Unit 1 – Introduction to Problem Solving and Mathematical Models
(22 days)
Activity 1.1 – Wild about Harry
Objectives: Practice communication skills, Organize information, Write a solution in sentences, Develop problemsolving skills
Activity 1.2 – The Classroom
Objectives: Organize information, Develop problemsolving strategies (draw a picture, recognize a pattern, do a simpler problem), Communicate problemsolving ideas
Activity 1.3 – Make Me an Offer
Objectives: Use basic steps for problemsolving, Translate verbal statements and algebraic equations, Use basic principles of algebra to solve realworld problems, Use formulas to solve problems A.1 and A.1  Algebraic Expressions A.4abdf and A.4ace  Linear Equations
Activity 1.4 – Proportional reasoning
Objectives: Use proportional reasoning as a problemsolving strategy, Write a proportion and then solve the resulting proportion 8.3 and 8.4  Proportional Reasoning
Activity 1.5 – Fuel Economy
Objectives: Apply rates directly to solve problems, Use proportions to solve problems, Use unit or dimensional analysis to solve problems 8.3 and 8.4  Proportional Reasoning
Activity 1.6 – Hot in Texas
Objectives: Identify input and output in situations, Identify trends in data, Identify independent and dependent variables, Represent functions as tables and graphs AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.7 – Fill ‘er Up
Objectives: Write the equation to define a function, Determine the domain and range, Identify independent and dependent variables of a function AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.8 – Mathematical Modeling
Objectives: Identify a mathematical model, Solve problems using formulas as models, Develop a function model to solve a problem, Recognize patterns and trends using tables AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.9 – Fundraiser Revisited
Objectives: Solve an equation numerically, Solve an equation graphically, Distinguish between a situation represented by a graph of distinct points versus a continuous graph AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.10 – Leasing a Copier
Objectives: Develop a mathematical model in the form of an equation, Solve an equation using an algebraic approach AFDA.4  Multiple Representations of Functions
Activity 1.11 – Comparing Energy Costs
Objectives: Develop mathematical models to solve problems, Write and solve equations of the form ax + b = cx + d, Use the distributive property, Solve formulas AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.12 – Summer Job Opportunities
Objectives: Use problemsolving skills to make decisions based on solutions of mathematical models AFDA.4  Multiple Representations of Functions
Activity 1.13 – Graphs Tell Stories
Objectives: Describe in words what a graph tells you, Sketch a graph to represent a situation, Identify increasing, decreasing, and constant parts of a graph, Identify minimum and maximum points,Use the vertical line test. AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 1.14 – Heating Schedule
Objectives: Use vertical shift, Use horizontal shift, Identify vertical and horizontal shifts, Write a new formula for a function for which its graph has been shifted vertically or horizontally AFDA.2  Transformations
Unit 2 – Linear Function Models and Problem Solving
(22 days)
Activity 2.1 – How Fast Did You Lose?
Objectives: Determine the average rate of change
Activity 2.2 – The Snowy Tree Cricket
Objectives: Identify linear functions by a constant rate of change, Interpret slope as an average rate of change, Determine slope of a line, Identify increase/decrease slope, Determine slope and equation of a horizontal and vertical line AFDA.1  Function Families
Activity 2.3 – Depreciation
Objectives: Identify situations that can be modeled by a linear function, Determine and identify meaning of x and yintercepts and zeroes, Develop slopeintercept of a line and use slopeintercept formula to find intercepts AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 2.4 – Family of Functions
Objectives: Identify effect of changes of a line on its equation and graph, Identify changes as a translation, reflection, or vertical stretch or shrink AFDA.1  Function Families AFDA.2  Transformations
Activity 2.5 – Predicting Population
Objectives: Write an equation given slope and yintercept in slopeintercept form y = mx + b, Determine error in a measurement or prediction, Interpret slope and yintercept in contextual situations, Use slopeintercept form to solve problems AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 2.6 – Housing Prices
Objectives: Determine equation from two given points, Interpret slope and yintercept in contextual situations, Use pointslope form y – k = m (x – h) to solve problems AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 2.7 – Body Fat Percentage
Objectives: Construct scatterplots, Recognize linear patterns of scatterplots related positively or negatively, Identify outliers, Line of best fit through points in scatterplot, Determine residuals in a data set, Determine line of best fit by leastsquar AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 2.8 – Plot Before Calculating
Objectives: Understand the need to first make a scatterplot of the data before calculating a correlation coefficient and regression line AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 2.9 – College Tuition
Objectives: Determine the equation of a regression line using a graphing calculator, Use the regression equation to interpolate and extrapolate AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 2.10 – Body Parts
Objectives: Collect and organize data in a table, Plot data in a scatterplot, Recognize linear patterns in paired data, Determine a linear regression equation AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions AFDA.8  Experiment/Survey
Activity 2.11 – Long Distance by Phone
Objectives: Graph a piecewise linear function, Write a piecewise linear function to represent a given situation, Determine if a piecewise function is continuous, Graph a function defined by y = x – c AFDA.1  Function Families BENCHMARK ASSESSMENT CUTOFF

Unit 3 – Systems of Linear Equations and Inequalities
(18 days)
Activity 3.1 – Business Checking Account
Objectives: Solve a system of two linear equations numerically, graphically, using substitution method, Recognize connections between the three methods, Interpret solution to system of equations from problem’s content AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 3.2 – Modeling a Business
Objectives: Solve a system of equations by any method, Determine breakeven point of linear system, Interpret breakeven points in contextual situations AFDA.1  Function Families
Activity 3.3 – Healthy Lifestyle
Objectives: Solve a 2 x 2 linear system algebraically using the substitution method and the addition method, Solve equations containing parentheses AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 3.4 – How Long Can You Live?
