Financial Algebra New Course Proposal

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Date _____November 6, 2011_______ 1. Teacher(s) submitting request John Walker

Teacher(s) expected to teach course John Walker 2. Department Pro-Tech 3. Course Title Financial Algebra 4. School year to be implemented 2012/13 5. Length of Course: __ ____ semester __X____ year 6. Course Credit: ______ required ____X__ elective 7. Appropriate grade level(s) 10-12 8. Anticipated number of students that will be involved 32 (current limit to computer lab) 9. Pre-requisite courses: Algebra I

10. Articulation with MHCC for credit? _____yes __X___no

11. This course can be repeated for credit: _____yes ___X__no

12. Explain why this course is needed. How will it benefit our students? How does it differ from current courses offered? How does this course enhance or relate to overall school goals and educational experiences appropriate for the 21st Century?

This course is proposed as a course that can be taken concurrently with Geometry, Algebra 2, or PreCalc. It is primarily geared as a course for students who may have experienced difficulty in Algebra 1 and/or Geometry and may not be ready for Algebra 2 or Precalculus. It will provide a Math Elective Credit It is

• A mathematically rigorous, algebra-based course. (Not an arithmetic-based personal finance course).

• Algebra 1 is the prerequisite, and Algebra 1 skills are reinforced throughout. • Includes selected topics from Algebra 2, Precalculus, Statistics, Probability and

Geometry that are taught at an ability-appropriate level for the Algebra 1-prerequisite audience.

• It is technology-dependent and applications-oriented.

NEW COURSE PROPOSAL FORM

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13. Course Description: (this must be in its final form when the proposal is made as it will be

used in the course planning guide) In Financial Algebra, the mathematics necessary for daily living is embedded in content that directly relates to financial decisions adults make in their daily lives. The mathematical formulas, functions, and representations used in Financial Algebra will assist you in making sense of the financial world through mathematical modeling and provide you with the ability to make sound financial decisions based on data. 14. General Course Outline: (briefly outline course objectives and what will be covered)

A. Semester I: See Attached Syllabus: B. Semester II (if applicable):

See Attached Syllabus:

15. List all state standards and graduation requirements that will be addressed in this course.

How does the course fit with district’s curriculum strands, standards-based instruction, career-related learning, and ongoing school goals?

See attached alignment with Common Core State Standards which are undergoing adoption in the State of Oregon for alignment.

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16. What methods or indicators will be used to evaluate the effectiveness of this class and/or

program? Successful integration of a learner into Algebra 2. 17. Budget: What additional materials and resources will be necessary to offer this course?

How will these requests be funded? Textbooks could be purchased at a cost of $3786.12 or a set of materials at $1000 could be

purchased and entire course converted to Moodle, which is the recommendation.

Funding is a part of the request

A. Operating Expenses:

1) Materials (textbooks, literature selections, etc.) $__1000____

2) Copying services $___________

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3) Office/classroom supplies $___________

4) Technology (software, etc.) $__________

B. Equipment $___________ C. Other Misc. Expenses $___________

D. List any items not covered: Course will be hosted on Integrated Media Moodle Server,

Class is dependant on daily technological and application utilization Instructor Training is $300 plus travel and expenses during summer 1000. Two Week stipend for instructor to convert materials – $ N/A

E. Total Estimated Cost of the course(s) $2000+Stipend

18. Assuming we receive no additional FTE, how will we staff sections of this course? Course will be staffed by assigning the IT teacher, who will be Math Endorsed, to two of four sections. As course is to be converted to a online learning management system, additional resources from either an Algebra I or 1.5 course could be assigned based on skills and experience in finance. 19. How will the master schedule be impacted by the adoption of this course? Two sections are foreseen to be conducted in Room 509, two sections would need to be in an additional lab with computers and projector access for instructor/students to access Learning Management on a daily basis. 20. Indicate whether research and best practice supports adoption of this course. Please

attach information from external sources (news articles, professional journals, research data, surveys, etc.) that support adoption of this course.

There are a number of articles and learning research to support connected learning through application. A quick Google search yields numerous Article from the NYTimes on April 9, 2010 Most Americans aren’t fluent in the language of money. Yet we’re expected to make big

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financial decisions as early as our teens … even though most of us received no formal instruction on financial matters until it is too late. All of this raises the question: What’s happening inside our classrooms? And how many schools even broach the topic? As it turns out, for a country that prizes personal responsibility, we’re doing very little. 21. If this proposal is an extension of, or addition to, a previous adopted course, please explain. Course may be considered as an alternate to Algebra 1.5. 22. Briefly explain the primary instructional practices that will be used to teach this course.

How do the practices align with the district’s instructional model? One can teach computer science concepts so that students have immediate visual feedback— at least in the beginning. They will truly understand what they have done right and wrong because they can see it. Students should not lose sight of computer science as they examine the details of the computer language. This undertaking is not too difficult since algorithms that solve a variety of robot tasks are both plentiful and provocative, as are the topics of study associated with them. Emphasis is placed on having creativity and imagination be their guides. A goal for students is to be enjoying computer science at the level that it is most inspiring—the conceptual level. This new course proposal has been approved by: Department _________________________________________ Date __________________

Department Chair Signature

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Principal _________________________________________ Date __________________ Principal Signature District _________________________________________ Date __________________ Director of K-12 Curriculum

Syllabus for Financial Algebra by Gerver & Sgroi Page 1

Financial Algebra

Syllabus & Essential Elements Chapter 1: The Stock Market (approximately 20 days) Students are introduced to basic business organization terminology in order to read, interpret and chart stock ownership and transaction data. 1-1 Business Organizations (1 day)

Objectives • Learn the basic vocabulary of business organizations. • Compute financial responsibility of business ownership based on ratios and

percents Key Terms

Capital, corporation, limited liability, partnership, personally liable profit, public corporation, shareholders, shares of stock, sole proprietorship

1-2 Stock Market Data (2 days)

Objectives • Use stock data to follow the daily progress of a corporate stock. • Write spreadsheet formulas.

Key Terms 52-week high, 52-week low, after-hours trading, cell, close, high, last, low, NASDAQ, net change, NYSE, sales in 100s, spreadsheet, stock market, trades, volume

1-3 Stock Market Data Charts (3 days)

Objectives • Interpret a stock bar chart. • Create a stock bar chart. • Interpret a stock candlestick chart. • Create a stock candlestick chart.

