Students will build new mathematical knowledge through problem solving.
8.PS.1 
Use a variety of strategies to
understand new mathematical content
and to develop more efficient
methods

8.PS.2 
Construct appropriate extensions to problem situations 
8.PS.3 
Understand and demonstrate how written symbols represent mathematical ideas 
Students will solve problems that arise in mathematics and in other contexts.
8.PS.4 
Observe patterns and formulate
generalizations

8.PS.5 
Make conjectures from generalizations 
8.PS.6 
Represent problem situations verbally, numerically, algebraically, and graphically 
Students will apply and adapt a variety of appropriate strategies to solve problems.
8.PS.7 
Understand that there is no one
right way to solve mathematical problems but that different methods have advantages and disadvantages

8.PS.8 
Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem 
8.PS.9 
Work backwards from a solution 
8.PS.10 
Use proportionality to model problems 
8.PS.11 
Work in collaboration with others to solve problems 
Students will monitor and reflect on the process of mathematical problem solving.
8.PS.12 
Interpret solutions within the given constraints of a problem 
8.PS.13 
Set expectations and limits for possible solutions 
8.PS.14 
Determine information required to solve the problem 
8.PS.15 
Choose methods for obtaining required information 
8.PS.16 
Justify solution methods through logical argument 
8.PS.17 
Evaluate the efficiency of different representations of a problem 
Students will recognize reasoning and proof as fundamental aspects of mathematics.
8.RP.1 
Recognize that mathematical ideas can be
supported by a variety of strategies 
Students will make and investigate mathematical conjectures.
8.RP.2 
Use mathematical strategies to reach a conclusion 
8.RP.3 
Evaluate conjectures by distinguishing relevant from
irrelevant information to reach a conclusion or make
appropriate estimates 
Students will develop and evaluate mathematical arguments and proofs.
8.RP.4 
Provide supportive arguments for conjectures 
8.RP.5 
Develop, explain, and verify
an argument using mathematical ideas and language 
Students will select and use various types of reasoning and methods of proof.
8.RP.6 
Support an argument by using a
systematic approach to test more
than one case 
8.RP.7 
Devise ways to
verify results or use counterexamples to refute incorrect
statements

8.RP.8 
Apply inductive
reasoning in making and supporting mathematical conjectures 
Students will organize and consolidate their mathematical thinking through
communication.
8.CM.1 
Provide a correct, complete, coherent, and clear
rationale for thought process used in problem solving

8.CM.2 
Provide an organized argument which explains rationale for strategy selection

8.CM.3 
Organize and accurately label work 
Students will communicate their mathematical thinking coherently and
clearly to peers, teachers, and others.
8.CM.4 
Share organized mathematical ideas through the
manipulation of objects, numerical tables, drawings, pictures, charts,
graphs, tables, diagrams, models and symbols in written and
verbal form

8.CM.5 
Answer clarifying questions from others

Students will analyze and evaluate the mathematical thinking and
strategies of others.
8.CM.6 
Analyze mathematical solutions shared by others 
8.CM.7 
Compare strategies used and solutions found by others in relation to their own work

8.CM.8 
Formulate mathematical questions that elicit,
extend, or challenge strategies, solutions, and/or conjectures of others 
Students will use the language of mathematics to express mathematical ideas precisely.
8.CM.9 
Increase their use of mathematical vocabulary and language when communicating with others 
8.CM.10 
Use appropriate language, representations, and
terminology when describing objects, relationships, mathematical
solutions, and rationale 
8.CM.11 
Draw conclusions about mathematical ideas through
decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing 
Students will recognize and use connections among mathematical ideas.
8.CN.1 
Understand and make connections
among multiple representations of the same mathematical idea

8.CN.2 
Recognize connections between
subsets of mathematical ideas 
8.CN.3 
Connect and apply a variety of strategies to solve
problems 
Students will understand how mathematical ideas interconnect and build
on one another to produce a coherent whole.
8.CN.4 
Model situations mathematically,
using representations to draw conclusions and formulate
new situations 
8.CN.5

Understand how concepts, procedures, and mathematical
results in one area of mathematics can be used to solve
problems in other areas of mathematics 
Students will recognize and apply mathematics in contexts outside of mathematics.
8.CN.6 
Recognize and provide examples of
the presence of mathematics in their daily lives 
8.CN.7 
Apply mathematical ideas to
problem situations that develop outside of
mathematics 
8.CN.8 
Investigate the presence of
mathematics in careers and areas of interest

8.CN.9 
Recognize and apply mathematics to
other disciplines, areas of interest, and societal issues 
Students will create and use representations to organize, record, and
communicate mathematical ideas.
8.R.1 
Use physical objects, drawings, charts, tables, graphs,
symbols, equations, or objects created using technology as representations 
8.R.2 
Explain, describe, and defend mathematical ideas using representations

8.R.3 
Recognize, compare, and use an array of representational forms

8.R.4 
Explain how different representations express the same relationship 
8.R.5 
Use standard and nonstandard representations with accuracy and detail 
Students will select, apply, and translate among mathematical representations
to solve problems.
8.R.6 
Use representations to explore problem situations 
8.R.7 
Investigate relationships between different representations and their impact on a given problem 
8.R.8 
Use representation as a tool for exploring and
understanding mathematical ideas 
Students will use representations to model and interpret physical, social,
and mathematical phenomena.
8.R.9 
Use mathematics to show and understand physical phenomena (e.g.,
make and interpret scale drawings of figures or scale models of objects) 
8.R.10 
Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks) 
8.R.11 
Use mathematics to show and understand mathematical
phenomena (e.g., use tables, graphs, and
equations to show a pattern underlying a function)

