Number System
Irrational Numbers
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
8.NS.A.1
Size of Irrational Numbers
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions
8.NS.A.2
Expressions & Equations
Properties of Exponents
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.A.1
Square & Cube Root
Use square root and cube root symbols to represent solutions to equations.Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
8.EE.A.2
Scientific Notation I
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.EE.A.3
Scientific Notation II
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology
8.EE.A.4
Proportional Relationship
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.B.5
Slope
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.B.6
Equation Solutions
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results.
8.EE.C.7.a
Solve Equations
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.EE.C.7.b
System of Equations
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
8.EE.C.8.a, 8.EE.C.8.b
Linear Equations
Solve real-world and mathematical problems leading to two linear equations in two variables.
8.EE.C.8.c
Functions
Functions
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.A.1
Rate of Change
Compare properties of two functions each represented in a different way.
8.F.A.2
Function of Linear Equation
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
8.F.A.3
Construct Function
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B.4
Geometry
Transformation of Points
Verify experimentally the properties of rotations, reflections, and translations.
8.G.A.1
Transformation of Lines
Verify experimentally the properties of rotations, reflections, and translations.
8.G.A.1
Transformation of Angles
Verify experimentally the properties of rotations, reflections, and translations.
8.G.A.1
Congruent Shapes
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.A.2, 8.G.A.4
Transformation of Shapes
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.A.3
Angles
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
8.G.A.5
Pythagorean Theorem I
Explain a proof of the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.B.6, 8.G.B.7
Pythagorean Theorem II
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.G.B.8, 8.G.B.7