Key Terms Candlestick chart, stock bar chart, stock chart

1-4 Simple Moving Averages (3 days)

Objectives • Understand how data is smoothed. • Calculate simple moving averages using the arithmetic average formula. • Calculate simple moving averages using the subtraction and addition method. • Graph simple moving averages using a spreadsheet.

Key Terms Arithmetic average (mean), crossover, fast moving average, lagging indicators, simple moving average (SMA), slow moving average, smoothing techniques


1-5 Stock Market Ticker (1 day) Objectives

• Understand stock market ticker information. • Determine the total value of a trade from ticker information. • Determine trade volumes from ticker information.

Key Terms Daily money flow, directional arrow, Dow Jones Industrial Average (DJIA), downtick, money flow, negative money flow, net money flow, positive money flow, stock symbol, ticker, ticker symbol, total value of a trade, trading price, trading volume, uptick

1-6 Stock Transactions (2 days)

Objectives • Learn the basic vocabulary of buying and selling stock. • Compute gains and losses from stock trades.

Key Terms Gross capital gain, gross capitol loss, odd lot, portfolio, round lot, trade

1-7 Stock Transaction Fees (2 days)

Objectives • Compute the fees involved in buying and selling stocks. • Become familiar with the basic vocabulary of stock trading.

Key Terms At the market, broker fee, commission, discount broker, limit order, net proceeds, stockbroker

1-8 Stock Splits (3 days)

Objectives • Calculate the post-split outstanding shares and share price for a traditional split. • Calculate the post-split outstanding shares and share price for a reverse split. • Calculate the fractional value amount that a shareholder receives after a split.

Key Terms Fractional part of a share, market capitalization (market cap), outstanding shares, penny stock, reverse stock split, stock split, traditional stock split

1-9 Dividend Income (2 days)

Objectives • Understand the concept of shareowners splitting the profit for the corporation they

own. • Compute dividend income. • Compute the yield for a given stock. • Compute the interest earned on corporate bonds.

Key Terms

Common stock, corporate bonds, dividend, dividend income, face value, growth stock, income stock, matures, preferred stock, yield


Chapter 1 Mathematics Topics Constructing, using, and interpreting algebraic ratios and proportions

Given investment ratios of the form r1 : r2 : ...: rn−1 : rn and a total T, write and solve the

investment equation r1x + r2x + ...+ rn−1x + rn x = T and determine the investment amount associated with each ratio

Determining, using, and interpreting percent increase/decrease of stock transaction prices

Determining, using, and interpreting percent net change of stock transaction prices

Constructing and interpreting stock bar and candlestick charts

Given a set of n closing prices, p1, p2, p3, ..., pn−1, pn , calculate and interpret d-day simple moving averages by applying the Arithmetic Average Formula and the Subtraction/Addition Method

Use and interpret stock market ticker notation of the form SYM PK@D#C where SYM is the corporation symbol, Px1000 is the transaction amount (K=1000), D is the transaction price per share, # is either (increase) or (decrease), and C is the change from the previous day’s closing price

In situations where w represents the purchase price for a set number of shares, y represents the selling price of that same number of shares , and x represents the percent

increase/decrease of an investment, use the equation x =y − w

w to determine the percent

increase of an investment

In any a-for-b stock split, let P represent the pre-split price per share, calculate the post-

split price per share using ba× P

In any a-for-b stock split, let D represent the pre-split number of shares, calculate the

post-split number of shares using ab× D

Calculate the stock yield percentage using the formula Yield =AC×100, where A

represents the annual dividend per share and C represents the current price per share


Chapter 2: Modeling a Business (approximately 20 days) Statistical analysis plays a very important role in the modeling of a business. Using linear, quadratic, and regression equations in that process assist students in getting a complete picture of supply, demand, expense, revenue, and profit as they relate to the sale of a product. 2-1 Interpret Scatterplots (2 days)

Objectives • Graph bivariate data. • Interpret trends based on scatterplots. • Draw lines and curves of best fit.

Key Terms Bivariate data, causal relationship, correlation, data, explanatory variable, negative correlation, positive correlation, response variable, scatterplot, trend, univariate data

2-2 Linear Regression (3 days)

Objectives • Be able to fit a regression line to a scatterplot. • Find and interpret correlation coefficients. • Make predictions based on lines of best fit.

Key Terms Correlation coefficient, domain, extrapolation, interpolation, least squares line, linear regression line, line of best fit, moderate correlation, range, strong correlation, weak correlation

2-3 Supply and Demand (2 days)

Objectives • Understand the slopes of supply and demand curves. • Find points of equilibrium.

Key Terms Demand, demand function, equilibrium, function, markup, retail price, shift, supply, wholesale price, widget

2-4 Fixed and Variable Expenses (2 days)

Objectives • Understand the differences between fixed and variable expenses. • Create an expense equation based on fixed and variable expenses.

Key Terms Breakeven point, expense equation, fixed expenses, loss, profit, revenue, revenue equation, variable expenses


2-5 Graphs of Expense and Revenue Functions (3 days) Objectives

• Write, graph, and interpret the expense function. • Write, graph, and interpret the revenue function. • Identify the point of intersection of the expense and revenue functions. • Identify breakeven points and explain them in the context of the problem.

Key Terms Axis of symmetry, leading coefficient, maximum value, nonlinear function, parabola, quadratic equation, second degree equation, vertex of a parabola

2-6 Breakeven Analysis (2 days)

Objectives • Determine the breakeven prices and amounts using technology and/or algebra.

Key Terms Quadratic formula, zero net difference

2-7 The Profit Equation (3 days)

Objectives • Determine a profit equation given the expense and revenue equations. • Determine the maximum profit and the price at which that maximum is attained.