Objectives: Solve linear inequalities, Use properties to solve inequalities, Solve compound inequalities, Use interval notation to represent a set of real numbers by an inequality AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 3.5 – Will Trees Grow?
Objectives: Graph a linear inequality in two variables, Solve a system of inequalities, Determine corner points of the solution set of a system of inequalities AFDA.5  Identifying Constraints and Linear Programming
Activity 3.6 – Helping Hurricane Victims
Objectives: Determine objective function where quantity is maximized/minimized, Determine constraints of limitations on objective function, Translate constraints into a system of inequalities, Use linear programming method to solve problem with maximized/ AFDA.4  Multiple Representations of Functions AFDA.5  Identifying Constraints and Linear Programming
Activity 3.7 – Healthy Burgers
Objectives: Determine objective function where quantity is minimized, Determine constraints of limitations on objective function, Translate constraints into a system of inequalities, Use linear programming method to solve problem with minimized set of con AFDA.5  Identifying Constraints and Linear Programming
Activity 3.8 – The Labor of Recycling
Objectives: Solve a linear programming problem with integer solutions AFDA.5  Identifying Constraints and Linear Programming
Unit 4 – Problem Solving with Quadratic and Variation Function Models
(17 days)
Activity 4.1 – The Amazing Property of Gravity
Objectives: Evaluate and graph functions of form y = ax2, Interpret coordinates of points on graph of y = ax2 , Solve equation of form ax2 = c graphically and by taking square roots AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 4.2 – Baseball and the Sears Tower
Objectives: Identify functions of the form y = ax2 + bx + c as quadratic functions, Explore the roles of a, b, c as they relate to the graph of y = ax2 + bx + c AFDA.1  Function Families AFDA.2  Transformations
Activity 4.3 – The Shot Put
Objectives: Determine vertex or turning point and axis of symmetry of parabola, Identify domain, range, x and yintercept, and vertex as a maximum/minimum, Interpret practical meaning of vertex and intercepts in given problem, Identify vertex from y = a AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 4.4 – Per Capita Personal Income
Objectives: Solve quadratic equations numerically and graphically, Determine zeroes of a function using technology AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 4.5 – Sir Isaac Newton
Objectives: Factor expressions by removing the greatest common factor, Factor trinomials using trial and error, Use zeroproduct principle to solve equations, Solve quadratic equations by factoring AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 4.6 – Ups and Downs
Objectives: Use the quadratic formula to solve quadratic equations, Identify the solutions of a quadratic equation with points on the corresponding graph, Determine the zeroes of a function AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 4.7 – Air Quality in Atlanta
Objectives: Determine quadratic regression models using the graphing calculator, Solve problems using quadratic regression models AFDA.1  Function Families AFDA.3  Best Fit
Activity 4.8 – A Thunderstorm
Objectives: Recognize equivalent forms of a direct variation statement, Determine the constant of proportionality in a direct variation problem, Solve direct variation problems AFDA.1  Function Families
Activity 4.9 – The Power of Power Functions
Objectives: Identify a direct variation function, Determine the constant of variation, Identify the properties of graphs of power functions defined by y = kxn, Graph transformations of power functions AFDA.1  Function Families AFDA.2  Transformations
Activity 4.10 – Speed Limits
Objectives: Determine the domain, range, vertical and horizontal asymptotes of function defined by y = k/x, Sketch graph of functions y = k/x, Determine properties of graphs with equation y = k/x AFDA.1  Function Families
Activity 4.11 – Loudness of a Sound
Objectives: Graph an inverse variation function defined by equation y = k/xn, Describe properties and vertical/horizontal asymptotes of graphs with equation y = k/xn, Determine constant of proportionality AFDA.1  Function Families

Unit 5 – Modeling with Exponential and Logarithmic Functions
(29 days)
Activity 5.1 – Going Shopping
Objectives: Define growth factor and decay factor, Determine growth factors and decay factors from percent increases/decreases, Apply growth factors and decay factors to problems involving percent increases/decreases
Activity 5.2 – Take an Additional 20% Off
Objectives: Define consecutive growth and decay factors, Determine a consecutive growth/decay factor from two or more consecutive percent changes, Apply consecutive growth/decay factors to solve problems involving percent changes
Activity 5.3 – Inflation
