The Lovett School Middle School Math Curriculum
Middle School Math Curriculum The Lovett School Vision for Learning Lovett offers experiences that inspire our students to love learning. We encourage them to think critically, communicate effectively, engage creatively, and collaborate purposefully. We provide the opportunities and resources that help our students develop independence and self-direction and extend their learning beyond the walls of the classroom as they grow intellectually, emotionally, physically, aesthetically, morally, and spiritually. 6th Grade Pre-Algebra Prep Course Description Pre-Algebra Prep: This math course begins the transition from arithmetic skills to the study of more advanced mathematical concepts. The course includes units that explore relationships amongst operations with fractions and decimals; operations with signed numbers; ratio, rates, proportion, and percent; expressions and equations; geometry; and coordinate plane. In addition, there will be an introduction to basic pre-algebra concepts, integrated throughout the units of study. Students discuss, practice, and select appropriate calculation techniques and problem-solving strategies. The course combines a discovery approach with traditional skill-building practice and review. In depth projects lead to real-life mathematical and interdisciplinary understandings. Essential Questions 1. 2. 3. 4. 5. 6. 7.
How may the various problem-solving methods be applied effectively? Can a specific problem be solved in multiple ways? What are the characteristics of geometric shapes? Why are these characteristics important? What are the inherent patterns and rules of mathematics? How may the patterns and rules of mathematics be used to solve various problems and equations? When is it appropriate to use a rate, ratio, proportion or percentage? What are the most efficient operational methods for working with decimals and fractions in various situations; why? 8. How can mathematical knowledge and understanding be expressed clearly to others? Assessment 1. Use formative assessments in the form of activities, quizzes, homework and classroom participation. 2. Formative assessments will be used as feedback to assess mastery level of content. 3. Practice work outside of class will be used as a connection from one class to the next, and prompt discussions/clarification when needed. 4. Students will participate in classroom activities that have them interact with the world around them and make connections to the class content in their daily lives. Examples include, but are not limited to a design project, coordinate plane project, and data collection project. 5. Use summative assessments in the form of unit tests, projects, cumulative reviews, and semester exams. 6. Each formative and summative assessment will be used as checkpoints to build and connect the content skills from unit to unit.
Skills Benchmarks 1. Students will be able to demonstrate multiple methods for solving problems and provide support for an efficient choice among those methods. 2. Students will be able to present knowledge and understanding of mathematical concepts clearly both verbally and in writing. 3. Students will be able to perform operations with decimals and fractions efficiently. 4. Students will be able to understand and articulate the difference amongst a ratio, proportion, and a rate. 5. Students will be able to plot points on a coordinate plane. 6. Students will be able to differentiate between the various characteristics of geometric shapes and use them as asked or needed mathematically and in real world problems. 7. Students will be able to recognize and use bar graphs, pie/circle graphs, and line graphs. Units · · · · · · · · · ·
Positive and negative numbers and the number line Fraction and decimal multiplication and division Operations with positive and negative numbers Ratios Unit rates and rates (bar graphs) Percent (pie/circle graphs) Expressions Equations and Inequalities Geometry (line graphs) Coordinate plane
Textbooks and Resources Math in Focus: Singapore Math, Course 1 Marshall Cavendish, Student eBook, 2012 Additional Teacher Selected Resources Revised September 2019
7th Grade Pre-Algebra Course Description Pre-Algebra: Students use multiple approaches to solving problems as they develop the ability to think logically and deepen their number sense. Algebraic ideas are used as students write and solve equations and inequalities that model real-world situations. In-depth projects lead to real-life mathematical and interdisciplinary understandings. Essential Questions 1. How is algebra related to real-life and how do I apply it to what I know? 2. How are variables used to substitute for numbers? 3. Can problems be solved using different methods? 4. What are the types of real numbers, their relationships to each other, and their uses? 5. What are the different ways that linear relationships be expressed in multiple ways? 6. How can you represent collected data in a meaningful way? Assessment (i.e. How do we know that students have reached the benchmarks below?) 1. Formative assessments (quizzes) 2. Homework 3. Unit Tests (Summative) 4. Open-Note Cumulative Reviews 5. Projects (Summative) 6. Cumulative semester assessment Skills Benchmarks (i.e. What is that we expect them to learn?) 1. Students will be able to identify and define variables within problems. 2. Students will be able to understand the relationships among types of real numbers. 3. Students will be able to demonstrate an understanding of linear relationships. 4. Students will be able to create and solve algebraic equations and inequalities. 5. Students will be able to analyze and display data and statistics. Displays may include line, bar, and circle graphs, scatterplots, and histograms. 6. Students will be able to use appropriate technologies to enhance their mastery of concepts. Units 1. 2. 3. 4. 5. 6. 7. 8.