Key Terms Maximum profit, profit

2-8 Mathematically Modeling a Business (2 days)

Objectives • Recognize the transitive property of dependence as it is used in a business model. • Use multiple pieces of information, equations, and methodologies to model a new

business. Key Terms

Dependence, transitive property of dependence Chapter 2 Mathematics Topics

Constructing and interpreting scatterplots

Operations with functions

Evaluating functions and using them to model situations

Translating verbal situations into algebraic linear functions

Translating verbal situations into quadratic functions


Creating rational functions of the form x

bmxxf +=)(

Translating verbal situations into linear and quadratic inequalities

Solving linear systems of equations and inequalities such as:

Solving systems of linear equations and inequalities in two variables

Identifying domains for which f(x) > g(x), f(x) = g(x), and f(x) < g(x)

Identifying form, direction, and strength from a scatterplot

Finding, interpreting, and graphing linear regression equations

Determining domains for which prediction using a regression line is considered

extrapolating or interpolating

Finding and interpreting the Pearson Product-Moment Coefficient of Correlation

Finding the axis of symmetry abx

2−

= , vertex ⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −−

abf

ab

2,

2, roots, and the

concavity of parabolic curves

Using the quadratic formula a

acbabxthencbxaxif

24

20

22 −

±−

==++

Finding and interpreting quadratic regression equations

Solving linear-quadratic systems of equations and inequalities such as:


Finding absolute and relative extrema

Causation vs. correlation for bivariate data

Identifying explanatory and response variables

Identifying and diagramming lurking variables such as:

Using the slope-intercept form of a linear equation bmxy +=

Interpreting slope as a rate of change xy

ΔΔ

Using the transitive property of dependence

Determining the zero net difference

Writing algebraic formulas for use in spreadsheets

Rational Expressions

Algebraic fractions, ratios, and proportions Writing literal equations


Solving linear equations and inequalities

Calculating moving averages

Reading and interpreting data in pictorial representations

Algebraic representations of percent, percent increase and percent decrease

Expressing averages as rational functions

Translating verbal expressions into algebraic formulas for use in a spreadsheet


Chapter 3: Banking Services (approximately 15 days) Banks offer a complete array of paper and electronic services that make access to money easy. In this chapter, students learn the function and computation of interest in short-term, long-term, single deposit and periodic deposit accounts. 3-1 Checking Accounts (2 days)

Objectives • Understand how checking accounts work. • Complete a check register.

Key Terms Automatic teller machine (ATM), canceled, check, check clearing, checking account, check register, credit, deposit, deposit slip, direct deposit, drawer, debit, electronic funds transfer (ETF), endorse, hold, insufficient funds, interest, joint account, overdraft protection, payee, personal identification number (PIN), maintenance fee, single account

3-2 Reconcile a Bank Statement (2 days)

Objectives • Reconcile a checking account with a bank statement by hand and by using a

spreadsheet. Key Terms

Account number, balancing, bank statement, ending balance, outstanding checks, outstanding deposits, reconciling, starting balance, statement period

3-3 Savings Accounts (1 day)

Objectives • Learn the basic vocabulary of savings accounts. • Compute simple interest using the simple interest formula.

Key Terms Certificate of deposit (CD), interest, interest rate, maturity, minimum balance, money market account, principal, savings account, simple interest, simple interest formula, statement savings

3-4 Explore Compound Interest (2 days)

Objectives • Understand the concept of getting interest on your interest. • Compute compound interest using a table.

Key Terms Annual compounding, compound interest, crediting, daily compounding, quarterly compounding, semiannual compounding

3-5 Compound Interest Formula (2 days)

Objectives • Become familiar with the derivation of the compound interest formula. • Make computations using the compound interest formula.


Key Terms Annual percentage rate (APR), annual percentage yield (APY), compound interest formula

3-6 Continuous Compounding (2 days)

Objectives • Compute interest on an account that is continuously compounded.

Key Terms Continuous compounding, continuous compound interest formula, exponential base (e), finite, infinite, limit

3-7 Future Value of Investments (2 days)

Objectives • Calculate the future value of a periodic deposit investment. • Graph the future value function. • Interpret the graph of the future value function.

Key Terms Biweekly, future value of a periodic deposit investment, future value of a single deposit investment, periodic investment

3-8 Present Value of Investments (2 days)

Objectives • Calculate the present value of a single deposit investment. • Calculate the present value of a periodic deposit investment.

Key Terms Present value, present value of a periodic investment, present value of a single deposit investment

Chapter 3 Mathematics Topics Using the simple interest formula PRTI = and its algebraic equivalents

Understanding compounding via iteration

Deriving the compound interest formula ntnrB )1( +=

Computing compound interest with and without the formula

Applying the compound interest formula

Introduction to limit notation bxfLimax

=→

)(


Approximating e by examining the sequence ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛ +

x

x11

Defining the natural base e using the rational and exponential expression limit notation x

x xLim ⎟⎠⎞

⎜⎝⎛ +

∞→

11

Applying the natural base e in the continuous compounding formula rtPeB =

Identifying baxy = as exponential decay when x < 1

Identifying baxy = as exponential growth when x > 1

Modeling a geometric series of the type ∑−

=

1

0

n

b

bax

Graphing exponential functions of the type baxy =

Analyzing rational functions and their limits of the form dcxbax

m

n

xLim

±±

∞→ where n=m, n

>m, and n< m

Using the compound interest formula to derive the present value of a single deposit

investment formula nt

nr

BP

⎟⎠⎞

⎜⎝⎛ +

=

1

Using the compound interest formula to derive the present value of a periodic deposit

investment formula

11 −⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛

= nt

nr

nrB

P


Using the future value of a periodic deposit investment formula

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ +

=

nr

nrP

B

nt11

Adapting all banking formulas for input into a spreadsheet


Chapter 4: Consumer Credit (approximately 15 days) The understanding and use of credit is extremely important to the consumer since actions taking in the present can have long standing ramifications in the future. Becoming familiar with credit terminology and regulations is critical in making wise credit decisions. Credit comes at a price and in this chapter students learn how to use and manipulate the credit formulas in order to make wise credit choices that fit their needs, current financial situation, and future goals. 4-1 Introduction to Consumer Credit (2 days)

Objectives • Become familiar with the basic vocabulary of credit terms. • Become familiar with types of lending institutions. • Compute finance charges for installment purchases.

Key Terms Asset, credit, creditor, credit rating, credit reporting agency, debtor, down payment, earning power, FICO score, finance charge, installment plan, interest

4-2 Loans (3 days)

Objectives • Read monthly payments from tables. • Compute monthly payments using a formula. • Compute finance charges on loans.

Key Terms Annual percentage rate, balloon payment, collateral, cosigner, lending institution, life insurance, prepayment penalty, prepayment privilege, principal, promissory note, wage assignment, wage garnishment

4-3 Loan Calculations and Regression (2 days)

Objectives • Calculate the present value of a single deposit investment. • Calculate the present value of a periodic deposit investment.

