# Math Curriculum – Grade 8

The middle school Math program is closely aligned with the New York State Learning Standards for Mathematics and share the same goals to provide students with the knowledge and understanding of mathematics necessary to function in a world very dependent upon the application of mathematics. Focus in the curriculum is meant to give students an opportunity to understand concepts and practice with them in order to reach a deep and fluent understanding. Coherence in the curriculum means progressions that span grade levels to build students’ understanding of ever more sophisticated mathematical concepts and applications. Rigor means a combination of fluency exercises, chains of reasoning, abstract activities, and contextual activities throughout the module.

The Mathematics standards presented by the New York State Learning Standards describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

The New York State Learning Standards include six instructional shifts to facilitate student proficiency in mathematics with a focus on shifting instructional methodology on the Practice Standards.  The Practice standards include:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

For additional information regarding state standards go to the NYS Learning Standards for Mathematics.

In Grade 8, instructional time will focus on three critical areas:

1. Through their learning in the Number System, the Expressions, Equations, and Inequalities, and the Probability and Statistics domains, students:

• recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin;
• understand that the slope (m) of a line is a constant rate of change, as well as how the input and output change as a result of the constant rate of change;
• interpret a model in the context of the data by expressing a linear relationship between the two quantities in question and interpret components of the relationship (such as slope and y-intercept) in terms of the situation;
• solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line; and
• use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to represent, analyze, and solve a variety of problems.

2. Through their learning in the Functions and the Expressions, Equations, and Inequalities domains, students:

• grasp the concept of a function as a rule that assigns to each input exactly one output;
• understand that functions describe situations where one quantity determines another; and
• translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations of the function), and describe how aspects of the function are reflected in the different representations.

3. Through their learning in the Geometry domain, students:

• use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems;
• show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines;
• understand the statement of the Pythagorean Theorem and its converse, and why the Pythagorean Theorem holds; and
• apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons

Grade 8 Accelerated Mathematics/ Algebra I