## Overview

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*This course is ideal for accelerating students as an alternative to the traditional developmental math sequence and preparing them for a college-level statistics, liberal arts math, or STEM-prep course.*

** MyMathLab for Foundations for Mathematical Reasoning** is the first in a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center’s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways and a supporting student success course.

**is the common starting point for all three mathematics pathways and is designed to build the mathematical skills and understanding necessary for success in a quantitative literacy, statistics, or algebra course.**

*Foundations for Mathematical Reasoning*

## Table of contents

**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

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