| Date |
Sections |
Topics |
Prerequisite Skills |
Student learning outcomes
|
| Week 1 |
Lesson 1.A |
Data |
Understand what is a learning community
|
- Collect data from daily life
- Work positively in a group to make a decision
|
| Week 1 |
Lesson 1.B |
Learning Community |
Example |
Seek and give help to one another inside and outside of class
|
| Week 1 |
Lesson 1.C |
First-degree equation involving percentages |
Determine the original amount, given the percentage that a given number is of the original
|
- Create a first-degree equation involving percentages and solve for the variable
- Apply and justify selection strategies to election results and decisions about other issues
|
| Week 1 |
Lesson 1.D |
Ranking methods |
Example |
Example
|
| Week 1 |
Lesson 2.A |
Graphical Display
|
- Be able to read and interpret graphical displays
- Know the definition of mean
- Know the definition of median
|
- Analyze a variety of graphical displays and interpret them in context
- Compute the mean of a set of data
- Construct a dot plot or histogram from data
|
| Week 1 |
Lesson 2.C |
Analyzing graphical displays |
Compare side-by-side graphical displays
|
Be able to read and interpret graphical displays |
Write a contextual analysis of a graphic display in a formal paper including appropriate mathematical language and explanations
|
| Week 1 |
Lesson 3.A |
Sampling |
Students should know the symbols for pop. Mean, sample mean, pop. Standard deviation, sample standard deviation
|
- Explain the difference between populations and samples
- Use the characteristics of a sample to describe the population
- Analyze the conclusions of a study and explain the limitations on inferences made
|
| Week 1 |
Lesson 3.B |
Mean and Central Limit Theorem |
Students should know how to determine the mean of a data set |
Graph sample means and use the central limit theorem to estimate the population mean
|
| Example |
Lesson 3.C |
Standard Deviation |
Students should be able to calculate the size of a portion given the size of the whole and a percentage
|
- Use standard deviation to interpret the spread of a data set
- Calculate the percentage of data in a graph region
|
| Example |
Lesson 4.A |
Probability
|
Students should be able to convert between fractions, decimals, and percentages |
- Calculate theoretical probability of two or more independent events
- Calculate AND and OR probabilities for independent events
|
| Example |
Lesson 4.B |
Conditional Probability |
Students should be able to determine a conditional probability |
Calculate conditional probabilities for two or more dependent events
|
| Example |
Lesson 5.A |
Conversions
|
- Be able to calculate unit ratios
- Be able to use ratios to convert units
- Be able to perform dimensional analysis
|
- Recognize when converting units is needed
- Use conversion to make comparisons
|
| Example |
Lesson 5.B |
Index numbers
|
- Be able to convert ratios to decimals and percentages, and divide
- Be able to describe types of averages
|
- Perform calculations involving index numbers
- Make and justify decisions and evaluate claims using index numbers
|
| Example |
Lesson 5.C |
Weighted averages |
Should be able to calculate mean
|
- Calculate weighted averages
- Use weighted averages to analyze data and draw conclusions about the data
|
| Example |
Lesson 5.D |
Expected Value |
Be able to calculate, percentages, means, and weighted averages
be able to find the mean of a data set
|
- Calculate expected value
- Make predictions about real world scenarios
|
| Example |
Lesson 6.A |
Weighted moving average graphs
|
- Weighted moving average
- Graph points
- Find the mean of a data set
|
- Calculate and compare simple and weighted moving averages
- Analyze graphs of moving average data
|
| Example |
Lesson 6.B |
Weighted moving average graphs continued
|
- Weighted moving average
- Find the mean of a data set
- Ue a spreadsheet to do calculations and create graphs
|
- Calculate and compare simple and weighted moving averages
- Write a contextual analysis of a graphical display
- Write a ratio or percentage and explain its meaning within a context
|
| Example |
Lesson 7.A |
Ratios and percentages |
Be able to write and simplify fractions, create a pie graph, convert fractions to percentages
|
- Determine percentages based on part-to-whole ratios
- Write a ratio or percentage and explain in meaning within a context
- Read a budget, determine values of line items, and draw conclusions about the overall distributions of funds
|
| Example |
Lesson 7.B |
Part-to-part ratios & Part-to-whole ratios |
Example |
Construct a pie graph based on ratios and percentages
|
| Example |
Lesson 7.C |
Absolute change (additive reasoning) & Relative change (multiplicative reasoning) |
Students should be able to create a line graph from data
|
- Analyze data in a spreadsheet and graphs
- Develop reasonable hypothesis supported by evidence
- Create line graphs and describe patterns in graphs
|
| Example |
Lesson 7.D |
Adjusting claims and hypothesis |
Students should be able to create a line graph from data |
Analyze data in a spreadsheet and graphs to compare changes in categories
|
| Example |
Lesson 7.E |
Debt-to-income (DTI) ratios |
Be able to write ratios and proportions, solve proportions, calculate percentages from ratios |
- Calculate a DTI ratio
- Draw conclusions from DTI about the appropriateness of the percentage of income spent on housing and debt
|
| Example |
Lesson 7.F |
Proportional reasoning |
Write rates, convert ratios to percentages
|
- Interpret ratios and percentages as rates of change
- Compare ratios and percentages
- Interpret graphical displays
- Compare mathematical relationships using a variety of representations
|
| Example |
Lesson 8.A |
Mathematical (Linear) relationships
|
- Be able to plot ordered pairs, sketch graphs of linear equations, construct a linear equation given the slope and y intercept