Objectives: Recognize exponential function as a rule for applying a growth/decay factor, Graph exponential functions from numerical data and with technology, Recognize exponential functions from equations AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 5.4 – The Summer Job
Objectives: Determine growth/decay factor of exponential function, Identify properties of graph of exponential function y = bx , Graph exponential functions using transformations AFDA.1  Function Families AFDA.2  Transformations
Activity 5.5 – Cellular Phones
Objectives: Determine the growth/decay factor and doubling/halving time for exponential function, Graph exponential functions defined by y = abx, Identify the meaning of a in y = abx in practical situation AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 5.6 – Population Growth
Objectives: Determine annual growth/decay rate of exponential function, Graph an exponential function having equation y = a (1 + r)x AFDA.4  Multiple Representations of Functions AFDA.1  Function Families
Activity 5.7 – Time Is Money
Objectives: Distinguish between simple and compound interest, Apply compound interest formula to lumpsum investment earning compound interest, Apply the continuous compounding formula A = Pert AFDA.1  Function Families
Activity 5.8 – Continuous Growth and Decay
Objectives: Discover relationship between exponential functions y = abt and continuous growth/decay exponential functions y = aekt, Solve problems of continuous growth/decay models, Graph base e exponential functions using transformations AFDA.1  Function Families AFDA.2  Transformations
Activity 5.9 – Bird Flu
Objectives: Determine equation of exponential function that best fits given data, Make predictions using exponential regression equation, Determine if linear or exponential model best fits the data AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 5.10 – The Diameter of Spheres
Objectives: Define logarithm, Write exponential statement in logarithmic form, Write logarithmic statement in exponential form, Determine log and ln values using a calculator AFDA.1  Function Families
Activity 5.11 – Walking Speed of Pedestrians pt 1
Objectives: Determine the inverse of exponential function, Identify properties of graph of logarithmic function, Graph natural logarithmic function using transformations AFDA.1  Function Families AFDA.2  Transformations AFDA.4  Multiple Representations of Functions
Activity 5.12 – Walking Speed of Pedestrians pt 2
Objectives: Compare average rate of change of increasing logarithmic, linear, and exponential functions, Determine regression equation of a natural logarithmic function with equation y = a + b ln x that best fits a set of data AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 5.13 – The Elastic Ball
Objectives: Apply the log of a product property, quotient property, power property, Discover change of base formula AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Activity 5.14 – Prison Growth
Objectives: Solve exponential equations both graphically and algebraically AFDA.1  Function Families AFDA.3  Best Fit AFDA.4  Multiple Representations of Functions
Activity 5.15 – Frequency and Pitch
Objectives: Solve logarithmic equations both graphically and algebraically AFDA.1  Function Families AFDA.4  Multiple Representations of Functions
Unit 6 – Probability Models
(29 days)
Activity 6.1 – Chances Are!
Objectives: Determine relative frequencies for data, Determine both theoretical and experimental probabilities, Simulate experiment and observe law of large numbers, Identify and understand properties of probabilities AFDA.6  Probabilities
Activity 6.2 – Choices
Objectives: Apply multiplication principle of counting, Determine sample space for probability distribution and complementary probabilities, Display sample space with tree diagram, Use Venn diagrams to illustrate relationships between events AFDA.6  Probabilities
Activity 6.3 – Experimenting with Probabilities
Objectives: Distinguish between independent and dependent events, Calculate probability involving “and” statements using multiplication formula and “or” statements using the addition formula, Identify mutually exclusive events AFDA.6  Probabilities
Activity 6.4 – Conditional Probabilities
Objectives: Identify conditional probability problem, Determine conditional probabilities using sample space or data from table and using a formula AFDA.6  Probabilities
Activity 6.5 – First Serve
Objectives: Use conditional probabilities to solve problems AFDA.6  Probabilities
Activity 6.6 – Colorful Probabilities
Objectives: Solve probability problems involving M&M candies AFDA.6  Probabilities AFDA.8  Experiment/Survey
Activity 6.7 – Selecting and Rearranging Things
Objectives: Determine the number of permutations, Determine the number of combinations, Recognize patterns modeled by counting techniques AFDA.6  Probabilities
Activity 6.8 – How many Boys (or Girls)?
