 # Mathematics

## Middle School

Using National Sciences Foundation rationale, our middle school mathematics curriculum makes important real life connections to math and science applications beyond the classroom. Students learn the importance of mathematics in various careers and understand the interdisciplinary connections between mathematics they are studying and the arts, sciences, and even history and language arts through the cross-curricular connections that are made throughout the year. Whether a student is beginning middle school mathematics, working in a regular Algebra or Geometry class or taking honors classes, mathematics courses help him learn to think logically, critically, and analytically while preparing for the rigors of the advanced mathematics courses of high school.

All middle school mathematics courses meet or exceed the Common Core State Standards for Mathematics (CCSSM). The CCSSM consists of two sets of standards, the Standards for Mathematical Practice and the Standards for Mathematical Content. The Standards for Mathematical Practice describe the process, practices, and dispositions of mathematicians. These eight Standards for Mathematical Practice are the same across all grade levels, K-12 to emphasize that students are developing these processes, practices, and dispositions throughout their school career. The Standards for Mathematical practice are shown below.

1. Make sense of mathematics and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

The Standards for Mathematical Content outline the concepts and skills that are important at each grade level. For example, at grade 6, these standards focus on these areas:

• Ratios and Proportional Relationships.
• The Number System.
• Expressions and Equations
• Geometry
• Statistics and Probability.

One big difference between the CA Mathematical standards and the CCSSM mathematical content is that CCSSM contain fewer standards and fewer topics to study at each grade level. WIth fewer topics, you can spend more time on concepts and achieve greater mastery of these concepts.

To assure our mathematics courses build on student learning, all incoming students take a computer based mathematics placement test and are placed in an appropriate course to assure success in either regular or accelerated classes. Individualized placement assures all students will have an excellent foundation for high school mathematics. (See our course descriptions and prerequisites for additional information.)

Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and enhance the curriculum. On-line technology such as video tutors and practice tests and additional practices are also made available.

## CCS Math 6

(Common Core State Standards for Mathematics – Grade 6)

Mathematics is a powerful tool with far-reaching applications in daily life. In this class, you will learn that mathematics is all around us. Building mathematical skills and an understanding of concepts is an ongoing process. Connection to real life application is made to areas like entertainment, nutrition, economics, and even recreation such as model airplanes and physical fitness and sports. The importance of mathematics in careers such as engineering, wildlife statisticians, architecture and other areas are also studied.

This is a 1 year mathematics course to prepare students for CCS Math 7. Topics covered are listed below.

• Number Properties and Decimals: Orders of operations with whole numbers and decimals
• Expressions and Equations: Writing algebraic expressions and solving one step equations.
• Number Theory: Prime factorization, GCF and LCM.
• Fractions: Multiplying and dividing proper/improper and mixed fractions.
• Ratios and Percents: Unit rates and equivalent fractions. Converting percents, fractions, and decimals.
• Integers and Rational Numbers: Comparing and ordering integers and solving one step inequalities.
• Coordinate Planes: Graphing points and polygons on the coordinate planes.
• Geometry and Measurement: Areas, volume and surface areas of various polygons.
• Data and Graphs: Mean, median, mode, box and whisker plots, frequency tables and histograms.

Technology such as the Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and to enhance the curriculum. On-line technology such as video tutor and practice tests are also made available. Test taking strategies and test prep is also covered in this class.

## CCS Math 7

(Common Core State Standards for Mathematics – Grade 7)
Prerequisite: Grade of “C” or better in CCS Math 6.

Mathematics is a powerful tool with far-reaching applications in daily life. In this class, you will learn that mathematics is all around us. Building mathematical skills and an understanding of concepts is an ongoing process. Connection to real life application is made to areas like entertainment, nutrition, economics, and even recreation such as model airplanes and physical fitness and sports. The importance of mathematics in careers such as engineering, wildlife statisticians, architecture and other areas are also studied.

This is a 1 year mathematics course to prepare students for CCS Math 8. Topics covered are listed below.

• Integers and Rational Numbers: Comparing and ordering integers, fractions/decimals and rational numbers.
• Equations: Simplifying algebra expressions, solving one step and two step equations
• Inequalities: Graphing and solving one step and two step inequalities.
• Ratios, Rates, and Proportions: Similar figures, using proportions, nit rates and scale drawings.
• Percents: Solving percent proportions and equations, interest rates and percent of change.
• Geometry and Area: Angle measures, areas of polygons, circles and composite figures.
• Surface Area and Volume: Three dimensional figures.
• Probability: Theoretical and experimental probability of multiple and compound events.

Technology such as the Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and to enhance the curriculum. On-line technology such as video tutor and practice tests are also made available. Test taking strategies and test prep is also covered in this class.

## CCS Math 8

(Common Core State Standards for Mathematics – Grade 8)
Prerequisite: Grade of “C” or better in CCS Math 7.

