Math III - Chapter by Chapter - Summaries

Chapter 1

Students begin the year reviewing variables, variable expressions, and integers. They extend their understanding of the order of operations by performing operations with integers. They also develop inductive reasoning skills using visual patterns and number patterns. The chapter ends with graphing integers in the coordinate plane.

Chapter 2

Students review properties of numbers and how to use them to solve equations. They use their equation solving skills to solve real-world problems and extend their skills to solving inequalities.

Chapter 3

Students use a variety of strategies to estimate decimal sums, differences, products, and quotients to evaluate when calculated answers are reasonable. They apply their decimal computation skills to real-life applications, such as finding measures of central tendency and using formulas. Students solve one-step equations that include decimals.

Chapter 4

Students use number theory to understand and work with rational numbers. They also simplify expressions using properties of exponents. The chapter concludes with a connection to scientific notation, which pulls together many of the concepts of the chapter and shows their particular applications.  

Chapter 5

In their study of fractions, students continue using estimates to determine when calculated answers are reasonable. Students further their understanding of algebra by solving equations containing fractions. They extend their study of numbers to include powers of products and quotients.

Chapter 6

Students learn to use proportional reasoning to solve real world problems, including ones involving indirect measurement, and mark up and discount. They use ratios to understand probability. Throughout the chapter, the interrelationship of fractions, decimals, and percents is emphasized.

Chapter 7

Students extend their equation solving skills to two- and multi-step equations, including solving equations with variables on both sides. They apply their skills to two-step inequalities and transforming formulas. Students end the chapter applying their skills from Chapter Six and Seven to find simple and compound interest.

Chapter 8

Students identify mathematical patterns and use their algebra skills to write rules for the patterns. Based on their understanding of patterns, they represent functions using tables, rules, and graphs. They graph linear equations and inequalities and extend their graphing skills to help solve systems of linear equations and inequalities.

Chapter 9

Students develop spatial thinking and apply their knowledge of geometry to the real-world. Students use logical reasoning to explain the relationships among figures, including pair of angles, congruent triangles, and types of polygons. In the final lessons of the chapter, students focus on the connection between congruence and transformations in the coordinate plane.

Chapter 10

Students begin the chapter with the study of area of two-dimensional figures. Then students apply this knowledge to find surface area of solid figures. They extend their use of formulas to include volume. Students apply algebraic reasoning and formulas to solve real-world problems involving solid figures, and they explore how changing the dimensions of a figure affects its surface area and volume.

Chapter 11

Students extend their knowledge of real numbers to include irrational numbers. They use their knowledge in a variety of geometric contexts through a rich source of applications of the Pythagorean Theorem. The concluding lessons introduce students to Trigonometry.

Chapter 12

Students learn about visual representations of relationships by interpreting and creating data displays. They further their understanding of data analysis by studying theoretical and experimental probability. They apply probability concepts to real-world situations using simulations.

Chapter 13

Students build on their knowledge of the coordinate plane by graphing nonlinear functions. They extend their algebra skills to include adding and subtracting polynomials, multiplying polynomials by monomials, and multiplying binomials.