Mathematical communication and problem solving are key themes of the seventh grade curriculum.

Problem Solving is having students apply their mathematical knowledge to puzzles and unfamiliar situations without giving them a road-map to follow. During problem solving tasks students will often work together in groups to share and debate ideas. Our emphasis is as much on describing one's thinking process as on finding the solution. Some problem solving tasks will come home as long term homework projects.

Mathematical Communication: Most Fayerweather students are adept at solving problems by the beginning of seventh grade, but it is still challenging for middle school students to present the steps of their solution in a manner that is clear to a third party. In preparation for more formal math studies, we strongly emphasize mathematical communication in seventh grade. This includes using standard mathematical notation, organizing work carefully on a page, and a great deal of writing. Our writing projects include:

• Warm-ups – quick write & share activities.
• Journal Entries – putting information that we have been working on into their own words.
• Posters/Displays – Revised drafts of above.
• Test Reflections – capturing their test taking experience before getting teacher feedback.
• Problem Solving Reports
• Clear problem statements that include statements of constraints and questions.
• Accurate use of vocabulary.
• Clear use of words, diagrams and tables to present information.
• Clear presentation of sequence of student's solution (first... then...)
• Accuracy of solution (if applicable)

The math units of 7th grade are:

• Accentuate the Negative/Order of Operations A study of rational numbers and the computational skills of working negative numbers and complex mathematical expressions.
  
• Relating Relationships Representing the relationships between dependent variables with graphs, tables, words and equations. Students gather data on related variables through projects and activities. Through graphing and tables they analyze the data for mathematical patterns. Students will be able to compare and interpret different representations of data. We will look at linear, exponential and quadratic relationships.
• Probably Pascal's A look into probability and the patterns of Pascal's triangle.
• Monster Dogs/Shrinking Mammals A study of three dimensional geometry. We will do work with nets, surface area, volume, similarity, and scale factors.
• Algebra Working with the first chapters of Introduction to Algebra by K.E. Martin-Gay, we will review number systems, operations on rational numbers and then move into using variables to represent and solve problems.

Assessment & Tests As a means of preparing students for high school we do give graded tests in seventh grade. The purpose of these tests is to de-mystify the process of test taking. Each test is used as an opportunity to discuss preparation habits and test-taking skills. The grades are only for student feedback. Our assessment of student accomplishment is based on our observations of classwork and homework.

In eighth grade math, students continue the study of Algebra I that they began the previous spring. Over the course of the year, students will complete an in-depth Algebra I course, designed to prepare them to place out of Algebra I when they go to high school. Our text for Algebra I is Beginning Algebra by K. Elayn Martin-Gay.

Following a review of their work from the spring, students begin to work on graphing linear equations and inequalities. They explore the question of what makes a line unique, and study how to calculate the slope and intercepts of a line both graphically and algebraically. They then study the many ways one can use an equation to plot a line and the many ways one can find the algebraic equation that represents given pieces of linear data. They conclude their study of graphing with an exploration of linear inequalities, and some non-linear functions.

Their next area of study is exponential expressions and polynomials. Using their basic knowledge of exponential notation, they explore what happens when you multiply two exponential expressions, divide them, or raise one exponential expression to another power. From these explorations they deduce the rules of working with exponents. They then work on adding and subtracting exponential expressions, which leads into a study of polynomials. After learning polynomial terminology, they learn to accurately add, subtract multiply and divide polynomials.

Next students use both algebraic and graphing strategies to solve systems of linear equations and inequalities. Real-world problems included business models (cost efficiency, comparing sales rates, pricing) and physics (acceleration, velocity/distance/time problems).

Their study of Algebra I concludes with an exploration of roots, radicals and quadratic equations. They use their knowledge of algebra to solve quadratic equations, graph quadratic functions and to derive the quadratic formula. Using the quadratic formula and Pythagorean theorem they conclude the year working through several types of real world applications.