Common Core Learning Standards s1

Common Core Learning Standards

GRADE 8 Mathematics

EXPRESSIONS & EQUATONS

Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Work with radicals and integer exponents. / Properties of exponents / Divide the numerical expressions with integer exponents with like bases by subtracting the exponents. / § Base
§ Exponent
§ Integer
§ Expression
§ Monomial
§ Coefficient
§ Numerical expression
Evaluate numerical expressions with integer exponents.
8.EE.1.
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,
= / Write a numerical expression with a negative exponent as an equivalent numerical expression with a positive exponent (write the base as a fraction).
Multiply numerical expressions with integer exponents with like bases by adding the exponents.
Add and subtract and divide numerical expressions with integer exponents.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Work with radicals and integer exponents. / Square roots and cube roots / Calculate the solution to x2 = p, where p is a positive rational number by taking the square root of both sides. / § Square root
§ Cube root
§ Squared
§ Cubed
§ Solution
§ Perfect square
§ Perfect cube
§ Exponent
§ Inverse operation
§ Index
§ Rational
§ Irrational
Calculate the solution to x3 = p, where p is a positive rational number by taking the cube root of both sides.
8.EE.2.
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational. / Evaluate a square root of a perfect square.
Name numbers that are perfect squares and non-perfect squares.
Evaluate a cube root of a perfect cube.
Name numbers that are perfect cubes and non-perfect cubes.
Identify that non-perfect squares and non-perfect cubes are irrational numbers (focus on ).
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Work with radicals and integer exponents. / Scientific notation / Compare the magnitude (size) of 2 or more numbers written in scientific notation. / § Scientific Notation
§ Magnitude
§ Standard Form
§ Estimate
§ Expand
Rewrite numbers in standard form in scientific notation.
8.EE.3.
Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 X and the population of the world as 7 X , and determine that the world population is more than 20 times larger. / Expand numbers written in scientific notation into standard form.
Divide numbers in scientific notation to compare their sizes.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Work with radicals and integer exponents. / Operations with scientific notation / Add, subtract, multiply, and divide numbers written in scientific notation, applying laws of exponents. / § Scientific notation
§ Decimal notation
§ Powers of 10
§ Standard form
§ Exponents
Find appropriate units for very large and small quantities.
8.EE.4.
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 (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. / Demonstrate on the calculator and identify that E on the calculator means x 10a.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Understand the connections between proportional relationships, lines, and linear equations. / Graphing relationships / Identify the slope of a linear relationship from equations, tables, and graphs. / § Proportions
§ Unit rate
§ Slope
§ Direct variation
Create and label an appropriate quadrant I graph.
8.EE.5.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance time equation to determine which of two moving objects has greater speed. / Describe unit rate as the slope of a graph.
Compare two different proportional relationships represented in different ways (graph vs. table vs. equation vs. verbal description).
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Understand the connections between proportional relationships, lines, and linear equations. / Linear equations / Determine the slope of a line by counting the rise over the run of the given line. / § Slope
§ Y-intercept
§ Slope intercept form
§ Similar triangles
§ Non-vertical line
§ Origin
§ Constant rate of change
Explain why the slope of a line is the same for any two points on the graph using rise over run.
8.EE.6.
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. / Explain slope as a constant rate of change (rise over run).
Given a line that passes through the origin, write the equation for the line in the form y = mx, where the slope is found using rise over run.
Given a line that passes the vertical axis at point other than the origin, write the equation for the line in the form y = mx + b, where the slope is found using rise over run and b is where the line intercepts the vertical axis.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Analyze and solve linear equations and pairs of simultaneous linear equations. / Solving linear equations / Solve a linear equation with one solution. / § Equation
§ Variable
§ Infinite solution
§ Linear
§ No solution
§ Inverse operation
§ Distributive property
§ Combine like terms
Solve a linear equation with infinitely many solutions.
8.EE.7a.
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 (where a and b are different numbers). / Solve a linear equation with no solution.
Check the solution to an equation.
Explain the differences between one solution, no solution, and infinitely many.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Analyze and solve linear equations and pairs of simultaneous linear equations. / Multi-step equations / Simplify equations using the distributive property, combining like terms, and inverse operations. / § Distributive property
§ Combine like terms
§ Coefficient
§ Inverse operations
§ Equations
§ Rational numbers
Solve multi-step linear equations with rational number coefficients.
8.EE.7b.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. / Add, subtract, multiply, and divide rational numbers.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Analyze and solve linear equations and pairs of simultaneous linear equations. / Systems of linear equations / Define the solution to a linear system of equations as the intersection point on a graph. / § System of equations
§ Solution
§ Point of intersection
Graph a system of linear equations.
8.EE.8a.
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. / Identify the point of intersection to a system of linear equations.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Analyze and solve linear equations and pairs of simultaneous linear equations. / Systems of equations algebraically / Solve a system of linear equations algebraically with one solution. / § Elimination
§ Substitution
§ Algebraically
§ Graphically
§ One solution
§ No solution
§ Infinitely many solutions
§ Systems of equations
Solve a system of linear equations algebraically with no solution.
8.EE.8b.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. / Solve a system of linear equations algebraically with infinitely many solutions.
Estimate the solution of a system of linear equations by graphing.
Solve simple systems of linear equations by inspection.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Analyze and solve linear equations and pairs of simultaneous linear equations. / Real world situations / Write a system of linear equations from a word problem. / § Intersect
§ Linear equation
§ Solution
§ Variable
§ Slope/rate of change
§ Y-intercept
§ Constraints
§ Coordinate plane
Solve a system of linear equations created from a word problem.
8.EE.8c.
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. / Graph points on a coordinate plane.
Calculate the slope of a line using the slope formula.
Create an appropriate coordinate plane based on the constraints of a word problem.
Rigorous Sample Tasks / Scaffolded Sample Tasks