linear equations s to
context. solve real-world problems.  In items that require the student to write a system of
MFAS: Constraints on Equations inequalities to represent a constraint, the system is
limited to a 2 x 2 with integral coefficient.

 Items must be set in a real-world context and may use

ALGEBRA NATION: Section 2 (Video 7) function notation.

SMP #4

MAFS.912.A-REI.3.5  solve a system of equations using the  Items must be placed in a mathematical context.
elimination method.  Items that require the student to solve a system of
Prove that given a system of two equations in
two variables, replacing one equation by the  solve a system of equations by equations are limited to a system of 2 x 2 linear
sum of that equation and a multiple of the substitution. equations with integral coefficients if the equations are
other produces a system with the same written in the form Ax + By = C.
solutions. 
MFAS: Solution Sets of Systems  Items may result in infinitely many solutions or no
solution.

ALGEBRA NATION : Section 4 (Video 6 & 7)
SMP # 3

Systems of Linear Equations & Inequalities (continued)

Essential Question(s):

How do you solve systems of equations using various methods?

How do solve systems of inequalities by graphing?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-REI.3.6  explain why some linear systems have no

solutions or infinitely many solutions.  Items that require the student to solve a system of

Solve systems of linear equations exactly and  solve a system of linear equations equations are limited to a system of 2 x 2 linear

approximately (with graphs), focusing on pairs of linear algebraically (by substitution or elimination) equations with integral coefficients if the equations

equations in two variables. to find an exact solution. are written in the form Ax + By = C.

 graph a system of linear equations and  Items that require the student to graph a system of

MAFS: Solving a System of Equations 1 determine the approximate solution to the equations or inequalities to find the solution are

ALGEBRA NATION: Section 4 system of linear equations by estimating limited to a 2 x 2 system.
(Videos 5-7) the point of intersection.  Items may be set in a real-world or mathematical

context.

SMP # 7  Items may result in infinitely many solutions or no
solution.

MAFS.912.A-REI.4.11  explain that a point of intersection on the  Items may be set in a mathematical or real-world

graph of a system of equations represents context and may use function notation.

Explain why the x-coordinates of the points where the a solution to both equations.  Items must designate the place value accuracy

graphs of the equations y=f(x) and y=g(x) intersect are  infer that the x-coordinate of the points of necessary for approximate solutions.

the solutions of the equations intersections are solutions for f(x) = g(x).

f(x) =g(x).  determine the approximate solutions to a

MFAS: Graphs and Solutions system of equations using a graphing
calculator.

ALGEBRA NATION: Section 4 (Video 5)

SMP #2, 4, 5  graph the solutions to a linear inequality in  Items may be set in a real-world or mathematical
MAFS.912.A-REI.4.12
two variable as a half-plane, excluding the context.
Graph the solutions to a linear inequality in two
variables as a half-plane (excluding the boundary in boundary for non-inclusive inequalities.  Items that require the student to graph a system of
the case of a strict inequality), and graph the solution
set to a system of linear inequalities in two variables  graph the solution set to a system of linear equations or inequalities to find the solution are
as the intersection of corresponding half-planes.
inequalities in two variables as the limited to a 2 x 2 system.

intersection of their corresponding half

plane.

MFAS: Graphing Linear Inequalities
Linear Inequalities in the Half-Plane
Graph a System of Inequalities

ALGEBRA NATION: Section 4 (Video 8 & 9)

SMP #5

Systems of Linear Equations & Inequalities (continued)

Essential Question(s):

How do you solve systems of equations using various methods?

How do solve systems of inequalities by graphing?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:
The students will:
I can:
MAFS.912.A-SSE.1.1
 define expression, term, factor, and co-  In items that require the student to transform a
Interpret expressions that represent a
quantity in terms of its context. efficient. quadratic equation to vertex form, the coefficient of

a. Interpret parts of an expression, such  group the parts of an expression differently the linear term must be an even factor of the
as terms, factors and coefficients.
in order to better interpret their meaning. coefficient of the quadratic term.
b. Interpret complicated expressions by
viewing one or more of their parts as a  interpret the real-world meaning of the term,  For A-SSE.2.3b and A-SSE.1.1, exponential
single entity.
factors, and co-efficient of an expression in expressions are limited to simple growth and
SMP: # 7
terms of their units. decay. If the number e is used then its

approximate value should be given in the stem.

 For A-SSE.2.3a and A-SSE.1.1, quadratic

expressions should be univariate.

 For A-SSE.2.3b, items should only ask the student

to interpret the y value of the vertex within a real-

world context.

Exponents & Exponential Functions

Standard Essential Question(s): Assessment Limits/ Stimulus
The students will: How can you perform operations with exponents?
MAFS.912.F-BF.1.1 How can you perform operations with rational exponents? Attributes:
How do you graph and use exponential functions?
Write a function that describes a  In items where the student must write
relationship between two quantities. Learning Targets a function using arithmetic operations
a. Determine an explicit expression, or by composing functions, the
a recursive process, or steps for I can: student should have to generate the
calculation from a context. new function only.
b. Combine standard function types  Define explicit and recursive expressions of a function.
using arithmetic operations.  Identity the quantities being compared in a real-world problem.  In items that require the student to
MFAS: Saving for a Car  Write an explicit and/or recursive expressions of a function to describe a construct arithmetic or geometric
sequences, the real-world context
ALGEBRA NATION: Section 4 (Video real-world problem. should be discrete.
1)
SMP: #4, 7  explain that recursive formula tells me how a sequence starts and tells  In items that require the student to
MAFS.912.F-BF.1.2: me how to use the previous value(s) to generate the next element of the construct a linear or exponential
sequence. function, the real-world context should
Write arithmetic and geometric be continuous.
sequences both recursively and with  explain that an explicit formula allows me to find any element of a
an explicit formula, use them to sequence without knowing the element before it.  In items where the student writes a
model situations, and translate recursive formula, the student may be
between the two forms.  distinguish between explicit and recursive formulas for sequences. expected to give both parts of the
 define an arithmetic sequence as a sequence of numbers that is formed formula.

so that the difference between consecutive terms is always the same  The student may be required to
known as a common difference. determine equivalent recursive
 determine and define geometric sequence as a sequence of numbers formulas or functions.
that is formed so that the ratio of consecutive terms is always the same
known as the common ratio.
 determine the common difference between two terms in an arithmetic
sequence.
 explain how to change a term of an arithmetic sequence into the next
term and write a recursive formula for the sequence, = −1 + .
 write an explicit formula for an arithmetic sequence, = 1 + ( − 1)..
 write an explicit formula for geometric sequence = 1−1
 decide when a real world problem models an arithmetic sequence and
write an equation to model the situation.

