2017-2018 - washoe county school district · 2017-2018 # 2201/2202 algebra ... students have...

2017-2018 # 2201/2202 Algebra 1

#228 Middle School Algebra 1

#776 Accelerated Algebra 1

#217 VMS Algebra 1

#7769/7770 Foundations in Algebra 1

Course Guide

Critical Areas in Algebra 1

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the

middle grades. Because it is built on the middle grades standards, this is a more ambitious version of Algebra I

than has generally been offered. 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.

(1) 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. Now,

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.

(2) 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.

(3) This unit builds upon prior students’ prior experiences with data, providing students with more formal

means of assessing how a model fits data. Students use regression techniques to describe approximately

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.

(4) Critical Area 4: In this unit, students build on their knowledge from unit 2, 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.

(5) 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 zeros 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.

Possible book sections – Code Key

Text Sections referenced are from 2007 McDougal Littell Algebra 1 - #.#

On Core sections – OC

Eureka Math – Module #, Lesson # = Mod#, L#

2017-2018

Algebra 1 Unit 1 (Review) – Semester 1

Topics Possible Book

Sections

Review - Evaluate and simplify expressions linear, quadratic, and exponential expressions. 1.2, OC1.2

Review - solve multi-step linear equations from grade 8, Use real numbers and

properties: associative, commutative, distributive, inverse and identity.

(A.SSE.2, A.REI.1, A.REI.3)

3.3, 3.4, OC2.1

Introduce - solve and graph on number line mulit-step linear inequalities. (review one and

two step inequalities from grade 7) (A.SSE.2, A.REI.1, A.REI.3) 6.3, 6.4, OC2.2

Write and solve single variable linear equations and inequalities to model real life

situations. (N.Q.1, N.Q.2, N.Q.3, A.CED.1, A.CED.3, A.SSE.1) OC1.4, OC2.3

Rearrange formulas and solve literal equations and inequalities for one variable.

(A.REI.1, A.REI.3, A.CED.4, A.SSE.2) OC2.4, OC2.5, 3.8

22 (50 min periods)

Standards to be taught Reason quantitatively and use units to solve problems. (Use N.Q.1, N.Q.2, N.Q.3 throughout year)

N.Q.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.

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Interpret the structure of expressions.

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. *

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For

example, interpret �(1 + �)� as the product of P and a factor not depending on P.

A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

Create equations that describe numbers or relationships.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations

arising from linear and quadratic functions, and simple rational and exponential functions.

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities,

and interpret solutions as viable or non-viable options in a modeling context. For example, represent

inequalities describing nutritional and cost constraints on combinations of different foods.

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

For example, rearrange Ohm’s Law � = � to highlight resistance R.

Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.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.

Solve equations and inequalities in one variable.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients

represented by letters.

2017-2018

Algebra 1 Unit 2 (Discrete Functions & Patterns) – Semester 1


Sections

Referrence Eureka Math Module 3, Lessons 1-3 throughout Unit 2

Develop conceptual understanding of functions, function notation and vocabulary (input,

output, domain, range, sequence, recursive, explicit form, recursive form, element,

average rate of change, interval, arithmetic, geometric, dependent variables, independent

variables). Plot functions in a coordinate plane. (F.IF.1, F.IF.2, F.IF.3, F.IF.4, F.IF.5)

1.6, 1.7, OC1.5

Examine a table of values, a discrete graph, or a sequence of numbers to determine if

there is an additive rate of change (linear) or multiplicative rate of change (exponential).

Identify the sequence accordingly as either arithmetic or geometric. (F.IF.6, F.LE.1)

5.3Ext

Arithmetic - from a table of values, coordinate graph, or a sequence of numbers write

explicit and recursive forms of a function using function and subscript notation for both.

Identify domain and range in terms of context.

• explicit form: these forms are equivalent; � = (� � �) + �, � = � + (� � 1�� ,

�� 1� � ��1�, where d is common difference and ��1� ��

• recursive form: � �� , where � and common difference, d,

can be determined from sequence, function form ��1� ��,

�� 1� � �

(F.IF.1, F.IF.2, F.IF.3, F.BF.1a, F.BF.2, F.LE.1a, F.LE.2)

OC5.1

Alg 2 OC9.1, OC9.2

Math Resources

Geometric - from a table of values, coordinate graph, or a sequence of numbers write

explicit and recursive forms of a function using function and subscript notation for both.

Interpret domain and range in terms of context.

