#### Quarter 4

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 problem-solving skills

Activity 1.2 – The Classroom
Objectives: Organize information, Develop problem-solving strategies (draw a picture, recognize a pattern, do a simpler problem), Communicate problem-solving ideas

Activity 1.3 – Make Me an Offer
Objectives: Use basic steps for problem-solving, Translate verbal statements and algebraic equations, Use basic principles of algebra to solve real-world 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 problem-solving 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 problem-solving 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 y-intercepts and zeroes, Develop slope-intercept of a line and use slope-intercept 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 y-intercept in slope-intercept form y = mx + b, Determine error in a measurement or prediction, Interpret slope and y-intercept in contextual situations, Use slope-intercept 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 y-intercept in contextual situations, Use point-slope 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 least-squar
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 break-even point of linear system, Interpret break-even 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 y-intercept, 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 zero-product 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 lump-sum 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

Activity 7.3 – The Class Survey pt 1
Objectives: Organize data with frequency tables, dotplots, and histograms, Organize data using stem-and-leaf 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 well-defined 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 z-score of a given numerical data value in a normal distribution, Identify the properties of a standard normal curve, Solve problems using the z-scores of a s
A.9 and AII.11 and *AII.11 - Normal Curve
AFDA.7 - Normal Distribution

Activity 7.11 – Part-time Jobs
Objectives: Determine the area under the standard normal curve using the z-table, 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 x-values in normal distribution using z-scores and using percentiles, Determine percent of data of two values of normal distribution, Determine percentile of x-score and x-value 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

38 Days 41 Days 52 Days 49 Days