Students will understand meanings of operations and procedures, and how they
relate to one another.
Operations
8.N.1 
Develop and apply the laws of exponents for multiplication
and division 
8.N.2 
Evaluate expressions with integral exponents 
8.N.3 
Read, write, and identify
percents less than 1% and greater than
100% 
8.N.4 
Apply percents to:
 Tax
 Percent increase/decrease
 Simple interest
 Sale price
 Commission
 Interest rates
 Gratuities

Students will compute accurately and make reasonable estimates.
Estimation
8.N.5 
Estimate a percent of quantity,
given an application 
8.N.6 
Justify the reasonableness of answers using
estimation 
Students will represent and analyze algebraically a wide variety of problem
solving situations.
Variables and Expressions
8.A.1 
Translate verbal sentences into
algebraic inequalities 
8.A.2 
Write verbal expressions that
match given mathematical expressions 
8.A.3 
Describe a situation involving
relationships that matches a given graph 
8.A.4 
Create a graph given a
description or an expression for a
situation involving a linear or
nonlinear relationship 
8.A.5 
Use physical models to perform operations with
polynomials 
Students will perform algebraic procedures accurately.
Variables and Expressions
8.A.6 
Multiply and divide monomials 
8.A.7 
Add and subtract polynomials (integer coefficients) 
8.A.8 
Multiply a binomial by a
monomial or a binomial (integer
coefficients) 
8.A.9 
Divide a polynomial by a
monomial (integer coefficients) Note:
The degree of the denominator is less
than or equal to the degree of the
numerator for all variables. 
8.A.10 
Factor algebraic expressions using the GCF 
8.A.11 
Factor a trinomial in the form
ax^{2 }+ bx + c; a=1 and c
having no more than three sets of
factors

Equations and Inequalities
8.A.12 
Apply algebra to determine the measure of angles formed by or
contained in parallel lines cut by a transversal and by intersecting lines 
8.A.13 
Solve multistep inequalities
and graph the solution set on a number
line 
8.A.14 
Solve linear inequalities by
combining like terms, using the
distributive property, or moving
variables to one side of the inequality
(include multiplication or division of
inequalities by a negative number) 
Students will recognize, use, and represent algebraically patterns,
relations, and functions.
Patterns, Relations, And Functions
8.A.15 
Understand that
numerical information can be represented in multiple
ways: arithmetically, algebraically, and graphically 
8.A.16 
Find a set of ordered pairs to
satisfy a given linear numerical pattern
(expressed algebraically); then plot the
ordered pairs and draw the line 
8.A.17 
Define and use correct
terminology when referring to function
(domain and range) 
8.A.18 
Determine if a relation is a function

8.A.19 
Interpret multiple
representations using equation, table of
values, and graph 
Students
will use visualization and spatial reasoning to analyze characteristics and
properties of geometric shapes.
Constructions

8.G.0 
Construct the following using a straight edge and compass:
 Segment congruent to a segment
 Angle congruent to an angle Perpendicular bisector
 Angle bisector

Students will identify and justify geometric relationships, formally and
informally.
Geometric Relationships
8.G.1 
Identify pairs of vertical angles as congruent 
8.G.2 
Identify pairs of supplementary and complementary
angles 
8.G.3 
Calculate the missing angle in
a supplementary or complementary pair 
8.G.4 
Determine angle pair
relationships when given two parallel
lines cut by a transversal 
8.G.5 
Calculate the missing angle
measurements when given two parallel
lines cut by a transversal 
8.G.6 
Calculate the missing angle
measurements when given two intersecting
lines and an angle 
Students will apply transformations and symmetry to analyze problem solving
situations.
Transformational Geometry
8.G.7 
Describe and identify transformations in the plane, using proper
function notation (rotations, reflections, translations, and dilations) 
8.G.8 
Draw the image of a figure under rotations of 90 and 180 degrees 
8.G.9 
Draw the image of a figure under a reflection over a given line 
8.G.10 
Draw the image of a figure under a translation

8.G.11 
Draw the image of a figure under a dilation 
8.G.12 
Identify the properties
preserved and not preserved under a
reflection, rotation, translation, and
dilation 
Students will apply coordinate geometry to analyze problem solving
situations.
Coordinate Geometry
8.G.13 
Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change 
8.G.14 
Determine the yintercept of a
line from a graph and be able to explain
the yintercept 
8.G.15 
Graph a line using a table of values 
8.G.16 
Determine the equation of a line given the slope
and the yintercept 
8.G.17 
Graph a line from an equation in slopeintercept
form (y=mx+b) 
8.A.18 
Solve systems of equations graphically (only linear,
integral solutions, y=mx+b
format, no vertical/horizontal lines) 
8.A.19 
Graph the solution set of an inequality on a
number line 
8.A.20 
Distinguish between linear and
nonlinear equations ax^{2} + bx
+ c; a=1 (only graphically) 
8.A.21 
Recognize the characteristics
of quadratics in tables, graphs,
equations, and situations 
Students will determine what can be measured and how, using appropriate
methods and formulas.
Units of Measurement
8.M.1 
Solve equations/proportions to convert to equivalent
measurements within metric and customary measurement systems Note: Also
allow Fahrenheit to Celsius and vice versa. 
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06/20/2006