# Mathematics Standards and Course Descriptions

# Coronado Middle School Courses

## Mathematics

### 6th Grade

#### Standards: Teaching and Learning Objectives

In Grade 6, instructional time will focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

#### The focus within the four critical areas will include the following:

**Ratios and Proportional Relationships**

- Understand ratio concepts and use ratio reasoning to solve problems.

**The Number System**

- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- Multiply and divide multi-digit numbers and find common factors and multiples.
- Apply and extend previous understandings of numbers to the system of rational numbers.

**Expressions and Equations**

- Apply and extend previous understandings of arithmetic to algebraic expressions.
- Reason about and solve one-variable equations and inequalities.
- Represent and analyze quantitative relationships between dependent and independent variables.

**Geometry**

- Solve real-world and mathematical problems involving area, surface area, and volume.

**Statistics and Probability**

- Develop understanding of statistical variability.
- Summarize and describe distributions.

**Mathematical Practices**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

#### Course Descriptions

**Math 6A**

This class is a comprehensive examination of the entire math 6 standards and half of the 7th grade standards covers and a variety of topics at an accelerated pace with a focus on problem solving. Students in this course demonstrate a passion for math, are cognitively and developmentally mature to handle the rigor of math concepts at a high level, and are critical, independent thinkers in the area of mathematics. Students who successfully complete this course and show a mastery of all standards in Math 6 are typically recommended for Math 7A the next year.

**Math 6**This class is an examination of the Math 6 standards. The focus of this class is based on connecting ratio and rate to whole number multiplication and division, and using concepts of ratio and rate to solve problems, completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers, writing, interpreting, and using expressions and equations, and developing understanding of statistical thinking. Students who successfully complete this course and show mastery of the standards are typically recommended for the Math 7 the next school year. This Math 6 class is a challenging class for many due to the nature of the work involved.

### 7th Grade

#### Standards: Teaching and Learning Objectives

In Grade 7, instructional time will focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

#### The focus within the four critical areas will include the following:

**Ratios and Proportional Relationships**

- Analyze proportional relationships and use them to solve real-world and mathematical problems.

**The Number System**

- Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

**Expressions and Equations**

- Use properties of operations to generate equivalent expressions.
- Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

**Geometry**

- Draw, construct and describe geometrical figures and describe the relationships between them.
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

**Statistics and Probability**

- Use random sampling to draw inferences about a population.
- Draw informal comparative inferences about two populations.
- Investigate chance processes and develop, use, and evaluate probability models.

**Mathematical Practices**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

#### Course Descriptions

**Math 7A**

This class is a comprehensive examination of the entire math 7 standards and covers half of the 8th grade standards and a variety of topics at an accelerated pace with a focus on developing understanding of and applying proportional relationships, developing understanding of operations with rational numbers and working with expressions and linear equations, solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and drawing inferences about populations based on samples. Students in this course demonstrate a passion for math, are cognitively and developmentally mature to handle the rigor of math concepts at a high level, and are critical, independent thinkers in the area of mathematics. Students who successfully complete this course and show a mastery of all standards in Math 7 are typically recommended for Algebra 1A the next year.

**Math 7**This class is an examination of the Math 7 standards. The focus of this class is based on developing understanding of and applying proportional relationships, developing understanding of operations with rational numbers and working with expressions and linear equations, solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and drawing inferences about populations based on samples. Students who successfully complete this course and show mastery of the standards are typically recommended for the Algebra 1 or Math 8 the next school year. Math 7 is a challenging class for many due to the nature of the work involved.

### 8th Grade

#### Standards: Teaching and Learning Objectives

In Grade 8, instructional time will focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

#### The focus within the four critical areas will include the following:

**The Number System**

- Know that there are numbers that are not rational, and approximate them by rational numbers.

**Expressions and Equations**

- Work with radicals and integer exponents.
- Understand the connections between proportional relationships, lines, and linear equations.
- Analyze and solve linear equations and pairs of simultaneous linear equations.

**Functions**

- Define, evaluate, and compare functions.
- Use functions to model relationships between quantities.

**Geometry**

- Understand congruence and similarity using physical models, transparencies, or geometry software.
- Understand and apply the Pythagorean Theorem.
- Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

**Statistics and Probability**

- Investigate patterns of association in bivariate data.

**Mathematical Practices**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

#### Course Descriptions

**Geometry**This is a college preparatory course designed to provide a strong base for advanced study in mathematics. Major topics include: geometric reasoning, geometric constructions, lines and polygons, congruence, circles, area, the Pythagorean Theorem, volume, similarity, trigonometry, and geometric proof. The first quarter of Algebra II topics will be studied. Students who complete this course with an 85% or better are expected to advance to Algebra II Honors

**Algebra 1**

This class is a comprehensive examination of the Algebra 1 standards and covers a variety of topics at an accelerated pace with a focus on word problems and application of concepts. Content will be focused on real numbers, linear equations, polynomials, factoring, ratios, proportions, systems of linear equations, functions, inequalities, rational and irrational numbers, quadratic functions, and statistics. Students who successfully complete this course and show a mastery of all standards are typically recommended for Geometry Honors or Geometry the next year. Algebra 1A is a California graduation requirement.

**Math 8**

This course prepares students for a full year of Algebra 1 in high school. This class includes all of the California Common Core Math 8 standards including; formulating and reasoning about expressions and equations, modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations, grasping the concept of a function and using functions to describe quantitative relationships, analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.