Exponents & Exponential Functions (continued)

Essential Question(s):
How can you perform operations with exponents?
How can you perform operations with rational exponents?
How do you graph and use exponential functions?

Standard Learning Targets Assessment Limits/ Stimulus
The students will:
MAFS.912.F-IF.1.3 I can: Attributes:

Recognize that sequences are functions,  write a function from a list of numbers by making the whole number  Functions represented algebraically
sometimes defined recursively, whose the inputs and the elements the outputs.. are limited to linear, quadratic, or
domain is a subset of the integers. exponential.
 define and write a recursive formula using a previous value to
MFAS: Which Sequences are generate the next element of the sequence.  Functions may be represented using
Functions? tables, graphs or verbally. Functions
 explain that an explicit formula allows me to find any element of a represented using these
representations are not limited to
sequence. linear, quadratic or exponential.
 distinguish between explicit and recursive formulas for sequences.
 Functions may have closed domains.
 recognize arithmetic sequences as linear functions.  Functions may be discontinuous.
 Items may not require the student to
ALGEBRA NATION: Section 4 (Video 1)
use or know interval notation. Key
SMP #2, 7, 8 features include x-intercepts, y-
intercepts; intervals where the
MAFS. 912.F-IF.2.4  locate the information that explains what each quantity represents. function is increasing, decreasing,
positive, or negative; relative
 interpret the meaning of an ordered pair. maximums and minimums;
symmetries; and end behavior.
For a function that models a relationship  determine if negative inputs and/or outputs make sense in the

between two quantities, interpret key problem.

features of graphs and tables in terms of  identify and explain the x and y intercept.
the quantities, and sketch graphs
 define intervals of increasing and decreasing of a table or graph.
showing key features given a verbal

description of the relationship.

NO CALCULATOR

MFAS: Elevation Along a Trail

ALGEBRA NATION: Section 8 (Bonus
Video)

SMP: #1, 7, 8

Standard Exponents & Exponential Functions Assessment Limits/ Stimulus Attributes:
The students will:
Essential Question(s):  Exponential functions are limited to
MAFS.912.F-IF.3.7e How can you perform operations with exponents? simple exponential growth and decay
How can you perform operations with rational exponents? functions and to exponential functions
Graph function expressed symbolically and How do you graph and use exponential functions? with one translation. Base e should not
show key features of the graph, by hand in be used.
simple cases and using technology for Learning Targets
more complicated cases. I can:

e. Graph exponential and logarithmic  graph exponential functions.
functions, showing intercepts and  identify data that displays exponential behavior.
end behavior, and trigonometric  describe the end behavior of a rational function by
functions showing period, midline
and amplitude. interpreting the graph.
 state the end behavior of a rational function when

looking at a graph of the function.

MFAS: Graphing a Linear Function

SMP #7, 8

MAFS.912.F-IF.3.8b  use the properties of exponents to transform  Exponential functions are limited to

expressions. simple exponential growth and decay

Write a function defined by an expression  use the properties of exponents to interpret functions and to exponential functions

in different but equivalent forms to reveal expressions for exponential functions in a real-world with one translation. Base e should not
and explain different properties of the context. be used.

function.  Items may specify a required form

b. Use properties of exponents to interpret using an equation or using common
expressions for exponential function. terminology such as standard form.

MAFS.912.A-SSE.1.2
Use the structure of an expression to
identify ways to rewrite it.

MFAS: Launch from a Hill

ALGEBRA NATION: Section 1 (Video 3 &
4)

SMP #2, 4, 7

Exponents & Exponential Functions

Standard Essential Question(s): Assessment Limits/ Stimulus Attributes:
The students will: How can you perform operations with exponents?
MAFS.912.F-IF.3.9 How can you perform operations with rational exponents?  Items may not require the student to use or
How do you graph and use exponential functions? know interval notation. Key features
Compare properties of two functions each include x-intercepts, y-intercepts; intervals
represented in a different way (algebraically, Learning Targets where the function is increasing,
graphically, numerically in tables, or by verbal I can: decreasing, positive, or negative; relative
descriptions).  identify exponential functions as growth or decay. maximums and minimums; symmetries;
 represent functions with a table or graph by evaluating and end behavior.
MFAS: Comparing Linear and Exponential
Functions several values of x.  Items may be set in a real-world or
 differentiate between exponential and linear functions. mathematical context.
SMP #6, 7
 define a exponential function.  Functions may be represented using
MAFS.912.F-LE.1.1  demonstrate that an exponential function has a constant tables, graphs or verbally.

Distinguish between situations that can be multiplier or equal intervals.  Exponential functions should be in the form
modeled with linear functions and with  identify situations that display equal ratios of change a(b) x+ k.
exponential functions.
a. Prove that linear functions grow by equal over equal intervals and can be modeled with exponential  Items may require the student to choose a
differences over equal intervals, and that functions. parameter that is described within the real-
exponential functions grow by equal factors  distinguish between situations modeled with linear world context.
over equal intervals. functions and with exponential functions when presented
b. Recognize situations in which one quantity with a real-world problem.  Items should be set in a real-world context.
changes at a constant rate per unit interval
relative to another.
c. Recognize situations in which a quantity
grows or decays by a constant percent rate per
unit interval relative to another.
NO CALCULATOR

MFAS: How Does Your Garden Grow?

SMP #3, 4, 8

Standard Exponents & Exponential Functions Assessment Limits/ Stimulus
The students will:
Essential Question(s): Attributes:
MAFS.912.F-LE.1.2 How can you perform operations with exponents?
How can you perform operations with rational exponents?  In items where the student
Construct linear and exponential functions, How do you graph and use exponential functions? constructs an exponential
including arithmetic and geometric function, at least two sets of pairs
sequences, given a graph, a description of Learning Targets must have consecutive inputs.
a relationship, or two input-output pairs I can:
(include reading these from a table).  In items that require the student
 determine if a function is exponential given a sequence, to construct an exponential
a graph, a verbal description or a table. function, the real-world context
should be continuous.
 describe the algebraic process used to construct the
exponential function that passes through two points.

 solve problems involving exponential growth and
exponential decay.

 construct arithmetic and geometric sequences.

