Mathematics

Mathematics

The mathematics program in fifth and sixth grades provides a solid foundation in numbers and basic operations and introduces the students to graphing, number theory, probability, statistics, algebra, and geometry. Intensive instruction in algebra begins in seventh grade. Students learn to analyze data with the help of a graphing calculator and software applications such as Microsoft Excel and Geometer’s Sketchpad. The mathematics curriculum in the Middle School is designed to challenge the most intuitive students and to support the students who are less facile in their approach to the subject.

Mathematics – 5 

The 5th grade mathematics program is designed to reinforce basic skills acquired in the Lower School and to facilitate the application of these skills in solving more advanced mathematical equations with accuracy and confidence. Organized around a variety of problem settings, the TERC Investigations Curriculum encourages higher-level thinking and problem solving. Students solve problems while observing patterns and relationships. They conjecture, test, discuss, verbalize, and generalize about these relationships while making connections with the applications of mathematical ideas in the world outside of school. The text materials provide a range of learning experiences that encourage student progress in use of concepts, facts, skills, and problem solving. The program is organized in topic modules that move the student from concrete experiences to abstract understanding. Electronic media supplement and reinforce topics introduced in class. The Internet serves as a resource for projects, additional problems, and review activities.

The following topics are covered during the year:

1. Number theory: exponents, order of operations, divisibility rules, common factors, and common multiples.

2. Fractions: review of fraction concepts, mathematical operations with fractions, equivalent fractions, reducing to lowest terms, mixed numbers and improper fractions.

3. Decimals: decimal place value, mathematical operations using decimals, conversion from decimals to fractions and fractions to decimals.

4. Percentages: calculations with percentages, finding the percent of a number, conversions among fractions, decimals, and percentages.

5. Geometry: points, lines, rays, and planes; perimeter and area of polygons and circles.

6. Integers: mathematical operations of addition, subtraction, multiplication, and division with integers.

7. Data and statistics: creating and interpreting line graphs and bar graphs, calculating mean, median, mode, and range.

8. Concepts of algebra: use of variables, solving basic one- and two-step equations.

Texts:

TERC Investigations Curriculum, Grade 5

Prentice Hall, Mathematics – Course 1

Numerous supplementary materials

Mathematics – 6

The 6th grade mathematics curriculum reinforces and applies concepts and skills taught in 5th grade. In addition, students are familiarized with new concepts in geometry and develop their understanding of percentages by calculating percent change and analyzing real-world applications. An introduction to formal logic leads to a study of beginning algebraic skills and proofs. Electronic media supplement and reinforce topics introduced in class. The Internet serves as a resource for projects, additional problems, and review activities. Students participate in the Math Olympiad, which is a series of five competitions during the year. Each Olympiad competition consists of five challenging word problems.

The following topics are covered during the year:

1. Number theory: exponents, order of operations, properties of arithmetic, and applications of prime factorization.

2. Sets of numbers: operations with integers, fractions, and decimals.

3. Measurement and proportions: unit conversions and dimensional analysis; scientific notation; significant digits and calculations with precision; applications of unit rates.

4. Percentages: applications of percentages, including interest, tax, tips, sale prices, and percent change.

5. Geometry: review of planar figures; perimeter and area of polygons, circles, and composite shapes; sector area and arc length of circles; volume and surface area of prisms, cylinders, pyramids, cones, and spheres; similar figures; radicals, Pythagorean Theorem, and applications.

6. Formal logic: conditional statements, Venn Diagrams, truth tables, basic proofs using deductive logic.

7. Pre-algebra: simplifying algebraic expressions, solving one-variable linear equations.

Texts:

Prentice Hall Mathematics – Course 2

Connected Mathematics Project, Grade 7 

Introductory Algebra – 7

Introductory Algebra – 7

In the 7th grade, students begin the formal study of algebra. Students become facile with the use of variables and algebraic equations to solve problems and with graphing as a means of representing functions. Along the way, they encounter real-world applications, share strategies and present solutions to their classmates, and complete projects related to the unit of study. Throughout the course, students model data with algebraic functions. To support their work, students use the Texas Instruments Graphing calculator as well as iPad applications such as Desmos.

The following topics are covered during the Introductory Algebra course:

1. Properties of Algebra: translating English into algebraic expressions, applying the order of operations, calculating with integers, simplifying and factoring algebraic expressions.

2. Concepts and notation of sets and subsets; sets of numbers: natural, whole, integers, rational, irrational, and real.

3. Functions, relations, and multiple representations thereof, including tables and graphs.

4. Problem solving and setting up and solving equations.

5. Linear equations: standard form, slope-intercept form, point-slope form, direct variation; graphs of linear functions.

