MyLab Math for Foundations of Mathematical Reasoning -- Student Access Kit

MyMathLab for Foundations for Mathematical Reasoning was developed by the Charles A. Dana Center at The University of Texas—Austin. The Dana Center brings together experienced faculty from two- and four-year institutions to author, review, field-test, and revise the New Mathways Project curricular materials.   The Dana Center develops and scales effective math and science innovations to support educators, administrators, and policy makers in creating seamless transitions throughout the K14 system for all students. Their work, based on research and two decades of experience, focuses on K—16 mathematics and science education with an emphasis on strategies for improving student engagement, motivation, persistence, and achievement. They develop innovative curricula, tools, protocols, and instructional supports and deliver powerful instructional and leadership development.  

Lesson 1: Reasoning With Large Numbers

Part A: How Big Is a Billion?



Scale measurements of groups to represent individual elements
Scale measurements to represent larger quantities of individual elements

Part B: Building a Learning Community



Identify ways in which this course is different from other math courses in both content and structure

Part C: How Big Is a Billion? (Continued)



Convert between units of measure
Calculate quantities in billions

Part D: Building a Learning Community (Continued)



Create a positive learning environment and a sense of community in the classroom
Identify their responsibilities in the course as individual learners and members of a learning community

 

Lesson 2: Representing And Analyzing Large And Small Numbers

Part A: Doubling Population



Describe quantities in the millions and billions
Use data to estimate a doubling time
Compare and contrast growth via doubling times

Part B: Scientific Notation



Represent large and small numbers in scientific notation
Convert numbers from scientific notation to standard notation

Part C: Ratios in Water Use



Recognize when it is appropriate to express a ratio as a percentage
Calculate ratios of large numbers
Estimate ratios of large numbers

Part D: Analyzing Water Footprints



Write and interpret numbers in scientific notation
Perform operations with scientific notation using a calculator

 

Lesson 3: Estimation And Percentages

Part A: Large Numbers in the Media



Evaluate reasonableness
Rewrite quantitative statements to improve clarity

Part B: Seeking Help



Identify when they need to ask for help

Part C: Estimating Sale Prices



Use a few standard benchmarks to estimate percentages (i.e., 1%, 10%, 25%, 33%, 50%, 66%, 75%)
Estimate the percent of a number, including situations involving percentages less than one

Part D: Calculating Sale Prices



Determine when an estimate or an exact calculation is appropriate
Calculate the percent one number is of another
Calculate the percent of a number, including situations involving percentages less than one

Part E: Developing Self-Regulation



Evaluate the accuracy of your self-assessment to this point
Make a plan to continue to improve your self-assessment and use it to regulate your learning

 

Lesson 4: Utilizing Charts And Spreadsheets

Part A: Budgeting Operations



Write a calculation in at least two different ways based on equivalent forms of fractions/decimals
Write a calculation in at least two different ways based on relationship of multiplication and division
Write a calculation in at least two different ways based on properties and order of operations

Part B: Budgeting with Spreadsheets



Apply mathematical knowledge about properties and operations in using spreadsheet technology

Part C: Graph Analysis



Calculate absolute and relative change from a line graph

Part D: Using Graphs to Understand Change



Estimate the absolute size of the portions of a pie chart if given the base value
Use data displayed on two graphs to estimate a third quantity

 

Lesson 5: Displaying Data

Part A: Displaying Table Data



Read a stem-and-leaf plot and a back-to-back plot
Identify important features of a stem-and-leaf plot

Part B: Relative Frequency Tables



Choose appropriate bin size and sort data into bins
Report frequencies and relative frequencies

Part C: Displaying Data: Histograms



Analyze histograms
Create a histogram from a frequency table

Part D: Shapes of Distributions



Analyze dotplots
Describe the shape of distributions

 

Lesson 6: Statistical Summaries

Part A: Measures of Central Tendency



Compare the mean and median from the shape of a distribution
Create a data set that meets certain criteria for measures of central tendency

Part B: Brain Power



Identify how the growth view of intelligence relates to learning math

Part C: Making Decisions with Data



Use data to make informed decisions
Identify the mean, median, or mode in contextual problems
Match data sets with appropriate statistics

Part D: Boxplots



Analyze boxplots
Interpret the mean, median, or mode in terms of the context of the problem

 

Lesson 7: Applying Numeracy Skills To Financial Situations

Part A: The Credit Crunch



Apply quantitative reasoning and math skills in various contexts

Part B: More Credit Crunch



Apply skills and concepts from previous lessons in new contexts
Interpret a numerical expression in context
Write a spreadsheet formula to compute interest

Part C: A Taxing Situation



Perform multi-step calculations using information from a real-world source
Rewrite multi-step calculations as a single expression

Part D: A Taxing Situation (Continued)



Generate an algorithm for performing multi-step calculations
Explain the meaning of a calculation within a context

 

Lesson 8: Assessing Risk

Part A: What’s the Risk?