MFAS: Writing a Function from Ordered
Pairs

ALGEBRA NATION: Section 8 (Video 1, 3-
5)

SMP #2, 7, 8  identify the names and definitions of the parameters a,b,  Items should be set in a real-
MAFS.912.F-LE.2.5
and c in the exponential function () = ∙ + world context.
Interpret the parameters in a linear or
exponential function in terms of a context.  explain the meaning of the constant a of an exponential  Items may use function notation.
NO CALCULATOR function when the exponential function models a real-
world relationship.  Exponential functions should be
MFAS: Interpreting Exponential Functions in the form a(b)x + k.

ALGEBRA NATION: Section 8 (Video 7)  explain the meaning of the y-intercept and other points

SMP #2, 4 on an exponential function when the exponential function

models a real-world relationship.

 explain the meaning of the constant b of an exponential

function when the exponential function models a real-
world relationship

 explain the meaning of the constant c of an exponential

function when it models a real-world relationship.

Exponents & Exponential Functions

Essential Question(s):

How can you perform operations with exponents?

How can you perform operations with rational exponents?

How do you graph and use exponential functions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:  Expressions should contain no more
than three variables.
MAFS.912.N-RN.1.1
 Items should not require the student
 evaluate and simplify expressions containing zero to do more than two operations.

Explain how the definition of the meaning of and integer exponents.

rational exponents follows from extending the  multiply monomials and apply multiplication

properties of integer exponents to those properties of exponents to evaluate and simplify

values, allowing for a notation for radicals in expressions.

terms of rational exponents.  rewrite equivalent expressions between radicals

NO CALCULATOR and rational exponents.

ALGEBRA NATION: Section 1 (Video 5)  apply properties of rational exponents to simplify
MAFS.912.N-RN.1.2 expressions.

Rewrite expressions involving radicals and
rational exponents using the properties of
exponents.
NO CALCULATOR

MFAS: Rational Exponents 1

ALGEBRA NATION: Section 1 (Video 5-7)

SMP #3, 7, 8  explain that a point of intersection on the graph of  Items may be set in a mathematical
MAFS.912.A-REI.4.11
a system of equations represents a solution to both or real-world context and may use
Explain why the x-coordinates of the points
where the graphs of the equations y=f(x) and equations. function notation.
y=g(x) intersect are the solutions of the
equations  infer that the x-coordinate of the points of  Items must designate the place value
f(x) =g(x).
intersections are solutions for f(x) = g(x). accuracy necessary for approximate

solutions.

MFAS: Graphs and Solutions

ALGEBRA NATION: Section 4 (Video 5)

SMP #2, 4, 5

Exponents & Exponential Functions

Essential Question(s):

How can you perform operations with exponents?

How can you perform operations with rational exponents?

How do you graph and use exponential functions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-SSE.1.1  define expression, term, factor, and co-efficient.

 understand and explain how to group the parts  In items that require the student to transform

Interpret expressions that represent a quantity in of an expression differently in order to better a quadratic equation to vertex form, the

terms of its context. interpret their meaning. coefficient of the linear term must be an even

a. Interpret parts of an expression, such as terms,  interpret the real-world meaning of the term, factor of the coefficient of the quadratic term.
factors and coefficients.
b. Interpret complicated expressions by viewing one factors, and co-efficient of an expression in terms  For A-SSE.2.3b and A-SSE.1.1, exponential
or more of their parts as a single entity.
of their units. expressions are limited to simple growth and

decay. If the number e is used then its

approximate value should be given in the

MAFS.912.A-SSE.2.3  define an exponential function. stem.
 rewrite exponential functions using the  For A-SSE.2.3a and A-SSE.1.1, quadratic
Choose and produce an equivalent form of an
expression to reveal and explain properties of the properties of exponents. expressions should be univariate.
quantity represented by the expression.  For A-SSE.2.3b, items should only ask the

c. Use the properties of exponents to transform student to interpret the y value of the vertex
expressions for exponential functions. within a real-world context.
 Items should require the student to choose
how to rewrite the expression.

MFAS: Population Drop

ALGEBRA NATION: Section 5 (Video 2-5)
SMP #7

MAFS.912.A-SSE.2.4  define a finite geometric series and common
ratio.
Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1), and use the  derive the formula for the sum of a finite
formula to solve problems. geometric series, = 1((1 − )/(1−)).

 express the sum of a finite geometric series.

 calculate the sum of a finite geometric series.
 recognize real-world scenarios that are modeled

by geometric sequences.

 use the formula for the sum of a finite geometric
series to solve real-world problems.

Polynomials

Essential Question(s):

How do you perform operations with polynomials? How do you factor polynomials using various methods?

How do you perform operations with rational expressions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-APR.1.1  identify and describe a polynomial.  Items set in a real-world context should not result

 define and interpret expressions, terms, in a non-real answer if the polynomial is used to

Understand that polynomials form a system factors, and coefficients of an expression in solve for the unknown.

analogous to the integers, namely, they are closed terms of their units.  In items that require addition and subtraction,

under the operations of addition, subtraction, and  apply arithmetic operation of addition, polynomials are limited to monomials, binomials,
multiplication; add, subtract, and multiply subtraction, and multiplication to polynomials. and trinomials. The simplified polynomial should
polynomials. contain no more than six terms.
NO CALCULATOR  apply the definition of a polynomial to explain  Items requiring multiplication of polynomials are
why adding, subtracting, or multiplying two

ALGEBRA NATION: Section 1 (Video 1) polynomials always produces a polynomial. limited to a product of: two monomials, a
monomial and a binomial, a monomial and a

trinomial, two binomials, and a binomial and a

MAFS.912.A-SSE.1.1 trinomial.
 Items may require the student to write the answer

Interpret expressions that represent a quantity in in standard form.
terms of its context.  Items may require the student to recognize

equivalent expressions.

a. Interpret parts of an expression, such as terms,  Items may require the student to rewrite
factors, and coefficients. expressions with negative exponents, but items
b. Interpret complicated expressions by viewing one must not require the student to rewrite rational
or more of their parts as a single entity. expression as seen in the standard MAFS.912.A-
APR.4.7.

