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8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work:
problem solving is important, takes significant time and repeated efforts, and requires reflection.
Essential Question - What are the specific strategies that have wide application in attacking problems and
can help in problem solving?
FP.8.1 12 NO.3.8.2 Solve, with and without appropriate with and without appropriate mental computation
Solve, with and without appropriate technology, multi-step problems using a technology: technology
technology, multi-step problems using a variety of methods and tools (Ex. objects, *represent multi-step problems using distributive property
variety of methods and tools (i.e. objects, mental computation, paper and pencil) manipulatives (including 2 or more rational numbers
mental computation, paper and pencil) steps) like terms
*solve problems mentally problem-solving
Note: This is identical to the 7th grade SLE. *solve multi-step problems with strategy
paper and pencil
FP.8.1 6 NO.3.8.1 Compute, with and without appropriate with and without appropriate rational numbers
Compute, with and without appropriate technology, with rational numbers in technology: distributive property
technology, with rational numbers in multi- multi-step problems *select an appropriate problem- like terms
step problems (positive and negative solving strategy equation
rational numbers) *translate word problems (Ex. write problem-solving
an equation) strategies
*compute with positive and negative
rational numbers in one-step
problems
*compute with positive and negative
rational numbers in multi-step
problems
rev. 05-2009 1 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FIRST NINE WEEKS
1. Enduring Understanding - Real numbers are either rational or irrational.
1a. Essential Question - Why use exponents?
C.8.4 NO.1.8.1 A. Read, write and compare numbers with and without appropriate scientific notation * Place value
Read, write, compare and solve problems, less than one in scientific notation with technology: standard form
with and without appropriate technology, and without appropriate technology *use patterns of exponents to written form
including numbers less than one in B. Solve problems involving numbers evaluate zero and negative exponent
scientific notation less than one in scientific notation with exponents power
and without appropriate technology *use the properties of exponents to base
simplify expressions
*convert from written form to
standard form (Ex. ten
million↔10,000,000)
*convert from standard form to
scientific notation (Ex. 3,456↔3.456
x 103)
*convert from scientific notation to
standard form (Ex. 3.456
x103↔3,456)
*compare numbers in scientific
notation
*identify problem-solving strategies
*compute with scientific notation
rev. 05-2009 2 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
C.8.4 3 NO.1.8.2 Demonstrate, with and without with and without appropriate review scientific
Convert between scientific notation and appropriate technology, conversion technology: notation
standard notation, including numbers from between scientific notation and standard *use patterns of exponents to standard form
zero to one notation, including numbers from zero to evaluate zero and negative written form
one exponents convert
*use the properties of exponents to exponent
simplify expressions power
*convert from written form to base
standard form (Ex. ten
million↔10,000,000)
*convert from standard form to
scientific notation (Ex. 3,456↔3.456
x 103)
*convert from scientific notation to
standard form (Ex. 3.456
x103↔3,456)
*compute with scientific notation
1b. Essential Question - What kinds of numbers make up the set of real numbers?
2 NO.1.8.4 Identify and justify classifications of *use the relationship of the number real numbers
Understand and justify classifications of numbers in the real number system systems to classify real numbers classify
numbers in the real number system *use characteristics of the number integers
systems to justify classification of value
real numbers
2 NO.1.8.3 A. Compare and order real numbers *classify real numbers number line * Compare decimals
Compare and order real numbers including including irrational numbers, with or *simplify different forms of numbers natural numbers * Convert fractions to
irrational numbers and find their without appropriate technology including fractions, square roots, and rational numbers decimals
approximate location on a number line (Use B. Locate the approximate placement of absolute values irrational numbers
technology when appropriate) real numbers including irrational numbers *compare and order real numbers real numbers
on a number line *locate irrational numbers on a square root
number line absolute value
rev. 05-2009 3 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
1 NO.2.8.5 A. Model and develop computational *model and develop algorithms for fractions
Model and develop addition, subtraction, skills in addition, subtraction, rational number operations with denominator
multiplication and division of rational multiplication and division of rational manipulatives numerator
numbers (positive and negative rational numbers *solve equations with positive and rational numbers
numbers) Ex. negative rational numbers common
Ex. 8 1/2 + 2 3/4 *translate word problem to equation denominator
8 1/2 + 2 3/4 B. Apply computational skills in addition, least common
subtraction, multiplication and division of denominator
rational numbers simplify
Ex. number sentence
8 1/2 + 2 3/4
FP.8.1 NO.2.8.2 Describe and apply the inverse and *identify inverse operations inverse property
Understand and apply the inverse and identity properties *apply inverse operations identity properties
identity properties *identify the inverse property (addition,
*apply the inverse property multiplication)
*identify the identity properties
(addition and multiplication)
*apply the identity properties
(addition and multiplication)
1c. Essential Question - How do operations with rational numbers compare to operations with integers?