Objectives: Recognize components of binomial experiment, Calculate binomial probabilities AFDA.6  Probabilities

Unit 7 – Problem Solving with Graphical and Statistical Models
(22 days)
Activity 7.1 – Visualizing Trends
Objectives: Recognize how scaling of the axes of a graph can misrepresent the situation
Activity 7.2 – Bald Eagle Population
Objectives: Read tables, Read and interpret bar graphs, Read and interpret circle graphs
Activity 7.3 – The Class Survey pt 1
Objectives: Organize data with frequency tables, dotplots, and histograms, Organize data using stemandleaf plots AFDA.8  Experiment/Survey
Activity 7.4 – The Class Survey pt 2
Objectives: Determine measures of central tendency, including the mean, median, mode and midrange, Recognize symmetric and skewed frequency distributions, Distinguish between percentiles and quartiles AFDA.7  Normal Distribution AFDA.8  Experiment/Survey
Activity 7.5 – Sampling a Population
Objectives: Know difference between census and sample, Identify characteristics of simple random sample, Know what bias in a sample means, Select a simple random sample, Identify how size of sample affects result AFDA.8  Experiment/Survey
Activity 7.6 – Highway Proposal – Yes or No?
Objectives: Identify the characteristics of a welldefined sample survey, Know how to collect a stratified sample, Identify ways in which a sample might be biased AFDA.8  Experiment/Survey
Activity 7.7 – Statistical Survey
Objectives: Design and execute a statistical survey AFDA.8  Experiment/Survey
Activity 7.8 – What’s the Cause?
Objectives: Understand the purpose and principles of experimental design, Know when a causal relationship can be established, Understand the importance of randomization, control treatments and blinding AFDA.8  Experiment/Survey
Activity 7.9 – A Switch Decision
Objectives: Measure the variability of a frequency distribution A.9 and AII.11 and AII.11  Normal Curve
Activity 7.10 – What is Normal?
Objectives: Identify a normal distribution, List the properties of a normal curve, Determine the zscore of a given numerical data value in a normal distribution, Identify the properties of a standard normal curve, Solve problems using the zscores of a s A.9 and AII.11 and AII.11  Normal Curve AFDA.7  Normal Distribution
Activity 7.11 – Parttime Jobs
Objectives: Determine the area under the standard normal curve using the ztable, Standardize a normal curve, Determine the area under the standard normal curve using a calculator AFDA.7  Normal Distribution
Activity 7.12 – Who Did Better?
Objectives: Compare xvalues in normal distribution using zscores and using percentiles, Determine percent of data of two values of normal distribution, Determine percentile of xscore and xvalue of percentile in normal distribution AFDA.7  Normal Distribution
Unit 8 – Problem Solving with Financial Models
(21 days)
Activity 8.1 – Income and Expenses
Objectives: Solve problems involving personal finances
Activity 8.2 – Time Is Money Revisited
Objectives: Distinguish between simple and compound interest, Apply compound interest formula and present value formula, Determine future value, effective interest rate and present value
Activity 8.3 – Saving for Retirement  Optional
Objectives: Distinguish between ordinary annuity and annuity due, Determine future value of an ordinary annuity, an annuity due and present value of an ordinary annuity, Solve problems involving annuities
Activity 8.4 – Buy or Lease?
Objectives: Determine the amortization payment on a loan using a formula and using technology, Solve problems involving repaying a loan or liquidating a sum of money by amortization model
Activity 8.5 – Buy Now, Pay Later
Objectives: Determine amount financed, installment price, finance charge of an installment loan, installment payment, annual percentage rate, unearned interest on a loan if paid before it is due, and interest on a credit card
Activity 8.6 – Home Sweet Home
Objectives: Determine amount of down payment and points in a mortgage, monthly mortgage payment, total interest on a mortgage, Prepare partial amortization schedule, Determine if borrowers qualify for a mortgage
Activity 8.7 – Which Is the Best Option?
Objectives: Use the financial models developed to solve problems
Review and Exam