MFAS: Adding Polynomials

SMP: #7, 8

MAFS.912.A-APR.2.2  divide polynomials using long division and

synthetic division and apply the Remainder

Know and apply the Remainder Theorem: For a Theorem (when appropriate) to check the

polynomial p(x) and a number a, the remainder on answer.

division by x-a is p(a), so p(a)=0 if and only if (x-a) is  apply the Remainder Theorem to determine if a

a factor of p(x). divisor (x-a) is a factor of the polynomials p(x).

Polynomials (continued)

Essential Question(s):

How do you perform operations with polynomials? How do you factor polynomials using various methods?

Can you identify excluded values of rational functions?

How do you perform operations with rational expressions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-APR.2.3  identify zeros of factored quadratics.  The leading coefficient should be an

 identify the multiplicity of the zeroes of a factored quadratic. integer and the polynomial’s degree is

Identify zeroes of polynomials when  explain how the multiplicity of the zeroes provides a clue as to how restricted to 3 or 4.
 The polynomial function should not have
suitable factorizations are available, and the graph will behave when it approaches and leaves the x-
a zero with multiplicity.
use the zeroes to construct a rough intercept.

graph of the function defined by the  sketch a rough graph using the zeroes of a polynomial and other  The polynomial should be given in
polynomial. easily identifiable points such as the y-intercepts. factored form.

MFAS: Zeros of a Cubic  In items that require the student to
interpret the vertex or a zero of a

ALGEBRA NATION: Section 7 (Video 1) quadratic function within a real-world
context, the student should interpret both

SMP: #1, 8 the x-value and the y-value.

MAFS.912.A-APR.3.4  verify polynomial identities (sums and differences of like powers.

− = ( − )( + )

Prove polynomial identities and use + = ( + )( − + )
them to describe numerical − = ( − )( + + ).
relationships.
 factor polynomials completely by applying the polynomial identities.

 use polynomial identities to describe numerical relationships.

MAFS.912.A-APR.4.6  define rational expressions.

 determine the best method of simplifying the given rational

Rewrite simple rational expressions in expression (inspection, long division, computer algebra system).

different forms; write () in the form  simplify rational expressions by inspection (e.g., 45²+9 = 5x + 1).
()
9
() + () , where a(x), b(x), q(x), and
 simplify rational expressions using long division.
()
 simplify complicated rational expressions using a graphing
r(x) are polynomials with the degree of
calculator.
r(x) less than the degree of b(x) , using  write a rational expression () where a(x) is the dividend and b(x)

inspection, long division, or, for the ()

more complicated examples, a graphing is the divisor in the form : q(x) +() where q(x) is the quotient and
calculator.
()

r(x) is the remainder

 (e.g., ³−2+4−10 = x² - 3x + 10 + −30 ).
+2 +2

Polynomials (continued)

Essential Question(s):

How do you perform operations with polynomials? How do you factor polynomials using various methods?

Can you identify excluded values of rational functions?

How do you perform operations with rational expressions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912A-REI.1.1  apply order of operations and inverse  Items may ask the student to complete steps in

operations to solve equations. a viable argument.

Explain each step in solving a simple equation as  construct an argument to justify my  Items should not require more than four

following from the equality of numbers asserted at solution process. procedural steps to reach a solution.

the previous step, starting from the assumption

that the original equation has a solution. Construct

a viable argument to justify a solution method.

NO CALCULATOR

MFAS: Does it Follow?

SMP: #2, 3

MAFS.912.A-REI.2.4  identify and factor a perfect square  In items that require the student to solve a
simple quadratic equation by inspection or by
trinomial. taking square roots, equations should be in the
form ax2 = c or ax2 + d = c, where a, c, and d
Solve quadratic equations in one variable.  solve quadratic equations by are rational numbers and where c is not an
integer that is a perfect square and c –d is not
a. Use the method of completing the square to inspection, finding square roots, and an integer that is a perfect square.

transform any quadratic equation in x into an factoring.  Items may require the student to recognize that
equation of the form (x – p)² = q that has the a solution is non-real but should not require the
student to find a non-real solution.
same solutions. Derive the quadratic formula
 Items should be set in a mathematical context.
from this form.  Items may use function notation.

b. Solve quadratic equations by inspection  Items may require the student to recognize
equivalent solutions to the quadratic equation.
(e.g., for x² = 49), taking square roots,
 Responses with square roots should require
completing the square, the quadratic formula the student to rewrite the square root so that
the radicand has no square factors.
and factoring, as appropriate to the initial

form of the equation. Recognize when the

quadratic formula gives complex solutions

and write them as a ± bi for real numbers a

and b.

MFAS: Complete the Square - 1

ALGEBRA NATION: Section 5 (Video 3 & 4)

SMP: #7, 8

Polynomials (continued)

Essential Question(s):

How do you perform operations with polynomials? How do you factor polynomials using various methods?

Can you identify excluded values of rational functions?

How do you perform operations with rational expressions?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-SSE.1.2  identify clues in the structure of expressions  In items that require the student to write

(e.g., like terms, common factors, difference equivalent expressions by factoring, the given

Use the structure of an expression to of squares, perfect squares) in order to expression may have integral common factors, be

identify ways to rewrite it. rewrite it another way. a difference of two squares up to a degree of 4,

 explain why equivalent expressions are be a quadratic, ax2 + bx + c, where a > 0 and a, b,

equivalent. and c are integers, or be a polynomial of four

MFAS: Finding Missing Values  apply models for factoring and multiplying terms with a leading coefficient of 1 and highest

polynomials to rewrite expressions. degree of 3.
 Items that require an equivalent expression found
ALGEBRA NATION: Section 1 (Video 3

& 4) by factoring may be in a real-world or

mathematical context.