Express and interpret ratios in non-standard forms (i.e., 1 out of 20) and standard forms, such as percentages and natural frequencies out of multiples of 10
Identify missing information needed to calculate risk

Part B: An Apple a Day



Identify major factors in determining risks of disease
Make quantitative comparisons between data
Write a statement that interprets data from a table using multiple categories

Part C: Reducing the Risk



Create graphs that show absolute change calculated from a rate
Compute absolute changes

Part D: Is Reducing the Risk Worth It?



Create graphs that show both absolute and relative changes in a rate (percent)
Compute absolute and relative changes

 

Lesson 9: Reasoning With Probabilities

Part A: Comparing Categorical Data



Correctly identify the quantities involved in a verbal statement about percentages based on specific data
Calculate percentages and convert from a decimal representation to a percent
Read and use information presented in a two-way table

Part B: Interpreting Percentages



Correctly identify variable quantities involved in a general verbal statement about percentages

Part C: Do You Trust the Test?



Extract relevant information from a two-way table
Select the appropriate values to calculate probabilities

Part D: Do You Trust the Test? (Continued)



Calculate probabilities from information given in a two-way table
Calculate and interpret probabilities of errors: percent of positive results that are false positives and percent negative results that are false negatives

 

Lesson 10: Reasoning With Ratios And Proportions

Part A: Population Density



Calculate population density as a unit rate
Compare and contrast populations using their population densities

Part B: Density Proportions



Calculate population densities
Calculate population density proportions from density ratios
Solve a proportion by first finding a unit rate and then multiplying appropriately

Part C: State Population Densities (Optional)



Estimate between which two powers of 10 a quotient of large numbers lies
Use unit rates to estimate population

Part D: Apportionment



Calculate a relative change
Explain the difference between a relative change and absolute change

 

Lesson 11: Geometric Reasoning

Part A: Formulating a Plan



Use formulas from geometry
Evaluate an expression in a geometric formula

 

Part B: The Costs of Geometry



Perform calculations that involve rates and measures to support financial decisions
Solve complex problems requiring multiple pieces of information and steps
Evaluate an expression involving estimating cost

Part C: Modifying and Combining Formulas



Use formulas from geometry and perform calculations that involve rates and measures to support financial decisions
Write an expression to solve a problem involving estimating cost

 

Lesson 12: Dimensional Analysis

Part A: Texting Distance



Use units to determine which conversion factors are needed for dimensional analysis
Use a conversion factor to convert a rate

Part B: The Cost of Driving



Write a rate as a fraction
Use a unit factor to convert a rate
Use dimensional analysis to help determine the factors in a series of operations to obtain an equivalent measure

Part C: The True Cost of Driving



Organize multiple pieces of information and steps involved in complex problems

Part D: Can the True Cost Vary?



Use variables to analyze multiple pieces of information and steps involved in complex problems
Investigate how changing certain values can affect the result of a calculation

 

Lesson 13: Analyzing Formulas

Part A: Algebra Reaction (Optional)



Evaluate an expression involving a square root

Part B: Breaking Down a Formula



Evaluate a rational expression

Part C: Analyzing Change in Variables



Establish a strategy to explore the pattern of changes in one variable of an expression while holding other variables fixed

Part D: Analyzing Change in Variables (Continued)



Informally describe the change in one variable as another variable changes

 

Lesson 14: Applying Formulas

Part A: Body Mass Index



Explicitly write out the order of operations to evaluate a given formula involving multiplication and division

Part B: Target Weight



Solve for a variable in an equation involving only multiplication and division
Explicitly write out the order of operations to solve a given equation involving multiplication and division

Part C: Blood Alcohol Content



Explicitly write out the order of operations to evaluate a given formula involving multiplication, addition, and division.

Part D: Balancing Blood Alcohol



Solve for a variable in an equation
Explicitly write out the order of operations to solve a given equation involving multiplication, addition, and division.

 

Lesson 15: Proportional Reasoning

Part A: Proportional Reasoning in Art



Set up a proportion based on a contextual situation
Solve a proportion

 

Part B: Proportion Solutions



Set up a proportion to solve a scaling problem
Solve a proportion using algebraic methods

 

Part C: Solving Equations



Solve equations that require simplification before solving
Solve for a variable in terms of other variables

Part D: More Work with Equations (Optional)



Solve equations in a variety of forms, such as simple quadratic equations (by square root function) and simple cubic equations (by cube root function)
Recognize when they do not have enough tools to solve an equation

Part E: Proportional Viewing (Optional)



Set up a proportion to solve an aspect ratio problem

 

Lesson 16: Creating Linear Models

Part A: Describing Rates



Calculate slope in direct variation situations
Express slope with appropriate units
Interpret slope in a problem situation

Part B: Comparing Rates



Compare slopes in a problem situation using appropriate units

Part C: Interpreting Change



Calculate slope from two points in a linear relationship

Part D: Where Do We Start?



Determine the y-intercept in a linear relationship
Determine the equation of a linear relationship

Part E: Predicting Costs



Calculate the y-intercept of any linear relationship given two points
Write an equation that represents a linear relationship given two data points
Use the linear equation to make predictions