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

# MyLab Math for Foundations of Mathematical Reasoning -- Student Access Kit, 1st edition

1st edition

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## 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. Foundations for Mathematical Reasoning 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.

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

• 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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