Key Terms Cubic function, cubic regression, monthly payment calculator, natural logarithm

4-4 Credit Cards (2 days)

Objectives • Become familiar with the basic vocabulary of credit cards. • Compute an average daily balance.

Key Terms Average daily balance, charge card, credit card, debit card, Electronic Funds Transfer Act, Fair Credit Billing Act, Fair Debt Collection Practices Act, impulse buying, mean, revolving charge account, Truth-In-Lending Act

4-5 Credit Card Statement (2 days) Objectives

• Identify and use the various entries in a credit card statement.


Key Terms

Account number, APR, available credit, average daily balance, billing cycle, billing date, credit card statement, credit line, debit/credit, finance charge, late charges, minimum payment, monthly periodic rate, new balance, new purchases, number of days in billing cycle, payments/credits, payment due date, previous balance, transactions

4-6 Average Daily Balance (3 days)

Objectives • Calculate the average daily balance using the credit calendar. • Calculate the finance charge using the credit calendar.

Key Terms Average daily balance, billing date, credit calendar

Chapter 4 Mathematics Topics Using algebraic proportions

Finding and interpreting cubic regression equations of the form

dcxbxaxy +++= 23

Using slope-intercept form bmxy +=

Using and interpreting exponential growth and decay equations

Computing the average daily balance

Applying the monthly payment formula

t

tr

rrPM

12

121

121

121

12

−⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

=

Using slope-intercept form y=Mx+b where

t

tr

rrPM

12

121

121

121

12

−⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

=


Using the formula Rbxr

rrPFC

t

t −+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

=

12

121

121

121

12 where FC = finance

charge and R = retail price

Using inverse functions to introduce the natural logarithm function xy ln= as

xy elog= and as the inverse of xey =

Using the formula

t

tr

rrPM

12

121

121

121

12

−⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

= to solve for the exponent t where

⎟⎠⎞

⎜⎝⎛ +

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

121ln12

12lnln

r

rp

Mp

M

t

Modeling the average daily balance using the formula ∑=

n

i

nn

d1

Calculating the finance charge using the formula 121

APRn

dFCn

i

n ⎟⎠

⎞⎜⎝

⎛= ∑

=

Creating algebraic formulas and applying them for use in spreadsheets


Chapter 5: Automobile Ownership (approximately 20 days) Whether it is a used or new car, ownership requires an understanding of the mathematics that models purchasing, insuring, depreciating, and driving that car. 5-1 Classified Ads (2 days)

Objectives • Compute the cost of classified ads for used cars. • Compute the cost of sales tax on automobiles.

Key Terms Cusp, domain, piecewise function, sales tax, split function

5-2 But or Sell a Car (2 days)

Objectives • Compute the mean, media, mode, range, quartiles, and interquartile range.

Key Terms Arithmetic average, ascending order, bimodal, data, descending order, interquartile range (IQR), lower quartile, mean, measures of central tendency, outlier, quartiles, range, resistant, skew, statistics, subscripts, median, outlier, upper quartile

5-3 Graph Frequency Distributions (2 days)

Objectives • Create a frequency distribution from a set of data. • Use box-and-whisker plots and stem-and-leaf plots to display information. • Use linear regression to negotiate the purchase or sale of a car.

Key Terms Box-and-whisker plot, boxplot, frequency, frequency distribution, modified boxplot, stem-and-leaf plot

5-4 Automobile Insurance (3 days)

Objectives • Learn about different types of automobile insurance coverage. • Compute insurance costs. • Compute payments on insurance claims.

Key Terms Actuary, automobile insurance, bodily injury liability (BI), car rental insurance, claim, collision insurance, comprehensive insurance, deductible, emergency road service insurance, liable, liability insurance, negligent, no-fault insurance , personal injury protection (PIP), premium, property damage liability (PD), surcharge, uninsured/underinsured motorist protection insurance (UMP)

5-5 Linear Automobile Depreciation (2 days)

Objectives • Write, interpret, and graph a straight line depreciation equation.

Key Terms


Appreciate, depreciate, slope, straight line depreciation, straight line depreciation equation

5-6 Historical and Exponential Depreciation (2 days)

Objectives • Write, interpret, and graph an exponential depreciation equation. • Manipulate the exponential depreciation equation in order to determine time,

original price, and depreciated value. Key Terms

Dollar value, exponential decay, exponential depreciation, historical data, historical depreciation

5-7 Driving Data (2 days)

Objectives • Write, interpret and use the distance formula. • Use the formula for the relationship between distance, fuel economy, and gas

usage. Key Terms

Currency exchange rate, distance formula, electronic odometer, English Standard System, fuel economy measurement, kilometers per liter, mechanical odometer, Metric System, miles per gallon, odometer, speedometer, trip odometer

5-8 Driving Safety Data (2 days)

Objectives • Calculate reaction time and distance in the English Standard System. • Calculate and use the braking distance in both English Standard and Metric

Systems. • Calculate and use the total stopping distance in both the English Standard and

Metric Systems. Key Terms

Braking distance, reaction distance, reaction time, thinking time, total stopping distance

5-9 Accident Investigation Data (3 days)

Objectives • Determine the minimum skid speed using the skid mark formula. • Determine the minimum skid speed using the yaw mark formula.

Key Terms Accident reconstructionist, anti-lock braking system (ABS), braking efficiency, chord, drag factor, middle ordinate, shallow skid mark, skid distance, skid mark, skid speed formula, yaw mark

Chapter 5 Mathematics Topics Systems of linear equations


Modeling exponential depreciation as

.1 and price purchase is P where <= xPxy b

Transforming raw data into a frequency distribution

Creating and interpreting stem and leaf plots and side-by-side steam plots such as

Creating and interpreting box and whisker plots and side-by-side boxplots

Creating and interpreting modified box and whisker plots

Computing measures of dispersion LH xxR −= and .13 QQIQR −=

Computing Q1, Q2, Q3, and Q4 manually and with the graphing calculator

Using the expressions )(5.11 IQRQ − and )(5.13 IQRQ + to determine outliers

Compute and interpret percentiles

Measures of central tendencyn

xx

n

ii∑

== 1 , median and mode

Creating and interpreting piecewise (split) functions of the form

Determining the domains of a piecewise function from verbal situations

Graphing piecewise functions using mutually exclusive domains


Identifying the cusp of a piecewise function at a change in slope such as

Using multi-variable square root functions such as the skid length DfnS 30= .