6. Linear inequalities: solving inequalities in one variable and graphing solutions on a number line.

7. Fitting lines to data: manually drawing best-fit lines, running linear regressions on graphing calculators.

8. Systems of linear equations: solving by graphing, substitution, and linear combinations.

9. Introduction to exponential and radical expressions.

Texts:

Martin-Gay, Elayn. Algebra I, Pearson, 2016.

Connected Mathematics Project, Grades 7 and 8

Algebra I – 7

In the 7th grade, students begin the formal study of algebra. Students become facile with the use of variables and algebraic equations to solve problems and with graphing as a means of representing functions. Along the way, they encounter real-world applications, share strategies and present solutions to their classmates, and complete projects related to the unit of study. Throughout the course, students model data with algebraic functions. To support their work, students use the Texas Instruments Graphing calculator as well as iPad applications such as Desmos. 

The following topics are covered during the Algebra I course:

1. Properties of Algebra: translating English into algebraic expressions, applying the order of operations, calculating with integers, simplifying and factoring algebraic expressions.

2. Concepts and notation of sets and subsets; sets of numbers: natural, whole, integers, rational, irrational, and real.

3. Functions, relations, and multiple representations thereof, including tables and graphs.

4. Problem solving and setting up and solving equations.

5. Linear equations: standard form, slope-intercept form, point-slope form, direct variation; graphs of linear functions.

6. Linear inequalities: solving inequalities in one variable and graphing solutions on a number line.

7. Fitting lines to data: manually drawing best-fit lines, running linear regressions on graphing calculators.

8. Systems of linear equations: solving by graphing, substitution, and linear combinations.

9. Absolute value inequalities.

10. Introduction to polynomials: classifying by number of terms; classifying by degree; adding, subtracting, and multiplying polynomials.

11. Quadratic equations: solving by graphing, factoring, completing the square, and the quadratic formula.

12. Quadratic functions: graphing using vertex form, intercept form, and standard form; applications of quadratic functions.

13. Quadratic inequalities, solving algebraically and graphically.

14. Radical equations: irrational numbers, simplifying radical expressions, and solving radical equations.

15. Exponential expressions: rules of exponents, operations with numbers expressed in scientific notation.

Texts:

Martin-Gay, Elayn. Algebra I, Pearson, 2016.

Connected Mathematics Project, Grades 7 and 8

Intermediate Algebra – 8 

In the 8th grade, students continue the study of algebra through a function-based curriculum, as they move from linear functions to absolute value, quadratic, and exponential functions. Technology, including the Texas Instruments Graphing calculator, Desmos, and Microsoft Excel, and real-world applications reinforce the increasingly complex concepts. Students are expected to make written analyses of increasing sophistication, along with occasional projects and presentations, as part of their regular work in and out of class.

The following topics are covered during the Intermediate Algebra course:

1. Review of systems of linear equations and use of linear systems in data modeling.

2. Inequalities and absolute value relations, both in one and two variables.

3. Systems of linear inequalities and concepts of linear programming.

4. Quadratic equations: solving by graphing, factoring, completing the square, and the quadratic formula.

5. Quadratic functions: graphing using vertex form, intercept form, and standard form; applications of quadratic functions, including applications of the Pythagorean Theorem.

6. Quadratic inequalities: solving algebraically and graphically.

7. Radical functions: irrational numbers, solving radical equations, and graphing radical functions.

8. Rational expressions: mathematical operations with rational expressions and solving rational equations.

9. Exponential functions and their applications.

Texts:

Martin-Gay, Elayn. Algebra 2, Pearson, 2016

Connected Mathematics Project, Grade 8

Algebra II – 8

Algebra II - 8

In the 8th grade, students continue the study of algebra through a function-based curriculum, as they move from linear functions to absolute value, quadratic, and exponential functions. Technology, including the Texas Instruments Graphing calculator, Desmos, and Microsoft Excel, and real-world applications reinforce the increasingly complex concepts. Students are expected to make written analyses of increasing sophistication, along with occasional projects and presentations, as part of their regular work in and out of class.

The following topics are covered during the Algebra II course:

1.           Systems of linear inequalities and concepts of linear programming.

2.           Radical functions: irrational numbers, solving radical equations, and graphing radical functions.

3.           Rational functions: mathematical operations with rational expressions, solving rational equations, graphing basic rational functions.

4.           Exponential functions and their applications.

5.           Introduction to logarithms and logarithmic functions.

6.           Introduction to trigonometry.

7.           Arithmetic and geometric sequences and series.

8.           Probability.

Texts:

Martin-Gay, Elayn. Algebra 2, Pearson, 2016

Connected Mathematics Project, Grade 8