Applied Algebra
Edition: 1
Copyright: 2023
Pages: 286
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Applied Algebra is designed for a one semester course for students entering college at the developmental level. It enhances students’ algebraic, critical reasoning, and communication skills, and to promote a growth mindset towards learning.
It provides a guided inquiry approach through collaborative exploration, concept formation, and application where students learn algebraic concepts and their meaning in real-world contexts.
The publication focuses on fewer concepts, mainly linear, exponential, and quadratic functions, but treat them conceptually, in more depth, and interconnected for better retention.
The movie Groundhog Day is a good metaphor for our book’s concept. Each day the lead character wakes up on the same day, Groundhog Day, repeating the same routine while struggling with a situation. He starts to predict what is going to happen each day, he learns a little bit more, and gets closer to solving the problem. By the end he understands what he needs to do.
Readers are taken through a similar experience. Each section starts with a launch exploration based on the common threads of the same routine: when given a situation, they identify the variables, make tables, draw graphs, search for patterns, and write equations.
Introduction
0 Math Foundations in a Nutshell
0.1 Fundamental Arithmetic: The Integers
Launch Exploration: Grouping and Regrouping
Numeration
Addition of Counting Numbers
Subtraction
Multiplication
Division
Number Zero
Order of Operations
Distributivity of Multiplication over Addition
Wrapping Up
Exercises
0.2 Fundamental Arithmetic: The Rationals
Mental Math
Divisibility of Numbers
Launch Exploration: Part of a Whole
Ordinary Fractions
Adding and Subtracting Fractions
Fraction Multiplication
Division by Fractions
Decimal Fractions
Rounding
Percent
Wrapping Up
Exercises
0.3 Elementary Algebra: Expressions and Equations
Launch Exploration: Find the ’Heap’
Ratios and Proportions
Powers and Radicals
Intro to Algebraic Expressions
Intro to Algebraic Equations
Wrapping Up
Exercises
0.4 Elementary Geometry: Shapes and Measures
Launch Exploration: Perimeter and Area
Primitive Notions
Angles and Circles
Parallel Lines
Triangles
Rectangles and Parallelograms
Perimeter versus Area
Volumes
Wrapping Up
Exercises
1 Quantitative Analysis, Problem Solving, and Functions
1.1 Quantitative Analysis: Constants and Variables
Launch Exploration: Shopping and Fencing
Analyzing a Situation: Quantities and Units
Analyzing a Situation: Constants and Variables
Values of a Variable – Discussion
Wrapping Up
Exercises
1.2 Algebraic Relations: Translations and Formulas
Launch Exploration: Building a Patio
Operations and Relations - Key Phrases
Quantitative Relations in Situations
Units Agreement
Wrapping Up
Exercises
1.3 Problem Solving with Linear and Power Systems
Launch Exploration: Building a Deck
Solving Linear Systems by Substitution
Linear Systems - More Examples
Power Equation – A Basic Example of a Nonlinear Equation
Mapping Diagrams
Power Systems
Critical Thinking
Wrapping Up
Exercises
1.4 Introduction to Modeling with Functions
Launch Exploration: Buying Protein Bars
Function Notation - How to Write About Functions
Real-World Domain and Range
Graphs - How to Visualize Functions
Analyzing a Graph
The Initial Value of a Function
What is a Function?
