Preparation for College Mathematics Second Edition

Preparation for College Mathematics coverThe new edition of Preparation for College Mathematics now covers even more intermediate-level algebraic topics and increases focus on application, conceptual understanding, and the development of the academic mindset. Request an examination copy.

The goal of this newly enhanced title is to develop holistic learners who are adequately prepared for subsequent, higher-level math courses on their path to college success.

View a free sample of the new edition of Preparation for College Mathematics.

 


NEW features include:

  • Strategies for Academic Success – study skills and learning strategies build stronger learners with tips on note taking, time management, test taking, and more
  • Chapter Projects – discovery-based projects promote collaboration and practical applications of mathematics
  • Concept Checks – exercise sets assess students’ conceptual understanding of topics before each practice set
  • Applications – exercise sets for each section challenge students to apply topics learned to real-world contexts
  • Extra Material – more advanced topics cover all learning outcomes to prepare students for future college math courses
  • Writing & Thinking – opportunities for students to independently explore and expand on chapter concepts

 


Table of Contents:

1. Whole Numbers

Introduction to Whole Numbers
Addition and Subtraction with Whole Numbers
Multiplication with Whole Numbers
Division with Whole Numbers
Rounding and Estimating with Whole Numbers
Problem Solving with Whole Numbers
Solving Equations with Whole Numbers (x + b = c and ax = c)
Exponents and Order of Operations
Tests for Divisibility
Prime Numbers and Prime Factorizations

2. Integers

Introduction to Integers
Addition with Integers
Subtraction with Integers
Multiplication, Division, and Order of Operations with Integers
Simplifying and Evaluating Expressions
Translating English Phrases and Algebraic Expressions
Solving Equations with Integers (ax + b = c)

3. Fractions, Mixed Numbers, and Proportions

Introduction to Fractions and Mixed Numbers
Multiplication with Fractions
Division with Fractions
Multiplication and Division with Mixed Numbers
Least Common Multiple (LCM)
Addition and Subtraction with Fractions
Addition and Subtraction with Mixed Numbers
Comparisons and Order of Operations with Fractions
Solving Equations with Fractions
Ratios and Rates
Proportions
Probability

4. Decimal Numbers

Introduction to Decimal Numbers
Addition and Subtraction with Decimal Numbers
Multiplication and Division with Decimal Numbers
Estimating and Order of Operations with Decimal Numbers
Statistics: Mean, Median, Mode, and Range
Decimal Numbers and Fractions
Solving Equations with Decimal Numbers

5. Percents

Basics of Percent
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations
Applications of Percent
Simple and Compound Interest
Reading Graphs

6. Measurement and Geometry

US Measurements
The Metric System: Length and Area
The Metric System: Weight and Volume
US and Metric Equivalents
Angles and Triangles
Perimeter
Area
Volume and Surface Area
Similar and Congruent Triangles
Square Roots and the Pythagorean Theorem

7. Solving Linear Equations and Inequalities

Properties of Real Numbers
Solving Linear Equations: x + b = c and ax = c
Solving Linear Equations: ax + b = c
Solving Linear Equations: ax + b = cx + d
Working with Formulas
Applications: Number Problems and Consecutive Integers
Applications: Distance-Rate-Time, Interest, Average, and Cost
Solving Linear Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities

8. Graphing Linear Equations and Inequalities

The Cartesian Coordinate System
Graphing Linear Equations in Two Variables
Slope-Intercept Form
Point-Slope Form
Introduction to Functions and Function Notation
Graphing Linear Inequalities in Two Variables

9. Systems of Linear Equations

Systems of Linear Equations: Solutions by Graphing
Systems of Linear Equations: Solutions by Substitution
Systems of Linear Equations: Solutions by Addition
Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
Applications: Interest and Mixture
Systems of Linear Equations: Three Variables
Matrices and Gaussian Elimination
Systems of Linear Inequalities

