Mathematics Analysis

PA Common Core Math Standards

• CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. 
• CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. 
• CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. 
• CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. 
• CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. 

• Real world representation of numbers form an equation.
• Steps to solve systems of equations.
• Steps to solve linear equations.
• Features of linear equations and linear graphs such as slope and y-intercept. 
• How quantitative data is represented on a graph.

• When cost equals revenue, a business is at a break even point.
• When supply equals demand, we have the best market price.
• Businesses use prediction equations to data driven decisions.

• Determine which real world values are represented in an equation.
• Define the units of measure for a solution.
• Recognize when equations should be set equal to each other.
• Solve equations using inverse operations.
• Organize values as independent and dependent variables.
• Interpret solutions to help make real world decisions.

• How can I create a cost and revenue equation?
• What is a fair market price?
• How can past data help make decisions for tomorrow?
   

• How do you find the cost of running a business?
• What are the procedures for finding a break even point using linear equations?
• Can you describe the relationship between supply and demand?
• What is the line of best fit?
• What information does a prediction formula give to a business?
   

• Instructor’s Notes
• Online Resources, including https://www.rossmanchance.com/applets/2021/regshuffle/regshuffle.htm
• Classroom Discussions and Demonstrations  
   

• Fixed Cost 
• Variable Cost
• Cost Equation
• Revenue 
• Break Even Point
• Supply 
• Demand
• Market Price
• Scatter Plot
• Line of Best Fit
• Prediction Equation
• Correlation
• Slope 
• Y-Intercept

• Online modules in Schoology
• Quizzes
• Creating a Business Assessment
   

PA Common Core Math Standards

• CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. 
• CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs and data displays.  
   

• How rates and time can impact a simple interest formula.
• How rates and time can impact a compound interest formula.
• How banking and credit create profits.
• The frequency of money being compounded, such as quarterly, monthly, annually.  

• How compound interest works faster than simple interest.
• Amortization formula shows how interest can impact a loan.
• Loans, investments, and credit all will impact budgeting. 

• Describe principal payments versus interest payments.
• Determine how often interest is applied to a simple interest calculation.
• Determine how often interest is applied to a compound interest calculation.
• Compare the growth rates of simple versus compound interest formulas.
• Find monthly payments for different types of interest loans. 

• Why does compound interest grow faster than simple interest?
• How does an amortization loan work? 
• Does credit help me or hurt me financially?
   

• Where does the interest on a simple loan get applied?
• Where does the interest on a compound loan get applied?
• How do I find the payments on a student loan, car, or house?
• Which retirement investment is best for me?
• How does credit really work?

• Instructor’s Notes
• Online Resources including Cars.com, Carfax.com, Zillow.com, Realtor.com 
• Classroom Discussions and Demonstrations 
   

• Credit
• Credit Score
• Simple Interest
• Bonds
• Discount Loans
• Compound Interest
• Amortization
• Leasing
• Mortgage
• Social Security
• 401K
• Pension

• Online modules in Schoology
• Quizzes
• Budgeting Assessment
   

PA Common Core Math Standards

• CC.2.4.HS.B.6  Use the concepts of independence and conditional probability to interpret data.
• CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. 
• CC.2.4.HS.B.8 Use probability to make decisions.

• Sample space is a list of all possible outcomes. 
• Probability is always a portion of a whole, or a fraction between 0 and 1. 
• One outcome might change the probability for another outcome. 
• Probability works only when doing many repetitions. 

• Basic probability is used in everyday life such as weather, insurance, medicine. 
• To find probability I need to first know all the possible outcomes
   

• Describe the sample space for an event.
• Determine the number of outcomes in favor.
• Combine the probability from multiple events.
• Support a decision based on the expected probability.  

• What do we mean when we say something is likely to happen?
• How do I determine all the possible outcomes?
   

• What is a sample space?
• How do I find the probability?
• What is the additive rule and product rule for probability?
• Is this probability rare, unlikely, or likely?
   

• Instructor’s Notes
• Online Resources
• Classroom Discussions and Demonstrations
   

• Total number of outcomes
• Sample Space
• Probability Formula
• Independent Events

• Online modules in Schoology
• Quizzes
• Spades Assessment
   

PA Common Core Math Standards

• CC.2.4.HS.B.6  Use the concepts of independence and conditional probability to interpret data.
• CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. 
• CC.2.4.HS.B.8 Use probability to make decisions.

• The difference between outcomes in favor and outcomes against an event. 
• Mutually exclusive events can’t happen at the same time.
• One outcome might change the probability for another outcome. 
• What a good sample looks like. 

• Find the probability for compound events.
• Odds are not the same as probability, but similar.

• Calculate the odds in favor and odds against.  
• Create Venn Diagrams for events that are not mutually exclusive. 
• Find the probability of an event not happening. 
• Support a decision based on the expected probability.

• How are odds and probability related?
• How do I determine probability when an event can be 2 things at the same time?

• What is a Venn Diagram?
• How can you calculate the expected value from a game or trial?
• Odds; where is the total?
• Does this everyday event use probability? 

• Instructor’s Notes
• Online Resources
• Classroom Discussions and Demonstrations

•  
• Compound Events
• Union
• Intersection
• Multiplication Counting Principle
• Mutually Exclusive
• Odds
•  

• Online modules in Schoology
• Quizzes
• Spades Assessment
   

PA Common Core Math Standards

• CC.2.2.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. 
• CC.2.2.HS.B.2 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. 

• When to use mean or median as a measure of center.
• When to use range or standard deviation as a measure of spread.
• How to read the scale or legend of a graphical display.
• What the signs of a bias sample are. 

• Measuring the center and spread of a data set.
• Graphical displays can be misleading.
• Determining a representative sample.

• Calculate mean, median, range, and standard deviation. 
• Determine if a data is an outlier. 
• Recognize how to measure center and spread when you know there is an outlier.
• Examine or collect data and decide if it is representative or biased.
• Explain how a graphical display can be misleading. 

• Which measure of center and spread is best?
• Why is this information misleading?
   

• Online modules in Schoology
• Quizzes
   

• Can you find all the measures of center and spread?
• Can you find any outliers?
• Which measures are resistant to outliers?
• Why is this graph misleading?
• Why is the sample not representative?
   

• Instructor’s Notes
• Online Resources, including https://stapplet.com/ 
• Classroom Discussions and Demonstrations 

• Mean, Median, Mode
• Standard Deviation
• Outlier
• Box Plot
• Histogram
• Discrete
• Continuous