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Math Lit

By Kathleen Almy, Heather Foes

Published by Pearson

Published Date: Jun 25, 2013

Description

Math Lit, by Kathleen Almy and Heather Foes, provides a one-semester alternative to the traditional two-semester developmental algebra sequence for non-STEM (Science, Technology, Engineering, and Math) students. This new approach offers an accelerated pathway to college readiness through developmental math, allowing non-STEM students to move directly into liberal arts math or introductory statistics, while also preparing STEM students for intermediate algebra. Through its emphasis on contextual problem-solving, the Almy/Foes worktext and its accompanying MyMathLab® course help students understand and practice the major themes of numeracy, proportional reasoning, algebraic reasoning, and functions.

Table of Contents

CYCLE 1

 

Part 1: Gear Up

1.1 Focus Problem, Step 1: Understand the Problem

  • Exposure to an open-ended problem on a medical error
    • Previews the use of rates and units and Polya’s problem solving process

1.2 Getting Started: Syllabus

  • Group activity to learn course policies
    • Develops critical reading skills

1.3 Getting Started: Skills

  • Venn diagrams are used to explore prerequisite knowledge
    • Reviews prerequisite skills
    • Develops Venn diagrams

1.4 Getting Started: Groups

  • Personality test to improve group dynamics
    • Develops knowledge of the Cartesian coordinate system
    • Develops the ability to plot and read ordered pairs
    • Exposes students to the term variable

1.5 A Tale of Two Numbers (FP)

  • Exploration of ratios and rates used in daily life
    • Previews scaling fractions
    • Develops ratio and rates concepts including notation

1.6 Part and Whole

  • Conceptual review of fraction operations
    • Reviews fraction concepts and operations
    • Develops the skill of drawing a picture

1.7 The Elusive A in Math

  • Assess traits necessary to success in mathematics
    • Develops pie and bar graphs
    • Connects equivalent fractions and scaling
    • Previews working with axes and increments on them

1.8 Two by Two

  • Visualizing situations with scatterplots
    • Develops scatterplots
    • Applies pie graphs and plotting points

1.9 Multiply or Divide? (FP)

  • Daily situations that involve unit conversions by multiplying or dividing
    • Develops unit conversions
    • Applies student success knowledge from 1.7

Part 1 Recap

 

Part 2: Shift Gears

1.10 Focus Problem, Step 2: Devise a Plan

  • Revisit focus problem and develop a plan to solve it
    • Applies knowledge gained to date

1.11 Higher or Lower? (FP)

  • Compare two pay structures with graphs, tables, and Excel
    • Previews integers, equations, like terms, and the commutative property
    • Develops percent calcuations, the concept of a function, and generalizing a calculation
    • Applies scaling

1.12 The X Factor

  • Important algebraic vocabulary
    • Develops the terms equation, expression, constant, variable, term
    • Applies Venn diagrams
    • Reviews pi

1.13 Take Two and Call Me…

  • Interpreting a graph that accompanies a medicine
    • Connects scaling with units and rates
    • Develops understanding of rates and units
    • Applies independent/dependent variables, function concepts, and reading ordered pairs

1.14 Good Eats (FP)

  • Understanding nutrition labels and nutrition guidelines
    • Develops the concept of proportionality
    • Applies fraction and percent skills

1.15 General Number

  • Generalizing patterns with variables
    • Exposes students to Fibonacci sequence
    • Develops generalizing a pattern, inductive and deductive reasoning
    • Previews simplifying expressions

1.16 Up and Down (FP)

  • Percent situations from daily life
    • Previews integers
    • Develops the concept of percent change
    • Applies the skills of finding the percent of a number and increasing or decreasing a number by a percent

1.17 The Social Network

  • Exploration of viral growth on the internet
    • Previews order of operations and slope concepts
    • Develops the concepts of linear and exponential growth
    • Applies the idea of generalizing a pattern
    • Exposes students to building a mathematical model
    • Connects exponential growth and percent of increase

Part 2 Recap

 

Part 3: Wind Down

1.18 Focus Problem, Step 3: Carry Out the Plan

  • Revisit focus problem and solve it
    • Applies knowledge gained to date

1.19 Cookie Monster

  • Recipe conversion to decrease its size
    • Connects conversions with scaling
    • Applies fraction skills
    • Applies unit conversion skills