SMP: #7

MAFS.912.A-SSE.2.3  factor a quadratic expression to find the  Quadratic expressions should be univariate.

zeros of the function it represents.  Items should only ask the student to interpret the

Choose and produce an equivalent form  identify zeros of factored quadratics. y value of the vertex within a real-world context.

of an expression to reveal and explain  identify the multiplicity of the zeroes of a  Items should require the student to choose how to

properties of the quantity represented by factored quadratic. rewrite the expression.

the expression.  identify and factor a perfect square

a. Factor a quadratic expression trinomial.

to reveal the zeroes of the  complete the square of ax2+bx+c to write the
function it defines.
quadratic in the form (x-p)2=q.

MFAS: Jumping Dolphin

ALGEBRA NATION: Section 5 (Video 2-
5)

SMP: #7

Quadratic Functions & Equations

Essential Question(s)

How do you solve quadratics equations by various methods?

Can you analyze functions with successive differences and ratios?

How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.F-BF.2.3  explain why f(x) + k translates the original graph of f(x)  Functions represented algebraically are limited to

up k units and why f(x) –k translates the original graph of linear, quadratic, or exponential.

Identify the effect on the graph of F(x) down k units.  Functions represented using tables or graphs are not
limited to linear, quadratic, or exponential.
replacing f(x) by f(x) + k, k (f(x),  determine the value of k given the graph of a
 Functions may be represented using tables or
f(kx),and f(x+k) for specific values of k. ( transformed function. graphs.

positive and negative) ; find the value of  Functions may have closed domains.
 Functions may be discontinuous. Items should have
k given the graphs. Experiment with
a single transformation.
cases and illustrate an explanation of  Items may require the student to explain or justify a

the effects on the graph using

technology.

MFAS: Saving for a Car transformation that has been applied to a function.
 Items may require the student to explain how a graph

ALGEBRA NATION: Section 3 (Video is affected by a value of k.
10)  Items may require the student to find the value of k.
 Items may require the student to complete a table of
SMP #5, 7
values.

MAFS.912.F-IF.2.4  locate the information that explains what each quantity  Students will find the zeros of a polynomial function

represents. when the polynomial is in factored form.

For a function that models a relationship  interpret the meaning of an ordered pair.  Students will use the x-intercepts of a polynomial

between two quantities, interpret key  determine if negative inputs and/or outputs make sense function and end behavior to graph the function.

features of graphs and tables in terms of in the problem and interpret the meaning of an ordered  Students will identify zeros, extreme values, and

the quantities, and sketch graphs pair. symmetry of the graph of a quadratic function.

showing key features given a verbal  identify and explain the intercepts. Students will identify intercepts and end behavior for

description of the relationship.  define intervals of increasing and decreasing of a table a quadratic function.

NO CALCULATOR or graph.  Students will graph a linear function using key

MFAS: Elevation Along a Trail  identify and explain relative maximums and minimums. features.

 identify reflective and rotational symmetries in a table or  Students will graph a quadratic function using key

graph. features.
ALGEBRA NATION: Section 3(Video 7)  explain why the function has symmetry in the context of  Students will graph an exponential function using key

SMP: #1, 7, 8 the problem. features.

 identify and explain positive and negative end behavior  Students will identify and interpret key features of a

of a function. graph within the real-world context that the function

represents.

Quadratic Functions & Equations (Continued)

Essential Question(s)

How do you solve quadratics equations by various methods?

Can you analyze functions with successive differences and ratios?

How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets Assessment Limits/ Stimulus

The students will: I can: Attributes:

MAFS.912.F-IF.2.6  define and explain interval, rate of change and average rate of  Items requiring the student to calculate

change. the rate of change will give a specified

Calculate and interpret the average rate of  calculate the average rate of change of a function, represented interval that is both continuous and

change of a function (presented either by function notation, a graph or a table over a specific interval. differentiable.

symbolically or as a table) over a specified  interpret the meaning of the average rate of change in the context of  Items should not require the student to

interval. Estimate the rate of change from the problem. find an equation of a line.
a graph.

MFAS: Identifying Rate of Change

ALGEBRA NATION: Section 3 (Video 8)

SMP #4, 5  explain that the parent function for quadratic functions is the  exponential functions are limited to
MAFS.912.F-IF.3.7
parabola f(x)=x2. simple exponential growth and decay
Graph functions expressed symbolically
and show key features of the graph, by  explain that the minimum or maximum of a quadratic is called the functions and to exponential functions
hand in simple cases and using
technology for more complicated cases. vertex. with one translation. Base e should not

c. Graph polynomial functions, identifying  identify whether the vertex of a quadratic will be a minimum or be used.
zeros when suitable factorizations are
available, and showing end behavior. maximum by looking at the equation.  For F-IF.3.7a, quadratic functions that

MFAS: Graphing a Linear  find the y-intercept of a quadratic by substituting 0 for x and are given in the form y = ax2 + bx + c,
Function
evaluating. a, b, and c must be integers. Quadratic
ALGEBRA NATION: Section 3 (Video 9)  estimate the vertex of a quadratic by evaluating different values of x. functions given in vertex form y = a(x –

SMP: #7, 8  use calculated values while looking for a minimum or maximum to h) 2 + k, a, h, and k must be integers.
decide if the quadratic has x-intercepts. Quadratic functions given in other
forms should be able to be rewritten
 estimate the x-intercepts of a quadratic by evaluating different values and adhere to one of the two previous
of x. forms.

 graph a quadratic using evaluated points.

 use technology to graph a quadratic and to find precise values for the

x-intercept(s) and the maximum or minimum.

Quadratic Functions & Equations (continued)

Essential Question(s)

How do you solve quadratics equations by various methods?

Can you analyze functions with successive differences and ratios?

How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.F-IF.3.8a  explain that there are three forms of quadratic  Items that require the student to transform a

functions: standard form (f(x)=ax2+bx+c), vertex form quadratic equation to vertex form, the coefficient of

Write a function defined by an expression (f(x)=a(x-h)2+k), and factored form (f(x)=a(x-x1)(x-x2) the linear term must be an even factor of the

in different but equivalent forms to reveal and that the graph of a quadratic function is a parabola. coefficient of the quadratic form.

and explain different properties of the  convert a standard form quadratic to factored form by

function. factoring and to vertex form by completing the square.

a. Use the process of factoring and  write the function that describes a parabola in all three
completing the square in a forms when given a graph with x-intercepts, y-intercept,
quadratic function to show zeros, and vertex labeled.
extreme values, and symmetry of

the graph, and interpret these in

terms of a context.

