Grade 8
Glastonbury Public Schools Mathematics Curriculum
Algebra: What is algebra?
Mathematics is learned through questions that arise while solving well-constructed problems. Our students begin with problems, they use strategies to solve the problems, and they learn the necessary mathematics along the way. Many classroom investigations are designed so that students will collaboratively or individually discover the mathematical properties. The properties are then discussed in class, summarized, and become part of the students’ mathematical knowledge to be applied to future problems.
The discovery of the mathematics is an essential part of the development of each student’s confidence as a mathematician. Knowledge that is gained through inquiry is more likely to be remembered for the long term. Teachers and parents work together to promote this discovery of math through investigation, problem solving, and reasoning. Our goal is that students in Glastonbury Public Schools will understand that mathematics makes sense.
Over the course of this year, through inquiry and problem solving students will develop the conceptual understanding of many algebra topics and prepare for the formal study of algebra in the following years.
Unit 1: Volume and Irrational Numbers
Over the course of unit 1, volume problems create the need for an understanding of irrational numbers. Students build and understand the formulas for the volume of cylinders, cones, and spheres, and use them to find volumes and missing dimensions. In this way, the need to understand irrational numbers is created. Students learn how to find rational approximations for irrational numbers and when a solution should be written precisely or approximately.
Common Core State Standards: 8.NS.A.1, 8.NS.A.2, 8.G.C.9, 8.EE.A.2,
Unit 2: Pythagorean Theorem
Students will discover the Pythagorean Theorem through observations of patterns. They will use the theorem to solve a variety of problems including distance on the coordinate plane. Students will then experience and explain a variety of geometric proofs of the theorem and develop a general understanding of proof.
Common Core State Standards: 8.G.B.6, 8.G.B.7, 8.G.B.8, 8.EE.A.2, 8.NS.A.1, 8.NS.A2.
Unit 3: Using Angle Measures (One Variable Equations)
To begin Unit 3 students will be confronted with a problem that doesn’t seem to have a solution. Students discover the relationship between angles formed by parallel lines and a transversal and the relationships between the angles of triangles, both interior and exterior. Algebra is used to solve for missing angles measures and students encounter problems with no real solutions.
Common Core State Standards: 8.G.B.6, 8.G.B.7, 8.G.B.8, 8.EE.A.2, 8.NS.A.1, 8.NS.A.2
Unit 4: Functions and Linear Equations
Students begin Unit 4 by graphing the relationships between the change in the radius of a cylinder and the changing volumes. “Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among table, equation, graph and verbal representations and partial representations of functions.”
Common Core State Standards: 8.F.A.1, 8.F.A.2, 8.F.A.3, 8.F.B.4, 8.F.B.5, 8.EE.B.5, 8.EE.B.6,
Unit 5: Systems of Linear Equations
In Unit 5 students begin the study of simultaneous equations using a problem that creates a need to analyze two relations simultaneously. The benefit of using a graph becomes apparent through the nature of the problem. They build the understanding of the meaning of the solution to a system first graphically, then analytically. A variety of methods are then used to solve simple systems of equations: inspection, substitution with y = ax + b and y = cx + d and finally, substitution with one equation in standard form. The graphing calculator is introduced as a method for solving systems, then also for solving equations in one variable.
Common Core State Standards: 8.EE.C.8A, 8.EE.C.8B, 8.EE.C.8C, 8.EE.C.7a, 8.EE.C.7b
Unit 6: Scientific Notation and Properties of Exponents
Students will discover the need for an efficient way to write and work with very large and very small numbers. The work with scientific notation will lead to the articulation of the patterns discovered in exponential expressions leading to the power properties. Although the patterns with exponents (properties) will be communicated through algebraic symbols, students will realize that the memorization of the rules is not required. Instead, the patterns make sense and can always be reasoned logically by expanding and compressing the expression.
Unit 7: Transformations
Students will express translations previously learned algebraically using mapping. They will discover the relationship between rigid transformations (isometries) and congruence. Then the work will focus on dilations and similarity. Students will discover that although the definition of similarity involves the proportionality of sides of similar shapes and the congruence of angles, students deduce that similarity of triangles can be determined using only 2 pairs of congruent angles.
Common Core State Standards: 8.G.A.1A, 8.G.A.1.B, 8.G.A.1.C, 8.G.A.2, 8.G.A.3, 8.G.A.4, 8G.A.5
Unit 8: Bivariate Data
In unit 8, students explore associations between sets of data. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation. Association is also explored through representations in two-way tables using percents and ratios.
Common Core State Standards: 8.SP.A.1, 8.SP.A.2, 8.SP.A.3, 8.SP.A.4