1.20 Picture This

  • Matching scenarios with graphs
    • Exposes students to fitting data with a curve
    • Connects scatterplots and types of change

1.21 Infinity and Beyond

  • Exploration of Sierpinski triangles and their patterns
    • Connects area and perimeter to generalizing a pattern
    • Applies concepts of area and perimeter
    • Exposes students to Sierpinski triangles
    • Connects proportionality to similar triangles

1.22 Error and Estimation: Liquid Medicine

  • Impact of being inaccurate with liquid medicine
    • Exposes students to volume concepts
    • Applies the concepts of constant and variable
    • Applies the concepts of independent and dependent variables
    • Applies unit conversions
    • Previews order of operations

1.23 Focus Problem, Step 4: Look Back

  • Reflect on focus problem and cycle as a whole
    • Debriefs the focus problem solution

 

Cycle Wrap-up

  • Active test preparation exercises
    • Reviews topics, skills, and concepts from the cycle
    • Connects cycle skills and concepts to apply them to new problems

 

 

 

CYCLE 2

 

Part 1: Gear Up

2.1 Focus Problem, Step 1: Understand the Problem

  • Exposure to an open-ended problem on baseball’s magic number
    • Previews the use of expressions, formulas, and integers

2.2 It’s All Relative (FP)

  • Work with atoms and ions to develop integer concepts
    • Develops integer concepts
    • Previews integer operations

2.3 Sign and Size, Part 1 (FP)

  • Real-life situations to develop signed number addition/subtraction rules
    • Develops integer operations of addition and subtraction
    • Applies integer concepts and operations to realistic scenarios

2.4 Sign and Size, Part 2

  • Use of patterns to develop signed number multiplication/division rules
    • Develops integer operations multiplication and division
    • Defines real numbers
    • Exposes students to imaginary numbers
    • Reviews the concept of square roots

2.5 An Ounce of Prevention

  • Grades situations to understand means
    • Develops means conceptually and numerically
    • Previews order of operations

2.6 Measure Up

  • Geometric formulas with units to develop exponent rules
    • Develops whole number exponent properties
    • Applies geometric formulas
    • Applies the use of units in calculations

2.7 Count Up (FP)

  • Common situations with like terms
    • Develops like terms
    • Applies knowledge of formulas
    • Exposes students to polynomial terminology and addition/subtraction

Part 1 Recap

 

Part 2: Shift Gears

2.8 Focus Problem, Step 2: Devise a Plan

  • Revisit focus problem and develop a plan to solve it
    • Applies knowledge gained to date

2.9 Order Up

  • Order of operations and their use in formulas
    • Develops the order of operations
    • Applies order of operations to evaluating formulas
    • Previews inverse operations necessary for equation solving

2.10 Does Order Matter?

  • Uses of the commutative and associative properties in algebra and mental math
    • Develops the commutative and associative properties
    • Develops mental math skills
    • Applies percent skills and adding like terms

2.11 Fair Share

  • Development and application of the distributive property
    • Develops the distributive property and mental math skills
    • Applies the commutative property
    • Applies the distributive property to multiplying polynomials
    • Reviews like terms and whole number exponent properties

2.12 Seat Yourself (FP)

  • Pattern recognition using a tables and chairs situation
    • Applies the distributive property and connects it to like terms
    • Develops the ability to write expressions

2.13 Punt, Pass, Kick

  • Pythagorean Theorem off a grid
    • Develops the Pythagorean Theorem
    • Develops conceptual and numeric approaches to equation solving
    • Previews concepts related to solving equations
    • Connects Pythagorean triples to similar triangles

2.14 Ramp Up

  • Slope on and off a grid
    • Develops slope concepts and calculations
    • Connects slope to linearity
    • Applies Pythagorean Theorem and unit conversions

2.15 Shortest Distance (Optional)

  • Pythagorean Theorem on a grid to measure distances
    • Applies Pythagorean Theorem, slope, and the order of operations
    • Develops the distance formula and measurement skills
    • Connects slope and the distance formula

Part 2 Recap

 