Using ⎟⎠⎞

⎜⎝⎛= 260

528075.0 sRD to determine reaction distance

Using 2)1(.5 sBD = to compute the breaking distance

Using 22 )1.0(5

60528075.0 ssTSD +⎟

⎠⎞

⎜⎝⎛= to compute total stopping distance

Manipulating RDT

TDRRTD === and ,, to determine distance, rate, and time

Using )(GMPGD = to compute miles per gallon

Using geometry theorems involving chords intersecting in a circle and radii perpendicular to chords to determine yaw mark arc length

Finding radius 28

2 MM

Cr += where C is chord length and M is middle ordinate

Computing arc lengths

Using dilations kD to transform formulas between the English Standard and Metric measurement systems

Applying all algebraic formulas from the chapter for use in spreadsheets


Chapter 6: Employment Basics (approximately 10 days) Employment is an integral part of our daily lives. Knowing how salaries are computed, benefits bestowed, and wage taxes calculated allow the employee the opportunity to make smart employment choices both before accepting a job and during the period of employment in that job. 6-1 Look for Employment (1 day)

Objectives • Compute periodic salary based on annual contract salary. • Interpret abbreviations in classified ads. • Express classified ad prices as piecewise functions.

Key Terms Benefits, discount, employment agency, fee paid, Form W-4: Employee’s Withholding Allowance Certificate, resume

6-2 Pay Periods and Hourly Rates (2 days)

Objectives • Compute weekly, semimonthly, and biweekly earnings given annual salary. • Compute hourly pay and overtime pay given hourly rate.

Key Terms

Biweekly, direct deposit, double-time pay, gross pay, hourly rate, monthly pay, overtime hours, overtime hourly rate, semimonthly, time-and-a-half overtime, weekly pay

6-3 Commissions, Royalties, and Piecework Pay (2 days)

Objectives • Compute pay based on percent commission. • Compute piecework pay. • Understand advantages and disadvantages of pay based on production.

Key Terms

Commission, pieceworker, piecework rate, royalty 6-4 Employee Benefits (2 days)

Objectives • Understand and calculate the value of certain employee benefits.

Key Terms Base period, childcare leave, employee benefits, family health care, individual health care, insurance, paid vacation time, paid holiday time, pension, retirement plans, stock ownership plans, unemployment insurance, worker’s compensation

6-5 Social Security and Medicare (3 days)

Objectives • Compute paycheck deductions for Social Security. • Compute paycheck deductions for Medicare.


Key Terms Federal Insurance Contributions Act, FICA tax, maximum taxable income, Medicare tax, Social Security, Social Security tax.

Chapter 6 Mathematics Topics

Identifying continuous and discontinuous functions by their graphs

Interpreting jump discontinuities

Writing an interpreting domains and piecewise functions of the forms

and

Graphing exponential pay schedules such as

Graphing piecewise functions with cusps such as

Using measures of central tendency and rational functions such as

rttrrxa

++

=5.140)(

Geometric sequences such as nn xra = with common ratio r


Expressing percent increases and decreases as rational functions

Reading and interpreting data


Chapter 7: Income Taxes (approximately 20 days) The Federal income tax laws and forms need not be a maze of complexities. In this chapter, students see how mathematics can be used to model and understand our progressive tax system. Through the creation of functions and the analysis of graphic representations of those functions, students gain insight into their income reporting and tax paying obligations. 7-1 Tax Tables, Worksheets, and Schedules (3 days)

Objectives • Express tax schedules algebraically. • Compute Federal income taxes using a tax table and tax schedule.

Key Terms Head of household, Income tax, Internal Revenue Service, married filing jointly, married filing separately, property tax, qualifying widower, sales tax, tax, taxable income

7-2 Modeling Tax Schedules (3 days)

Objectives • Construct income tax graphs using piecewise functions derived from tax

schedules. Key Terms

Flat tax, progressive tax system, proportional tax, regressive tax schedule, tax bracket

7-3 Income Statements (2 days)

Objectives • Interpret and use the information on a pay stub, W-2 form and 1099 form..

Key Terms Cafeteria plan, flexible spending account, Form 1099, Form W-2, gross pay, net pay, paycheck, pay stub, take-home pay, tax-deferred contribution, withholding tax

7-4 Forms 1040EZ and 1040A (4 days)

Objectives • Complete Form 1040EZ. • Complete Form 1040A.

Key Terms Dependent, exemption, Form 1040A, Form 1040EZ, Form 1040, itemize, standard deduction

7-5 Form 1040 and Schedules A and B (6 days)

Objectives • File Form 1040 with itemized deductions. • Understand the difference between a tax credit and a tax deduction.

Key Terms Form 1040, Schedule A-Itemized Deductions, Schedule B-Interest and Dividend Income, tax avoidance, tax credit, tax evasion, voluntary compliance



Introducing point-slope form )( 11 xxmyy −=− and converting

it to slope-intercept form bmxy +=

Graphing continuous polygonal functions with multiple slopes and cusps

Translating verbal expressions into literal rational, exponential, and linear

equations.

Expressing domains using compound inequality notation of the form

21 ttandtt <≥

Expressing domains using compound inequality notation of the form

21 ttandtt ≤> , interval notation of the form 21 txt ≤< , and tax schedule

notation of the form “over 1t but not over 2t ”

Given a compound inequality statement, modeling a tax bracket to determine the tax using a linear equation of the form )( 1txpay −+= where y is the tax, a is the base tax, p is the tax percentage expressed as a decimal, t1 is the lower boundary of the domain, and x is the taxable income

Converting point-slope form to slope-intercept form of a linear equation

Writing equations in point-slope form

Modeling algebraically a tax schedule of the form


Using a piecewise function of the form

where f(x) represents the tax liability function for taxpayers using a given tax schedule with taxable incomes on a given domain

Graphing piecewise functions of the form

on the coordinate plane.

Identifying the cusps of piecewise functions from the function notation

Interpreting the graphs, slopes, and cusps of continuous polygonal functions with

multiple slopes and cusps

Translating verbal expressions into literal equations

Adapting all algebraic formulas in the unit for use in spreadsheets


Chapter 8: Independent Living (approximately 15 days) A “place of my own to call home” comes in many forms and with varying degrees of financial responsibilities. In this chapter, students work their way through the mathematics that models moving, renting, and purchasing a place to live. 8-1 Find a Place t Live (3 days)

Objectives • Calculate the affordability of a monthly rent. • Determine the relationship between square footage and monthly rent. • Determine lease signing costs. • Calculate moving expenses..

