# Mathematics

Will I ever use this? Why do I need to know this?

Learning to think mathematically is useful and something needed. Math is a tool, not just an end in itself, so McCallie teachers strive to spark a joy of numbers and utilize real-life situations in teaching math. Many times boys who initially believed they were “bad at math” find they are quite good once the rote memorization style of problem-solving is replaced by explanations that uncover the beauty and usefulness of math.

## Courses

- Math 610 - 6th Grade Mathematics
- Math 611 - 6th Grade Mathematics Accelerated
- Math 710 - 7th Grade Mathematics
- Math 711 - 7th Grade Mathematics Accelerated
- Math 721 - 7th Grade Algebra 1 Accelerated
- Math 810 - 8th Grade Pre-Algebra
- Math 820 - 8th Algebra 1
- Math 821 - 8th Grade Algebra 1 Accelerated
- Math 830 - 8th Grade Geometry

## Math 610 - 6th Grade Mathematics

**Course Description:**

The purpose of the sixth grade math course is to provide boys with fluency in math skills to prepare them for higher math study. While much of the work involves drill on essential skills, a great deal of time is spent on problem-solving and higher order reasoning skills. Traditionally, math is the most difficult subject to assimilate into thematic instruction. The nature of the material is extremely sequential and often is not easily related to a thematic unit at the time that the unit is being implemented. Therefore, in many ways, math is a stand-alone course. However, the boys may complete a relevant, but small, math project for each integrated unit. Grade: 6

**Academic Goals:**

- Estimation.
- Rounding numbers.
- Identification and construction of geometric shapes.
- Adding, subtracting, multiplying, and dividing proper and improper fractions.
- Lowest common denominator, least common multiple, and greatest common factor.
- Area, perimeter, and circumference of rectangles, circles, triangles, trapezoids, and parrallelograms.
- Order of operations with the use of negative numbers.
- Reading, drawing, and interpreting line and bar graphs.
- Frequency tables.
- Introduction to algebraic topics and variables.
- Word problems.
- Negative numbers.
- Squares and square roots.
- Ratio and proportion.
- Finding the mean, median, and mode of sets of numbers.
- Research paper on famous mathematicians.
- Place value.
- The accelerated section(s) will explore additional topics:
- classification of angles
- Pythagorean Theorem
- simplifying multi-variable expressions
- coordinate system
- exponents

**Instructional Methods:**

- Direct one-on-one instruction.
- Classroom and group discussion.
- Giving students opportunities to find alternate forms of solving problems by allowing them to work with partners.
- Daily practice problems done as review of previous day's work.
- Calling on students randomly.
- Applicability to real world problems.
- The use of cooperative learning to encourage interaction and the exchange of ideas.
- Peer tutoring.
- Classroom as well as outside the classroom activities.
- Note taking and communication of concepts.
- Student-teacher interaction.

**Evaluation:**

- Student and group presentations.
- Extra credit opportunities.
- Full period quizzes and tests.
- T-squares competition.
- Extended projects done in groups or by students themselves.
- Creating and solving their own types of problems related to a particular topic.
- Graded homework.
- Internet exercises.
- Student-teacher interaction.

## Math 611 - 6th Grade Mathematics Accelerated

**Course Description:**

The purpose of the sixth grade math course is to provide boys with fluency in math skills to prepare them for higher math study. While much of the work involves drill on essential skills, a great deal of time is spent on problem-solving and higher order reasoning skills. Traditionally, math is the most difficult subject to assimilate into thematic instruction. The nature of the material is extremely sequential and often is not easily related to a thematic unit at the time that the unit is being implemented. Therefore, in many ways, math is a stand-alone course. However, the boys may complete a relevant, but small, math project for each integrated unit. Grade: 6

**Academic Goals:**

- Estimation.
- Rounding numbers.
- Identification and construction of geometric shapes.
- Adding, subtracting, multiplying, and dividing proper and improper fractions.
- Lowest common denominator, least common multiple, and greatest common factor.
- Area, perimeter, and circumference of rectangles, circles, triangles, trapezoids, and parrallelograms.
- Order of operations with the use of negative numbers.
- Reading, drawing, and interpreting line and bar graphs.
- Frequency tables.
- Introduction to algebraic topics and variables.
- Word problems.
- Negative numbers.
- Squares and square roots.
- Ratio and proportion.
- Finding the mean, median, and mode of sets of numbers.
- Research paper on famous mathematicians.
- Place value.
- The accelerated section(s) will explore additional topics:
- classification of angles
- Pythagorean Theorem
- simplifying multi-variable expressions
- coordinate system
- exponents