Part 3: Wind Down

2.16 Focus Problem, Step 3: Carry Out the Plan

  • Revisit focus problem and solve it
    • Applies knowledge gained to date

2.17 Parts of Speech

  • Operations vs. operators
    • Applies the distributive property
    • Develops understanding of operations

2.18 In the Swing of Things (Optional)

  • Investigation of a pendulum formula
    • Applies the order of operations
    • Connects functions to the order of operations
    • Applies function concepts

2.19 Error and Estimation: Rounding (Optional)

  • Impact of being inaccurate with a financial formulas
    • Applies the order of operations
    • Develops understanding of the role of accuracy and precision

2.20 Focus Problem, Step 4: Look Back

  • Reflect on focus problem and cycle as a whole
    • Debriefs the focus problem solution

 

Cycle Wrap-up

  • Active test preparation exercises
    • Reviews topics, skills, and concepts from the cycle
    • Connects cycle skills and concepts to apply them to new problems

 

CYCLE 3

 

Part 1: Gear Up

 

3.1 Focus Problem, Step 1: Understand the Problem

  • Exposure to an open-ended problem about comparing e-readers
    • Previews the use of linear equations

3.2 Rule of Thumb

  • Explore weighted means with grade situations
    • Applies means and rates in a new context
    • Develops weighted means

3.3 Working Hard for the Money (FP)

  • Correlation between profession and income, unemployment rate
    • Applies means and weighted means
    • Applies making scatterplots
    • Develops correlation, median, and mode
    • Previews finding the trend line
    • Previews slope-intercept form
    • Applies scaling concepts
    • Connects measures of center to geometry

3.4 A Fine Balance (Optional)

  • Using chemical equations to understand solutions to equations
    • Connects algebraic ideas with chemistry notation
    • Develops the concept of solutions to equations
    • Previews algebraic identities

3.5 Just a Pinch

  • Measuring natural variation using standard deviation
    • Develops standard deviation concepts and calculations
    • Applies means, order of operations, and signed numbers
    • Previews equation solving concepts

3.6 Separate but Equal (FP)

  • Real-life scenarios that can be solved numerically and with one-step equations
    • Develops one-step equations and understanding of equation solving
    • Connects algebraic and numeric methods of equation solving

3.7 On the Rise

  • Analyze an article about food packaging using algebra, geometry, and statistics
    • Applies mean, median, standard deviation, and bar graphs
    • Develops Pareto charts
    • Applies writing and solving one-step equations

Part 1 Recap

 

Part 2: Shift Gears

 

3.8 Focus Problem, Step 2: Devise a Plan

  • Revisit focus problem and develop a plan to solve it
    • Applies knowledge gained to date

3.9 Game On (FP)

  • Use pictures and algebra to solve two-step and multi-step equations
    • Develops solving of linear equations
    • Develops identities and contradictions

3.10 Quarter Wing Night (FP)

  • Determine the number of buffalo wings in varying scenarios
    • Applies equation solving techniques
    • Applies percent concepts

3.11 Eastbound and Down (FP)

  • Analyzing gas price scenarios with and without a car wash
    • Applies equation solving techniques
    • Connects linear equation solving and graphing
    • Reviews linearity, slope, and rate of change
    • Previews systems of equations

3.12 Get in Line (FP)

  • Explore linear situations algebraically and on a graph
    • Develops slope-intercept form and its uses in graphing
    • Connects linearity between tables, graphs, and equations
    • Exposes students to the concept of domain

3.13 Gas Up and Go (Optional)

  • Study Distance = Rate x Time to explore variation
    • Develops direct and inverse variation
    • Exposes students to combined variation
    • Applies equation solving

Part 2 Recap

 

Part 3: Wind Down

3.14 Focus Problem, Step 3: Carry Out the Plan

  • Revisit focus problem and solve it
    • Applies knowledge gained to date

3.15 Value of a Dollar (Optional)

  • Determine the amount of time worked to pay for a tank of gas
    • Develops rational functions
    • Applies direct and inverse variation

3.16 When is the Algebra Worth It? (Optional)

  • Assess when algebra is useful
    • Applies and extends equation solving techniques
    • Exposes students to non-linear equation solving