• explicit form: � �� where �common ratio (rate of change) are obtained

from the sequence, �� 1� ∙ �� where ��1� ��

• recursive form: � � ∙ �� where � and common ratio (rate of change) are

obtained from the sequence, ��1� �� and �� ∙ �� 1�

(F.IF.1, F.IF.2, F.IF.3, F.BF.1a, F.BF.2, F.LE.1a, F.LE.2)

8.6Ext

Alg 2 OC9.3

Math Resources

Compare properties of two functions (Arithmetic/Geometric) each represented in a

different way (algebraically, graphically, numerically and in table or a verbal description).

(F.IF.9)

Math Resources

17 (50 min periods)

Standards to be taught Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential

functions.

a. Prove that linear functions can be modeled by equal differences over equal intervals, and that

exponential functions grow by equal factors over equal intervals.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a

graph, a description of a relationship, or two input-output pairs (including reading these from a table).

Understanding the concept of a function and use function notation.

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns

to each element of the domain exactly one element of the range. If f is a function of and � is an

element of its domain, the �(�) denotes the output of f corresponding to the input �. The graph of f is

the equation � = �(�).

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that

use function notation in terms of a context.

F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of

the integers.

2017-2018

Interpret functions that arise in applications in terms of the context.

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and

tables in terms of the quantities, and sketch graphs showing key features given a verbal description of

the relationship.

F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it

describes.*

F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table)

over a specified interval. Estimate the rate of change from a graph.*

Build a function that models a relationship between two quantities.

F.BF.1 Write a function that describes a relationship between two quantities.*

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to

model situations, and translate between the two forms.

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically,

numerically and in table or a verbal description.

2017-2018

19 (50 min periods)

Standards to be taught Understand the concept of a function and use function notation.


to each element of the domain exactly one element of the range. If f is a function of and � is an

element of its domain, the �(�) denotes the output of f corresponding to the input �. The graph of f is

the equation � = �(�).

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that





the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing,

positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*


describe.*



Analyze functions using different representations.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases

and using technology for more complicated cases. *

a. Graph linear and quadratic functions show intercepts, maxima and minima.

b. Graph square root, cube root and piecewise-defined functions, including step functions and absolute

value functions.



Interpret expression for functions in terms of the situation they model.


graph, a description of a relationship, or two input-output pairs (including reading these from a table).

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Algebra 1 Unit 3 (Linear) – Semester 1


Sections

Make connections using tables, graphs and ordered pairs, to create linear equations in

two variables (slope intercept, standard form, (h,k) form) to model mathematical and

real-world situations. (A.CED.2, A.CED.3, F.IF.1, F.IF.2, F.IF.4, F.LE.2)

5.1, 5.3, OC2.8,

OC4.5,

Graph linear equations in two variables to model mathematical and real-world

situations. (A.CED.2, A.REI.10, F.IF.4, F.IF.7a) OC2.6, OC4.2, OC4.5

Analyze key features of graphs (domain, range, end behavior (all notations), increasing

and decreasing, intercepts, rate of change) (A.REI.10, F.IF.4, F.IF.5, F.IF.6, F.LE.5, F.BF.3) OC4.3

Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically and in table or a verbal description). (F.IF.9, F.BF.3) Math Resources

Create and graph linear inequalities to model mathematical and real-world situations.

(A.CED.3, A.REI.12) 6.7, OC2.7, OC2.8

Create, and graph, a single linear function with a restricted domain to build a foundation

for piecewise functions. (F.IF.4, F.IF.5, F.IF.7b) Math Resources

2017-2018

Build new functions form existing functions.

F.BF.3 Identify the effect on the graph of replacing �(�) by �(�) + �, � ∙ �(�), ��, �� (� + �) for

specific values of k (both positive and negative); find the value of k given the graphs. Experiment with

cases and illustrate an explanation of the effects on the graph using technology.


A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.


and interpret solutions as viable or nonviable options in a modeling context.

Represent and solve equations and inequalities graphically.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the

coordinate plane, often forming a curve (which could be a line).

A.REI.12 Graph the solutions to linear inequality in two variables as a half-plane (excluding the boundary in the

case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables

as the intersections of the corresponding half-planes.

2017-2018

Algebra 1 Unit 4 (Systems) – Semester 1


Sections

Solve Linear Systems by graphing – addressing systems with no solution, one solution, or

infinite solutions. (A.REI.6, A.REI.11, F.IF.9) 7.1

Solve Linear Systems by Substitution and Elimination (A.REI.5, A.REI.6, A.REI.11) 7.2-7.5

Model mathematical and real-world situations with linear systems.