The Real Number System Rational Number Operations Algebraic Expressions Algebraic Equations and Inequalities Ratios, Rates, Percent, and Dimensional Analysis/Unit Conversion Direct Proportions, Linear Equations, and Slope Statistics Volume and Surface Area of Solids
Textbooks and Resources Math in Focus, Course 2 (Singapore Math by Marshall Cavendish) Simple Calculator (or TI-84 or above for future use)
Revised: September, 2019
7th Grade Advanced Pre-Algebra Course Description Advanced Pre-Algebra: This course provides students with a rigorous study of pre-algebra and algebraic concepts. Students use reasoning, abstract thinking skills, and communication skills to investigate and develop these concepts and deepen their number sense. In depth projects lead to real-life mathematical and interdisciplinary understandings. Essential Questions 1. How can real-world problems be translated into equations and inequalities and solved? 2. Can a specific problem be solved in multiple ways? 3. What are the most efficient methods for solving specific equations and why are they most efficient? 4. How do I know if my solution is reasonable? 5. Why are there rules in math? Do I really need to use them? 6. Why is it important for me to be mathematically literate in today’s world? 7. What problem-solving strategies work best for me? How can I use them? 8. How can I apply what I know to a new situation? Assessment 1. Formative Assessments (Quizzes) 2. Summative Assessments (Unit Tests, Projects, Semester Exam) 3. Homework 4. Class Activities 5. Cumulative Quizzes 6. Open-Note Cumulative Reviews Skills Benchmarks 1. Students will be able to create algebraic equations and inequalities to model real world problems. 2. Students will be able to identify and analyze mathematical patterns to develop mathematical ideas and apply them to new situations. 3. Students will be able to solve algebraic equations and explain the meaning of their solutions. 4. Students will demonstrate an understanding of linear relationships, including slope. 5. Students will be able to analyze and display data and statistics. Displays may include line, bar, and circle graphs, scatterplots, and histograms. 6. Students will be able to use appropriate technologies to enhance their mastery of concepts. 7. Students will be able to demonstrate multiple methods for solving problems and provide support for an efficient choice among those methods. 8. Students will be able to present knowledge and understanding of mathematical concepts clearly.
Units 1. 2. 3. 4. 5.
The Real Number System Rational Number Operations Algebraic Expressions Algebraic Equations and Inequalities Ratio, Rates, Percent, and Dimensional Analysis/Unit Conversion
6. 7. 8.