**Instructional Methods:**

- Direct one-on-one instruction.
- Classroom and group discussion.
- Giving students opportunities to find alternate forms of solving problems by allowing them to work with partners.
- Daily practice problems done as review of previous day's work.
- Calling on students randomly.
- Applicability to real world problems.
- The use of cooperative learning to encourage interaction and the exchange of ideas.
- Peer tutoring.
- Classroom as well as outside the classroom activities.
- Note taking and communication of concepts.
- Student-teacher interaction.

**Evaluation:**

- Student and group presentations.
- Extra credit opportunities.
- Full period quizzes and tests.
- T-squares competition.
- Extended projects done in groups or by students themselves.
- Creating and solving their own types of problems related to a particular topic.
- Graded homework.
- Internet exercises.
- Student-teacher interaction.

## Math 710 - 7th Grade Mathematics

**Course Description:**

Seventh grade math is designed to teach and to practice the fundamentals of math and to introduce concepts in beginning algebra. More emphasis in the second semester will be put on problem solving, and placement in the accelerated section is based upon previous grades and testing (ISEE, McCallie's Math Placement Test, and ERB). The accelerated class goes faster and presents more challenging word problems than the regular sections, and they do lots of work with factoring quadratic equations. Grade: 7

**Academic Goals:**

- Least common multiple.
- Adding, subtracting, multiplying, and dividing fractions, mixed numbers, and negative numbers.
- Perimeter, area, and circumference of rectangles, triangles, circles, and semicircles.
- Surface area and volume of prisms, rectangular solids, and right solids.
- Order of operations including work with powers.
- Evaluating variable expressions.
- Overall average.
- Reading and drawing bar graphs and broken line graphs.
- Solving linear equations, inequalities, proportions, and percent equations.
- Graphing points and linear equations in a coordinate plane.
- Understanding and applying the Pythagorean Theorem.
- Interpret scatter plots.
- Identify and use properties of addition and multiplication.
- Solve problems by using formulas.
- Express numbers in standard and scientific notation.
- Solving real world assessment problems by using the Woodbury Jasper Series from Vanderbilt University.
- Algebra word problems involving integer, age, cost, distance, work, mixture, and miscellaneous problems.
- Basic use of the graphing calculator.
- Factoring quadratic equations.
- Using unit multiplers to make both unit conversions and square unit conversions.
- Accelerated section(s) will include the following additional topics:
- Solve polynomial equations by factoring.
- b. Use the quadratic equation.
- c. More challenging word problems that require use of their quadratic factoring skills.

**Instructional Methods:**

- Direct instruction.
- Demonstration technique.
- Study of text, especially definitions and example problems.
- Daily work (guided practice).
- Collaborative problem sets.
- One-on-one instruction (back work).
- Note taking.
- Hands on, real world project.
- Cooperative learning strategies.
- Spiraling of former problems.

**Evaluation:**

- In-class, full period tests.
- Graded daily work.
- Extended projects.
- Class participation.
- Students working problems on the board.
- Enrichment problems.

## Math 711 - 7th Grade Mathematics Accelerated

**Course Description:**

Seventh grade math is designed to teach and to practice the fundamentals of math and to introduce concepts in beginning algebra. More emphasis in the second semester will be put on problem solving, and placement in the accelerated section is based upon previous grades and testing (ISEE, McCallie's Math Placement Test, and ERB). The accelerated class goes faster and presents more challenging word problems than the regular sections, and they do lots of work with factoring quadratic equations. Grade: 7