(N.Q.1, N.Q.2, N.Q.3, A.CED.2, A.CED.3, A.REI.6, A.REI.11) OC3.6

Solve Systems of Linear Inequalities (A.REI.12) 7.6

Model mathematical and real-world situations with systems of linear inequalities

(N.Q.1, N.Q.2, N.Q.3, A.REI.12) OC3.6

16 (50 min periods)

Standards to be taught Reason quantitatively and use units to solve problems. (Use N.Q.1, N.Q.2, N.Q.3 throughout year)

N.Q.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.

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.










Solve systems of equations.

A.REI.5 Prove that given a system of two equations in two variables, replacing one equation by the sum of that

equation and a multiple of the other produces a system with the same solutions.

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of

linear equations in two variables.


A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations � = �(�) and � = �(�)

intersect are the soutions of the equation �(�) = �(�); find the solutions approximately, e.g., using

technology to graph the functions, make tables of values, or find successive approximations. Include

cases where �(�) and/or �(�) are linear, polynomial, rational, absolute value, exponential, and

logarithmic funtions.*

A.REI.12 Graph the solutions to linear inequality in two variables as a half-plane (excluding the boundary in the

case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables

as the intersections of the corresponding half-planes.

2017-2018

Algebra 1 Unit 5 (Statistics) – Semester 1


Sections

Understand and interpret data:

• Represent data with plots on the real number line (dot plots, histograms, and

box plots). (S.ID.1)

• Use statistics appropriate to the shape of the data distribution to compare

center (median, mean) and spread (interquartile range, standard deviation) of

two or more different data sets. (S.ID.2)

• Interpret differences in shape, center, and spread in the context of the data

sets, accounting for possible effects of extreme data points (outliers). (S.ID.3)

(Eureka Module 2)

OC9.1-OC9.4, 13.8

Summarize categorical data for two categories in two-way frequency tables. Interpret

relative frequencies in the context of the data (including joint, marginal, and conditional

relative frequencies). Recognize possible associations and trends in the data. (S.ID.5)

OC9.5

5 (50 min periods)

Summarize, represent, and interpret data on a single count or measurement variable.

S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and

spread (interquartile range, standard deviation) of two or more different data sets.

S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for

possible effects of extreme data points (outliers).

Summarize, represent, and interpret data on two categorical and quantitative variables.

S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative

frequencies in the context of the data (including joint, marginal, and conditional relative frequencies).

Recognize possible associations and trends in the data.

2017-2018

Algebra 1 Unit 6 (Absolute Value) - Semester 2


Sections

Graph and interpret linear piecewise functions with mathematical and real-world

situations. Given a graph, write a piecewise function. (Step functions are not necessary

for Algebra 1) (A.CED.2, A.CED.3, A.REI.10, F.IF.2, F.IF.4, F.IF.5, F.IF.7b)

OC6.1

Understanding that an absolute value function is a piecewise function by graphing:

�(�) = � �� ≥ 0−� �� < 0

(A.CED.2, A.CED.3, A.REI.10, F.BF.3, F.IF.2, F.IF.4, F.IF.5, F.IF.7b)

Math Resources

Graph �(�) = |� − ℎ| + � using tables and transformations (translate,

shrink/compress, stretch, reflect) and combinations of transformations. Interpret key

features of the graph. Given a graph or table, write the absolute value function.

(A.CED.2, F.IF.2, F.IF.4, F.IF.5, F.IF.7b, F.BF.3, A.REI.10)

OC6.2

ext 6.5, OC6.3, OC6.4

Solve absolute value equations (not inequalities)

• First establish conceptual understanding by solving graphically, to explain why

the x-coordinates of the points where the graphs of the equations � = �(�) and

� = �(�) intersect are solutions to the equation �(�) = �(�).

• Then establish procedural understanding by solving algebraically, using procedures

and number lines.

(A.CED.1, A.CED.2, F.IF.4, A.REI.11)

(Mod3, L16), OC6.5

Math Resources

Model mathematical and real-world situations with absolute value functions.

(A.CED.1, A.CED.2, A.CED.3, F.IF.2, F.IF.4, F.IF.5, F.IF.7b) 6.5, OC6.6

9 (50 min periods) Standards to be taught










F.IF.2 Use function notation, evaluate functions for inputs in their domain, and interpret statements that





the relationship. Key features include: intercepts; intervals where the function is increasing,

decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and

periodicity.*


describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n

engines in a factory, then the positive integers would be an appropriate domain for the function.*



and using technology for more complicated cases.*

b. Graph piecewise functions including absolute value functions.

