# Math

There are a range of Math courses offered at Phoenix; Math 7, Accelerated Math 7, Math 8, Accelerated Math 8, HS Math 1 and HS Math 2. Student placement is based upon multiple criteria including: State/Local Test scores from 4th, 5th, and 6th grades, 6th grade teacher recommendations and evaluations, and the successful completion of prerequisite courses needed for placement in the Accelerated classes. The accelerated courses (7/8) take 3 years of math (7, 8, and HS Math 1) and condense that material into just 2 years of classroom experience. These classes, just as they are named, move through the material at a rigorous pace and a high level of student dedication is required for success.

**Mathematics | Grade 7**

**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.

**In Grade 7, instructional time will focus on four critical areas:**

**(1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems.**

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 by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. 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.

**(2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers.**

Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. 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 and equations in one variable and use these equations to solve problems.

**(3) 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.

**(4) 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.

**Mathematics | Grade 8**

**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.

**In Grade 8, instructional time will focus on three critical areas:**

**(1) Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems.**

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, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m•A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. 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.

**(2) 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 and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.

**(3) 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 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.

**Accelerated Math Offerings**

There is an option to take the Accelerated Math 7 class when you are entering Phoenix Middle School. This decision will be based on the suggestion of the 6th grade math teacher, test scores, student desire, and teacher discretion. If a student completes the Accelerated math 7 class, then they will automatically enter into Accelerated Math 8 during 8th Grade year. After completing BOTH years of accelerated courses, the student will have earned credit for the Math 7 class, Math 8 class, and the High School MATH 1 class. Upon entering High School, the student will go directly into the High School Math 2 class. Students must Master both Accelerated courses in order to earn the High School Credit.

HS Math 1 and HS Math 2 are offered at Phoenix in an effort to keep our students in the building all day. Placement in these classes is in sequence after successful completion of the Math 8 course either in Elementary school or during 7th grade year. These course are directly aligned to the graded course of study / CCSS for the Math 1/2 classes taught at the high school and successful completion of these courses provides the student with the HS credit for the class, but the grade in this class DOES NOT apply to the student’s eventual HS G.P.A.