3.17 Error and Estimation: Volume

  • Revisit and quantify liquid medicine overfilling error
    • Applies slope-intercept form and graphing
    • Applies percent of change and unit conversions

3.18 Focus Problem, Step 4: Look Back

  • Reflect on focus problem and cycle as a whole
    • Debriefs the focus problem solution

 

Cycle Wrap-up

  • Active test preparation exercises
    • Reviews topics, skills, and concepts from the cycle
    • Connects cycle skills and concepts to apply them to new problems

 

CYCLE 4

 

Part 1: Gear Up

4.1 Focus Problem, Step 1: Understand the Problem

  • Exposure to an open-ended problem about making sense of a large number
    • Previews dimensional analysis

4.2 A Matter of Change (FP)

  • Work with more involved conversion problems
    • Develops dimensional analysis
    • Previews scientific notation

4.3 Little Giants (FP)

  • Explores very large and very small numbers
    • Develops scientific notation
    • Connects dimensional analysis to scientific notation
    • Applies Pareto charts and medians
    • Previews negative exponents and compound inequalities

4.4 Outwit and Outlast (FP)

  • Situations with proportionality, explored numerically and algebraically
    • Develops solving proportions algebraically
    • Connects scaling with algebraic methods of solving
    • Applies rates
    • Exposes students to concepts of apportionment

4.5 Chances Are (Optional)

  • Simple probability situations from daily life
    • Develops theoretical and experimental probabilities
    • Connects area to probability
    • Applies scientific notation
    • Previews compound inequalities

4.6 A Model Approach (FP)

  • Working with numbers in scientific notations from science scenarios
    • Develops negative exponents
    • Connects scientific notation to exponent rules
    • Applies exponent rules, unit conversions, and solving proportions algebraically

Part 1 Recap

 

Part 2: Shift Gears

4.7 Focus Problem, Step 2: Devise a Plan

  • Revisit focus problem and develop a plan to solve it
    • Applies knowledge gained to date

4.8 Chain, Chain, Chain

  • Linear relationships in alkanes
    • Exposes students to domain
    • Develops writing linear models using y = mx + b
    • Connects equation solving to linear models

4.9 Hot and Cold

  • Analyzing and developing temperature formulas
    • Develops factoring the greatest common factor
    • Develops solving equations for a variable
    • Applies slope-intercept form and equation solving

4.10 Going Viral

  • Statistics and models of viral marketing in social media
    • Exposes students to solving an exponential equation
    • Develops exponential models
    • Connects functions to exponential growth
    • Connects slope, growth, and statistics
    • Develops understanding of the concept of size
    • Applies factoring the GCF

4.11 The Cost of College (Optional)

  • Comparing tuition and fee structures
    • Develops solving systems with graphing and substitution
    • Connects graphing and algebraic methods of solving systems
    • Applies solving literal equations, solving equations, graphing lines
    • Applies writing equations of lines

4.12 Tuition Increases (Optional)

  • Exploring the effects of a tuition increase on revenue
    • Develops quadratic function modeling
    • Connects linear, exponential, and quadratic functions
    • Applies systems of equations
    • Applies multiplying binomials

Part 2 Recap

 

Part 3: Wind Down

4.13 Focus Problem, Step 3: Carry Out the Plan

  • Revisit focus problem and solve it
    • Applies knowledge gained to date

4.14 Outliers (Optional)

  • Modeling height using belly button height
    • Exposes students to residuals, the Golden ratio, and compound inequalities
    • Develops z-scores
    • Connects issues of size and scale to statistics
    • Applies standard deviation and mean

4.15 A Little Less (FP)

  • Large scale effects of plastic saving measures
    • Applies dimensional analysis
    • Develops concepts of size and scale

4.16 Error and Estimation: Order of Magnitude Optional

  • A new scale to make sense of size
    • Develops order of magnitude
    • Applies scientific notation and exponent rules

4.17 Focus Problem, Step 4: Look Back

  • Reflect on focus problem and cycle as a whole
    • Debriefs the focus problem solution

Cycle Wrap-up

  • Active test preparation exercises
    • Reviews topics, skills, and concepts from the cycle
    • Connects cycle skills and concepts to apply them to new problems

 

*(FP): Indicates a lesson essential to solving the focus problem

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    Alan Bass
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