Mathematics is a powerful tool with far-reaching applications in daily life. In this class, you will learn that mathematics is all around us. Building mathematical skills and an understanding of concepts is an ongoing process. Connection to real life application is made to areas like entertainment, nutrition, economics, and even recreation such as model airplanes and physical fitness and sports. The importance of mathematics in careers such as engineering, wildlife statisticians, architecture and other areas are also studied.

This is a 1 year mathematics course to prepare students for CCS Algebra 1. Topics covered are listed below.

• Real Numbers and the Coordinate Plane: Square roots, irrational numbers and Pythagorean theorem.
• Solving Linear Equations: Simplifying algebra expressions, solving multi-step equations.
• Introduction to Functions: Linear and non linear functions.
• Graphing Functions: Graphing linear functions and slope.
• Systems of Linear Equations: Solving systems of equations by graphing/substitution/elimination.
• Exponents: Multiplying scientific notation and exponents.
• An Introduction to Geometry: Congruent figures, parallel lines and proving similar figures.
• Transformation: Translation/reflection/rotation/dilation of points and figures.
• Geometry and Measurement: Volumes of prisms, cylinders, pyramids, cones, spheres.
• Data Analysis: Scatter plots and trend lines.

Technology such as the Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and to enhance the curriculum. On-line technology such as video tutor and practice tests are also made available. Test taking strategies and test prep is also covered in this class.

## CCS Algebra 1

(Common Core State Standards for Mathematics – Algebra 1)
Prerequisite: Grade of “C” or better in CCS Math 8
Note: Meets graduation requirement for Algebra.

This class is designed to help students learn algebra and see how it connects to the real world. There are many opportunities to make connections from concrete models to abstract concepts. Career guidance and real examples of how mathematics is used in many types of careers is also studied. We work through problems in zoology and finance and even make interdisciplinary connections to earth science, biology and physics. This class prepares students for proficiency examinations such as the SAT/ACT and the CAHSEE. Throughout the year students will see the practical value of algebra and see how it relates directly to a students life.

This is a 1 year mathematics course to prepare students for Geometry. Algebra is an advanced mathematics course for students who are college bound. Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Topics covered are listed below.

• Solving multi-step equations, rates, ratios proportions and unit conversions.
• Solving and graphing multi-step inequalities, compound and absolute value inequalities.
• Linear and nonlinear functions, arithmetic sequences and relations, slopes, equations of various lines.
• Solving systems of equations and inequalities using substitution and elimination, graphing systems.
• Exponents and exponential functions, zero and negative exponents, rational exponents and radicals.
• Factoring and solving quadratic functions and equations.
• Simplifying and solving radical expressions and equations, Pythagorean theorem and trig ratios.
• Data analysis and probability, using matrices, central tendencies and dispersions, theoretical and experimental probability and compound events.

Technology such as the Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and to enhance the curriculum. On-line technology such as practice tests and additional practices are also made available.

## CCS Geometry

(Common Core State Standards for Mathematics – Geometry)
Prerequisite: Grade of “C” or better in CCS Algebra 1
Note: Meets graduation requirement for Geometry

This class is designed to help students learn geometry and see how it connects to the real world. There are many opportunities to make connections from concrete models to abstract concepts. Career guidance and real examples of how mathematics is used in many types of careers is also studied. We work through problems in zoology and finance and even make interdisciplinary connections to earth science, biology and physics. This class prepares students for proficiency examinations such as the SAT/ACT and the CAHSEE. Throughout the year students will see the practical value of Geometry and see how it relates directly to a students life.

This is a 1 year mathematics course to prepare students for Algebra 2. Geometry is an advanced mathematics course for students who are college bound. Symbolic reasoning and thinking mathematically are central in Geometry. Through the study of Geometry, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, geometric skills and concepts are developed and used in a wide variety of problem-solving situations. Topics covered are listed below.

• Understanding points, lines and planes and angles.
• Pattens and inductive reasoning and conditional statements.
• Proving lines parallel and perpendicular, constructing parallel and perpendicular lines.
• Proving congruent triangles by SSS, SAS, ASA, AAS and CPCC, congruence in right triangles.
• Midsegments, perpendicular and angle bisector in triangles, medians and altitudes.
• Polygons and quadrilaterals, various parallelograms, trapezoids and proofs in coordinate geometry.
• Proving similar triangles, ratios, proportions and proportions in triangles.
• Pythagorean theorem and its converse, laws of sines and cosines, special right triangles.
• Translation, reflections, rotation, dilation transformation.
• Areas of polygons, circles, and sectors, perimeters and areas of similar figures and geometric probability.
• Surface area and volumes of solid figures and spheres.
• Tangent lines, chords and arcs, inscribed angles and segment lengths.
• Experimental and theoretical probability, compound models and permutations and combinations.

Technology such as the Apple Ipads are used to promote mastery over foundational math skills and to reinforce concepts and to enhance the curriculum. On-line technology such as practice tests and additional practices are also made available.

CCS Middle School – (pdf)

CCS ECDS Roadmap for Mathematics – (pdf)