## Mathematics

#### Middle School

Mathematics is the universal language. It allows us to make sense of the natural world—to observe, quantify, analyze, make connections, and solve problems in every field of study. The ability to comprehend, develop, and utilize mathematical concepts is invaluable throughout life; all global citizens need strong fluency in this area. This is best done by learning to draw reasonable conclusions from information found in various sources. Whether from observation, words, data, or graphs, students use the tools of mathematics to analyze information and become adept at problem solving (course descriptions follow).

Students are encouraged to welcome new challenges, question and justify their conjectures and solutions, test the reasonableness of solutions, develop facility and understanding of mathematical operations and procedures, and use them appropriately to make sense of the world.

The Middle School math program is unleveled in the sixth grade. One day a week is designated for extension or review, individualized for the students. Seventh and eighth grade math classes will be leveled; levels will be determined by student demonstration of knowledge and teacher recommendation. Students have the opportunity to complete two full years of algebra.

#### Math 6

In the problem-centered math 6 curriculum, students employ the inquiry approach to learn new concepts. The purpose of this format is to begin the exploration of rigorous math in a real world context. Students become contributors to what is learned in class by posing and exploring their own questions. They are encouraged to think critically and share their results and conjectures as they collaborate with their classmates. They develop the ability to ask effective questions, assess their own work, and learn communication and presentation skills. These skills become the foundation of their future development in all levels of mathematics.

This course develops students’ mathematical reasoning as they explore problems dealing with factors and multiples; the distributive property; comparisons with ratios, rates, and percentages; arithmetic operations with fractions; the basics of perimeter and area - extending to surface area and volume using triangles and parallelograms; computations and operations involving decimals and percentages; analyzing and relating tables, graphs, variables, expressions, equations, and inequalities; organizing, representing, describing and analyzing data; and lastly, measuring variability.

#### Pre-Algebra 7

This course continues the exploration approach to develop understanding of the following concepts: shapes and designs using families of polygons, designing polygons, triangles and quadrilaterals; extending knowledge of the number system to operations with rational numbers and the properties of these real number operations; stretching and shrinking shapes, scaling perimeter and area, and solving problems involving similar figures; comparing rates, ratios, percentages and proportions; walking rates, exploring linear relationships using graphs, tables and equations, exploring slope and connecting rates and ratios; conjecturing about chance, testing with experimental probability, making decisions based on theoretical probability, binomial outcomes and analyzing compound events; building and learning properties of rectangular prisms, quantifying area and circumference of circles, volume and surface area of cylinders, cones and spheres; and making sense of variability and samples, and solving real world population problems.

#### Pre-Algebra 8

This course will continue the inquiry approach to develop understanding of the following topics: data patterns, linear models and equations, inverse variation, variability and associations in numerical and categorical data and coordinate grids; analyzing triangles and circles using the Pythagorean Theorem; exploring exponential growth and decay, exponential functions, and patterns of exponents; transformations using coordinates, congruence, dilations and similar figures; making sense of symbols using expressions, functions and solving equations; and solving systems of two variables, linear systems, systems of functions and inequalities.

#### Algebra 1A

Algebra is the foundation of all of the subsequent mathematics courses. It is a problem-solving tool for modeling real world occurrences - both symbolically and graphically. “Owning” algebra is the key to successful understanding and navigation of future courses like geometry, trigonometry, calculus and higher math, and thus lays the groundwork for study in science, economics, medicine, computers, and many other fields, including those which have yet to be imagined. Students develop conceptual understanding and technical facility with algebraic procedures to support their continued study of mathematics.

This course begins the study of algebra—the abstract modeling of the real world. In this course, students build the foundation for higher math through the following work: reviewing operations of real numbers, expressions and variables; solving equations and inequalities; understanding ratios, rates, percentages, proportions, and similar figures while solving problems; working with sets, unions and intersections; recognizing patterns and understanding the concept of functions; studying, modeling and graphing linear functions and developing trend lines; and solving systems of linear functions and inequalities.

#### Algebra 1B

This course continues the study of algebra. Students review real numbers, functions, linear functions, and solving equations. They develop facility by delving deep into the following skills: working with integral, zero, negative and rational exponents, and exponential functions; solving problems involving exponential growth and decay; operating with polynomials and factoring; recognizing and graphing quadratic functions and solving quadratic equations by factoring, completing the square, and the quadratic formula; solving systems of linear and quadratic functions; simplifying radicals and operations with radical expressions, graphing square root functions, and solving radical equations; simplifying rational expressions and solving rational equations; solving problems involving direct and inverse variation; organizing and analyzing data using matrices, statistical graphs, measures of central tendency and dispersion; and exploring probability, permutations and combinations.