- Write a linear equation based on a verbal description/or that passes through 2 points
- Solve a 2-step linear equation
|
- Compare mathematical relationships using a variety of representations
- Write a linear equation given a slope and y intercept
|
| Example |
Lesson 8.B |
Proportionality vs. Linearity |
Determine when 2 quantities are proportional |
Explain, compare, and contrast linear and proportional relationships
|
| Example |
Lesson 8.C |
Simple and Compound Interest (Linear and Exponential Models)
|
- Write a percentage as a decimal
- Perform calculations with percentages
|
- Describe the difference between simple and compound interest in practical and mathematical terms
- Compare and contrast patterns in linear and exponential models
|
| Example |
Lesson 8.D |
Regression
|
- Read a scatterplot
- Interpret the slope of a line in context
|
- Create a scatterplot and regression equation using technology and estimate the parameters of the line of best fit
- Interpret the parameters (slope, y-intercept, coefficient of determination) of a simple linear regression
|
| Example |
Lesson 8.E |
Piecewise Linear Function
|
- Use a percentage rate to calculate tax
- Use constant rates of change to write a linear equation
- Identify the slope of a linear function
- Solve a linear equation for a given output
|
- Model a progressive income tax system algebraically and graphically
- Compare a progressive income tax system to a flat tax system and explain advantages and disadvantages of different income tax systems
|
| Example |
Lesson 9.A |
Depreciation
|
- Graph ordered pairs
- Identify the value of the output variable, given the input value, using a graphical and symbolic representation of the relationship between two variables
|
- Interpolate and extrapolate using a graphical representation of the relationship between two variables
- Use a symbolic model to find the exact value of one variable, given the value of the other variable, and relate those values to the context of the problem
|
| Example |
Lesson 9.B |
Geometric interpretation of interpolation
|
- Graph data from a scenario
- Create proportions using the sides of similar triangles and solve them
|
- Create a proportion between corresponding sides of similar triangles
- Use variables with subscripts
|
| Example |
Lesson 9.C |
Univariate, Bivariate, Correlation and Causation
|
- Calculate measures of central tendency
- Analyze data and visual displays of univariate and bivariate data and describe trends
|
- Create a line graph for univariate data
- Determine, informally, the correlation between bivariate data
- Analyze data and related graphs and describe the trend of the data
|
| Example |
Lesson 9.D |
Univariate, Bivariate, Correlation and Causation |
Create and interpret a scatterplot |
Explain why, even if there is a strong correlation, a change in one variable may not cause a change in the other
|
| Example |
Lesson 10.A |
Time series model of exponential growth |
Use formulas in spreadsheets
|
- Develop a time series model for the Fibonacci problem
- Test whether data are exponential by comparing the rate of growth to the population size
|
| Example |
Lesson 10.B |
Linear and Exponential Models
|
- Create a table of values and scatterplot in a spreadsheet
- Calculate the average rate of growth for a period of time
- Calculate the first differences in a data set
|
- Evaluate the mathematical appropriateness of a model give historical data
- Determine whether a data set suggests a linear or exponential relationship
- Use an appropriate model to predict a future outcome
|
| Example |
Lesson 11.A |
Continuous Growth
|
- Analyze the relationship of input and output values in a problem situation
- Determine whether numerical and graphical relationships are increasing at a constant rate, at an increasing rate or at a decreasing rate
|
- Sketch a model for a population that increases at an increasing rate and a decreasing rate
- Identify behavior in a graph, draw conclusions about the behavior, and predict future outcomes
|
| Example |
Lesson 11.B |
Carrying Capacity and Logistic Growth Rate
|
- Calculate absolute and relative change
- Read delta notation for absolute change
|
- Develop discrete models of natural phenomena and use the models to predict future values
- Calculate the carrying capacity and logistic growth rate of a real-world scenario
|
| Example |
Lesson 11.C |
Logistic Growth Model |
Determine the increasing and/or decreasing behavior of outputs in a table |
Explore the changes of the values of the parameters of a logistic growth model and describe the effect of those changes on the model
|
| Example |
Lesson 11.D |
Complex Population Growth and Decay Models
|
- Find the constant of proportionality and express variables that are jointly proportional
- Determine how jointly proportional variables affect each other in an abstract model
|
Develop a parameterized time series model with more than two dependent variables in a spreadsheet
|
| Example |
Lesson 11.E |
Analyzing Complex Population Growth and Decay Models |
Extract data from an academic article and create models for the data
|
- Determine parameters to match a model’s predictions against historical data
- Create a spreadsheet involving the formulas of the model to predict future behavior
|
| Example |
Lesson 12.A |
Periodic Function
|
- Plot points on coordinate axis
- Analyze the shape of a graph and find 12A coordinate values on a graph
|
- Sketch a graph that depicts a periodic phenomenon
- Identify the period and amplitude of a periodic function
- Compare and contrast the graphs of different periodic models
|
| Example |
Lesson 12.B |
The Sine Function
|
- Plot points on a graph
- Understand that constants (Parameters) in an equation control the relationship between the dependent variable and independent variable
|
- Describe the effect that changing one or more parameters has on the graph of a sine function
- Change the parameters of the sine curve to match given criteria
|