**Academic Goals:**

- Least common multiple.
- Adding, subtracting, multiplying, and dividing fractions, mixed numbers, and negative numbers.
- Perimeter, area, and circumference of rectangles, triangles, circles, and semicircles.
- Surface area and volume of prisms, rectangular solids, and right solids.
- Order of operations including work with powers.
- Evaluating variable expressions.
- Overall average.
- Reading and drawing bar graphs and broken line graphs.
- Solving linear equations, inequalities, proportions, and percent equations.
- Graphing points and linear equations in a coordinate plane.
- Understanding and applying the Pythagorean Theorem.
- Interpret scatter plots.
- Identify and use properties of addition and multiplication.
- Solve problems by using formulas.
- Express numbers in standard and scientific notation.
- Solving real world assessment problems by using the Woodbury Jasper Series from Vanderbilt University.
- Algebra word problems involving integer, age, cost, distance, work, mixture, and miscellaneous problems.
- Basic use of the graphing calculator.
- Factoring quadratic equations.
- Using unit multiplers to make both unit conversions and square unit conversions.
- Accelerated section(s) will include the following additional topics:
- Solve polynomial equations by factoring.
- b. Use the quadratic equation.
- c. More challenging word problems that require use of their quadratic factoring skills.

**Instructional Methods:**

- Direct instruction.
- Demonstration technique.
- Study of text, especially definitions and example problems.
- Daily work (guided practice).
- Collaborative problem sets.
- One-on-one instruction (back work).
- Note taking.
- Hands on, real world project.
- Cooperative learning strategies.
- Spiraling of former problems.

**Evaluation:**

- In-class, full period tests.
- Graded daily work.
- Extended projects.
- Class participation.
- Students working problems on the board.
- Enrichment problems.

## Math 721 - 7th Grade Algebra 1 Accelerated

**Course Description:**

Algebra 1 is designed to give the boys the basis needed to carry on and be successful in and beyond the McCallie math program. The foundation of numbers, number systems, variables, equations, and functions will be laid through such specific topics as a review of the number systems, introduction to variables and their uses, solving and graphing both equalities and inequalities, functions and their graphs, and more. Algebra 1 is the first step to more complex and higher order thought. Accelerated topics will also be studied, such as matrices, solving 3 equations in 3 unknowns, imaginary numbers, completing the square to solve and sketch quadratics, and trigonometric functions and relationships. A TI-83 Plus (or Silver edition) or TI-84 Plus is a requirement of this course. Grade: 7

**Academic Goals:**

- First semester course content will include:
- By the end of the first semester, students will be able to:
- Second semester course content will include:

**Instructional Methods:**

- Direct instruction.
- Demonstration models.
- Question and answer sessions (oral responses).
- One-on-one help sessions (back work).
- Note taking.
- Reading and studying of the text.
- Daily work.
- Discussion and use of TI-83 Plus Calculator

**Evaluation:**

- Graded daily work.
- Quizzes.
- In-class, full period tests.
- Class participation.
- Extra credit and/or enrichment problems.
- Oral presentations in class.
- Two-hour, written semester exams consisting of short calculation questions covering the topics explored throughout the year. Also the exams will contain problem solving questions, some covering topics discussed during the year and others where concepts outlined in the question must be applied in order to find a solution. (These concepts would be an extension of the ones discussed in class.)
- Bi-weekly Web assignments

## Math 810 - 8th Grade Pre-Algebra

**Course Description:**

This course is designed for students who have not yet demonstrated adequate skills in pre-algebra topics. The course begins with a brief review of the arithmetic of signed numbers, rational numbers, and an introduction to the concept of variables using formulas. Other topics include percent, ratio, proportions, solving basic first-degree equations, and a thorough study of introductory plane geometry. During the second semester, the course will introduce many algebraic topics such as combining like terms, using the distributive property to simplify expressions, multiplying/dividing polynomials, solving complex first-degree equations, and learning concrete methods for applying algebraic skills to real world problems. Grade: 8

**Academic Goals:****Instructional Methods:****Evaluation:**

- By the end of the first semester, students will be able to:
- Use order of operations to evaluate expressions and apply the properties of the rational numbers.
- Solve proportions using cross-multiplication and apply proportions to real world situations.
- Solve percent equations and formulate percent equations that solve real world problems.
- Solve problems involving special polygons, parallel lines, supplementary angles, complementary angles, and vertical angles.
- Use geometric formulas to calculate perimeters and areas of plane figures.
- Use geometric formulas to calculate surface areas and volumes of three-dimensional solids.
- Take good notes in class and learn how to study for tests, quizzes, and the semester exams.

- Second semester course content will include:
- Pythagorean Theorem.
- Algebraic symbol manipulation.
- Equation solving.
- Formal algebraic problem-solving techniques.
- Introduction to coordinate geometry.