FP.8.1 1 NO.2.8.4 Apply rules (conventions) for order of *use rules for order of operations: numerical
Apply rules (conventions) for order of operations to rational numbers •grouping symbols ( ), [ ], fraction bar expression
operations to rational numbers (positive and •exponents evaluate
negative rational numbers) •multiplication & division left to right order of operations
•addition & subtraction left to right acronym (Ex.
*solve problems with integers and PEMDAS,
positive rational numbers using order GEMDAS)
of operations rational numbers
1d. Essential Question - How are roots and powers related?
C.8.4 3 NO.3.8.5 Calculate and find approximations of *estimate the square root, check with square roots
Calculate and find approximations of square roots with appropriate technology technology and find a closer approximating
square roots with appropriate technology approximation reasonable estimate
Note: Corresponding framework in 7th *find the square root with technology
grade includes absolute value
rev. 05-2009 4 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
C.8.4 1 NO.2.8.3 Solve problems using inverse *translate word problem to numerical inverse operations
Use inverse relationships (addition and relationships (addition and subtraction, equation for four properties (+,
subtraction, multiplication and division, multiplication and division, squaring and *use identity or inverse properties -, x, ÷) (review)
squaring and square roots) in problem square roots) in problem solving (addition and subtraction, squaring numbers
solving situations situations multiplication and division, squaring square root
and square roots) to solve one-step odd/even numbers
equation perfect square
*use identity or inverse properties prime
(addition and subtraction, composite
multiplication and division, squaring
and square roots) to solve two-step
equation
2. Enduring Understanding - Patterns and relationships can be represented graphically, numerically,
symbolically, and verbally.
2a. Essential Question - How can a pattern be identified?
4 A.4.8.1 Identify the value of the nth term in a *determine the rule of a pattern or pattern recognition
Find the nth term in a pattern or a function pattern or a function table function functions
table *write the rule as an algebraic input tables
expression or equation output tables
*express the rule in terms of x domain
*identify the value of the nth term in range
the pattern or function table nth term
5 A.4.8.2 Using real-world situations, describe or using real-world situations to: patterns
Using real-world situations, describe patterns express patterns in words, tables, *determine the rule for a geometric pictorial
in words, tables, pictures, and symbolic pictures, and symbolic representations pattern of shapes or a real-world representation
representations event input/output table
*describe the pattern with words real-world situations
*describe the pattern with a table symbolic
*describe the pattern with a picture representations
*describe the pattern with a symbolic
representation (Ex. graph)
rev. 05-2009 5 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
2b. Essential Question - How are patterns and relationships useful in working with algebraic expressions?
FP.8.1 9 A.5.8.3 A. Translate sentences into algebraic *translate phrases and sentences algebraic equations
Translate sentences into algebraic equations equations and inequalities into algebraic expressions inequalities
and inequalities and combine like terms B. Combine like terms within polynomials *translate sentences into algebraic combining like terms
within polynomials equations polynomials
*translate sentences into algebraic monomials
inequalities
*identify like terms in a polynomial
*add monomials
*subtract monomials
*combine like terms in a polynomial
FP.8.1 4 A.5.8.4 Write and evaluate algebraic expressions *write algebraic expressions using evaluate
Write and evaluate algebraic expressions using rational numbers rational numbers algebraic
using rational numbers *evaluate algebraic expressions expressions
using rational numbers rational numbers
NO.3.8.4 Apply factorization to find LCM and GCF *find prime factorization of algebraic prime numbers
Apply factorization to find LCM and GCF of algebraic expressions expressions relatively prime - 2
of algebraic expressions Ex. *use prime factorization to find the integers are
Ex. 4x2 y3 GCF of an algebraic expression relatively prime if
4x2y3 6xy2 *use prime factorization to find the they have no
6xy2 LCM of an algebraic expression common factors
GCF=2xy2
except 1 (Ex. 6 and
GCF=2xy2 LCM=12x2y3 5, or 6 and 25)
LCM=12x2y3 composite numbers
prime factorization
factor tree
monomial
least common
multiple
greatest common
factor
algebraic expression
multiple
common multiple
rev. 05-2009 6 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
SECOND NINE WEEKS
1. Enduring Understanding - Patterns and relationships can be represented graphically, numerically,
symbolically, and verbally.