Function Equations
Wrapping Up
Exercises
2 Linear Functions
2.1 Introduction to Linear Relationships
Launch Exploration: Growing Plants
Linear Function Tables
Another Plant Example
Constant Rate of Change
Linear Function Equations
Positive and Negative Rates of Change
Wrapping Up
Exercises
2.2 Analyzing Linear Functions
Launch Exploration: Linear Graphs
Analyzing Linear Graphs
Writing Linear Function Equations from Graphs
Writing Linear Function Equations from Tables
Comparing Slopes
Wrapping Up
Exercises
2.3 Linear Modeling
Launch Exploration: Window Washers
Creating and Using Linear Models
More Linear Modeling
Wrapping Up
Exercises
3 Exponential Functions
3.1 A New Pattern - Introduction to Exponential Functions
Launch Exploration: Growing Bacteria
Exponential Function Tables
Exponential Function Equations
Exponential Growth versus Decay
Writing Equations from Two Data Points
Wrapping Up
Exercises
3.2 Analyzing Exponential Functions
Launch Exploration: Graphing an Exponential
Domain and Range for Exponentials
Zoom In and Out on Exponential Graphs
Asymptotes and Intercepts
An Exponential Decay Example
Comparing Exponential Graphs
Solving Exponential Equations with Logarithms
Analyzing Exponential Functions in Context
Writing Equations from Exponential Graphs
Wrapping Up
Exercises
3.3 Problem Solving with Exponentials
Launch Exploration: A Growing Colony
Relative Rate of Change
Relative Rate of Growth
Relative Rate of Decay
Relative Rates in Equations
Exponential Modeling
Linear versus Exponential
Wrapping Up
Exercises
4 Quadratic Functions
4.1 Problem Solving with Quadratic Equations
Launch Exploration: A Room with a Given Area
The Quadratic Formula
Creating and Using Quadratic Equations
The Number of Real Solutions
Special Cases of Quadratic Problems
Wrapping Up
Exercises
4.2 Another New Pattern - Intro to Quadratic Functions
Launch Exploration: A Square Garden
Quadratic Function Equations
Quadratic Function Tables
Quadratic Function Graphs
Why Are Parabolas So Special?
Not All U-Shapes Are Parabolas!
Writing Quadratic Function Equations from Tables
Wrapping Up
Exercises
4.3 Finding Features of Parabolas Algebraically
Launch Exploration: Analyzing Parabolas
Symmetry and Vertex
Direction
The Vertex Formula
Intercepts
Finding All the Features of a Parabola
Wrapping Up
Exercises
4.4 Analyzing Quadratic Functions
Launch Exploration: A Projectile Motion Graph
Throwing a Ball on the Moon
The Profit of Kandy-n-Kakes
Maximizing Area Inside a Fence
Wrapping Up
Exercises
Index
If you are tired by the usual turgid textbooks on introductory algebra, you have found the antidote - an excellent teaching tool, with successive topics following in seamless flow; this material is visually pleasing, uncluttered and inviting, well grounded in a narrative mode. Anton and Santoro’s accomplishment in offering a rigorous, yet engaging introductory manual, is salutary.
Mircea Pitici, PhD, the editor of "The Best Writings on Mathematics" series by Princeton University Press
Applied Algebra is designed for a one semester course for students entering college at the developmental level. It enhances students’ algebraic, critical reasoning, and communication skills, and to promote a growth mindset towards learning.
It provides a guided inquiry approach through collaborative exploration, concept formation, and application where students learn algebraic concepts and their meaning in real-world contexts.
The publication focuses on fewer concepts, mainly linear, exponential, and quadratic functions, but treat them conceptually, in more depth, and interconnected for better retention.
The movie Groundhog Day is a good metaphor for our book’s concept. Each day the lead character wakes up on the same day, Groundhog Day, repeating the same routine while struggling with a situation. He starts to predict what is going to happen each day, he learns a little bit more, and gets closer to solving the problem. By the end he understands what he needs to do.
Readers are taken through a similar experience. Each section starts with a launch exploration based on the common threads of the same routine: when given a situation, they identify the variables, make tables, draw graphs, search for patterns, and write equations.
Introduction
0 Math Foundations in a Nutshell
0.1 Fundamental Arithmetic: The Integers
Launch Exploration: Grouping and Regrouping
Numeration
Addition of Counting Numbers
Subtraction
Multiplication
Division
Number Zero
Order of Operations
Distributivity of Multiplication over Addition
Wrapping Up
Exercises
0.2 Fundamental Arithmetic: The Rationals
Mental Math
Divisibility of Numbers
Launch Exploration: Part of a Whole
Ordinary Fractions
Adding and Subtracting Fractions
Fraction Multiplication
Division by Fractions
Decimal Fractions
Rounding
Percent
Wrapping Up
Exercises
0.3 Elementary Algebra: Expressions and Equations
Launch Exploration: Find the ’Heap’
Ratios and Proportions
Powers and Radicals
Intro to Algebraic Expressions
Intro to Algebraic Equations
Wrapping Up
Exercises
0.4 Elementary Geometry: Shapes and Measures
Launch Exploration: Perimeter and Area
Primitive Notions
Angles and Circles
Parallel Lines
Triangles
Rectangles and Parallelograms
Perimeter versus Area
Volumes
Wrapping Up
Exercises
1 Quantitative Analysis, Problem Solving, and Functions
1.1 Quantitative Analysis: Constants and Variables
Launch Exploration: Shopping and Fencing
Analyzing a Situation: Quantities and Units
Analyzing a Situation: Constants and Variables
Values of a Variable – Discussion
Wrapping Up
Exercises
1.2 Algebraic Relations: Translations and Formulas
Launch Exploration: Building a Patio
Operations and Relations - Key Phrases
Quantitative Relations in Situations
Units Agreement
Wrapping Up
Exercises
1.3 Problem Solving with Linear and Power Systems
Launch Exploration: Building a Deck
Solving Linear Systems by Substitution
Linear Systems - More Examples
Power Equation – A Basic Example of a Nonlinear Equation
Mapping Diagrams
Power Systems
Critical Thinking
Wrapping Up
Exercises
1.4 Introduction to Modeling with Functions
Launch Exploration: Buying Protein Bars
Function Notation - How to Write About Functions
Real-World Domain and Range
Graphs - How to Visualize Functions
Analyzing a Graph
The Initial Value of a Function
What is a Function?
