Mathematics

Mathematics 8 Mathematics Course Description

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

formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations;
grasping the concept of a function and using functions to describe quantitative relationships;
analyzing two‐ and three‐dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Numbers and Operations

Determine whether a number is rational or irrational. For example, √18 is irrational because its decimal expansion (4.24264069…) does not repeat.
Convert a terminating or repeating decimal into a rational number. For example, 0.363636...is equal to 36/99 which can be reduced to 4/11.
Estimate the value of an irrational number without a calculator. For example, √20 is between 4 and 5 because it is between √16 and √25.
Use rational approximations of irrational numbers to compare and order irrational numbers. For example, √35 is less than 6, and 2√10 is more than 6, so √35 < 2√10 .
Locate rational and irrational numbers on a number line.

Geometry

Identify and apply the properties of rotations, reflections, and translations.
Using coordinates, describe the effects of dilations, translations, rotations, and reflections on two‐ dimensional figures.
Apply the converse of the Pythagorean Theorem to show that a triangle is a right triangle. For example, a triangle with side lengths 5 cm, 6 cm and 8 cm is not a right triangle because 52 +62 ≠ 82.
Apply the Pythagorean Theorem to find unknown side lengths in right triangles.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. For example, the distance between (3, 7) and (6, 3) is 5 because (3– 6)2 + (7– 3)2 =52.
Apply formulas for the volumes of cones, cylinders, and spheres to solve problems.

Algebraic Concepts

Apply one or more properties of integer exponents to generate equivalent expressions. For example, (32 × 33)‐2 = 1/(310).
Use square root and cube root symbols to represent the solutions to exponential equations. For example, if x2 = 30 then x = ± √30.
Estimate very large or very small numbers using multiplication by a power of 10. For example, the population of the United States is about 3 × 108 (300,000,000).
Solve problems using scientific notation.
Graph proportional relationships, interpreting the unit rate as the slope.
Derive the equation y = mx and the equation y = mx + b for lines based on the slope and the y‐intercept.
Solve linear equations in one variable. For example, given the equation 3(x– 2)+ 1 = 10, the solution is x = 5.
Solve and interpret the solution to a system of two linear equations. For example, given the linear system
3x+ 2y = 18 and 2x+ 5y = 23, the solution Is x = 4 and y = 3.
Determine whether a relation is a function. For example, y = 3x+ 2 is a function because the graph of y = 3x+ 2 passes the vertical line test.
Compare properties of two different functions presented in different ways.
Describe the functional relationship between two quantities using a graph.

Measurement, Data, and Probability

Construct scatter platos to look at relationship between two quantities.
Find the line of best fit for scatter plots that show a linear association.
Interpret the slope and the y-intercept of the line of best fit in the context of the problem.
Construct and interpret a two-way table using relative frequencies.

Algebra 1A is the first of a two-course Algebra study at the High School Level.

Algebra 1B is the second of a two-course Algebra study at the High School Level.