1a. Essential Question - Why are equations and inequalities useful?
FP.8.1 2 A.4.8.3 Interpret and represent a two-operation *determine the rule of a two- algebraic equation
Interpret and represent a two-operation function as an algebraic equation operation function algebraic
function as an algebraic equation Ex. *write the rule as an algebraic representation
Ex. y = 2x + 1 equation function
y = 2x + 1
FP.8.1 A.4.8.4 Use tables, graphs, and equations to using tables, graphs and equations: equation
Use tables, graphs, and equations to identify identify independent/dependent variables *identify the dependent (output) input/output
independent/dependent variables (input/output) variable of a function independent/depend
(input/output) *identify the independent (input) ent variables
variable of a function
FP.8.1 NO.2.8.1 Solve two-step equations using addition, *apply order of operations when properties of
Apply the addition, subtraction, multiplication subtraction, multiplication and division appropriate to solve two-step equalities (+, -, x, ÷)
and division properties of equality to two- properties of equality equations equation
step equations *apply addition, subtraction, solution
multiplication and division properties solving an equation
of equality to one-step equations with distributive property
whole numbers integers
*apply addition, subtraction,
multiplication and division properties
of equality to one-step equations with
integers
*apply addition, subtraction,
multiplication and division properties
of equality to one-step equations with
fractions
*apply addition, subtraction,
multiplication and division properties
of equality to one-step equations with
decimals
rev. 05-2009 7 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
2. Enduring Understanding - Proportional situations involve multiplicative relationships.
2a. Essential Question - What kinds of questions can be answered using proportional reasoning?
C.8.1 12 NO.3.8.6 Solve, with and without appropriate with and without appropriate percent
Solve, with and without appropriate technology, real-world percent problems technology: percent of change
technology, real-world percent problems including percent of increase or decrease *translate word problems to percent of increase
including percent of increase or decrease equations percent of decrease
*solve percent increase problems markup
*solve percent decrease problems discount
interest
principal
annual interest rate
percents above 100
percents below 1
C.8.1 3 NO.3.8.3 Use estimation to solve problems *solve problems with ratios rational numbers
Use estimation to solve problems involving involving rational numbers including ratio, *solve problems with proportions estimate
rational numbers including ratio, proportion, proportion, percent (increase or *solve problems with percent ratio
percent (increase or decrease) then judge decrease) then judge the increase proportion
the reasonableness of solutions reasonableness of solutions *solve problems with percent percent
decrease percent of change
*identify best solution in a percent percent of increase
increase/decrease problems percent of decrease
*judge the reasonableness of solution
solutions reasonableness
rev. 05-2009 8 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.1 1 A.5.8.1 Solve and graph two-step equations and with and without appropriate two-step equations
Solve and graph two-step equations and inequalities with one variable and verify technology in real-world applications: inequalities
inequalities with one variable and verify the the reasonableness of the result with real- *solve two-step equations involving variable
reasonableness of the result with real-world world application with and without one variable and verify the unknown
application with and without appropriate appropriate technology reasonableness of the result graphing two-step
technology *solve two-step inequalities involving equations
one variable and verify the graphing two-step
reasonableness of the result inequalities
*graph two-step equations involving
one variable and verify the
reasonableness of the result
*graph two-step inequalities involving
one variable and verify the
reasonableness of the result
C.8.4 1 NO.2.8.3 Solve problems using inverse *translate word problem to numerical inverse operations
Use inverse relationships (addition and relationships (addition and subtraction, equation for four properties (+,
subtraction, multiplication and division, multiplication and division, squaring and *use identity or inverse properties -, x, ÷) (review)
squaring and square roots) in problem square roots) in problem-solving (addition and subtraction, squaring numbers