Key Terms Apartment, application deposit, evict, expire, furnished, landlord, security deposit, single-family home, square footage, and tenant.

8-2 Read a Floor Plan (3 days) Objectives

• Compute the perimeter and the area of a polygon. • Compute areas of irregular regions. • Compute volumes of rectangular solids..

Key Terms Apothem, area, British Thermal Units (BTUs), congruent, floor plan, Monte Carlo Method, perimeter, volume.

8-3 Mortgage Application Process (3 days)

Objectives • Compute the monthly cost of paying for a house. • Understand the research thatis necessary before you purchase a home..

Key Terms Assessed value, adjustable-rate mortgage, back-end ratio, balloon mortgage, debt-to-income ratio, down payment, escrow, fixed-rate mortgage, foreclose, front-end ratio, homeowner’s insurance, interest-only market value, mortgage, mortgage, property tax, real estate tax.

8-4 Purchase a Home (4 days)

Objectives • Estimate closing costs. • Create an amortization table for a fixed-rate mortgage. • Create an amortization table for a fixed-rate mortgage with extra payments. • Investigate the amortization table for an adjustable rate mortgage.

Key Terms Adjustment period, arrears, attorney fee, closing, closing costs, discount points, earnest money deposit, hybrid ARM, initial rate, non-recurring costs, origination points, prepaid interest, title, title search, transfer tax.


8-5 Rentals, Condominiums, and Cooperatives (2 days) Objectives

• Compute costs of purchasing a cooperative or condominium. • Understand the advantages and disadvantages of different forms of homes.

Key Terms Board of directors, condominium, cooperative, co-op apartment, equity, landominium, maintenance fee


Using rational functions to compute back-end ratios of the form

12/3/12/

adchpmb ++++

= .

Using rational functions to compute front-end ratios of the form

12/12/12/

xhpmf ++

= .

Using the monthly payment formula

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ +

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

=

112

1

121

1212

12

t

t

r

rrP

M

Computing interest I = Cr

rrP

t

t

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ +

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

112

1

121

1212

12

where C is original cost

Using the apothem to compute the area of a regular polygon apA21

=

Using probability to find the area of irregular plane region (The Monte Carlo Method)

rectangle framing of arearegion irregular of area

generated points random of numberregion inside points of number

=

Using factors of dilations to draw to scale

Finding areas of irregular and shaded regions


Using rational functions to compute BTU’s, such as 60

rating BTU while≈

Solving proportions

Creating multi-variable tax assessment equations

Using exponential equations to model rent increases such as 1

1001

−

⎟⎠⎞

⎜⎝⎛ +=

DBAR

Modeling rent increases using exponential regression

Reading and interpreting data

Using the future value of a periodic deposit formula

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ +

=

nr

nrP

B

nt11

to make

comparisons to mortgage payments and increasing resale value of a home

Writing all algebraic formulas from the chapter for use in spreadsheets

Translating verbal expressions into literal equations


Chapter 9: Planning for Retirement (approximately 10 days) For most high school students, the notion of retirement is so far in the distant future that many rarely consider the fact that actions they take now can affect how they will live once they stop working. The focus of this chapter is on the fiscal plans that workers can make years ahead of their retirement date. This involves a detailed study of retirement savings plans, both personal and federal, employee pension programs, and life insurance. 9-1 Retirement Income from Savings (2 days)

Objectives • Calculate future values of retirement investments that are both signle deposit and

periodic. • Compare the tax savings by making contributions to pre-tax retirement savings

accounts. • Calculate an employer’s matching contribution to a retirement account.

Key Terms 401K, 403B, after-tax investments, individual retirement account (IRA), Keogh plan, retirement, Roth IRA, semi-retired, tax-deferred, tax-exempt, traditional IRA

9-2 Social Security Benefits (3 days) Objectives

• Understand the benefits paid by Social Security. • Understand how benefits are computed. • Compute Federal income tax on benefits that are paid under Social Security.

Key Terms Full-retirement age, Old-Age, Survivors, and Disability Insurance (OASDI), Social Security benefit, Social Security credit, Social Security statement

9-3 Pensions (2 days)

Objectives • Calculate pension benefits using various formulas. • Calculate pension benefits during and after vesting periods..

Key Terms Consumer Price Index (CPI), cost of living adjustment (COLA), deferred compensation, defined benefit plan, Employee Retirement Income Security Act, lump-sum payment, pension, Pension Benefit Guaranty Corporation, Pension Protection Act, qualified joint and survivor annuity, vested

9-4 Life Insurance (2 days)

Objectives • .Compute the cost of different types of life insurance. • Understand the advantages and disadvantages of different types of life insurance.


Key Terms Beneficiary, cash value, decreasing term insurance, face value, group term life insurance, increasing term insurance, level term insurance, mortality table, permanent life insurance, premium, term life insurance, universal life insurance, variable life insurance, whole life insurance


Using the future value of a periodic investment formula of the form

to predict balances after t years when given a periodic deposit amount, an investment return rate, and compounding information

Using the present value of a periodic investment formula of the form when given a future

value, a time in years, an investment return rate, and compounding information

Writing rational expressions as a combination of rational and polynomial expressions

Using inequalities to define domains when creating algebraic expressions

Analyzing the effect that a change in multipliers has to the value of an algebraic expression

Writing rational expressions to represent increase over time

Using and interpreting the greatest integer function of the form [ ]x

Determining and interpreting the expected value of a probability distribution where the

expected value is of the form )(1

in

ii xfx∑

=

Reading and interpreting data presented in multiple formats


Creating, interpreting, and graphing greatest integer functions of the form [ ]axy −=

Creating, interpreting, and graphing greatest integer functions of the form [ ] 1+−= axy

Understanding the algebraic and contextual differences between [ ]axy −= and

[ ] 1+−= axy

Incorporating the greatest integer function into a piecewise function of the form a when x ≤ b c(x) = x – d) when x > b and x is an integer a + c([x – d] + 1) when x > b and x is not an integer

Evaluating a piecewise function that includes a greatest integer function for various values on the domain of the piecewise function

Creating, interpreting, and graphing a system of a linear and a piecewise function and

determining the point of intersection as shown in the following graph:


Chapter 10: Prepare a Budget (approximately 10 days) This final chapter of the text calls upon the knowledge acquired in the preceding chapters in order to create, chart, and use a responsible personal budget. 10-1 Utility Expenses (2 days)

Objectives • Compute the cost of electric, gas, oil and water for a home. • Compute the cost of using specific appliances for specific lengths of time. • Compute the time is takes an energy-saving appliance to pay for itself

Key Terms Ccf, cubic foot, kilowatt-hour (kWh), meter, present reading, previous reading, utility, volume, watt, watt-hour

10-2 Electronic Utilities (2 days) Objectives

• .Compute the cost of cell phone calls, text messaging, Internet service, and cable television.