2017-2018


F.BF.3 Identify the effect on the graph of replacing �(�) by �(�) + �, � ∙ �(�), �(��), �� (� + �) for


cases and illustrate an explanation of the effects on the graph using technology. Include recognizing

even and odd functions from their graphs and algebraic expressions for them.


A.REI.10 Understand that the graph of an equations in two variables is the set of all its solutions plotted in the


A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations � = �(�) and

� = �(�) intersect are the soutions of the equation �(�) = �(�); find the solutions approximately,

e.g., using technology to graph the functions, make tables of values, or find successive

approximations. Include cases where �(�) and/or �(�) are linear, polynomial, rational, absolute

value, exponential, and logarithmic funtions.*

2017-2018

Algebra 1 Unit 7 – Semester 2

(Quadratic Functions in Vertex Form)


Sections

Vertex Form Eureka Module 4

Graph �(�) = (� − ℎ)% + � using tables and transformations (translate,

shrink/compress, stretch, reflect) and combinations of transformations. Interpret key

features of the graph. Given a graph or table, write the quadratic function in vertex

form. (A.CED.2, F.BF.3, F.IF.2, F.IF.4, F.IF.5, F.IF.6, F.IF.7a, A.REI.10)

10.1

OC7.1-OC7.3

Solve quadratics equations that are in vertex form.




• Then establish procedural understanding by solving algebraically, using square roots

and number lines.

(A.CED.1, A.CED.2, A.REI.4, A.REI.11, F.IF.4)

OC 7.4-OC7.5

Alg 2 – 4.5 #22-33

Model mathematical and real-world situations with quadratic functions in vertex form.

(A.CED.1, A.CED.2, A.CED.3, A.SSE.1, F.IF.2, F.IF.4, F.IF.5, F.IF.7a) OC7.6

13 (50 minute periods)

Standards to be taught Create equations that describe numbers or relationships.






and interpret solutions as viable or non-viable options in a modeling context

Interpret the structure of the expressions.






F.IF.2 Use function notation, evaluate functions for inputs in their domain, and interpret statements that





the relationship. Key features include: intercepts; intervals where the function is increasing,

decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and

periodicity.*


describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n

engines in a factory, then the positive integers would be an appropriate domain for the function.*



2017-2018




a. Graph linear and quadratic functions and show intercepts, maxima, and minima.




cases and illustrate an explanation of the effects on the graph using technology. Include recognizing



A.REI.4 Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of

the form (� − &)% = ' that has the same solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection (e.g., for �% = 49), taking square roots, completing the square,

the quadratic formula and factoring, as appropriate to the initial form of the equation.




A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations � = �(�) and � =�(�) intersect are the soutions of the equation �(�) = �(�); find the solutions approximately, e.g.,

using technology to graph the functions, make tables of values, or find successive approximations.

Include cases where �(�) and/or �(�) are linear, polynomial, rational, absolute value, exponential,

and logarithmic funtions.*

Algebra 1 Unit 8 (Quadratic Expressions) – Semester 2


Sections

Quadratic Expressions Eureka Module 4

Operations with Expressions – represent a quantity in terms of its context.

Conceptual understanding should be established using Area Models and Algebra Tiles.

• Addition

• Subtraction

• Multiplication

• Multiplication – Vertex Form to Standard Form

(A.SSE.1, A.SSE.2)

9.1, 9.2, OC8.1

Factoring Quadratic Expressions �% + *� + +

Conceptual understanding should be established using Area Models and Algebra Tiles

• Division

(A.SSE.2)

9.5, 9.6

16 (50 min periods)

Standards to be taught


A.SSE.1 Interpret expressions that represent a quantity in terms of its context.*





2017-2018

Algebra 1 Unit 9 – Semester 2

(Quadratic Functions in Intercept and Standard Form)


Sections

Intercept Form Eureka Module 4

Graph �(�) = (� − ')(� − &) using tables to establish conceptual understanding of

values p and q as x-intercepts on the graph (lay the foundation for Zero Product Property

later). Find and interpret the key features of the graph based on the x-intercepts (axis of

symmetry � = ,-.% ). Given a graph or table write the intercept form of the function.

(A.CED.2, F.IF.2, F.IF.4, F.IF.5, F.IF.6, F.IF.7a, F.IF.8a, A.REI.10)

p641, 10.3

Solve quadratics equations using intercept form.