10. Exponents and Polynomials

Rules for Exponents
Power Rules for Exponents
Applications: Scientific Notation
Introduction to Polynomials
Addition and Subtraction with Polynomials
Multiplication with Polynomials
Special Products of Binomials
Division with Polynomials
Synthetic Division and the Remainder Theorem

11. Factoring Polynomials

Greatest Common Factor (GCF) and Factoring by Grouping
Factoring Trinomials: x^2+bx+c
Factoring Trinomials: ax^2+bx+c
Special Factoring Techniques
Review of Factoring Techniques
Solving Quadratic Equations by Factoring
Applications: Quadratic Equations

12. Rational Expressions

Introduction to Rational Expressions
Multiplication and Division with Rational Expressions
Least Common Multiple of Polynomials
Addition and Subtraction with Rational Expressions
Simplifying Complex Fractions
Solving Rational Equations
Applications: Rational Expressions
Applications: Variation

13. Roots, Radicals, and Complex Numbers

Evaluating Radicals
Rational Exponents
Simplifying Radicals
Addition, Subtraction, and Multiplication with Radicals
Rationalizing Denominators
Solving Radical Equations
Functions with Radicals
Introduction to Complex Numbers
Multiplication and Division with Complex Numbers

14. Quadratic Equations

Quadratic Equations: The Square Root Method
Quadratic Equations: Completing the Square
Quadratic Equations: The Quadratic Formula
More Applications of Quadratic Equations
Equations in Quadratic Form
Graphing Quadratic Functions
More on Graphing Functions and Applications
Solving Polynomial and Rational Inequalities

15. Exponential and Logarithmic Functions

Algebra of Functions
Composition of Functions and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Common Logarithms and Natural Logarithms
Logarithmic and Exponential Equations and Change-of-Base
Applications: Exponential and Logarithmic Functions

16. Conic Sections

Translations and Reflections
Parabolas as Conic Sections
Distance Formula, Midpoint Formula, and Circles
Ellipses and Hyperbolas
Nonlinear Systems of Equations

Request an examination copy.

Want to learn more? Contact us at sales@hawkeslearning.com!

Missouri Math Pathways Initiative and Hawkes Learning

Below is information about the Hawkes materials regarding the new Missouri Math Pathways Initiative. We know this is an incredibly important topic of conversation across the state, and our goal is to deliver a curriculum uniquely designed to better prepare students for college-level math in Missouri.

New Missouri Pathways:

Pathway Corresponding Hawkes Text
Mathematical Reasoning and Modeling Viewing Life Mathematically
Precalculus Algebra Precalculus
Precalculus Precalculus
Statistical Reasoning Beginning Statistics
Pathway Corresponding Hawkes Text as a Corequisite
Mathematical Reasoning and Modeling Viewing Life Mathematically Plus Integrated Review
Precalculus Algebra College Algebra Plus Integrated Review
Precalculus Precalculus
Statistical Reasoning Beginning Statistics Plus Integrated Review

Hawkes Courseware

Hawkes courseware ensures students achieve mastery of course content through multimedia-rich lessons, unlimited practice problems with intelligent tutoring, and competency-based Certify assignments.

Chapter projects, simulations, and real-world games promote collaboration and show students the practical side of mathematics through activities using real-world applications of concepts taught. Offerings include new corequisite-ready courses that integrate foundational skills necessary for success in curriculum content.

Check out these two quick videos to learn more:

Mastery Learning:

Explain Error:


Quick Links

Request a review copy here.

Sign up for a demonstration of the accompanying courseware here.

Instructor advice on motivating students

Having trouble motivating your students to stay active and engaged in class? We understand that some days, it can be a struggle. Current and former instructors here at Hawkes Learning have provided advice on how to keep students motivated. Check it out below, then let us know what advice YOU have!

