Edits
•
Correct common errors in spelling, punctuation,
grammar, and capitalization
•
Use dictionary, thesaurus, technology, and
other available references
•
Make appropriate editing changes
independently
•
Use proofreading marks
Publishing
•
Reflect upon and analyze own writing to
determine a plan for improvement after
receiving feedback on published work
•
Maintain an up-to-date writing portfolio that
contains sequential samples of writing that
reflect skill progression
Evaluating/Analyzing Self
•
Read and discuss own work
•
See self as a writer
•
Use the seven-traits model to reflect on and
improve writing
•
Assess progress and set writing goals of
own writing
•
See writing as an ongoing process and a means
to communicate one’s thoughts and ideas
Evaluating/Analyzing Others
•
Use the seven-traits model as criteria to
assess writing
•
Offer specific constructive feedback to others
based on the seven-traits model of writing
•
Review writing of authors to analyze
effective writing
•
Reflect on writing of other authors to improve
own writing
•
Identify possible bias, stereotyping, or
propaganda in writing
•
Effectively articulate the qualities that make a
piece of writing effective
•
Listen while others share
MATH
The Number System
Know that there are numbers that are not rational,
and approximate them by rational numbers
•
Know that numbers that are not rational are
called irrational
•
Understand informally every number has
decimal expansion; for rational numbers show
that decimal expansion repeats eventually,
and convert decimal expansion which repeats
eventually into rational number
•
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
•
Identify word names and standard numerals for
integers, fractions, decimals, percents, absolute
value, radicals, and ratios
•
Understand and compute real world problems
involving rational numbers, percents, ratios, and
proportions
Algebra
Reasoning with equations and inequalities
•
Solve and graph equations and inequalities
using scientific and graphing calculators and
computer spreadsheets
•
Identify and graph solutions of linear equalities,
inequalities and equations
Arithmetic with polynomials and rational
expressions
•
Understand and solve equations containing
polynomials and trinomials
Expressions and Equations
Work with radicals and integer exponents
•
Know and apply the properties of integer
exponents to generate equivalent numerical
expressions
•
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
133
Eighth Grade
small perfect cubes; know that √2 is irrational
•
Use numbers expressed in the form of 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
•
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
•
Understand and solve problems by applying
the laws of exponents
•
Simplify, evaluate, and solve two-step algebraic
inequalities…using a variety of strategies,
concrete materials, and models
•
Solve problems using scientific notation
•
Graph and solve non-linear equations
•
Solve systems equations using graphing,
substitution, and elimination
Understand the connections between
proportional relationships, lines, and linear
equations
•
Graph proportional relationships, interpreting
the unit rate as the slope of the graph;
compare two different proportional
relationships represented in different ways
•
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
Analyze and solve linear equations and pairs of
simultaneous linear equations
•
Solve linear equations in one variable
•
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
•
Solve linear equations with rational number
coefficients, including equations whose solutions
require expanding expressions using the
distributive property and collecting like terms
•
Analyze and solve pairs of simultaneous
linear equations
•
Understand that solutions to system of two linear
equations in two variables correspond to points of
intersection of their graphs; 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
•
Solve real-world and mathematical problems
leading to two linear equations in two variables
Functions
Define, evaluate, and compare 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
•
Compare properties of two functions each
represented in a different way
•
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
•
Solve word problems and graphi non-linear
functions
•
Identify the trigonometric ratios using both
provided tables and scientific calculators
Use functions to model relationships between
quantities
•
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
•
Describe qualitatively functional relationship
between two quantities by analyzing a graph.
Sketch a graph that exhibits the qualitative features
Nobel Learning Curriculum Reference Guide
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