- By the end of the second semester, students will be able to:
- Apply properties of square roots to solve problems using the Pythagorean Theorem.
- Simplify, add, subtract, multiply, and divide algebraic expressions.
- Solve single variable algebraic equations.
- Write algebraic equations based on interpretation of verbal sentences.
- Plot points in the coordinate plane, write and graph linear equations in two variables, and determine slopes/intercepts of linear graphs.
- Develop and strengthen their study skills, organizational habits, and graphing calculator proficiency.

- Direct instruction.
- Demonstration techniques.
- Study of text: active reading of text, especially definitions and example problems.
- Oral questioning.
- Daily work (guided practice).
- One-on-one instruction (back work).
- Note taking.
- Cooperative learning.
- In-class, full period tests.
- Take-home tests.
- Quizzes.
- Graded daily work.
- Notebook checks and organization.
- Trimester exams.
- Extended projects.
- Extra credit.
- Test corrections.
- Class participation.
- Supplemental problem-solving exercises.

## Math 820 - 8th Algebra 1

**Course Description:**

This course is for those students who have completed a pre-algebra course. This course centers around various topics such as the concept of variable, equation solving, polynomials, and linear equations in two variables. Probability and statistics will also be examined. The graphing calculator, as well as other forms of technology, will be used extensively throughout the course. Grade: 8

**Academic Goals:****Instructional Methods:****Evaluation:**

- First semester course content will include:
- Algebraic techniques
- Equation solving
- Inequalities
- Proportion
- Geometric Measurement

- By the end of the first semester, students will be able to:
- Use order of operations to evaluate expressions and apply the properties of the rational numbers (calculator application).
- Write algebraic equations from verbal sentences, solve single variable algebraic equations, and solve multivariable equations for a specific variable.
- Solve, write and graph simple inequalities.
- Solve proportions using cross multiplication.
- Solve problems involving special polygons, parallel lines, supplementary angles, complementary angles, and vertical angles.

- Second semester course content will include:
- Angles and Measure
- Congruence
- Pythagorean Theorem
- Quadraric Equations
- Linear Equations
- Polynomials

- By the end of the second semester, students will be able to:
- Apply properties of square roots to solve problems using the Pythagorean Theorem.
- Solve problems involving the perimeter, area, volume, and other measurements of special polygons, circles, and geometric solids.
- Simplify, add, subtract, multiply, and divide polynomials.
- Solve proportions using cross multiplication and identify similar figures.
- Show two triangles are congruent using congruence axioms and theorems.
- Take good notes in class and learn how to study for tests, quizzes, and the semester exams.
- Develop and strengthen his study skills and organizational habits.
- Find the greatest common factor for a set of numbers or monomials, factor polynomials, factor polynomials of the form ax2 + bx + c, solve equations by factoring, use the quadratic formula to solve a quadratic equation, and graph a guadratic equation (calculator application).
- Identify similar figures.
- Plot points in the coordinate plane, write and graph linear equations, and solve a system of linear equations (calculator applications).
- Simplify, add, subtract, multiply, and divide polynomials.

- Direct instruction
- Study of text: active reading of text, especially definitions and example problems
- One-on-one instruction (back work)
- Note taking
- Semester exams
- Extra credit
- There will be a two hour exam at the end of the semester during the exam week in the fall and spring. The fall exam will be approximately 25 questions dealing with topics such as order of operations, solving algebraic equations and inequalities, and problems dealing with points, lines, and planes, polygons, and proportion. The spring exam will be approximately 25 questions dealing with topics such as similarity and congruence of geometric figures, rational and irrational numbers, area and volume of polygons and circles, operations with polynomials, factoring polynomials, and linear equations.

## Math 821 - 8th Grade Algebra 1 Accelerated

**Course Description:**

Algebra 1 is designed to give the boys the basis needed to carry on and be successful in and beyond the McCallie math program. The foundation of numbers, number systems, variables, equations, and functions will be laid through such specific topics as a review of the number systems, introduction to variables and their uses, solving and graphing both equalities and inequalities, functions and their graphs, and more. Algebra 1 is the first step to more complex and higher order thought. Accelerated topics will also be studied, such as matrices, solving 3 equations in 3 unknowns, imaginary numbers, completing the square to solve and sketch quadratics, and trigonometric functions and relationships. A TI-83 Plus (or Silver edition) or TI-84 Plus is a requirement of this course. Grade: 8

**Academic Goals:****Instructional Methods:****Evaluation:**

- First semester course content will include:
- Reviewing arithmetic properties and operations.
- Translating English into algebra.
- Real number operations.
- Absolute value.
- Solving linear equations and inequalities.
- Linear graphs and functions.
- Solve systems of equations using graphing, substitution, linear combinations and matrices
- linear programming

- By the end of the first semester, students will be able to:
- Properly handle the order of operations.
- Take word phrases or sentences and turn them into algebaic forms and/or equations.
- Understand absolute value, especially by using the graphing calculator.
- Solve both linear equations and inequalities.
- Graph relations and functions and distinguish their differences.