In-class

  • Consider announcing a 3-point bonus question before your first test, and make it a scavenger hunt. Ask for three things (one point each): 1. What is written on your office door? (This encourages students to find your office.) 2. What is one name of a tutor in the tutoring lab? (This encourages them to find the tutoring lab.) 3. What are the hours for the tutoring lab? (This knowledge helps them if they need to schedule an appointment.)
  • Take attendance. Even if attendance isn’t part of the grade, it shows students that you’re aware whether or not they come to class and participate.
  • Get students to speak. A few will always take the lead and constantly ask questions, while some will never open their mouths. Directly ask those students a question. Hearing their voice and knowing it’s being heard has a positive effect and can lead them to speak up without being prompted later on.

Online

  • Post discussions and message boards. Since you can’t talk face-to-face, the next best thing is to utilize these communications threads.
  • Remind students that they never stop learning because technology changes so often. Use the online environment to your advantage by showing students new communications tools and apps that they can adapt to and learn from.
  • Hold virtual office hours for students who have questions or need a little extra help.

Math

  • Have a large class? Consider the “shared birthday” problem. A class of 30 students has over a 70% chance of having at least one shared birthday among them. A class of 40 students has almost 90%. If you happen to have one or more shared birthdays in the class, they never forget it and it gets them interested from the start.
  • Collect noninvasive data from your class to use throughout the semester. Asking at the beginning of the term for information like students’ majors, favorite sport, and number of siblings gives you data to incorporate in your lessons that will keep students interested.
  • Math courses have historically had a stigma for math anxiety for some students. Be reassuring and encouraging to your students, and provide opportunities for success that will help supply confidence and a positive momentum through the course.

English

  • Give students options! Anytime students can decide on an element of their learning, they get more invested in the outcome. Let them choose a project partner, reading selection, or project option.
  • Allow students to revise and resubmit assignments based on your feedback to improve their grades and strengthen their learning.
  • Put students in the role of instructor. Assign them a reading passage that they are responsible for teaching to part or all of the class. Teaching is the best way to learn a new concept!

Have more tips? We’d love to hear them! Comment below with your tried and true tips on keeping students motivated and engaged.

Apply mathematical concepts to other fields

Sometimes, getting students excited about math isn’t easy. Nearly every math instructor has heard “When will I use this in real life?” at least once during their teaching career. Many students don’t see right away that they use math just about every day, and you can lose their interest in the subject if you don’t connect your course objectives to their lives outside of class. Thankfully, math applies to more fields than most students realize. Here are just a few ways to connect mathematical concepts to other areas and to get students more motivated to learn.

1. Create art with math.

Not all students see how subjects in STEM connect with the liberal arts. Some people mistakenly think the fields are separate and never the two shall meet. One great way to get rid of this misconception is to show how art can be created by using math. Creative Bloq shows eight examples of beautiful fractal art with suggestions on programs to use in order to create your own fractal masterpieces, such as Mandelbulb 3D and FraxHD.

The co-author of our Single Variable Calculus with Early Transcendentals textbook, Dr. Paul Sisson, used to incorporate art into his math classes when he taught at Louisiana State University – Shreveport. He encouraged students to use software to track complex numbers’ behaviors and create images to which students could assign different colors. Learn more from Math in the Media here.

2. Show students how to be fiscally responsible.

Chances are you have some students who don’t know much about personal finance beyond having a checking and savings account. Teaching them about budgeting, loans, interest, and more will benefit them now and in all the years to come. Students can start with concepts such as calculating tip and figuring out how much money they save when they buy discounted items before moving on to long-term financial decisions, such as putting a down payment on a house and paying a mortgage.

This post from Annenberg Learner summarizes the basics of simple and compound interest that you can incorporate into your class.

3. Calculate sports statistics.

Have students who want to be professional athletes, coaches, sports announcers, agents or just die-hard fans of the game? They’ll benefit from learning how much math goes into any sport. Everything from calculating batting averages in baseball to knowing touchdowns per pass attempt in football to determining the probability of winning a point in tennis can connect the concepts learned in class to some students’ favorite extracurricular activities. Plus, fantasy sports are especially popular, so you may even consider having your class join a fantasy league and see who wins!

