Math - Eighth Grade

These Open Educational Resources are comprehensive and coherent curricular materials that may be used to teach a course or grade level.

 

• Chapter 1 - Mathematical Foundation (UMSMP)
  This is Chapter 1 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Analyzing and Solving Linear Equations.
• Chapter 1 - Student Workbook (UMSMP)
  This is Chapter 1 of the Utah Middle School Math: Grade 8 student workbook. It covers analyzing and solving linear equations.
• Chapter 2 - Mathematical Foundation (UMSMP)
  This is Chapter 2 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Proportional and Linear Relationships.
• Chapter 2 - Student Workbook (UMSMP)
  This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships.
• Chapter 3 - Mathematical Foundation (UMSMP)
  This is Chapter 3 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Representations of a Line.
• Chapter 3 - Student Workbook (UMSMP)
  This is Chapter 3 of the Utah Middle School Math: Grade 8 student workbook. It covers Representations of a Line.
• Chapter 4 - Mathematical Foundation (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Functions.
• Chapter 4 - Student Workbook (UMSMP)
  This is Chapter 4 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Functions.
• Chapter 5 - Mathematical Foundation (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Simultaneous Linear Equations.
• Chapter 5 - Student Workbook (UMSMP)
  This is Chapter 5 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Simultaneous Linear Equations.
• Chapter 6 - Mathematical Foundation (UMSMP)
  This is Chapter 6 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Statistics: Investigate patterns of Association in Bivariate Data.
• Chapter 6 - Student Workbook (UMSMP)
  This is Chapter 6 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Statistics: Investigate patterns of Association in Bivariate Data.
• Chapter 7 - Mathematical Foundation (UMSMP)
  This is Chapter 7 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Rational and Irrational Numbers.
• Chapter 7 - Student Workbook (UMSMP)
  This is Chapter 7 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Rational and Irrational Numbers.
• Chapter 8 - Mathematical Foundation (UMSMP)
  This is Chapter 8 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Integer Exponents, Scientific Notation and Volume.
• Chapter 8 - Student Workbook (UMSMP)
  This is Chapter 8 of the Utah Middle School Math Grade 8 student workbook. It focuses on Integer Exponents, Scientific Notation and Volume.
• Chapter 9 - Mathematical Foundation (UMSMP)
  This is Chapter 9 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Transformations, Congruence and Similarity.
• Chapter 9 - Student Workbook (UMSMP)
  This is Chapter 9 of the Utah Middle School Math: Grade 8 student workbook. It focuses on these topics: Transformations, Congruence and Similarity.
• Chapter 10 - Mathematical Foundation (UMSMP)
  This is Chapter 10 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Angles, Triangles and Distance.
• Chapter 10 - Student Workbook (UMSMP)
  This is Chapter 10 of the Utah Middle School Math Grade 8 student workbook. It focuses Angles, Triangles and Distance.



 

Engage NY
• Grade 8 Math Module 1: Integer Exponents and Scientific Notation (EngageNY)
  In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent. Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other. This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form.
• Grade 8 Math Module 2: The Concept of Congruence (EngageNY)
  In this Grade 8 module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.
• Grade 8 Math Module 3: Similarity (EngageNY)
  In 8th grade Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles. The module begins with the definition of dilation, properties of dilations, and compositions of dilations. One overarching goal of this module is to replace the common idea of same shape, different sizes with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.
• Grade 8 Math Module 4: Linear Equations (EngageNY)
  In 8th grade Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
• Grade 8 Math Module 5: Examples of Functions from Geometry (EngageNY)
  In the first topic of this 15 day 8th grade module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two. Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line. Students compare linear functions and their graphs and gain experience with non-linear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.
• Grade 8 Math Module 6: Linear Functions (EngageNY)
  In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students work in algebra in Grade 9.
• Grade 8 Math Module 7: Introduction to Irrational Numbers Using Geometry (EngageNY)
  Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form ofx2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.



 

Georgia Standards of Excellence Curriculum Frameworks
• Grade 8 Unit 1: Transformations, Congruence, and Similarity (Georgia Standards)
  In this unit students will develop the concept of transformations and the effects that each type of transformation has on an object; explore the relationship between the original figure and its image in regards to their corresponding parts being moved an equal distance which leads to concept of congruence of figures; learn to describe transformations with both words and numbers; relate rigid motions to the concept of symmetry and to use them to prove congruence or similarity of two figures; physically manipulate figures to discover properties of similar and congruent figures; and focus on the sum of the angles of a triangle and use it to find the measures of angles formed by transversals (especially with parallel lines), find the measures of exterior angles of triangles, and to informally prove congruence.
• Grade 8 Unit 2: Exponents and Equations (Georgia Standards)
  In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational.
• Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)
  In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.
• Grade 8 Unit 4: Functions (Georgia Standards)
  In this unit students will recognize a relationship as a function when each input is assigned to exactly one unique output; reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output; produce a counterexample: an input value with at least two output values when a relationship is not a function; explain how to verify that for each input there is exactly one output; and translate functions numerically, graphically, verbally, and algebraically.
• Grade 8 Unit 5: Linear Functions (Georgia Standards)
  In this unit students will graph proportional relationships; interpret unit rate as the slope; compare two different proportional relationships represented in different ways; use similar triangles to explain why the slope is the same between any two points on a non-vertical line; derive the equation y = mx for a line through the origin; derive the equation y = mx + b for a line intercepting the vertical axis at b; and interpret equations in y = mx + b form as linear functions.
• Grade 8 Unit 6: Linear Models and Tables (Georgia Standards)
  In this unit students will identify the rate of change and the initial value from tables, graphs, equations, or verbal descriptions; write a model for a linear function; sketch a graph when given a verbal description of a situation; analyze scatter plots; informally develop a line of best fit; use bivariate data to create graphs and linear models; and recognize patterns and interpret bivariate data.
• Grade 8 Unit 7: Solving Systems of Equations (Georgia Standards)
  In this unit students will understand the solution to a system of equations is the point of intersection when the equations are graphed; understand the solution to a system of equations contains the values that satisfy both equations; find the solution to a system of equations algebraically; estimate the solution for a system of equations by graphing; understand that parallel lines have will have the same slope but never intersect; therefore, have no solution; understand the two lines that are co-linear share all of the same points; therefore, they have infinitely many solutions; and apply knowledge of systems of equations to real-world situations.



 

 

The Online Core Resource pages are a collaborative project between the Utah State Board of Education and the Utah Education Network. If you would like to recommend a high quality resource, contact Trish French (Elementary) or Lindsey Henderson (Secondary). If you find inaccuracies or broken links contact resources@uen.org.