• Establish conceptual understanding by solving graphically, to explain why



• Establish procedural understanding by solving algebraically, using factoring and

Zero Product Property.

(A.CED.1, A.CED.2, A.SSE.2, A.SSE.3a, A.REI.11, F.IF.4, F.IF.8a)

OC8.2, OC8.3, 10.3

Model mathematical and real-world situations w/quadratic functions in intercept form.

(A.CED.1, A.CED.2, A.CED.3, A.SSE.1, A.SSE.2, A.SSE.3a, F.IF.2, F.IF.4, F.IF.5, F.IF.7a, F.IF.8a) OC8.10

Standard Form Eureka Module 4

Convert standard form into vertex form by completing the square. Use algebra tiles and

area models to establish conceptual understanding. (F.IF.8a, A.SSE.2, A.SSE.3b) 10.5, OC8.4

Before using the quadratic formula, derive the quadratic formula from standard form

(extension of completing the square). Be prepared to justify steps when given a quadratic

equation in standard form transformed into the quadratic formula by using completing

the square. (A.SSE.2, A.REI.4b)

OC8.6

Graph � = �% + *� + + using tables to establish conceptual understanding and find the

axis of symmetry /� = − 0%12 and vertex (− 0

%1 , � /− 0%12). Find and interpret the key

features of the graph. Given a graph or table write the standard form of the

function. (F.IF.4, F.IF.5, F.IF.7a, F.IF.8a, A.REI.10)

10.2, OC8.8

Use the quadratic formula, factoring, or completing the square to find the zeros of a

quadratic function in any form. Reinforce the connection of finding zeros algebraically to

the graph of the function. (A.SSE.2, A.REI.4a, A.REI.4b)

10.6, OC8.5, OC8.7

Model mathematical and real-world situations w/quadratic functions in standard form.

(A.CED.1, A.CED.2, A.CED.3, A.SSE.1, A.SSE.2, A.SSE.3a, F.IF.2, F.IF.4, F.IF.5, F.IF.6, F.IF.7a, F.IF.8a) cc10.8A, OC8.10

Compare properties of two functions each represented in a different way (algebraically,

graphically, table, or verbal description). (F.IF.9)

*Note: At the end of this unit, students should be given mixed practice opportunities to:

• Convert between all forms of quadratic equations

• Graph quadratic functions in various forms

• Solve quadratic equations in various forms using any method

• Interpret and reinforce the key features of graphs that appear in each form

OC8.9, Math

Resources

20 (50 min periods)

Standards to be taught Create equations that describe numbers or relationships.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from

linear and quadratic functions, and simple rational and exponential functions.

2017-2018

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on

coordinate axes with labels and scales.

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret

solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing

nutritional and cost constraints on combinations of different foods.


A.REI.4 Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the

form (� − &)% = ' that has the same solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection (e.g., for �% = 49), taking square roots, completing the square, the

quadratic formula and factoring, as appropriate to the initial form of the equation.


A.REI.10 Understand that the graph of an equations in two variables is the set of all its solutions plotted in the coordinate

plane, often forming a curve (which could be a line).

A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations � = �(�) and � = �(�) intersect

are the soutions of the equation �(�) = �(�); find the solutions approximately, e.g., using technology to graph

the functions, make tables of values, or find successive approximations. Include cases where �(�) and/or �(�)

are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.




b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example,

interpret �(1 + �)� as the product of P and a factor not depending on P.


Write expression in equivalent forms to solve problems.

A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity

represented by the expression.*

a. Factor a quadratic expression to reveal the zeros of the function it defines.

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


F.IF.2 Use function notation, evaluate functions for inputs in their domain, and interpret statements that use function

notation in terms of a context.


F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in

terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative;

relative maximums and minimums; symmetries; end behavior; and periodicity.*

F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory,

then the positive integers would be an appropriate domain for the function.*

F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a

specified interval. Estimate the rate of change from a graph.*


F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using

technology for more complicated cases.*

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different

properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values,

and symmetry of the graph, and interpret these in terms of a context.

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically

and in table or a verbal description.

2017-2018

Algebra 1 Unit 10 (Exponential Functions) – Semester 2


Sections

Review: Know and apply the properties of integer exponents to generate equivalent

numerical expressions

**you only need to be able to manipulate the expression of an exponential function,

�% = 2�� etc. (spending time to work on all of the exponential properties is not

necessary at this point) (8.EE.1, A.SSE.3)

8.3

Given a table of values or data set, distinguish between situations that can be modeled

with linear functions and with exponential functions and write the function.