solving situations situations multiplication and division, squaring square root
and square roots) to solve one-step odd/even numbers
equation perfect square
*use identity or inverse properties prime
(addition and subtraction, composite
multiplication and division, squaring
and square roots) to solve two-step
equation
rev. 05-2009 9 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
3. Enduring Understanding - Linear relationships are characterized by a constant rate of change.
3a. Essential Question - What makes a relationship linear?
FP.8.1 2 A.6.8.2 Represent, with and without appropriate with and without appropriate linear
Represent, with and without appropriate technology, linear relationships technology: linear equation
technology, linear relationships concretely, concretely using tables, graphs and *identify the components of the slope relationship
using tables, graphs and equations equations intercept form for the equation of a slope
line intercept
*write equation of a line in slope
intercept form (y = mx + b)
*construct tables representing linear
relationships
*construct graphs representing linear
relationships
*construct equations representing
linear relationships
FP.8.1 A.6.8.3 Identify the independent/dependent *identify the independent variable in independent/depend
Differentiate between variables given a linear relationship in real-world problems ent variables
independent/dependent variables given a context *identify the dependent variable in
linear relationship in context real-world problems
3b. Essential Question - Why are linear functions useful?
FP.8.1 A.6.8.1 A. Describe, with and without appropriate with and without appropriate constant rate of
Describe, with and without appropriate technology, the relationship between the technology in real-world problems: change
technology, the relationship between the graph of a line and its equation *define the meaning of slope slope of a line
graph of a line and its equation, including B. Explain the meaning of slope as a (constant rate of change) slope intercept
being able to explain the meaning of slope constant rate of change (rise/run) and y- *identify positive, negative, undefined formula
as a constant rate of change (rise/run) and y- intercept in real-world problems and zero slope on a linear graph graph of a line
intercept in real-world problems *identify the meaning of the x- rise/run
intercept and y-intercept
*identify a graph by its slope and y-
intercept
*describe how the change of slope or
the y-intercept will affect the graph
rev. 05-2009 10 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.1 1 A.5.8.2 Solve and graph linear equations (in the *solve linear equations in slope linear equations
Solve and graph linear equations (in the form y=mx+b) intercept form horizontal lines
form y=mx+b) *graph linear equations in slope vertical lines
intercept form system of linear
*write equations in slope intercept equations
form solution of linear
equations
slope
intercept
coordinate points
ordered pairs
1 A.7.8.1 A. Use, with and without appropriate with and without appropriate predicted
Use, with and without appropriate technology, graphs of real-life situations technology: estimated
technology, graphs of real-life situations to to describe the relationships including *analyze a graph that represents a accumulation
describe the relationships and analyze graphs of change (cost per minute) and real-life event including graphs of graph of change
change including graphs of change (cost per graphs of accumulation (total cost) change and accumulation (e.g. cost graph of
minute) and graphs of accumulation (total B. Use, with and without appropriate per minute, total cost) accumulation
cost) technology, graphs of real-life situations *analyze a table that represents a
to analyze change including graphs of real-life event
change (cost per minute) and graphs of *make predictions of a real-life event
accumulation (total cost) based on its graph
*make predictions of a real-life event
based on its table
rev. 05-2009 11 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
4. Enduring Understanding - The characteristics of non-linear functions and their representations are useful
in solving real-world problems.
4a. Essential Question - How do linear and non-linear functions compare?
C.8.1 2 A.6.8.4 A. Represent, with and without with and without appropriate quadratic function
Represent, with and without appropriate appropriate technology, simple technology: exponential function
technology, simple exponential and/or exponential functions using verbal *identify tables, graphs, and formulas translate
quadratic functions using verbal descriptions, tables, graphs and formulas of simple exponential functions
descriptions, tables, graphs and formulas and translate among these *identify tables, graphs, and formulas
and translate among these representations representations of simple quadratic functions
B. Represent, with and without *construct tables, graphs, and
appropriate technology, simple quadratic formulas of simple exponential
functions using verbal descriptions, functions
tables, graphs and formulas and *construct tables, graphs, and
translate among these representations formulas of simple quadratic
functions
*translate between tables, graphs,
and formulas for exponential
functions
*translate between tables, graphs,
and formulas for quadratic functions
rev. 05-2009 12 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
THIRD NINE WEEKS
1. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, and areas of
two-dimensional figures.