Fantasy Sports and Mathematics is a website that includes the latest scores and injuries lists for various sports and sample math problems to use in class. This NYT blog post lists out ways to use sports analytics to teach math and includes additional resources ranging from a video demonstrating what it’s like to return a serve in professional tennis to a graphic showing how often football teams go for the fourth down.

4. Delve into the history of mathematics.

Students gain a deeper appreciation of the subject when they know who’s behind all those theories, formulas, and discoveries. Plus, they just might connect with the subject more when they know that people from similar demographics advanced the field.

A Buzzle article introduces readers to several achievements of African American mathematicians, ranging from those in the 18th century like Benjamin Banneker to the present day like Dr. William A. Massey.

This Smithsonian.com post highlights five influential female mathematicians throughout history, including Ada Lovelace and Emmy Noether. It gives a little background into these women’s lives, explains their accomplishments, and kicks the blatantly false stereotype that women aren’t good at math to the curb!

5. Have students write about how they think they’ll use math in their future careers.

Are your students still not feeling connected with the course content? Dedicate some class time to brainstorming how they’ll use math in the careers they’re planning to pursue. While at first some may assume they won’t use math at all in their chosen professions, they might surprise themselves once they think a little harder and dig deeper into a job’s tasks and expectations. They may want to interview someone in their field via email or phone to get an insider’s perspective into the kind of math skills needed to excel in the workplace.

On the blog Math for Grownups, author Laura Laing interviewed several professionals—including writers, academic advisors, and artists—asking them how they use math in their jobs. Her books Math for Grownups and Math for Writers delve into more detail on these topics and encourage folks who are hesitant about math or think they’re bad at it to rethink their perspective.


What are some lessons you’ve taught that encouraged students to apply math to other subjects and think outside the box? Let us know in the comments!

Updates to questions in select math products!

We’ve updated the default curriculum to include new questions just in time for the spring term. The updated questions provide a more uniform level of difficulty to give the overall lesson more consistency. Most do not require a calculator for your students to complete. In many cases, these questions cover lesson topics more comprehensively than before.

*Please note that these new questions are only available to students using the web platform at learn.hawkeslearning.com.*

To see the new questions, please log into your Assignment Builder to view your curriculum. These questions are marked as new and are always located at the very bottom of the lesson so that they’re easy to identify:

Here is a list of the new questions and where to find them:

  • Developmental Mathematics
    • Lesson 2.2
      • Questions 45-50
    • Lesson 2.3
      • Questions 10-16
  • Prealgebra and Introductory Algebra
    • Lesson 2.4
      • Questions 21-27
    • Lesson 2.6
      • Questions 18-21
  • Beginning Statistics Plus Integrated Review
    • Lesson 4.R.1
      • Questions 45-50
    • Lesson 4.R.2
      • Questions 10-16
  • Viewing Life Mathematically Plus Integrated Review
    • Lesson 7.R.1
      • Questions 45-50
    • Lesson 7.R.2
      • Questions 10-16
  • Developmental Math – North Carolina Curriculum
    • Lesson 2.2
      • Questions 21-27
    • Lesson 2.4
      • Questions 44-50
  • Foundations of Mathematics for Virginia
    • Lesson 1.4
      • Questions 45-50
    • Lesson 3.3
      • Based on instructor feedback, we’ve added one question on the topic of estimating square roots and replaced a few questions with new, more refined problem cases

 


If you have any questions about these updates, please contact your Training and Support Specialist or call 1-800-426-9538.

What did the NAEP discover about U.S. high school seniors?

According to the National Assessment of Educational Progress (NAEP), high school seniors in the United States haven’t improved their reading skills, and their math skills have declined since 2013.

Emma Brown reports, “Eighty-two percent of high school seniors graduated on time in 2014, but the 2015 test results suggest that just 37 percent of seniors are academically prepared for college course­work in math and reading — meaning many seniors would have to take remedial classes if going on to college.”

Read the original Washington Post article here or below.

Brown, Emma. “U.S. high school seniors slip in math and show no improvement in reading.” The Washington Post. The Washington Post, 27 April 2016. Web. 27 April 2016.