# Math

## Sixth Grade

*Math Course 1*

This course explores concepts in addition, subtraction, multiplication, and division of whole numbers, decimals, and fractions. In addition, topics of ratio, proportion, percents, basic geometry, probability, and statistics are explored using various types of graphs. On a daily basis, students in 6th Grade use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. The course emphasis helps students to develop multiple strategies to solve problems and to recognize the connections between concepts through cooperative learning. This is the introduction to the Common Core Math in the middle school. We use the College Preparatory Math Series (CPM).

## Seventh Grade

**Math Course 2**

Core Connections, Course 2 is the second of a three-year sequence of courses designed to prepare students for a rigorous college preparatory algebra course. It uses a problem-based approach with concrete models. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course meet all of the content standards and embed the “Mathematical Practices” of the Common Core State Standards released in June 2010.

Upon completion of this course, students should be able to:

- Model integers and operations with integers and rational numbers including using order of operations.
- Use linear models and equal ratios to represent part-whole relationships.
- Use percents and scale factors to determine percent increase or decrease, discounts and markups.
- Simplify variable expressions by combining like terms and using the Distributive Property.
- Solve linear equations including those with fractional coefficients and those with no solutions or infinite solutions.
- Solve and graph one-variable inequalities.
- Compare experimental and theoretical probabilities.
- Distinguish between dependent and independent events and calculate the probability of compound independent events.
- Represent probabilities of multiple events using systemic lists, charts, or tree diagrams.
- Design, conduct and analyze surveys.
- Collect and compare data and describe the distribution of sets of data.
- Solve distance, rate and time problems.
- Compare ratios and calculate unit rates.
- Recognize and solve problems involving proportional relationships.
- Recognize and use the properties of similar shapes and scale factors to solve problems.
- Describe angles, angle pairs and their measures.
- Compute area and perimeter of standard and compound shapes.
- Compute the volume of a variety of solids.

## Eighth Grade

**Math Course 3**

Core Connections, Course 3 is the third of a three-year sequence of courses designed to prepare students for a rigorous college preparatory algebra course. It uses a problem-based approach with concrete models. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course meet all of the content standards and embed the “Mathematical Practices” of the Common Core State Standards released in June 2010.

Upon completion of this course, students should be able to:

- Represent a linear function with a graph, table, rule, and context and should be able to find any representation when provided one of the others
- Solve systems of equations represented in tables and graphs.
- Symbolically manipulate expressions in order to solve problems including those with fractional coefficients.
- Solve contextual word problems using multiple strategies, including making tables, looking for patterns, drawing diagrams, and creating a table of guesses to assist with writing and solving a variable equation.
- Describe various transformations on a coordinate grid.
- Represent data using scatterplots and describe associations.
- Collect and analyze data and make predictions based on the trend of the data.
- Compare ratios, calculate unit rates and slope ratios.
- Analyze the slope of a line graphically, numerically, and contextually.
- Recognize and solve problems involving proportional relationships.
- Graph and analyze non-linear functions.
- Recognize and use the properties of similar shapes to solve problems.
- Use the Pythagorean Theorem and its converse to solve problems in 2 and 3 dimensions.
- Use square and cube roots.
- Represent and simplify expressions using positive and negative exponents.
- Represent and compare large and small numbers using standard and scientific notation.
- Perform operations with numbers represented in scientific notation.
- Use the relationships between angles created by parallel lines with transversals and the triangle sum theorem to solve problems.
- Compute the volume of a variety of solids.

**Math 1 - Algebra**

*Math 1: Core Connections Algebra* is the first course in a five-year sequence of college preparatory mathematics courses that starts with Algebra 1 and continues through Calculus. It aims to deepen and extend student understanding built in previous courses by focusing on developing fluency with solving linear equations, inequalities, and systems. These skills are extended to solving quadratic equations, exploring linear, quadratic, and exponential functions graphically, numerically, symbolically, and as sequences, and by using regression techniques to analyze the fit of models to distributions of data.

On a daily basis, students in *Core Connections Algebra *use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas.

The course is well balanced among procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and application). The lessons in the course meet all of the content standards of Appendix A of the *Common Core State Standards for Mathematics*. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.

Key concepts addressed in this course are:

- Represent linear, quadratic, and exponential relationships using graphs, tables, equations, and contexts.
- Symbolic manipulation of expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc.
- Analysis of the slope of a line multiple ways, including graphically, numerically, contextually (as a rate of change), and algebraically.
- Solving equations and inequalities using a variety of strategies, including rewriting (such as factoring, distributing, or completing the square), undoing (such as extracting the square root or subtracting a term from both sides of an equation), and looking inside (such as determining the possible values of the argument of an absolute value expression).
- Solving systems of two equations and inequalities with two variables using a variety of strategies, both graphically and algebraically.
- Representations of arithmetic and geometric sequences, including tables, graphs, and explicit or recursive formulas.
- Use of exponential models to solve problems, and to compare to linear models.
- Investigation of a variety of functions including square root, cube root, absolute value, piecewise-defined, step, and simple inverse functions.
- Use of function notation.
- Statistical analysis of two-variable data, including determining regression lines, correlation coefficients, and creating residual plots.
- The differences between association and causation, and interpretation of correlation of context.
- Comparison of distributions of one-variable data.