• Linear functions can be modeled by equal differences over equal intervals -

Recognize situations in which one quantity changes at a constant rate per unit

interval relative to another.

• Exponential functions grow by equal factors over equal intervals - Recognize

situations in which a quantity grows or decays by a constant percent rate per unit

interval relative to another.

• Compare the average rate of change between linear, exponential and quadratic

functions. (F.LE.1, F.LE.2)

OC5.7,

Math Resources

Graph and interpret exponential growth and decay functions (�(�) = *4, �(�) = *4 + �) with mathematical and real world situations.

(stick to translating up and down and vertical stretch and compression) (F.BF.3, F.LE.2)

8.5, 8.6 OC5.2-OC5.4, Make connections to OC5.1 and

discrete functions.

Solve simple equations involving exponents in mathematical situations.




• Then establish procedural understanding by solving algebraically, using simple

properties of exponents (reviewed above) (A.REI.1, A.REI.10, A.REI.11)

8.5, 8.6, OC5.5

Modeling with exponential growth and decay functions

(A.SSE.1, A.CED.1, A.CED.2, F.IF.1, F.IF.2, F.IF.4, F.IF.5, F.IF.6, F.IF.7e, F.LE.1, F.LE.2, F.LE.5)

8.5, 8.6, OC5.7, OC5.8,

p541

10 (50 min periods)

Standards to be taught Work with radical and integer exponents.

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Write expressions in equivalent forms to solve problems.





A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the

quantity represented by the expression.

c. Use the properties of exponents to transform expressions for exponential functions.






Understand solving equations as a process of reasoning and explain the reasoning.

2017-2018

A.REI.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.




A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations � = �(�) and � = �(�)

intersect are the soutions of the equation �(�) = �(�); find the solutions approximately, e.g., using

technology to graph the functions, make tables of values, or find successive approximations. Include

cases where �(�) and/or �(�) are linear, polynomial, rational, absolute value, exponential, and

logarithmic functions.



to each element of the domain exactly one element of the range. If f is a function of and x is an

element of its domain, the f(x) denotes the output of f corresponding to the input x. The graph of f is

the graph of the equation � = �(�).

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use

function notation in terms of a context.




the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing,

positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

F.IF.5 Relate the domain of a function to its graph and where applicable, to the quantitative relationship it

describes.*






e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and

trigonometric functions, showing period, midline and amplitude.

Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential

functions.

a. Prove that linear functions can be modeled by equal differences over equal intervals, and that

exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity 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.


graph, a description, or a two input-output pairs (include reading these from a table).

Interpret expression for functions in terms of the situation they model.

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Build new functions form existing functions.


specific values ok k (both positive and negative); find the value of k given the graphs. Experiment with

cases and illustrate an explanation o the effects on the graph using technology. Include recognizing


EOC Testing Window

2017-2018

TO BE TAUGHT AFTER THE EOC!

Algebra 1 Unit 11 (Exponents Properties) – Semester 2


Sections

Review properties of exponents, reivew integer exponents with numerical bases, (8.EE.1) 8.1-8.3

Explain and use Integer Exponents with variable bases to rewrite expressions

(N.RN.1, N.RN.2, N.RN.3)

Examples: Rewrite the following expressions using the properties of exponents:

(��5)�% (5��5)7(�8)�5 (59):9;9<:9= (9��5)�%

ext 8.3

Perform operations (add, subtract, multiply and rationalize) on Square Roots and Cube Roots

with numerical bases (N.RN.1, N.RN.2, N.RN.3)

Examples: Rewrite the following expressions using the properties of rational exponents:

√2 + √8 √21@√3B √3= + √81=

7√3 + √27 √72(√2) √8= + √54=

�√%

√%8√5

8√%7= √2@3√2 + 4√5B

11.2

• Limit simplifying to square roots and cube roots.

8 (50 min periods) Standards to be taught

Work with radical and integer exponents.

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Extend the properties of exponents to rational exponents.

N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties

of integer exponents follows from extending the properties of integer properties of integer exponents

to those values, allowing for a notation for radicals in terms of rational exponents. For example,

we define 5� 5⁄ to be the cube root of 5 because we want @5� 5⁄ B5 = 5(� 5⁄ )5 to hold, so. @5� 5⁄ B5 must

equal 5.

N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Use properties of rational and irrational numbers.

N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number

and an irrational number is irrational; and that the product of a nonzero rational number and an

irrational number is irrational.

2017-2018 - washoe county school district · 2017-2018 # 2201/2202 algebra ... students have...

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