ALGEBRA NATION: Section 5 (Video 2-5,  compare properties of two functions in different ways.  Functions represented algebraically are limited to
7), Section 6 (Video 1 & 6) For example, given a graph of one quadratic function linear, quadratic, or exponential.
and an algebraic expression for another, say which has
MFAS: A Home for Fido the larger maximum.  Functions may be represented using tables, graphs
or verbally.
SMP #2, 7
MAFS.912.F-IF.3.9  Functions represented using these representations
are not limited to linear, quadratic or exponential.
Compare properties of two functions each
represented in a different way  Functions may have closed domains.
(algebraically, graphically, numerically in  Functions may be discontinuous.
tables, or by verbal descriptions).  Items may not require the student to use or know
NO CALCULATOR
interval notation.
MFAS: Comparing Quadratics  Key features include x-intercepts, y-intercepts;

intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; and end
behavior.

SMP #6, 7

Quadratic Functions & Equations (continued)

Essential Question(s)
How do you solve quadratics equations by various methods?
Can you analyze functions with successive differences and ratios?
How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets  Assessment Limits/ Stimulus
The students will:
 I can: Attributes:

MAFS.912.F-LE.1.3  use graphs or tables to compare the output values of  Exponential functions represented

linear, quadratic, and exponential functions. in graphs or tables should be able

Observe using graphs and tables that a  estimate the intervals for which the output of one function to be written in the form a(b)x+ k.

quantity increasing exponentially eventually is greater than the output of another function when given a  For exponential relationships,

exceeds a quantity increasing linearly, table or graph. tables or graphs must contain at

quadratically, or (more generally) as a  use technology to find the point at which the graphs of two least one pair of consecutive
polynomial function. functions intersect. values.
NO CALCULATOR
 use the points of intersection to precisely list the intervals

for which the output of one function is greater than the

MFAS: Compare Quadratic and output of another function.
Exponential  use graphs or tables to compare the rates of change of

Functions linear, quadratic, polynomial, and exponential functions.
 explain why exponential functions eventually have greater

ALGEBRA NATION: Section 8 (Video 2) output values than linear or quadratic functions by
comparing single functions of each type.

SMP #2, 8  compare properties of two functions when represented in
different ways.

Quadratic Functions & Equations (continued)

Essential Question(s)

How do you solve quadratics equations by various methods?

Can you analyze functions with successive differences and ratios?

How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-REI.2.4  identify and factor a perfect square trinomial.  In items that require the student to transform

 complete the square of ax2+bx+c to write the a quadratic equation to vertex form, the

Solve quadratic equations in one variable. quadratic in the form (x-p)2=q. coefficient of the linear term must be an

 derive the quadratic formula by completing the even factor of the coefficient of the quadratic

a. Use the method of completing the square of ax2+bx+c. term.
square to transform any quadratic
equation in x into an equation of  determine the best method to solve a quadratic  In items that allow the student to choose the
the form (x – p)² = q that has the
same solutions. Derive the equation in one variable. method for solving a quadratic equation,
quadratic formula from this form.
 solve quadratic equations by inspection, finding equations should be in the form ax2 + bx + c
b. Solve quadratic equations by
inspection (e.g., for x² = 49), square roots, completing the square, the quadratic = d, where a, b, c, and d are integers.
taking square roots, completing
the square, the quadratic formula formula, and factoring.  Items may require the student to recognize
and factoring, as appropriate to
the initial form of the equation.  explain that complex solutions result when the that a solution is non-real but should not
Recognize when the quadratic radicand is negative in the quadratic formula (b2- require the student to find a non-real
formula gives complex solutions solution.
and write them as a ± bi for real 4ac<0).  The formula must be given in the item for
numbers a and b.
items that can only be solved using the

quadratic formula

 Items may require the student to complete a

missing step in the derivation of the

quadratic formula.

 Items should be set in a mathematical

context.

MFAS: Complete the Square - 1  Items may use function notation.
 Items may require the student to recognize

ALGEBRA NATION: Section 5 (Video 3 & equivalent solutions to the quadratic
4) equation.
 Responses with square roots should require

SMP: #7, 8 the student to rewrite the square root so that
the radicand has no square factors.

Quadratic Functions & Equations (continued)

Essential Question(s)

How do you solve quadratics equations by various methods?

Can you analyze functions with successive differences and ratios?

How do you identify and graph special functions (piecewise and absolute value)?

Standard Learning Targets Assessment Limits/ Stimulus Attributes:

The students will: I can:

MAFS.912.A-REI.4.11  explain that a point of intersection on  Items may be set in a mathematical or real-

the graph of a system of equations world context and may use function notation.

Explain why the x-coordinates of the points where represents a solution to both  Items must designate the place value accuracy

the graphs of the equations y=f(x) and y=g(x) equations. (See Assessment limits ) necessary for approximate solutions.

intersect are the solutions of the equations  infer that the x-coordinate of the  In items where a function is represented by an
f(x) =g(x). points of intersections are solutions equation, the function may be an exponential

MFAS: Graphs and Solutions for f(x) = g(x). function with no more than one translation, a
 determine the approximate solutions linear function, or a quadratic function.

SMP #2, 4, 5 to a system of equations using a
graphing calculator.

MAFS.912.A-SSE.2.3  explain the connection between the  Items should only ask the student to interpret

completed square form of a quadratic the y value of the vertex within a real-world

Choose and produce an equivalent form of an expression and the maximum or context.

expression to reveal and explain properties of the minimum values of the function it

quantity represented by the expression. defines.

b. Complete the square in a quadratic
expression to reveal the maximum or
minimum value of the function it defines.

