8th Grade Mathematics

Grade 8 mathematics focuses on three critical areas:
  • Reasoning about expressions and equations which includes modeling bivariate data with linear equations and solving linear equations and systems of linear equations
  • Grasping the concept of a function and using functions to describe qualitative relationships
  • Analyzing 2 and 3 dimensional space and figures using distance, angles, similarity and congruence and applying the Pythagorean Theorem

First Quarter

 During the first 9-weeks...
students will:
  • 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
  • translate among representations and partial representations of functions
  • describe how aspects of the function are reflected in the different representations
  • recognize equations for proportions (y/x = m) 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, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount mA.
  • understand and apply the Pythagorean theorem to find distances between points on the coordinate plane, find lengths and analyze polygons
They will also learn:
  • there are numbers that are not rational, and approximate them by rational numbers
  • numbers that are not rational are called irrational and understand that every number has a decimal expansion
  • for rational numbers, to show that the decimal expansion repeats and  use rational approximations of irrational numbers to compare the size of irrational numbers and approximately locate them on a number line diagram
  • the meaning behind square root and cubed root symbols 
Standards Addressed:
Functions: F.1,2,3,4
Geometry: G.6,7,8
Number System: NS.1,2
Expressions and Equations: EE. 2,5

Second Quarter

During the second 9-weeks...
Students will build on their work with functions from the first nine weeks to:
  • use linear equations and to represent, analyze, and solve a variety of problems. 
  • recognize equations for proportions (y/x = m) as special linear equations (y = mx + b),
  • understand that the constant of proportionality (m) is the slope​ 
  • understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount mA.
  • to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.
  • strategically choose and efficiently implement procedures to solve linear equations in one variable
  • use linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
  • give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions
  • 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.
  • translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations),
  • describe how aspects of the function are reflected in the different representations.
Standards Addressed:
​Functions: F.1,3,4
​Expressions and Equations: EE. 5,6,7 a,7b,

Third Quarter

During the third 9-weeks....
Students will:
  • 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 angle 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.
  • apply their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest.
  • analyze bivariate measurement data graphed on a scatterplot by describing shape, center, and spread.  "Shape” refers to a cloud of points on a plane, “center” refers to a line drawn through the cloud that captures the essence of its shape, and “spread” refers to how far the data points stray from this central line.
  • extend their understanding of “cluster” and “outlier” from univariate data to bivariate data.
  • summarize bivariate categorical data using two-way tables of counts and/or proportions, and examine these for patterns of association.
Standards Addressed:
​Geometry:  G.1,2,3,4,5
Statistics:  SP.1,2,3,4
​Functions:  F.5

Fourth Quarter

During the fourth 9-weeks......
Students will continue their work with Solid Geometry and Expressions and Equations.  
For Geometry they will:
  • build on their knowledge of volume to learn the formulas for cones, spheres and cylinders and use the formulas to solve real-world and mathematical problems.
For Expressions and Equations they will:
  • know and apply the properties of integer exponents to generate equivalent expressions
  • use numbers expressed in scientific notation to estimate very small and very large numbers and perform operations with numbers expressed in scientific notation
  • ​extend their knowledge of linear equations to solving pairs of simultaneous linear equations
Standards Addressed:
Geometry: 9
Expressions and Equations:
1,3,4,7,8
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