1a. Essential Question - How are areas of rectangles, parallelograms, triangles, trapezoids, and circles
related?
1 M.13.8.1 Draw and apply measurement skills with *read units of measure with different precision of
Draw and apply measurement skills with fluency to appropriate levels of precision tools (protractor, ruler, tape measure, measurement
fluency to appropriate levels of precision etc) accurate
*draw units of measure with different represent
tools (protractor, ruler, meter stick) estimate
*apply measurement skills (Ex. protractor
determine the perimeter of geometric ruler
shapes) meter stick
yard stick
standard/customary
units
metric units
rev. 05-2009 13 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.2 22 M.12.8.1 A. Select and use, with and without with and without appropriate perimeter formula
Understand, select and use, with and without appropriate technology, the appropriate technology: circumference
appropriate technology, the appropriate units units and tools to measure angles to *find angle measures formula
and tools to measure angles, perimeter, solve real-world problems *find the perimeter of polygons area formulas
area, surface area and volume to solve real- B. Select and use, with and without *use a graph to find area surface area
world problems appropriate technology, the appropriate *use formulas to find area volume formulas
units and tools to measure perimeter to *find the volume of prisms and protractor
solve real-world problems cylinders degrees
C. Select and use, with and without *find the volume of composite figures straight edge
appropriate technology, the appropriate *find the volume of pyramids and compass
units and tools to measure area to solve cones composite figures
real-world problems *find the surface area of prisms and interior angles
D. Select and use, with and without cylinders alternate interior
appropriate technology, the appropriate *find the surface area of pyramids angles
units and tools to measure surface area and cones complementary
to solve real-world problems supplementary
E. Select and use, with and without estimating
appropriate technology, the appropriate metric units
units and tools to measure volume to standard units
solve real-world problems square units
cubic units
FP.8.2 M.13.8.5 Estimate and compute the area of *use graph paper to estimate area of area of irregular
Estimate and compute the area of irregular irregular two-dimensional shapes irregular shapes shapes
two-dimensional shapes *find the area of basic geometric irregular shapes
shapes (square, rectangle, triangle, polygon
parallelogram) area
*compute the area of irregular two- estimate
dimensional shapes
2. Enduring Understanding - Geometric relationships exist between two-dimensional and three-dimensional
figures.
2a. Essential Question - How are two-dimensional and three-dimensional figures related?
G.11.8.1 Using isometric dot paper identify and *draw polyhedrons on isometric dot isometric dot paper
Using isometric dot paper interpret and draw different views of buildings paper polyhedron
draw different views of buildings *identify alternative two-dimensional two-dimensional
representations of three-dimensional three-dimensional
solids
rev. 05-2009 14 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.2 3 G.8.8.1 Compare and contrast the properties of *identify the properties of selected validate
Form generalizations and validate geometric shapes and validate findings geometric shapes conclude
conclusions about properties of geometric *compare and contrast the properties generalize
shapes of given geometric shapes line of symmetry
perpendicular
perimeter
area
volume
parallel
Pythagorean
Theorem
polygons
tessellation
two-dimensional
figures:
quadrilaterals
(rectangle, square,
parallelogram,
trapezoid, rhombus)
circle
ellipse
triangles (scalene,
isosceles,
equilateral, right,
acute, obtuse)
pentagons,
hexagons, octagon,
decagon, n-gon
three-dimensional
figures (pyramid,
cone, sphere,
cylinder, cube,
prism, tetrahedron)
rev. 05-2009 15 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.2 2 G.8.8.2 Make, with and without appropriate with and without appropriate two-dimensional
Make, with and without appropriate technology, and test conjectures about technology: figures (see G.8.8.1)
technology, and test conjectures about characteristics and properties between *identify the two-dimensional figure three-dimensional
characteristics and properties between two-dimensional figures and three- of the cross section of a three- figures (see G.8.8.1)
two-dimensional figures and three- dimensional objects dimensional solid from a model solid
dimensional objects Ex. *identify the two-dimensional figure polyhedron
Ex. circle vs. cylinder, square vs. cube of the cross section of a three- faces
circle vs. cylinder, square vs. cube dimensional solid from a drawing edge
vertex
defining properties of
shapes/figures
conjecture
cross-section
base
3. Enduring Understanding - Geometric figures can change position and maintain the same attributes on a
coordinate plane.
