# Middle School Mathematics Courses

This is a comprehensive list of the courses available in the SPS Math Course Catalog. Please refer to the webpage Example of Math Progressions for more details on course progressions. Contact schools for specific course offerings.

Semester 1: Students complete understanding of dividing fractions; study the rational number system; and write, interpret, and use expressions and equations.

Semester 2: Students use concepts of ratio and rate to solve problems; develop understanding of statistical thinking; and reason about relationships among shapes to find area, surface area and volume of geometric figures.

**Additional Math 6 Courses**

Math 6-M: Teachers will provide modifications in the content to meet student IEP goals. Students with an LRE score of 80-100 and who qualify in mathematics can be enrolled in this course.

Mathematics 6A is the first semester of a year-long course. In this course, students review fraction and decimal operations. This is a foundation for understanding and using long division strategies for whole numbers and decimals, as well as understanding and using strategies to divide fractions by fractions. Students use these operations to solve problems. Students’ understanding of the number system is extended to include negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. Students understand the use of variables in mathematical expressions. They write numeric and algebraic expressions and equations that correspond to given situations, evaluate expressions using the order of operations and mathematical properties, and use expressions and formulas to solve problems. Students use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students write and solve simple inequalities. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.

Mathematics 6B is the second semester of a year-long course. In this course, students identify and extend ratio relationships in tables and graphs. Students understand unit rate as a special ratio comparing a quantity to one of another quantity. Students understand how unit rate can be used to compare ratio relationships. Students solve ratio and rate problems using multiplicative reasoning. Students solve a wide variety of problems involving ratios and rates. Students begin to think statistically by understanding what a statistical question is. They create and describe data distributions. Students compute mean and median and determine which is a better measure of center based on the shape of the data distribution. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students revisit ratio reasoning to understand percent as a ratio of one quantity to 100. Students solve problems involving percent of a whole. Students reasoning about and compute area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They find the volume of a right rectangular prism with fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

Semester 1: Students develop understanding of operations with rational numbers and proportional relationships; apply proportional relationships; and work with expressions.

Semester 2: Students work with linear equations and inequalities; solve problems involving scale drawings and informal geometric constructions; solve problems involving area, surface area and volume; and draw inferences about populations based on samples.

**Additional Math 7 Courses**

Math 7-M: Teachers will provide modifications in the content to meet student IEP goals. Students with an LRE score of 80-100 and who qualify in mathematics can be enrolled in this course.

MESA Math 7: This class was designed to group together underrepresented ethnic groups in the math, engineering and science fields in order to increase their achievement.

Mathematics 7A is the first semester of a year-long course. In this course, students develop an understanding of the rational number system, recognizing fractions, decimals and percents as different representations of rational numbers. Students build on previous understandings to learn how to operate on rational numbers. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions. They extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings.

Mathematics 7B is the second semester of a year-long course. In this course, students write and solve equations in one variable involving rational numbers and use these equations to solve problems. Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8, they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Students develop, use and evaluate probability models.

Math 7/8 Compacted A prepares 7th grade students to take Algebra 1 in 8th by compacting the content of Math 7 and Math 8 into one year. Students develop understanding of operations with rational numbers and proportional relationships; apply proportional relationships; work with irrational numbers, radicals and integer exponents; and work with expressions, linear equations and inequalities. Only open to 7th grade students.

Mathematics 7/8 Compacted A is the first semester of a year-long course. This course is only open to 7th grade students. In this course, students develop an understanding of the rational number system, recognizing fractions, decimals and percents as different representations of rational numbers. Students build on previous understandings to learn how to operate on rational numbers. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions, write, and solve equations in one variable involving rational numbers and use these equations to solve problems. Students grow their knowledge of the real number system in their work with rational and irrational numbers, radicals and integer exponents. They extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease.

Mathematics 7/8 Compacted B is the second semester of a year-long course. This course is only open to 7th grade students. Students use linear equations to represent, analyze, and solve a variety of problems. Students strategically choose and efficiently implement procedures to solve linear equations in one variable. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change. Students express a linear relationship between two quantities with an equation and interpret the meaning of the slope and y-intercept in terms of the situation. Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Students develop, use and evaluate probability models. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students solve real-world and mathematical problems involving surface-area and volume involving cones, cylinders, and spheres. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students solve problems about scale drawings.

Semester 1: Students will reason about expressions and equations, including modeling bivariate data and solving linear equations; use functions to describe quantitative relationships; and work with irrational numbers, radicals and integer exponents.

Semester 2: Students will solve systems of linear equations; understand and apply the Pythagorean Theorem; and analyze two- and three-dimensional space and figures.

**Additional Math 8 Courses**

Math 8-M: Teachers will provide modifications in the content to meet student IEP goals. Students with an LRE score of 80-100 and who qualify in mathematics can be enrolled in this course.

Mathematics 8A is the first semester of a year-long course. In this course, students grow their knowledge of the real number system in their work with rational and irrational numbers, radicals and integer exponents. Students use linear equations to represent, analyze, and solve a variety of problems. Students strategically choose and efficiently implement procedures to solve linear equations in one variable. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change. Students express a linear relationship between two quantities with an equation and interpret the meaning of the slope and y-intercept in terms of the situation. Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations of functions, and they describe how aspects of the function are reflected in the different representations (table, graph, equation). Students also use a linear equation to describe the association between two quantities in bivariate data. At this grade, fitting the model, and assessing its fit to the data are done informally.

Mathematics 8B is the second semester of a year-long course. In this course, students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines.

Semester 1: Students model and analyze real-world and mathematical situations using linear and exponential equations and functions.

