Hillel's math program is designed to address the wide range of student needs in our school community. In Eighth grade, students are placed in a math course to enhance skills at an appropriate challenge level. Course offerings include Eighth Grade Math, Algebra 1, and Geometry.
In Grade 8, instructional time focuses on three critical areas: (1) formulating and reasoning about expressions and equations, including analyzing data that represent direct variation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
Algebra 1 consists of three critical units:
Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and use them to solve problems. Students also apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students also use regression techniques to describe the approximate linear relationship between quantities.
Students learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, and translate between representations. Students study exponential functions and compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students investigate systems of equations and inequalities.
Students analyze the structure in and learn to create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions. Additionally, students compare the key characteristics of quadratic functions to those of linear and exponential functions.
Geometry consists of five areas of study:
Students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Students identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. Students develop the Laws of Sine and Cosine in order to find missing measures of general (not necessarily right) triangles, building on students’ work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.
Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.
Students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course.
Students prove basic theorems about circles and study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations.