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.
• 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 an 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 numbers, 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 the 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.
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.
• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean theorem.
• Solve real-world and mathematical problems involving the 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 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 the 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 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 the 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 Math 2 class. Students must Master both Accelerated courses in order to earn 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 the 7th-grade year. These courses 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.
The Social Studies curriculum is designed for students to accomplish multiple objectives. Students will learn major concepts and themes from the following curriculum areas including History, Geography, Economics, and Government. Throughout the year, they will continue to develop and implement thinking, writing, reading, and listening skills within a social studies context. Through the social studies curriculum, students will continue to develop and apply skills in information gathering, organization, discussion, and presentation. In addition, students will be guided in the understanding of concepts and how to apply them to real-life situations. This content area helps students learn about the origination of values and how attitudes and values influence our actions and the actions of others. Students learn how to integrate concepts and factual information through inductive and deductive reasoning. Analyzing, synthesizing, and problem-solving are major objectives of the social studies program.
7th Grade World Geography/Ancient History
Students in the seventh grade Social Studies explore world events occurring between 1000 BCE and AD 1750. We will be examing the enduring impact of the early civilizations of Central & South America, West Africa, Greece, and Rome. The class will be analyzing the effects of geography, economics, religion, and governmental structures on human interaction. There are also many skills and methods social scientists use that will be introduced and practiced throughout the year.
Ancient World History continues our students' study of ancient world history and continues up through the early European exploration of North America. Comparative methods are used using contemporary events as a way for students to determine the meaning of our subject.
8th Grade American History
8th-grade social studies covers American History and the United States Government from colonization in the late 16th century to Reconstruction after the Civil War. This is the first sequence of American History that will be completed in the 10th-grade year with Reconstruction to the Present. The course of study contains the topics of colonization, independence, forming a new government, new challenges, expansion, industrialization, and the cause and effects of the Civil War.
Besides historical content, we will focus on the common core, citizenship, cause and effect relationships, opinion and fact, interpretation of resources, problem-solving, presentation skills, quality of work, and analyzing skills. Although content builds on past historical knowledge, our focus will be to look deeper at the origins of our country today.