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Common Core Learning Standards
GRADE 8 Mathematics
EXPRESSIONS & EQUATONS
Common Core Learning
Standards
Work with radicals and integer
exponents.
Concepts
Embedded Skills
Properties of
exponents
Divide the numerical expressions with integer
exponents with like bases by subtracting the
exponents.
Evaluate numerical expressions with integer
exponents.
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.
8.EE.1.
Know and apply the properties of integer
exponents to generate equivalent numerical
expressions. For example,
=
Vocabulary
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Base
Exponent
Integer
Expression
Monomial
Coefficient
Numerical
expression
Add and subtract and divide numerical expressions
with integer exponents.
Rigorous Sample Tasks
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Work with radicals and integer
exponents.
Concepts
Embedded Skills
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.
Calculate the solution to x3 = p, where p is a positive
rational number by taking the cube root of both
sides.
Evaluate a square root of a perfect square.
Name numbers that are perfect squares and nonperfect squares.
Evaluate a cube root of a perfect cube.
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.
Name numbers that are perfect cubes and nonperfect cubes.
Vocabulary
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Square root
Cube root
Squared
Cubed
Solution
Perfect square
Perfect cube
Exponent
Inverse
operation
Index
Rational
Irrational
Identify that non-perfect squares and non-perfect
cubes are irrational numbers (focus on ).
Rigorous Sample Tasks
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Work with radicals and integer
exponents.
Concepts
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.
Rigorous Sample Tasks
Embedded Skills
Vocabulary
Compare the magnitude (size) of 2 or more
numbers written in scientific notation.
Rewrite numbers in standard form in scientific
notation.
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Expand numbers written in scientific notation into
standard form.
Divide numbers in scientific notation to compare
their sizes.
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Scientific
Notation
Magnitude
Standard
Form
Estimate
Expand
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Work with radicals and integer
exponents.
Concepts
Embedded Skills
Add, subtract, multiply, and divide numbers written
Operations
with scientific in scientific notation, applying laws of exponents.
Find appropriate units for very large and small
notation
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.
Rigorous Sample Tasks
quantities.
Demonstrate on the calculator and identify that E
on the calculator means x 10a.
Vocabulary
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Scientific
notation
Decimal
notation
Powers of 10
Standard form
Exponents
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand the connections between
proportional relationships, lines, and
linear equations.
Concepts
Graphing
relationships
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.
Rigorous Sample Tasks
Embedded Skills
Identify the slope of a linear relationship from
equations, tables, and graphs.
Create and label an appropriate quadrant I graph.
Describe unit rate as the slope of a graph.
Vocabulary
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Proportions
Unit rate
Slope
Direct
variation
Compare two different proportional relationships
represented in different ways (graph vs. table vs.
equation vs. verbal description).
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand the connections between
proportional relationships, lines, and
linear equations.
Concepts
Embedded Skills
Linear
equations
Determine the slope of a line by counting the rise
over the run of the given line.
Explain why the slope of a line is the same for any
two points on the graph using rise over run.
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.
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.
Rigorous Sample Tasks
Vocabulary
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Slope
Y-intercept
Slope
intercept form
Similar
triangles
Non-vertical
line
Origin
Constant rate
of change
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze and solve linear equations
and pairs of simultaneous linear
equations.
Concepts
Solving linear
equations
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).
Rigorous Sample Tasks
Embedded Skills
Solve a linear equation with one solution.
Solve a linear equation with infinitely many
solutions.
Solve a linear equation with no solution.
Check the solution to an equation.
Explain the differences between one solution, no
solution, and infinitely many.
Vocabulary
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Equation
Variable
Infinite
solution
Linear
No solution
Inverse
operation
Distributive
property
Combine like
terms
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze and solve linear equations
and pairs of simultaneous linear
equations.
Concepts
Multi-step
equations
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.
Rigorous Sample Tasks
Embedded Skills
Simplify equations using the distributive property,
combining like terms, and inverse operations.
Solve multi-step linear equations with rational
number coefficients.
Add, subtract, multiply, and divide rational
numbers.
Vocabulary
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Distributive
property
Combine like
terms
Coefficient
Inverse
operations
Equations
Rational
numbers
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze and solve linear equations
and pairs of simultaneous linear
equations.
Concepts
Systems 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.
Rigorous Sample Tasks
Embedded Skills
Define the solution to a linear system of equations
as the intersection point on a graph.
Graph a system of linear equations.
Identify the point of intersection to a system of
linear equations.
Vocabulary
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System of
equations
Solution
Point of
intersection
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
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.
Solve a system of linear equations algebraically with
no solution.
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.
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.
Rigorous Sample Tasks
Vocabulary
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Elimination
Substitution
Algebraically
Graphically
One solution
No solution
Infinitely
many
solutions
Systems of
equations
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze and solve linear equations
and pairs of simultaneous linear
equations.
Concepts
Real world
situations
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.
Rigorous Sample Tasks
Embedded Skills
Write a system of linear equations from a word
problem.
Solve a system of linear equations created from a
word problem.
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.
Vocabulary
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Intersect
Linear
equation
Solution
Variable
Slope/rate of
change
Y-intercept
Constraints
Coordinate
plane
Scaffolded Sample Tasks
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.