- Second semester course content will include:
- Factoring of polynomials.
- Study of rational and irrational numbers.
- Quadratic equations and functions.
- Pythagorean Theorem.
- Solve and sketch quadratic functions
- Probability and Binomial expansion
- Complex numbers

- Direct instruction.
- Demonstration models.
- Question and answer sessions (oral responses).
- One-on-one help sessions (back work).
- Note taking.
- Reading and studying of the text.
- Daily work.
- Discussion and use of TI-83 Plus Calculator
- Graded daily work.
- Quizzes.
- In-class, full period tests.
- Class participation.
- Extra credit and/or enrichment problems.
- Oral presentations in class.
- Two-hour, written semester exams consisting of short calculation questions covering the topics explored throughout the year. Also the exams will contain problem solving questions, some covering topics discussed during the year and others where concepts outlined in the question must be applied in order to find a solution. (These concepts would be an extension of the ones discussed in class.)
- Bi-weekly Web assignments

## Math 830 - 8th Grade Geometry

**Course Description:**

Concepts are presented visually with the extensive use of The Geometer's Sketchpad. Students explore ideas analytically, then inductively, and finally deductively, developing insight, confidence, and increasingly sophisticated mathematical understanding. Topics will include studies of the Euclidean ideals: points, lines, and algebraic; therefore, much time will be spent reviewing algebraic skills and extending these skills to be better prepared for Honors Algebra 2. Grade: 8

**Academic Goals:**

- First semester course content will include:
- Review of Algebra skills
- Properties of polygons and circles
- Inductive reasoning and deductive reasoning
- Angle relationships
- Compass and straightedge constructions
- Discovering and proving triangle properties
- Discovering and proving quadrilateral properties
- Discovering and proving circle properties

- By the end of the first semester, students will be able to:
- Solve linear and quadratic equations
- Prove basic conjectures
- Use Triangle inequality theorem plus relationships between sides and angles
- Find the measure of vertical and linear angles
- Duplicate the basic Euclidean constructions
- Do basic triangle proofs
- Do basic quadrilateral proofs
- Do basic circle proofs

- Second semester course content will include:
- More review of Algebra skills
- Areas of polygons
- Pythagorean Theorem and special triangles
- Volume and surface area of polyhedrons
- Similarity
- Basic Trigonometry
- Law of Sines and Cosines
- Proofs

- By the end of the second semester, students will be able to:
- Graph linear systems
- Calculate area of triangles, quadrilaterals, and circles
- Solve a right triangle and solve 45-45-90 plus 30-60-90 triangles
- Calculate the surface area and voume of polyhedrons
- Calculate corresponding parts of similar figures
- Use sine, cosine, and tangent to find sides and angles in triangles
- Use Law of Sine and Cosine to find areas, angles, and side lengths
- Use direct and indirect proof to verify conjectures

**Instructional Methods:**

- Study of text; active reaching of text, especially definitions and example problems
- Oral questioning
- Daily work (guided practice)
- Collaborative problem sets
- One-on-one instruction (back work)
- Hands-on, real world project
- Cooperative learning strategies
- Note taking in class and from reading the book

**Evaluation:**

- In-class, full period tests
- Take home tests
- Quizzes
- Graded daily work
- Notebook checks
- Section outlines
- Semester exams
- Extended projects that require a formal write up and that will be graded with a rubric
- The exam in both fall and spring will take place during the two-hour slot set aside during exam week. the exam will consist of short and long computation and proofs. Each exam will include coordinate geometry (slope, distance formula, parallel lines, perpendicular lines), solving linear systems, circles, factoring, solving equations, parabolas, simplifying, right triangle trigonometry, 1 derive quad. formula, and a locus problem.
- Students will present to the class a formal presentation of a problem that will be graded with a rubric.