Middle School Curriculum Guide

Mathematics

The Middle School mathematics program serves as a bridge between the heterogeneous groupings of the Lower School and the multiple levels of subject instruction of the Upper School. In each class, teachers provide students with opportunities to communicate mathematically through participation in discussions and problem solving sessions, and work progresses at a pace designed so that all students can learn at a comfortable rate and find success. Technology enhances every class, with SMARTBoards, iPads, Desmos software for graphing, and laptops providing students with various methods of acquiring mathematical knowledge and discovering its applications. The Middle School program strives to develop a solid foundation in mathematics and a lifelong love for learning. As a result, students develop a curiosity about the mathematical world around them. Teachers evaluate student progress and adjust the program as necessary. In addition to traditional forms of assessment, teachers evaluate involvement, creativity, and eagerness for mental challenge.

MIDDLE SCHOOL MATHEMATICS DEPARTMENT COURSE BYPASS POLICY

Mathematics skills build sequentially upon each other, and the mathematics courses offered at RCDS are designed to span an academic year so that students can fully develop those skills alongside their peers. The Mathematics Department does not consider it necessary for students to bypass any course in order to excel in math.

There are rare times, however, when a student is prepared and chooses to focus intensively on a course and is able to develop the skills covered in a math course over a condensed period of time in order to bypass a year-long mathematics course in RCDS’s sequence. Bypassing a course in RCDS’s mathematics sequence can only be done with the approval of the Department, and courses can only be bypassed at the Honors level. Students may not bypass a course before sixth grade or beyond Algebra 2/Trigonometry.

Students wishing to be considered for a possible move ahead must complete the Bypass Form before the end of the current school year. The form (available from the Mathematics Department) must include the proposed summer course work/tutoring plans. The form will be reviewed by the Department, and a decision to approve or not will be shared by the end of the school year.

If the student’s request is approved, the student is responsible for completing the summer work by mid-August. The student will then be required to take a placement test at RCDS on a mutually agreed upon date in mid to late August. The student must pass the appropriate placement test with a grade of 90% or better in order to bypass the course and demonstrate preparedness to enter the successive honors level math course. Placement tests will not be given prior to the mid-August date, and students may only take the placement test once.

If the student does not pass the placement test at the Honors level, then the student will continue to be enrolled in the course that the student was assigned during course selection.

FIFTH-GRADE MATHEMATICS

The fifth-grade Mathematics program is a continuation of Singapore Math, the program used in the Lower School. Students work to master computation with whole numbers, fractions, and decimals, and improve their understanding of number sense, place value, estimation, fractional equivalents, and percents. Throughout each unit, importance is placed on acquiring problem solving strategies through independent and group work. Students strive to develop organizational skills and appropriate study habits. Quizzes and tests, as well as class performance and participation, are used to assess students.

By the end of the year, fifth-grade students should demonstrate reasonable mastery of the following:

basic whole number skills and operations
computation of fractions and decimals
fraction/decimal/percent equivalents
percent of a quantity
perimeter and area of rectangles
geometry, including measurement of angles, classifying triangles and quadrilaterals, and sum of angles of triangles and quadrilaterals.

SIXTH-GRADE MATHEMATICS

Sixth-grade Mathematics focuses on student mastery of computation skills while introducing complex problem solving and pre-algebra concepts. Various study skills applicable to math are presented throughout the year, and the production of organized and accurate solutions is emphasized. Problem solving strategies are discussed within each unit as students examine a wide variety of word problems. Students should demonstrate reasonable mastery of the following topics by the end of the year:

number theory and decimals
fractions
integers
pre-algebra topics including expressions and equations
percents, ratios, and proportions
business math - discount, sales tax, etc.
geometry
measurement.

SEVENTH-GRADE MATHEMATICS

Math in the seventh grade is offered in three distinct levels: Pre-Algebra, Advanced Pre-Algebra, and Honors Pre-Algebra. Students are enrolled in the class that will allow them to sharpen their mathematical skills and proceed comfortably onto the next level of mathematics, with a degree of challenge that is suitable to the level.