3a. Essential Question - Why graph geometric figures and transformations on a coordinate plane?
FP.8.2 G.10.8.1 Use coordinate geometry to explore the *find the length of line segment on a coordinate geometry
Use coordinate geometry to explore the links between geometric and algebraic coordinate plane geometric
links between geometric and algebraic representations of problems (lengths of *find the distance between points on representation
representations of problems (lengths of segments/distance between points, a coordinate plane algebraic
segments/distance between points, slope/perpendicular-parallel lines) *find the slope of a line on a representation
slope/perpendicular-parallel lines) coordinate plane perpendicular line
*find the slope of a perpendicular line parallel line
on a coordinate plane distance formula
*find the slope of a parallel line on a slope
coordinate plane Pythagorean
*find the missing side of a right Theorem
triangle
FP.8.2 M.13.8.4 Find the distance between two points on *find the length of a hypotenuse coordinate plane
Find the distance between two points in a a coordinate plane using the *find the length of a leg in a right Pythagorean
coordinate plane using the Pythagorean Pythagorean Theorem triangle Theorem
Theorem *use the Pythagorean Theorem to plane
find the distance between two points leg
on a coordinate plane hypotenuse
rev. 05-2009 16 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.2 7 G.8.8.3 Determine appropriate application of with and without appropriate congruence
Determine appropriate application of geometric ideas and relationships, such technology: similarity
geometric ideas and relationships, such as as congruence, similarity, and the *identify properties of given Pythagorean
congruence, similarity, and the Pythagorean Pythagorean Theorem, with and without geometric shapes Theorem
Theorem, with and without appropriate appropriate technology *identify the usage of congruency similarity vs.
technology within problems congruence
*identify the usage of similarity within best representation
problems
*identify the usage of the
Pythagorean Theorem within
problems
*identify the usage of geometric
ideas and properties
4 G.9.8.2 Draw the results of translations and *identify origin, x- and y-axis origin
Draw the results of translations and reflections about the x- and y-axis and *perform translations of two- x and y axis
reflections about the x- and y-axis and rotations of objects about the origin dimensional shapes on a coordinate coordinate plane
rotations of objects about the origin plane transformations
*draw results of translation of a two- (translation, rotation,
dimensional shape across the x- and reflection)
y-axis
*perform reflections of two-
dimensional shapes on a coordinate
plane
*draw results of a reflection of a two-
dimensional shape about the x- or y-
axis
*perform rotation of two-dimensional
shapes on a coordinate plane
*draw results of a rotation of a two-
dimensional shape about the origin
FP.8.2 2 G.9.8.1 Determine a transformation’s line of *identify the lines of symmetry in a line of symmetry
Determine a transformation’s line of symmetry and compare the properties of two-dimensional shape transformation
symmetry and compare the properties of the the figure and its transformation *identify the line of symmetry in a comparing properties
figure and its transformation transformation reflection
*identify the properties of a figure rotational symmetry
*compare the properties of a figure translation
and its transformation
rev. 05-2009 17 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
4. Enduring Understanding - Geometric figures can change size and/or position while maintaining
proportional attributes.
4a. Essential Question - How is proportionality of geometric figures used to solve problems?