MFAS: Rocket Town

ALGEBRA NATION: Section 5 (Video 2-5)

SMP #7

Radical Functions

Standard Essential Question(s) Assessment Limits/ Stimulus
The students will:
How do you graph and transform radical functions? Attributes:
MAFS.912.F-BF.2.4 How do you perform operations with radical functions?
 Functions represented
Find inverse functions. How do you solve radical equations? algebraically are limited to
Learning Targets linear, quadratic, or
a. Solve an equation of the form exponential.
b. f(x) = c for a simple function f that I can:
 Functions may be
has an inverse and write an  write the inverse of a function by solving f(x) = c; for x. represented using tables,
expression for the inverse.  explain that after f(x) = c; for x, c can be considered the input and x graphs or verbally.
c. Verify by composition that one
function is the inverse of another. the output.  Functions represented using
d. Read values of an inverse function  write the inverse of a function in standard notation by replacing the these representations are not
from a graph or a table, given that limited to linear, quadratic or
the function has an inverse. x in my inverse equation with y and replacing the c in my inverse exponential.
e. Produce an invertible function from equation with x.
a non-invertible function by  use the composition of functions to verify that g(x) and f(x) are  Key features include x- y-
restricting the domain. inverses by showing that g(f(x))=f(g(x)) = 1. intercepts; intervals where
 decide if a function has an inverse using the horizontal line test. the function is increasing,
SMP #7  use the definitions of functions, inverse functions, and 1:1 functions decreasing, positive, or
to explain why the horizontal line test works. negative; relative maximums
MAFS.912.F-IF.2.4  list values of an inverse given a table or graph of a function that has and minimums; symmetries;
an inverse. and end behavior.
For a function that models a relationship  identify and eliminate the part of the graph that caused it to fail the
between two quantities, interpret key vertical line test.
features of graphs and tables in terms of  state the domain of a relation that has been altered in order to pass
the quantities, and sketch graphs the horizontal line test.
showing key features given a verbal  write the inverse of the invertible function in function notation.
description of the relationship.
NO CALCULATOR  determine from a table and/or a graph information that explains
what each quantity represents.
MFAS: Uphill and Downhill
 determine if negative outputs make sense in the problem situation.
ALGEBRA NATION: Section 3 (Video 7)  identify the intercepts.
 use the definition of function to explain why there can only be one

y-intercept.
 use the problem situation to explain what an x-intercept means.
 interpret how the domain of a function is represented in its graph
 create a graph that matches the description and indicates all of the

key features of the function.

SMP #1, 7, 8

Radical Functions (continued)

Standard Essential Question(s) Assessment

The students will: How do you graph and transform radical functions? Limits/ Stimulus
How do you perform operations with radical functions?
Attributes:
How do you solve radical equations? N/A
Learning Targets
 Expressions
I can: should contain
no more than
MAFS.912.F-IF.3.7  explain that the parent function for square root function three variables.

Graph functions expressed symbolically and show key features of the () = √.  For N-RN.1.2,
graph, by hand in simple cases and using technology for more  sketch a graph of a square root function by hand using items should not
complicated cases. require the
convenient values for x. student to do
more than two
 graph square root functions and find intercepts using operations.

b. Graph square root, cube root, and piecewise-defined functions, technology.

including step functions and absolute value functions.

d. Graph rational functions, identifying zeros and asymptotes when

suitable factorizations are available, and showing end behavior.

MFAS: Graphing Root Functions

SMP #7, 8

MAFS.912.A-REI.1.2  define extraneous solutions.

 determine which numbers cannot be solutions of explain

Solve simple rational and radical equations in one variable, and give why they cannot be solution.

examples showing how extraneous solutions may arise.  generate examples of radical equations with extraneous
SMP #1, 3 solutions.

 solve a radical equation in one variable.

MAFS.912.N-RN.1.2  write radical expressions as expressions with radical

exponents.

Rewrite expressions involving radicals and rational exponents using the  write expressions with rational exponents as radical

properties of exponents. expressions.

NO CALCULATOR  add and subtract radical expressions.
MFAS: Rational Exponents 4  multiply radical expressions.
ALGEBRA NATION: Section 1 (Video 5-7)  simplify radical expressions with indices greater than 2 and
SMP #7
with variables and/or rational numbers in the radicand.

MAFS.912.N-RN.2.3  explain why the sum of two rational numbers is rational

 explain why the product of two rational numbers is rational

Explain why the sum or product of two rational numbers is rational; that  explain why the sum of a rational and irrational number is

the sum of a rational number and an irrational number is irrational; and irrational

that the product of a nonzero rational number and an irrational number is  explain why the product of a nonzero rational and irrational
irrational.
number is irrational.
NO CALCULATOR

MFAS: Product of Non-Zero Rational and Irrational Numbers

ALGEBRA NATION: Section 1(Video 8)

SMP #2, 3

Analyzing Univariate Data

Essential Questions:

How do you analyze data sets using statistics?

How do you describe and use the shape of distribution?

How do you use and compare measures of central tendency and variation?

Standard Learning Goals Assessment Limits/ Stimulus
The students will: I can:
Attributes:

MAFS.912.S-ID.1.1 Display data using the best representation.  Items may require the student to

Represent data with plots on the real number line  choose the best representation (dot plot, histogram, box plot) calculate mean, median, and
interquartile range for the purpose of
(dot plots, histograms, and box plots). for a set of data. identifying similarities and differences.

 decide if a representation preserves all the data values or  Items should not require the student to

MFAS: A Tomato Garden presents only the general characteristics of a data set. calculate the standard deviation.
ALGEBRA NATION: Section 9 (Videos 1-4)  construct a histogram for a set of data  Items should not require the student to
 construct a dot plot for a set of data and choose the
fit normal curves to data.
appropriate scale to represent data on a number line.  Data distributions should be

approximately normal.

MAFS.912.S-ID.1.2 Analyze and interpret sets of data given a display.  Data sets should be real-world and
quantitative.

Use statistics appropriate to the shape of the  describe the center of the data distribution (mean or median).
data distribution to compare center (median,  choose the histogram with the largest mean when shown
mean) and spread (interquartile range, standard
deviation) of two or more different data sets. several histograms.
 describe the spread of the data distribution (interquartile range

or standard deviation).

 choose the histogram with the greatest standard deviation

MFAS: Texting During Lunch Histograms when shown several histograms.
 choose the box-and-whisker plot with the greatest interquartile

ALGEBRA NATION: Section 9 (Video 5-8) range when shown several box-and-whisker plots.
 compare the distributions of two or more data sets by

examining their shapes, centers, and spreads when drawn on

MAFS.912.S-ID.1.3 the same scale.
 interpret the differences in the shape, center, and spread of a

Interpret differences in shape, center, and spread data set in the context of a problem.

in the context of the data sets, accounting for  identify the outliers for the data set.

possible effects of extreme data points (outliers).  predict the effect an outlier will have on the shape, center, and
spread of a data set.