Pre-Algebra

The central objectives of Pre-Algebra are to build upon the student's comprehension of basic mathematical concepts, introduce fundamental concepts of algebra, and deliver the curriculum at a pace that allows each student the time to comprehend and process the material. Building each student's foundation of knowledge is a major point of emphasis, as is increasing each student's confidence in his/her mathematical abilities. While the bulk of the curriculum centers around topics that students have seen previously, new topics are also introduced.

Advanced Pre-Algebra

The central objectives of Advanced Pre-Algebra are to continue the study of arithmetic in a theoretical framework, to develop more sophisticated techniques in problem solving, and to introduce the fundamental concepts of algebra. Throughout the course of the year, students build upon their mathematical foundation and develop their algebraic skills so that they are prepared to move into Algebra I in eighth grade. Students also are expected to demonstrate academic independence and require limited teacher support.

Honors Pre-Algebra

The central objective of the Honors Pre-Algebra course is to learn techniques for solving various types of problems that encourage students to discover solutions to problems. The students in the Honors program will move more quickly through the material and will be responsible for understanding by using basic algebraic concepts and skills. By the end of the year, Honors students should master problems based on arithmetic, and algebra, with considerable emphasis on word problems.

In all of the classes, seventh-grade students are expected to demonstrate reasonable mastery of the following concepts:

word problems involving algebra, percents, and geometry
operations with integers and real numbers
simplification and evaluation of algebraic expressions
solutions of linear equations
solutions and graphing of multistep inequalities
operations with monomials and polynomials
basic forms of factoring with algebraic expressions
perimeter, area, volume, and surface area.

EIGHTH-GRADE MATHEMATICS

Math in the eighth grade is offered in three distinct levels: Introduction to Algebra 1, Advanced Algebra 1, and Honors Algebra 1. Students are enrolled in the class that will allow them to sharpen their mathematical skills and proceed comfortably onto the next level of mathematics, with a degree of challenge that is suitable to the level.

Introduction to Algebra 1

Students in the Introduction to Algebra 1 level will cover a traditional Algebra 1 curriculum, which builds on the skills the student acquired in Pre-Algebra. The emphasis will be on developing students’ ability to work with integers and variables and to enhance their critical thinking skills. Upon completion of this course, students may enter Geometry or Advanced Geometry. For some students, retaking Algebra 1 will be the best option.

Advanced Algebra 1

The Advanced Algebra 1 course is the completion of the Algebra1 program begun in the seventh grade, through quadratic functions. The text offers exposure to all of the concepts and operations involved in any Algebra 1 course. This course is not as theoretical in nature as the Honors course but does give students a solid understanding of Algebra 1 and a strong foundation on which to build. Students must be highly motivated and have strong mathematical skills. At the end of the eighth-grade year, the students will have completed a full Algebra 1 course and may enter Geometry at the advanced level.

Honors Algebra 1

The Honors Algebra 1 course is the completion of the Algebra 1 course begun in Honors Pre-Algebra. The text offers a thorough and challenging exploration of the concepts and operations involved in a demanding Algebra 1 course. This course requires technical skill and speed, analytical facility, independence, and sharp reading skills. The pace is fast-moving and requires strong ability and motivation on the part of the student. At the end of the year, students will have completed a rigorous Honors Algebra 1 program, and those who are ready will enter the Honors program in Geometry in Grade 9. By the end of the eighth grade, students are expected to demonstrate reasonable mastery of the following topics:

various number properties and axioms
solutions to both linear and quadratic equations
operations with integers
operations with rational and irrational numbers and expressions.
exponents
inequalities
operations with polynomials
factoring by all methods
graphing both linear and quadratic functions
systems of equations and inequalities.

In This Section

Useful Links

MS Curriculum