Key Terms Electronic utilities

10-3 Charting a Budget (3 days)

Objectives • Create and use a budget check-off matrix. • Visualize and interpret a budget using a pie chart, a bar graph, a line graph, and a

budget line graph.. Key Terms

Bar graph, budget check-off matrix, budget line graph, budget matrix, column, electronic matrix, line graph, matrix, order of a matrix, pie chart, row, sector

10-4 Cash Flow and Budgeting (3 days)

Objectives • Develop and interpret a cash flow chart. • Develop and interpret a frequency budget plan. • Develop and interpret a year-long expense budget plan..

Key Terms Assets, cash flow, cash-flow matrix, debt reduction plan, debt-to-income ratio, year-long expense budget plan, envelope accounting system, frequency budget plan, net worth,


Using sectors and central angles of a circle to depict proportional categories on a pie chart when given categorical information


Creating and interpreting budget line equations of the type ByCxC yx =+ where xC

represents the cost of the first of two items and yC represents the cost of the second of

two items, x and y represent quantities under consideration and B represents an amount budgeted

Interpreting points on a budget line graphs in the context of their relationship to the

budget line as shown in the following display:

Comparing budget line graphs and interpreting them as transformations in the plane as

shown here:

Using inequalities to interpret regions and points in the plane in relation to a budget line graph

Using multiple representations to chart data such as


Using algebraic rational expressions to model ratios in context

Writing algebraic formulas for use in spreadsheets

Correlation of

Financial Algebra,

by Robert K. Gerver/Richard J. Sgroi, © 2011, ISBN 10: 0538449675;

ISBN 13: 9780538449670

To

Common Core State Standards For Mathematics

1

Financial Algebra by Gerver & Sgroi Common Core Standard

In Financial Algebra, the mathematics necessary for daily living is embedded in content that directly relates to financial decisions adults make in their daily lives. The mathematical formulas, functions, and pictorial representations used in Financial Algebra assist students in making sense of the financial world around them through mathematical modeling and, equip them with the ability to make sound financial decisions based on data.

Mathematics| High School Modeling★ Modeling Standards Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★).

Financial Algebra Chapter

& Section Financial Algebra

Page Numbers Common Core Standard

CHAPTER 1

C1 1-1 Pages 5-9 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

C1 1-2 (continued on next page)

Pages 10-15 Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

2

C1 1-2 (continued)

Pages 10-15 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

C1 1-3

Pages 16-21

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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.

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling.

C1 1-4

Pages 22-28


Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling.

C1 1-5

Pages 29-24

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.


Pages 36-39


Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Chapter & Section Page Numbers Common Core Standard

3

C1 1-6 (continued)

Pages 36-39

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

C1 1-7 Pages 40-45 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

C1 1-8

Pages 46-50

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

C1 1-9 Pages 51-56 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context

CHAPTER 2


Pages 65-69

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


4

C2 2-1 (continued)

Pages 65-69 Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Statistics and Probability★ - Interpret categorical and Quantitative Data S-ID Interpret Linear Models 9. Distinguish between correlation and causation.


Pages71-74

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling.

Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.


5

C2 2-2 (continued)

Pages 71-74 Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 7c. Fit a linear function for a scatter plot that suggests a linear association.

Statistics and Probability★ - Interpret categorical and Quantitative Data S-ID Interpret Linear Models 8. Compute (using technology) and interpret the correlation coefficient of a linear fit.


Pages 75-79

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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. ★ Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.★

Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.


6

C2 2-3 Pages 75-79

Statistics and Probability★-Interpret categorical and Quantitative Data S-ID Interpret Linear Models 8. Compute (using technology) and interpret the correlation coefficient of a linear fit.

C2 2-4

Pages 80-85

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Algebra - Reasoning with Equations and Inequalities A-REL Understand solving equations as a process of reasoning and explain the reasoning 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Algebra - Reasoning with Equations and Inequalities A-REL Solve systems of equations 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 12. Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Statistics and Probability★- Interpret categorical and Quantitative Data S-ID Interpret Linear Models 8. Compute (using technology) and interpret the correlation coefficient of a linear fit.


Pages 86-90




7

C2 2-5 (continued)

Pages 86-90

Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.★ a. Interpret parts of an expression, such as terms, factors, and coefficients.

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 4. Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula 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. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Functions- Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.


Pages 91-96

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.


8

C2 2-6 (continued)

Pages 91-96

Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 4. Solve quadratic equations in one variable. Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 4. Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula 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. Algebra - Reasoning with Equations and Inequalities A-REL Solve systems of equations 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions- Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions- Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.


9


Pages 97-102



Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Algebra - Reasoning with Equations and Inequalities A-REL Solve systems of equations 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


10

C2 2-7 (continued)

Pages 97-102

Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.


Pages 103-107


Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Algebra - Reasoning with Equations and Inequalities A-REL Solve systems of equations 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


11

C2 2-8 (continued)

Pages 103-107

Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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★

CHAPTER 3

C3 3-1 Pages 116-122 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★ Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1a.. Determine an explicit expression, a recursive process, or steps for calculation from a context.

C3 3-2 Pages 123-130 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

C3 3-3 Pages 131-136 Algebra - Creating equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

C3 3-4 Pages 137-142 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context


12

C3 3-4 Pages 137-142 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1a. Interpret parts of an expression, such as terms, factors, and coefficients Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity

C3 3-5

Pages 143-149

Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Functions - Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions.

C3 3-6 Pages 150-155 Number and Quantity - The Real Number System N-RN Extend the properties of exponents to rational numbers 1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Number and Quantity - The Real Number System N-RN Extend the properties of exponents to rational numbers 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

C3 3-7 Pages156-160 Functions - Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions.


13

C3 3-8

Pages 161-165

Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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.★ Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Functions- Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions.