Direct Proportions, Linear Equations, and Slope Geometry- Volume and Surface Area of Solids Statistics
Textbooks and Resources Math in Focus, Course 2 (Singapore Math by Marshall Cavendish) Simple Calculator (or TI-84 or above for future use)
Revised September 2019
8th Grade Algebra I Course Description This course is designed to help students develop the fundamentals of algebra. It includes studies of the real number system, simple linear equations and inequalities, systems of equations, graphing first-degree equations and inequalities in one and two variables, operations with and factoring of polynomials, application problems, linear, and quadratic functions. The students use graphing calculators to record and display data and to explore the concept of functions and their graphs. Students gain an understanding of basic algebraic concepts that will enable them to continue their study of Algebra I or begin a course in geometry in ninth grade. In depth projects lead to real-life algebra and interdisciplinary understandings. Essential Questions 1. How can real-world problems be translated into mathematical equations and solved? 2. Can a specific problem be solved in multiple ways? 3. What are the most efficient methods for solving specific equations; why? 4. How can real world problems be displayed graphically? 5. What are the special relationships in right triangles? 6. How can mathematical knowledge and understanding be expressed clearly to others? 7. What tools can be used to support mathematical learning and communication? Assessment 1. Quizzes – purely formative, designed to assess students’ comprehension of material prior to a graded work or a test. 2. Unit Tests – summative, occurring every 4-6 weeks. 3. Student Projects – compilation of data and units of knowledge, demonstrating ability to work with real-world problems and provide mathematical information and conclusions. 4. Graded Classwork – designed as graded checkpoints in between unit tests. Graded classwork may be done individually or working with others, depending on the nature of the assignment and at the discretion of the teacher. 5. Homework – Algebra homework serves to sharpen students’ mathematical skills, provide additional practice, challenge students to complete various problems that may look differently than they did in class, and build confidence in students' ability to master a concept. 6. Semester Exams – There is a final exam at the end of each semester, 2 exams in total. Each exam serves as a cumulative review of the material learned up until that date. The semester exams serve as a heavily weighted comprehensive review to thoroughly assess the students’ knowledge of the material. 7. Test Corrections – Following each test, students will complete test corrections to demonstrate knowledge of the types of errors they made, how frequently they produce these kinds of errors, how to re-do the question to solve it correctly, and how they can prevent this type of error from happening in the future.
Skills Benchmarks 1. Students should be able to translate real world problems into linear, quadratic equations, and inequalities (linear only). 2. Students should be able to use systems of equations to solve problems. 3. Students should be able to demonstrate multiple methods for solving problems and provide support for an efficient choice among those methods. 4. Students should be able to use laptops and graphing calculators for appropriate support. 5. Students should be able to present knowledge and understanding of algebraic concepts clearly through both mathematical work and verbal explanation. Units
1. 2. 3. 4. 5. 6.
Expressions, Equations, & Inequalities Linear Functions Systems of Equations Exponents & Radicals Polynomials and Factoring Quadratic Functions
Textbooks and Resources 1. Teacher-Created Workbook – Semester 1 2. Teacher-Created Workbook – Semester 2 3. TI-84 Graphing Calculator
Revised September 2019
7th and 8th Grade Advanced Algebra Course Description This fast-paced course provides a rigorous study of first year algebra concepts. Students in this course are expected to think critically and master problem solving that includes: working in the real number system; operations with and factoring of polynomials; first- and second- degree equations in one and two variables; quadratics; systems of equations; graphing first-degree equations and inequalities in one and two variables. In addition, students in this course conduct a thorough investigation of quadratic functions and rational expressions and functions. The students use graphing calculators and personal laptop software to record and display data and to explore the concept of functions and their graphs. Advanced Algebra I students complete projects that demonstrate the application of algebra concepts in a “real world” setting. Essential Questions 1. How can real-world problems be translated into mathematical equations and solved? 2. Can a specific problem be solved in multiple ways? 3. What are the most efficient methods for solving specific equations; why? 4. How can real world problems be displayed graphically? 5. How can angles be quantified, compared, measured and classified? 6. What are the special relationships in right triangles? 7. How can mathematical knowledge and understanding be expressed clearly to others? 8. What tools can be used to support mathematical learning and communication? Assessment 1. Quizzes – purely formative, designed to assess students’ comprehension of material prior to a graded work or a test. 2. Homework – also formative. Advanced Algebra homework serves to sharpen students’ mathematical skills, provide additional practice, challenge students to complete various problems that may look differently than they did in class, and build confidence in the students’ ability to master a concept. 3. Unit Tests – summative, occurring every 4-6 weeks. 4. Student Projects/Graded Classwork – compilation of data and units of knowledge, demonstrating ability to work with real-world problems and provide mathematical information and conclusions. Graded classwork may be done individually or working with others, depending on the nature of the assignment and at the discretion of the teacher. 5. Cumulative Reviews – summative and cumulative up to that point, 3-4 per semester. 6. Semester Exams – There is a final exam at the end of each semester, 2 exams in total. Each exam serves as a cumulative review of the material learned up until that date. The semester exams serve as a heavily weighted comprehensive review to thoroughly assess the students’ knowledge of the material. 7. Test Corrections – Following each test, students will complete test corrections to demonstrate knowledge of the types of errors they made, how frequently they produce these kinds of errors, how to re-do the question to solve it correctly, and how they can prevent this type of error from happening in the future.
