Mathematics
The Middle School mathematics program is designed to provide students with a solid foundation for their Upper School coursework. The program aims to solidify computation skills, build self-confidence in mathematical abilities and teach organizational skills demonstrated in student work. The process of arriving at one’s answer is more important than the answer itself. This philosophy gives the students a greater ability to interpret and solve real-world problems. Teachers use a variety of measures to assess and challenge students based on their current ability and achievement.
Students are recommended to the next level of mathematics, including advanced and honors levels, based on their performance in their current course. They are placed in the most appropriate class to meet both their current needs and potential for mathematical mastery and growth. There can be a dramatic change in students’ maturity, motivation and ability from the beginning of the school year to the finish. Thus, students are assessed on a trimester basis with a formal end-of-the-year diagnostic test. In addition, a review of a student’s performance in math competitions and ERB scores takes place.
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Prerequisite: Math 8 Honors or Math 7 Accelerated Honors
Math I Honors is the first of a three-year sequence of compacted courses. Students solidify and extend their understanding of functions, solving equations, geometric relationships, and data analysis, and continue to establish their understanding of linear and exponential sequences and functions. They expand their algebraic skills, focusing on solving equations and inequalities, including systems of linear equations and inequalities. Students develop explanations of geometric relationships of similarity and congruence through transformations and formal constructions, and formulate and present mathematical arguments. They extend their work from previous grades, working with linear models and linear regression equations. Additionally, students use histograms, dot plots, and box plots to describe and compare the shape, center, and spread of univariate data.
As an honors course, the Math I curriculum is regularly extended through enrichment topics in each unit. Students expand their knowledge of sequences to series formulas and sigma notation and focus on matrix-related topics. They explore matrix addition and multiplication and use matrices to solve systems of linear equations with elementary row operations and the multiplicative inverse. Matrices are also used to represent vector transformations. Students build proficiency in moving between different forms of quadratic equations, identifying the characteristics of a function from its equation, and using factoring and completing-the-square techniques. They also develop strategies to solve quadratic equations using various methods and are introduced to complex numbers as solutions.
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Integrated Math 5 emphasizes the development of sound computation and reasoning skills using whole numbers, fractions and decimals. Students develop competency in all whole-number operations and gain a firm foundation in those with fractions and decimals. Elementary statistics is introduced through data analysis. Development of basic number theory and geometry concepts continues. Problem-solving skills are stressed in this course.
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Integrated Math 6 builds on students’ understanding of fractions and decimals and continues to emphasize reasoning with rational numbers and the four basic operations. Exponents and roots are explored in greater depth and explicitly connected to geometric figures and real-world contexts. The course continues with a deeper exploration of the properties of numbers, introducing negative numbers and absolute value, which are integrated into solving linear equations and inequalities. Students also formalize their understanding of ratios and proportions, solve linear equations, and create graphical representations of data. Modeling strategies and multiple representations are heavily integrated into instruction.
All students will be expected to explain their mathematical reasoning both verbally and in writing. Students will have the option to complete more challenging tasks with greater rigor. These extensions will allow students who are ready to engage with the concept at a deeper level to explore and/or reason further. By completing challenges, extensions, and assessments, each student will have the opportunity to earn an “honors distinction” on their report card.
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The Honors program follows the scope and sequence of the Integrated Math 6 course. Students explore concepts in depth and further develop their problem-solving skills through enrichment and extension activities. They engage in questioning strategies utilized by the teacher that encourage them to explore the richness of the problems.
Students are expected to practice and use higher-level thinking strategies and construct arguments using verbal or written explanations. Furthermore, they refine their mathematical communication skills through discussions and written responses, critically evaluating their own thinking and that of other students.
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Integrated Math 7 is designed to develop students’ confidence further in their problem-solving abilities and to enable them to see the connections among the different algebraic, geometric, and data science topics introduced in the course, while preparing them for the rigors of upper-level mathematics.
All students will be expected to explain their mathematical reasoning both verbally and in writing. Students will have the option to complete more challenging tasks with greater rigor. These extensions will allow students who are ready to engage with the concept at a deeper level to explore and/or reason further. By completing challenges, extensions, and assessments, each student will have the opportunity to earn an “honors distinction” on their report card.
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Following the scope and sequence of Integrated Math 7, the Honors course is designed to develop students’ confidence further in their problem-solving abilities, enable them to see connections among the different algebraic, geometric, and data science topics introduced, and prepare them for the rigors of upper-level mathematics. Students explore concepts in depth and build skills through enrichment and extension activities. They engage in questioning strategies utilized by the teacher that encourage them to explore the richness of the problems. Students are expected to practice and use higher-level thinking strategies.
In this course, students solve real-world problems by applying algebraic and geometric concepts, model problem situations using symbolic and graphical representations, and construct arguments using verbal or written explanations. Furthermore, they refine their mathematical communication skills through discussions and written responses, critically evaluating their own thinking and that of other students.
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Integrated Math 8 helps students develop multiple strategies for solving problems and recognizing connections between algebraic and geometric concepts. Students will engage in problem-solving strategies, questioning, investigations, critical analysis, gathering and constructing evidence, and communicating rigorous arguments to their thinking. They build on the concepts and skills developed in Integrated Math 7 to understand the connections among proportional relationships, linear relationships, and the solution of linear equations and systems of linear equations. Students are introduced to function notation, and representing functions by graphing is emphasized. They expand their algebraic skills by simplifying expressions with radicals and integer exponents. Students explore a variety of geometric concepts, including rigid transformations, dilations, congruence, similarity, volume, angles, distance, and the Pythagorean theorem.
Math language and vocabulary, problem-solving techniques, and computation with algebraic expressions are stressed. The use of graphing technology on Desmos is integrated throughout. By the end of the course, students should be able to confidently connect varied mathematical concepts and apply strategies to solve problems they have never seen before.
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Following the scope and sequence of Integrated Math 8, the Honors course helps students develop multiple strategies to solve problems and to recognize the connections between algebraic and geometric concepts. They will engage in problem-solving strategies, questioning, investigations, critical analysis, constructing evidence, and communicating rigorous arguments about their thinking. Students explore concepts in depth and further develop skills through enrichment and extension activities. They engage in questioning strategies utilized by the teacher that encourage them to explore the richness of the problems. Students are expected to practice and use higher-level thinking strategies.
In this course, students solve real-world problems by applying algebraic and geometric concepts, model problem situations using symbolic and graphical representations, and construct arguments using verbal or written explanations. Furthermore, they refine their mathematical communication skills through discussions and written responses, critically evaluating their own thinking and that of other students.