CHAPTER 4

C4 4-1 Pages174-180 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★ Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1a. Determine an explicit expression, a recursive process, or steps for calculation from a context.


Pages181-186 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 2. Use the structure of an expression to identify ways to rewrite it.

Algebra - Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3c. Use the properties of exponents to transform expressions for exponential functions


14

C4 4-2 (continued)

Pages181-186 Functions - Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions. Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity Linear and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 5. Interpret the parameters in a linear or exponential function in terms of a context.

C4 4-3

Pages187-192

Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

C4 4-4 Pages 193-199 Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★

C4 4-5 Pages 200-205 Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Algebra - Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★

C4 4-6 Pages 206-210 Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★


15

CHAPTER 5

C5 5-1

Pages 220-223

Algebra - Creating equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Functions - Interpreting Functions F-LF Analyze functions using different representations 7b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

C5 5-2

Pages 224-230

Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 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. Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.


Pages 232-237

Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 1. Represent data with plots on the real number line (dot plots, histograms, and box plots).


16

C5 5-3 (continued)

Pages 232-237

Statistics and Probability★ - Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 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. Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on a single count or measurement variable 4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

C5 5-4

Pages 240-251

Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Statistics and Probability★- Interpret categorical and Quantitative Data S-ID Interpret Linear Models 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.


Pages 245-251

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Functions- Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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. Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima.


17

C5 5-5 (continued)

Functions - Interpreting Functions F-LF Analyze functions using different representations 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 1. Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 5. Interpret the parameters in a linear or exponential function in terms of a context.


Pages 252-258

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions -Interpreting Functions F-LF Analyze functions using different representations 7e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Functions - Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions. Functions - Interpreting Functions F-LF Analyze functions using different representations 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 1. Distinguish between situations that can be modeled with linear functions and with exponential functions c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


18

C5 5-6 (continued)

Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 5. Interpret the parameters in a linear or exponential function in terms of a context. Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.


C5 5-7 Pages 259-267 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

C5 5-8 Pages 268-273 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity Algebra -Seeing Structure in Expressions A-SSE Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

C5 5-9

Pages 274-282

Algebra - Reasoning with Equations and Inequalities A-REL Understand solving equations as a process of reasoning and explain the reasoning 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Geometry - Circles G-C Find arc lengths and areas of sectors of circles 5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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★


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CHAPTER 6

C6 6-1

Pages 291-295

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

C6 6-2 Page 299 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

C6 6-3 Pages 303-309 Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context..

C6 6-4 Pages 310-315 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Pages 310-315 Algebra - Reasoning with Equations and Inequalities A-REL Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Pages 310-315 Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★

Pages 310-315 Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

C6 6-5 Pages 316-321 Functions - Interpreting Functions F-LF Analyze functions using different representations 7b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Functions -Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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★


20

CHAPTER 7

C7 7-1 Pages 328-334 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 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.

C7 7-2

Pages 335-343

Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Functions - Interpreting Functions F-LF Understand the concept of a function and use function notation 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Functions - Interpreting Functions F-LF Analyze functions using different representations 7b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Functions - Interpreting Functions F-LF Analyze functions using different representations 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

C7 7-3 Pages 344-351 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★

Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★


Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.



21

C7 7-5 (continued)

Pages 365-376 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

CHAPTER 8

C8 8-1

Pages 387-392

Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.


Statistics and Probability★- Interpret Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables 7c. Fit a linear function for a scatter plot that suggests a linear association.

Statistics and Probability★- Interpret categorical and Quantitative Data S-ID Interpret Linear Models 8. Compute (using technology) and interpret the correlation coefficient of a linear fit.

C8 8-2 Pages 393-400 Geometry - Circles G-C Find arc lengths and areas of sectors of circles 5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.


Pages 401-410 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x)+r(x)/b(x), where a(x), b(x), q(x), r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection, long division, or, for the more complicated examples, a computer algebra system.


22

C8 8-3 (continued)

Pages 401-410 Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★

C8 8-4 Pages 411-421 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★

C8 8-5 Pages 422-429 Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1b. Interpret complicated expressions by viewing one or more of their parts as a single entity Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★ Functions – Linear, Quadratic, and Exponential Model F-LE Construct and compare linear and exponential models and solve problems 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

CHAPTER 9

C9 9-1 Pages 439-446 Functions - Interpreting Functions F-LF Analyze functions using different representations 8b. Use the properties of exponents to interpret expressions for exponential functions.

C9 9-2

Pages 447-455

Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Algebra - Creating Equations★ A-CED Creating equations that describe numbers or relationships 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

C9 9-3 Pages 456-466 Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★


23

C9 9-4

Pages 467-471

Statistics and Probability★- Using probability to Make decisions S-MD Calculate expected values and use them to solve problems 1. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Statistics and Probability★- Using probability to Make decisions S-MD Calculate expected values and use them to solve problems 2. (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Statistics and Probability★- Using probability to Make decisions S-MD Calculate expected values and use them to solve problems 4. (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. Statistics and Probability★- Using probability to Make decisions S-MD Calculate expected values and use them to solve problems 5. (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Functions- Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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★

CHAPTER 10

C10 10-1 Pages 482-487 Number and Quantity – Quantities★ N-Q Reason quantitatively and use units to solve problems 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. Number and Quantity - Quantities★ N-Q Reason quantitatively and use units to solve problems 2. Define appropriate quantities for the purpose of descriptive modeling

Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★

C10 10-2 Pages 489-495

Functions - Interpreting Functions F-LF Analyze functions using different representations 7b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.


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C10 10-3 Pages 496-507 Number and Quantity - The Complex Number System N-CM Perform Operations on matrices and use matrices in applications. 6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Algebra - Reasoning with Equations and Inequalities A-REL Represent and solve equations and inequalities graphically 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). Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 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★

Functions - Interpreting Functions F-LF Interpret functions that arise in applications in terms of the context 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.★ Functions - Interpreting Functions F-LF Analyze functions using different representations 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Functions - Interpreting Functions F-LF Analyze functions using different representations 7a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

C10 10-4 Pages 508-519 Algebra -Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context★ Functions - Building Functions F-BF Build a function that models a relationship between two quantities 1. Write a function that describes a relationship between two quantities ★


25

Chapters 1-10

Used throughout the text when constructing algebraic models for real life situations

Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.★

Algebra - Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context.★ b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

Functions - Building Functions F-BF Build a function that models a relationship between two quantities 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. b. Combine standard function types using arithmetic operations.


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