Skills Benchmarks
1. Students should be able to translate real world problems into linear, exponential, and quadratic equations and inequalities (linear only). 2. Students should be able to use systems of equations and inequalities to solve problems. 3. Students should be able to demonstrate multiple methods for solving problems and provide support for an efficient choice among those methods. 4. Students should be able to use laptops and graphing calculators for appropriate support. 5. Students should be able to present knowledge and understanding of algebraic concepts clearly through both mathematical work and verbal explanation. Units 1. 2. 3. 4. 5. 6. 7.
Expressions, Equations, & Inequalities in One Variable Linear Functions Systems of Equations & Inequalities Exponents & Radicals Polynomials & Factoring Quadratic Functions Algebraic Fractions & Rational Functions
Textbooks and Resources Teacher-Created Blue Workbook – Semester 1 Teacher-Created Blue Workbook – Semester 2 TI-84 Graphing Calculator
Revised September 2019
8th Grade Honors Geometry Course Description The honors level of geometry covers all topics included in the regular course but at an accelerated pace. Many concepts are extended and developed more completely; there is a greater emphasis on proof and solving non-routine problems; and the pace of the course affords the opportunity to explore additional topics, such as non-Euclidean geometries. Outside readings, projects, and/or independent research may be used to enrich this advanced study. Essential Questions 1. 2. 3. 4. 5.
What is the role of algebra in geometry? How does geometry differ from algebra? What is the role of proofs in the development of a deductive system? How does geometry enhance reasoning abilities/logical thinking? How does one use geometry to model real life situations?
Skills Benchmarks 1. Students will be able to construct a two-column proof involving parallel lines, congruent triangles and other polygons, similarity, and relationships within a circle. 2. Students will be able to solve right triangles using the Pythagorean Theorem, the relationships of sides in special right triangles, and the trig ratios. 3. Students will be able to apply the theorems of tangents, arcs, chords, and angles of a circle. 4. Students will be able to find the perimeter and area of triangles, quadrilaterals, regular polygons, and circles. 5. Students will be able to find the area and volume of prisms, pyramids, cylinders, cones, and spheres. 6. a. b. c. d. e.
Students will be able to use the algebra of geometry. Ratio and proportions Distance formula Midpoint formula Slopes of lines Equations of lines and circles
7. Students will be able to model real world applications using geometry. 8. Students will be able to apply transformations (translations, rotations, reflections and dilations) to geometric figures. (May be extension material)
Units 1. Points, Lines, Planes, and Angles 2. Deductive Reasoning 3. Parallel Lines and Planes 4. Congruent Triangles 5. Quadrilaterals 6. Inequalities in Geometry 7. Similar Polygons 8. Right Triangles 9. Circles 10. Areas of Plane Figures 11. Areas of Volumes and Solids 12. Coordinate Geometry 13. Transformations (Where time allows) Assessment 1. 2. 3. 4. 5. 6. 7.
Homework – formative only Quizzes – formative only Unit tests Test Corrections Cumulative Reviews Projects/Classwork Semester exams
Textbooks and Resources Text: Jurgensen, Ray C., Richard G. Brown, and John W. Jurgensen, Geometry, McDougal Littell TI-84 Graphing Calculator
Revised September 2019