5: Appendix A - Pre-Skills
- Page ID
- 216648
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 5.1: Whole Numbers
- Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is modeled and explained. As each operation is covered, discussions of algebraic notation and operation signs, translation of algebraic expressions into word phrases, and the use the operation in applications are included.
- 5.2: Integers
- While introducing the basic operations with negative numbers, students continue to practice simplifying, evaluating, and translating algebraic expressions. The Division Property of Equality is introduced and used to solve one-step equations.
- 5.2.1: Introduction to Integers
- 5.2.2: Introduction to Integers (continued)
- 5.2.3: Add Integers
- 5.2.4: Subtract Integers
- 5.2.5: Multiply and Divide Integers
- 5.2.6: Solve Equations Using Integers; The Division Property of Equality
- 5.2.7: Chapter Review
- 5.2.7.1: Key Terms
- 5.2.7.2: Key Concepts
- 5.2.8: Exercises
- 5.2.8.1: Review Exercises
- 5.2.8.2: Practice Test
- 5.3: Fractions
- Fraction circles and bars are used to help make fractions real and to develop operations on them. Students continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication Property of Equality to solve equations involving fractions.
- 5.3.1: Introduction to Fractions
- 5.3.2: Visualize Fractions
- 5.3.3: Multiply and Divide Fractions
- 5.3.4: Multiply and Divide Mixed Numbers and Complex Fractions
- 5.3.5: Add and Subtract Fractions with Common Denominators
- 5.3.6: Add and Subtract Fractions with Different Denominators
- 5.3.7: Add and Subtract Mixed Numbers
- 5.3.8: Solve Equations with Fractions
- 5.3.9: Chapter Review
- 5.3.9.1: Key Terms
- 5.3.9.2: Key Concepts
- 5.3.10: Exercises
- 5.3.10.1: Review Exercises
- 5.3.10.2: Practice Test
- 5.4: Decimals
- Basic operations with decimals are presented, as well as methods for converting fractions to decimals and vice versa. Averages and probability, unit rates and unit prices, and square roots are included to provide opportunities to use and round decimals.
- 5.4.1: Introduction to Decimals
- 5.4.2: Decimals
- 5.4.3: Decimal Notation and Place Value
- 5.4.4: Decimal Operations
- 5.4.5: Decimals and Fractions
- 5.4.6: Solve Equations with Decimals
- 5.4.7: Averages and Probability
- 5.4.8: Simplify and Use Square Roots
- 5.4.9: Chapter Review
- 5.4.9.1: Key Terms
- 5.4.9.2: Key Concepts
- 5.4.10: Exercises
- 5.4.10.1: Review Exercises
- 5.4.10.2: Practice Test
- 5.5: Percents
- Conversions among percents, fractions, and decimals are explored. Applications of percent include calculating sales tax, commission, and simple interest. Proportions and solving percent equations as proportions are addressed as well.
- 5.6: Percent, Decimals, and Fractions
- So, when you hear the word “percent,” think “parts per hundred.”
- 5.7: The Properties of Real Numbers
- The properties of real numbers are introduced and applied as a culmination of the work done thus far, and to prepare students for the upcoming chapters on equations, polynomials, and graphing.
- 5.7.1: Introduction to the Properties of Real Numbers
- 5.7.2: Rational and Irrational Numbers
- 5.7.3: Commutative and Associative Properties
- 5.7.4: Distributive Property
- 5.7.5: Properties of Identity, Inverses, and Zero
- 5.7.6: Systems of Measurement
- 5.7.7: Chapter Review
- 5.7.7.1: Key Terms
- 5.7.7.2: Key Concepts
- 5.7.8: Exercises
- 5.7.8.1: Review Exercises
- 5.7.8.2: Practice Test
- 5.8: Introduction to the Language of Algebra
- Mathematical vocabulary as it applies to the whole numbers is presented. The use of variables, which distinguishes algebra from arithmetic, is introduced early in the chapter, and the development of and practice with arithmetic concepts use variables as well as numeric expressions. In addition, the difference between expressions and equations is discussed, word problems are introduced, and the process for solving one-step equations is modeled.
- 5.8.1: Introduction to the Language of Algebra
- 5.8.2: Use the Language of Algebra
- 5.8.3: Evaluate, Simplify, and Translate Expressions
- 5.8.4: Solving Equations Using the Subtraction and Addition Properties of Equality
- 5.8.5: Find Multiples and Factors
- 5.8.6: Prime Factorization and the Least Common Multiple
- 5.8.7: Chapter Review
- 5.8.7.1: Key Terms
- 5.8.7.2: Key Concepts
- 5.8.8: Exercises
- 5.8.8.1: Review Exercises
- 5.8.8.2: Practice Test
- 5.9: Ratios and Rate
- A ratio compares two numbers or two quantities that are measured with the same unit. When a ratio is written in fraction form, the fraction should be simplified. To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units. A rate compares two quantities of different units. A rate is usually written as a fraction.
- 5.10: Solving Linear Equations
- A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with constants on both sides, variables on both sides, variables and constants on both sides, and fraction and decimal coefficients.
- 5.10.1: Introduction to Solving Linear Equations
- 5.10.2: Solve Equations Using the Subtraction and Addition Properties of Equality
- 5.10.3: Solve Equations Using the Division and Multiplication Properties of Equality
- 5.10.4: Solve Equations with Variables and Constants on Both Sides)
- 5.10.5: Solve Equations with Fraction or Decimal Coefficients
- 5.10.6: Chapter Review
- 5.10.6.1: Key Terms
- 5.10.6.2: Key Concepts
- 5.10.7: Exercises
- 5.10.7.1: Review Exercises
- 5.10.7.2: Practice Test
- 5.11: Math Models and Geometry
- The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean Theorem, and volumes and surface areas of solids. Distance-rate-time problems and formulas are included as well.
- 5.11.1: Introduction
- 5.11.2: Use a Problem Solving Strategy
- 5.11.3: Solve Money Applications
- 5.11.4: Use Properties of Angles, Triangles, and the Pythagorean Theorem
- 5.11.5: Use Properties of Rectangles, Triangles, and Trapezoids
- 5.11.6: Solve Geometry Applications- Circles and Irregular Figures
- 5.11.7: Solve Geometry Applications- Volume and Surface Area
- 5.11.8: Solve a Formula for a Specific Variable
- 5.11.9: Chapter Review
- 5.11.9.1: Key Terms
- 5.11.9.2: Key Concepts
- 5.11.10: Exercises
- 5.11.10.1: Review Exercises
- 5.11.10.2: Practice Test
- 5.12: Graphs
- This chapter is placed last so that all of the algebra with one variable is completed before working with linear equations in two variables. Examples progress from plotting points to graphing lines by making a table of solutions to an equation. Properties of vertical and horizontal lines and intercepts are included. Graphing linear equations at the end of the course gives students a good opportunity to review evaluating expressions and solving equations.
- 5.12.1: Introduction to Graphs
- 5.12.2: Use the Rectangular Coordinate System
- 5.12.3: Cartesian Coordinate System
- 5.12.4: Graphing Linear Equations
- 5.12.5: Graphing with Intercepts
- 5.12.6: Understand Slope of a Line
- 5.12.7: Graphing Functions Review before Modeling
- 5.12.7.1: Graphing Functions Exercises
- 5.12.8: Chapter Review
- 5.12.8.1: Key Terms
- 5.12.8.2: Key Concepts
- 5.12.9: Exercises
- 5.12.9.1: Review Exercises
- 5.12.9.2: Practice Test