Semester 2: Students model and analyze real-world and mathematical situations using linear, exponential, quadratic equations, inequalities and functions. Students will summarize, represent, and interpret single variable and bivariate categorical and quantitative data.

Students will receive high school credit on their transcript for this course.

Algebra 1A is the first semester of a year-long Algebra 1 course. In this course, students begin with simplifying expressions, solving linear and literal equations and justifying steps using mathematical properties. Next, students engage in a deeper analysis and formalization of functions in context. Students identify and describe function features such as domain and range, increasing and decreasing intervals, and discrete versus continuous. Students represent arithmetic sequences explicitly and recursively using function notation, then evaluate and interpret meaning of solutions within a context. Students build upon their prior knowledge of linear functions to model real-world situations using multiple representations and using multiple forms of linear equations. Students extend properties of exponents to rational exponents and use these properties to create equivalent expressions in both exponential and radical form. Students model and evaluate exponential growth and decay contexts (including geometric sequences) using multiple representations and fluently translate between representations. Students compare and contrast the properties of linear functions with exponential functions.

Algebra 1B is the second semester of a year-long Algebra 1 course. In this course, students model real life situations with quadratics functions using multiple representations and fluently translate between representations. Students manipulate quadratic functions by using algebraic properties to highlight key features, determine contextual information, and solve problems. Students graph quadratic functions to highlight key features. Students write and solve quadratic equations by factoring, completing the square, and using the quadratic formula. Students solve linear-linear, linear-exponential, and linear-quadratic systems of equations algebraically and graphically which model real-world situations. Students interpret their solution to a system in the context of the problem (which may include no solutions, one solution, two solutions, or infinite solutions). Students solve and graph one variable inequalities and graph two variable and systems of inequalities. Students write constraints and identify viable solutions for real-world problems using systems of linear inequalities. Students create a line of best fit given a scatter plot or data points. Students will be able to create an estimated line of best fit by hand and compute the least-squares line of best fit using technology. Students use technology to fit non‐linear curves to data. Students will create and interpret appropriate data displays and summary statistics of one-variable quantitative data.

Semester 1: Students formalize their understanding of angle relationships and triangle properties. Students use geometric transformations and formal constructions to study congruence and similarity. Students develop formal proofs of angle and triangle properties and relationships using precise language and notation.

Semester 2: Students establish properties of right triangles (including trigonometric ratios), quadrilaterals, and circles and use these properties to write formal proofs and solve real-world and mathematical problems. Students extend work with area and volume to investigate real-world modeling problems. Students further develop probability concepts, focusing on conditional probability, independence, and compound events.

Prerequisite: 1.0 Algebra 1 credit.

Geometry A is the first semester of a year-long Geometry course. In this course, students formalize vocabulary definitions and notation. Students write formal proofs of angle and line relationships and triangle properties established informally in prior courses. Students analyze parallel and perpendicular lines on the coordinate plane, establish the slope criteria for parallel and perpendicular lines, and use them to solve problems. Students use geometric tools to make formal constructions of common geometric figures. Students use constructions to explore geometric relationships, concepts, and theorems. Students formalize their understanding of rigid and non-rigid transformations. Students identify and perform transformations of geometric figures on the coordinate plane and in space utilizing construction skills. Students establish congruency of triangles through transformations and establish criteria for triangle congruence (ASA, SAS, SSS). Students write formal proofs to show triangle congruence. Students identify different types of triangles on the coordinate plane by calculating slopes, midpoints, and distances to determine the triangle’s properties. Students develop a formal definition of similarity and establish criteria that can be used to prove two triangles are similar. Students experiment with dilated shapes in space and on the coordinate plane, calculate and use scale factors and proportional relationships to solve for missing information, and apply the properties of similarity to solve real world problems and prove theorems about triangles.

Geometry B is the second semester of a year-long Geometry course. In this course, students use similarity to establish the trigonometric ratios for right triangles. Students solve real-world situations that can be modeled with right triangles using both the Pythagorean theorem and trigonometric ratios. Students formally prove the Pythagorean theorem using right triangle similarity and extend the Pythagorean theorem to the coordinate plane to develop the distance formula. Students establish and prove the characteristics and properties of special quadrilaterals and parallelograms both in space and on the coordinate plane. Students write formal proofs of quadrilateral properties. Students calculate the probability of single or compound events. Students identify independent and dependent events by calculating their conditional probabilities. Students calculate the probability of a union, intersection, or complements of events in order to make informed decisions. Students establish the geometric relationships among chords, arcs, angles, and lines that are within or intersecting with circles. Students construct the inscribed and circumscribed circle of a triangle. Students apply the definition of similarity and congruence based on transformations to prove all circles are similar. Students develop methods for computing areas and arc lengths of circles and establish the definition of radian measure. Students solve mathematical and modeling problems involving area and volume of two- and three-dimensional shapes.

An additional math class, taken concurrently with grade-level math designed to support student success in core math content.

This math course is designed for beginning-level, newly-immigrated English Language Learners of middle school age. The goals of the course are to develop basic English language proficiency, basic math content knowledge, and introduction to US school culture. Prerequisites: Middle school-aged newly immigrated English Language Learner.

ELD Math MS is designed for beginning-level, newly-immigrated English Language Learners of middle school age. The goals of the course are to develop basic English language proficiency, basic math content knowledge, and introduction to US school culture. Language development is focused on numbers, place value, whole number operations, fractions and fraction operations, decimals and decimal operations, integers, and geometric shapes and their properties. After this course, students may transition to a comprehensive middle school bilingual program.