Math - Grade Level Descriptions
Course Description
Sixth graders complete a year of dynamic College Preparatory Math (CPM) curriculum, rooted in the real world. Pre-algebra skills are developed, refined, and extended. CPM’s unique presentation encourages students to use Five Ways of Thinking – Comparing, Visualizing, Describing and Explaining, Multiple Ways of Seeing, and Sense Making. Through exploration, discussion, and practice, students gain an understanding of the mathematical reasoning behind core concepts. The goal is that a sense of fun will be preserved and a sense of wonder will be fostered in sixth-grade math.
Units of Study:
Chapter 1: Introduction and Representation
Section 1.1 Course Introduction Problems
Section 1.2 Representations
Section 1.3 Data Collection and Analysis
Chapter 2: Length and Integers
Section 2.1 Introduction to Length
Section 2.2 Introduction to Integer Operations
Section 2.3 Order of Operations
Section 2.4 Introduction to Variables
Chapter 3: Arithmetic Strategies and Area
Section 3.1 Place Value
Section 3.2 Area
Section 3.3 Multiplication and Area
Section 3.4 More Integer Operations
Chapter 4: Data and Portions
Section 4.1 Coordinate Graphing
Section 4.2 More Data Analysis
Section 4.3 Multiple Representations of Portions
Chapter 5: Geometry and Probability
Section 5.1 Characteristics of Shapes
Section 5.2 Introduction to Probability
Chapter 6: Similarity, Multiplying Fractions, and Equivalence
Section 6.1 Enlarging and Reducing Figures
Section 6.2 Multiplying Fractions
Section 6.3 Equivalent Fractions & Ratios
Chapter 7: Volume, Adding and Subtracting Fractions and Decimals
Section 7.1 Volume and Surface Area
Section 7.2 Adding Fractions and Decimals
Section 7.3 Adding Mixed Numbers
Chapter 8: Describing Quantities with Variables and Dividing Fractions
Section 8.1 Describing Patterns
Section 8.2 Writing Expressions with Variables
Section 8.3 Using Variables in Other Contexts
Section 8.4 Dividing Fractions
Chapter 9: Percent Applications, Proportions and Geometry
Section 9.1 Percent Applications
Section 9.2 Proportions
Section 9.3 Area and Volume
Chapter 10: Probability and Sampling
Section 10.1 Probability
Section 10.2 Sampling and Bias
Course Description
Seventh grade completes a Pre-Algebra curriculum, College Preparatory Math, Making Connections. The curriculum asks the students to use the following five ways of thinking as they explore mathematics: justifying, generalizing, making connections, reverse thinking, and applying and extending understanding. The course focuses on problem solving and on allowing students to discover generalizations and mathematical principles from student explorations. This curriculum guides the students toward understanding the reasons behind the math. Students do a combination of independent practice and group investigations.
Units of Study:
Chapter 1: Probability and Proportions
Chapter 2: Transformations and Area
Chapter 3: Building Expressions
Chapter 4: Proportional Reasoning and Statistics
Chapter 5: Inequalities and Descriptive Geometry
Chapter 6: Graphing and Solving Equations
Chapter 7: Slopes and Rates of Change
Chapter 8: Percents and More Solving Equations
Chapter 9: Proportions and Pythagorean Theorem
Chapter 10: Interest, Exponents, and Non-Linear Growth
Chapter 11: Three-Dimensional Measurement and Probability
Course Description
Eighth grade completes a comprehensive Algebra I curriculum using, Algebra Connections, a College Preparatory Math text. The approach of this curriculum is for students to use the following five ways of thinking as they explore mathematics: justifying, generalizing, making connections, reversing thinking, and applying and extending understanding. Students are asked to think in order to problem solve, not just memorize algorithms. This curriculum guides the students toward understanding the reasons behind the math. Students do a combination of independent practice and group investigations.
Units of Study:
The eighth grade completes Algebra Connections by Dietiker, Kysh, Sallee, Hoey, a College Preparatory Math text. The students begin Volume I in seventh grade and complete the entire book by June of eighth grade.
Volume I
Chapter 4: Multiple Representations
Students investigate the connections between the four representations of data: graphs, tables, patterns, and equations. They explore situations that can be represented linearly and learn to use y=mx+b to graph a line quickly. In addition, they begin to solve systems of equations both graphically and algebraically.
Chapter 5: Multiplication and Proportions
Students learn to multiply binomials and trinomials, solve multi-variable equations for one of the variables, and write and solve equations with equivalent ratios to solve problems involving proportional relationships.
Chapter 6: Systems of Equations
Students will solve contextual word problems by writing and solving equations. They will recognize systems of equations that have no solution or infinite solutions. Students learn multiple methods to solve a system of equations.
Volume II
Chapter 7: Linear Relationships
Students will build on their study of linear growth to develop an understanding of slope geometrically and as a measurement of steepness. Students will develop an algorithm to find the equation of a line given any two pieces of information: the slope and y-intercept, the slope and a point on the line, or two points on the line.
Chapter 8: Quadratics
Students will learn how to factor quadratic and simple cubic equations. They will solve quadratic equations using factoring, the Zero Product Property, and the Quadratic Formula. They will recognize how the solutions to a quadratic equation connect to the graph of a parabola. Students will apply this knowledge to physical problems, such as the motion of an object under the force of gravity.
Chapter 9: Inequalities
Students will solve and graph linear inequalities. They will solve systems of linear inequalities with two variables and will sketch the solution sets. Additionally, absolute value is introduced in several situations.
Chapter 10: Simplifying and Solving
Students will learn how to simplify rational expressions and use this knowledge to solve equations with complicated fractions. They will examine three methods for solving equations: looking inside (parentheses, square roots, absolute values, etc.), undoing the operation, and rewriting (distributing, simplifying, etc.).
Chapter 11: Functions and Relations
Students will determine whether a relation defines a function and the domain and range of that function. Students will be able to determine the difference between intercepts and intersections will identify the possible number of intersections between two relations.
Chapter 12: Algebraic Extensions
The final chapter revisits and expands on many of the core subjects of the course. Students are provided with the opportunity to pull together their knowledge from the entire course in order to solve challenging and meaningful problems.