MFAS: Comparing Distributions  decide whether to include the outliers as part of the data set or
ALGEBRA NATION: Section 9 (Video 9) to remove them.

 use the 68-95-99.7 Rule to estimate the percent of a normal

population that falls within 1, 2, or 3 standard deviations of the

SMP #1, 5 mean.

Analyzing Univariate Data (continued)

Essential Questions:

How do you analyze data sets using statistics?
How do you describe and use the shape of distribution?
How do you use and compare measures of central tendency and variation?

Standard Learning Goals Assessment Limits/ Stimulus
The students will: I can:
Attributes:

MAFS.912.S-ID.1.4 Recognize and interpret a data set with a normal
distribution.
Use the mean and standard deviation data set to
fit it to a normal distribution and to estimate  use mean and standard deviation of a set of data to
population percentages. Recognize that they are fit the data to a normal curve
data sets for which such a procedure is not
appropriate. Use calculators, spreadsheets, and  use the 68-95-99.7 Rule to estimate the percent of
tables to estimate area under the normal curve. a normal population that falls within 1, 2, or 3
standard deviations of the mean.
MFAS: Probability of Your Next Texting Thread
Range of Texting Thread  recognize that normal distributions are only
Label a Normal Curve appropriate for unimodal and symmetric shapes

 estimate the area under a normal curve using a
calculator, table, or spreadsheet

SMP #2, 5, 7

Analyzing Bivariate Data

Essential Questions:

How do you write an equation to model/show trends in data?

How can you decide whether a correlation exists between paired numerical data?

How can you find a linear model for a set of data and evaluate the goodness of fit?

Standard Learning Goals Assessment Limits/ Stimulus
The students will: I can:
Attributes:

MAFS.912.S-ID.2.5  read and interpret the data displayed in a two-way frequency  In data with only two categorical

table. variables, items should require the
student to determine relative
Summarize categorical data for two categories in  write clear summaries of data displayed in a two-way frequency frequencies and use the
frequencies to complete the table or
two-way frequency tables. Interpret relative table. to answer questions.

frequencies in the context of the data (including  calculate percentages using the ratios in a two-way frequency

joint, marginal, and conditional relative table to yield relative frequencies.

frequencies). Recognize possible associations and  calculate joint, marginal, and conditional relative frequencies.
trends in the data.
 interpret and explain the meaning of relative frequencies in the

MFAS: Breakfast Drink Preference context of a problem.
ALGEBRA NATION: SECTION 10 (VIDEOS 1-2)  make appropriate displays of joint, marginal, and conditional
SMP #2
distributions.
 describe patterns observed in the data.

MAFS.912.S-ID.2.6  identify the independent and dependent variable and describe  In items that require the student to

the relationship of the variables. interpret or use the correlation

Represent data on two quantitative variables on a  construct a scatter plot with an appropriate scale. coefficient, the value of the

scatter plot, and describe how the variables are  identify any outliers on the scatter plot. correlation coefficient must be given

related. Fit a function to the data; use functions  determine when linear, quadratic, and exponential models in the stem.

fitted to data to solve problems in the context of the should be used to represent a data set.  Items requiring the student to

data. Use given functions or choose a function  determine whether linear and exponential models are increasing calculate the rate of change will
suggested by the context. Emphasize linear, and decreasing. give a specified interval that is both

quadratic, and exponential models. Informally  use technology to find the function of best fit for a scatter plot. continuous and differentiable.
assess the fit of a function by plotting and  use the function of best fit to make predictions.  Items should not require the student
analyzing residuals. Fit a linear function for a  compute the residuals (observed value minus predicted value)
scatter plot that suggests a linear association. to find an equation of a line. Items
for the set of data and the function of best fit. assessing S-ID.3.7 should include
MFAS: Swimming Predictions  construct a scatter plot of the residuals. data sets.
ALGEBRA NATION: SECTION 10 (VIDEOS 3-5)  analyze the residual plot to determine whether the function is an  Data sets must contain at least six
data pairs. The linear function given
MAFS.912.S-ID.3.7 appropriate fit. in the item should be the regression
 sketch the line of best fit on a scatter plot that appears linear. equation.
Interpret the slope (rate of change) and the  write the equation of the line of best fit (y=mx+b) using  For items assessing S-ID.3.7, the
intercept (constant term) of a linear model in the rate of change and the y-intercept
context of the data. technology or by using two points on the best fit line. should have a value with at least a
 interpret the meaning of the slope in terms of the units stated in hundredths place value.

the data.
 interpret the meaning of the y-intercept in terms of the units

MFAS: Slope for the Foot Length Model stated in the data.

ALGEBRA NATION: SECTION 10 (VIDEOS 4-5)

Analyzing Bivariate Data

Essential Questions:

How do you write an equation to model/show trends in data?

How can you decide whether a correlation exists between paired numerical data?

How can you find a linear model for a set of data and evaluate the goodness of fit?

Standard Learning Goals Assessment Limits/ Stimulus
The students will: I can:
Attributes:

MAFS.912.S-ID.3.8  explain the correlation coefficient applies only to  In items that require the student

quantitative variables and linear models of best fit. to interpret or use the correlation

Compute (using technology) and interpret the  compute the correlation coefficient (r) using a graphing coefficient, the value of the
correlation coefficient of a linear fit. calculator or other appropriate technology. correlation coefficient must be
given in the stem.
MFAS: July December Correlation  use the correlation coefficient to determine if a linear model
is a good fit for the data (significance).

ALGEBRA NATION: SECTION 10 (VIDEO 5)  recognize that correlation does not imply causation and

that causation is not illustrated on a scatter plot.

 choose two variables that could be correlated because one

is the cause of the other and defend my selection.

MAFS.912.S-ID.3.9  determine if statements of causation seem reasonable or
unreasonable and defend my opinion.

Distinguish between correlation and causation.

MFAS: Does the Drug Cause Diabetes?

ALGEBRA NATION: SECTION 10 (VIDEO 5)

SMP #2, 3, 4, 5