Function Equations
Wrapping Up
Exercises
2 Linear Functions
2.1 Introduction to Linear Relationships
Launch Exploration: Growing Plants
Linear Function Tables
Another Plant Example
Constant Rate of Change
Linear Function Equations
Positive and Negative Rates of Change
Wrapping Up
Exercises
2.2 Analyzing Linear Functions
Launch Exploration: Linear Graphs
Analyzing Linear Graphs
Writing Linear Function Equations from Graphs
Writing Linear Function Equations from Tables
Comparing Slopes
Wrapping Up
Exercises
2.3 Linear Modeling
Launch Exploration: Window Washers
Creating and Using Linear Models
More Linear Modeling
Wrapping Up
Exercises
3 Exponential Functions
3.1 A New Pattern - Introduction to Exponential Functions
Launch Exploration: Growing Bacteria
Exponential Function Tables
Exponential Function Equations
Exponential Growth versus Decay
Writing Equations from Two Data Points
Wrapping Up
Exercises
3.2 Analyzing Exponential Functions
Launch Exploration: Graphing an Exponential
Domain and Range for Exponentials
Zoom In and Out on Exponential Graphs
Asymptotes and Intercepts
An Exponential Decay Example
Comparing Exponential Graphs
Solving Exponential Equations with Logarithms
Analyzing Exponential Functions in Context
Writing Equations from Exponential Graphs
Wrapping Up
Exercises
3.3 Problem Solving with Exponentials
Launch Exploration: A Growing Colony
Relative Rate of Change
Relative Rate of Growth
Relative Rate of Decay
Relative Rates in Equations
Exponential Modeling
Linear versus Exponential
Wrapping Up
Exercises
4 Quadratic Functions
4.1 Problem Solving with Quadratic Equations
Launch Exploration: A Room with a Given Area
The Quadratic Formula
Creating and Using Quadratic Equations
The Number of Real Solutions
Special Cases of Quadratic Problems
Wrapping Up
Exercises
4.2 Another New Pattern - Intro to Quadratic Functions
Launch Exploration: A Square Garden
Quadratic Function Equations
Quadratic Function Tables
Quadratic Function Graphs
Why Are Parabolas So Special?
Not All U-Shapes Are Parabolas!
Writing Quadratic Function Equations from Tables
Wrapping Up
Exercises
4.3 Finding Features of Parabolas Algebraically
Launch Exploration: Analyzing Parabolas
Symmetry and Vertex
Direction
The Vertex Formula
Intercepts
Finding All the Features of a Parabola
Wrapping Up
Exercises
4.4 Analyzing Quadratic Functions
Launch Exploration: A Projectile Motion Graph
Throwing a Ball on the Moon
The Profit of Kandy-n-Kakes
Maximizing Area Inside a Fence
Wrapping Up
Exercises
Index
If you are tired by the usual turgid textbooks on introductory algebra, you have found the antidote - an excellent teaching tool, with successive topics following in seamless flow; this material is visually pleasing, uncluttered and inviting, well grounded in a narrative mode. Anton and Santoro’s accomplishment in offering a rigorous, yet engaging introductory manual, is salutary.
Mircea Pitici, PhD, the editor of "The Best Writings on Mathematics" series by Princeton University Press