FP.8.2 7 G.8.8.3 Determine appropriate application of with and without appropriate congruence
Determine appropriate application of geometric ideas and relationships, such technology: similarity
geometric ideas and relationships, such as as congruence, similarity, and the *identify properties of given Pythagorean
congruence, similarity, and the Pythagorean Pythagorean Theorem, with and without geometric shapes Theorem
Theorem, with and without appropriate appropriate technology *identify the usage of congruency similarity vs.
technology within problems congruence
*identify the usage of similarity within best representation
problems
*identify the usage of the
Pythagorean Theorem within
problems
*identify the usage of geometric
ideas and properties
C.8.1 18 M.13.8.3 A. Apply proportional reasoning to solve *compare the dimensions of scale similarity
Apply proportional reasoning to solve problems involving indirect drawings and actual objects rates
problems involving indirect measurements, measurements *use proportions to find unknown scale
scale drawings or rates B. Apply proportional reasoning to solve scales or lengths scale drawing
problems involving scale drawings *use scales and scale drawings to indirect measure
C. Apply proportional reasoning to solve find unknown dimensions enlargement
problems involving rates *find scale factors reduction
*solve problems involving rates unit rate
ratio
proportional
dimensions
indirect
dilation
equal ratios
similar proportion
rev. 05-2009 18 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
5. Enduring Understanding - Selection of standard measurement tools and units depend on the real-world
situation.
5a. Essential Question - How are one-, two-, and three-dimensional measures related?
4 M.12.8.2 Describe and apply equivalent measures *describe and apply equivalent equivalent
Describe and apply equivalent measures using a variety of units within the same measurements using metric units units of measure:
using a variety of units within the same system of measurement *describe and apply equivalent Ex.
system of measurement measurements using standard seconds↔minutes↔
(customary) units hours↔days
inches↔feet↔yards
↔miles
ounces↔cups↔pint
s↔quarts↔gallons
benchmark prefixes
kilo-↔deci-↔centi-
↔milli-
grams
liters
meters
FP.8.2 M.13.8.2 Solve problems involving volume and with and without appropriate surface area
Solve problems involving volume and surface area of pyramids, cones and technology: volume of surface
surface area of pyramids, cones and composite figures, with and without *apply formulas for surface area and area
composite figures, with and without appropriate technology volume of geometric figures pyramids
appropriate technology (pyramids, cones, composite figures) cones
*solve real-world problems involving volume of cylinder
volume and surface area of volume of prism
geometric figures (pyramids, cones, volume of pyramid
composite figures) significant digits
composite figures
capacity
square units
cubic units
rev. 05-2009 19 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FOURTH NINE WEEKS
1. Enduring Understanding - Graphical representations and statistical measures influence interpretations
and predictions about data.
1a. Essential Question - How can the results of a statistical investigation be used to support an argument?
FP.8.3 2 DAP.14.8.1 Design and conduct investigations which *explore, identify, and use biased sample
Design and conduct investigations which include: appropriate sampling methods for conclude
include: •adequate number of trials experimental trials conclusion
•adequate number of trials •unbiased sampling *identify, design, and use appropriate conjecture
•unbiased sampling •accurate measurement survey tools for experimental trials equally likely
•accurate measurement •record-keeping *design and use accurate event
•record-keeping measurement instruments for experiment
experimental trials experimental
*design and use accurate record- probability
keeping instruments for experimental frequency table
trials mutually exclusive
event
population
random numbers
random sample
sample
sample space
sample survey
simulation
theoretical
probability
trial
unbiased sample
rev. 05-2009 20 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.3 2 DAP.14.8.2 Explain which types of display are *explain the use of the following data stem-and-leaf plot
Explain which types of display are appropriate for various data sets (scatter displays for various data sets: box-and-whisker plot
appropriate for various data sets (scatter plot plot for relationship between two variants •tree diagrams circle graph
for relationship between two variants and line and line of best fit) •scatter plots dependent variable
of best fit) •box-n-whisker plots double bar graph
•stem-and-leaf plots independent events
•line graphs independent variable
•various bar graphs line graph
•histograms line of best fit
•circle graphs (pie chart) outlier
•frequency tables range
tables
illustrate change
rate of growth
appropriate
representation
variant
FP.8.3 10 DAP.14.8.3 Interpret or solve real-world problems *correctly interpret and use various bar graph
Interpret or solve real-world problems using using data from charts, line plots, stem- data displays as addressed 14.8.2 correlation
data from charts, line plots, stem-and leaf and-leaf plots, double bar graphs, line *correctly determine and apply basic fractional part
plots, double-bar graphs, line graphs, box- graphs, box-and-whisker plots, scatter mathematical calculations (i.e. histogram
and-whisker plots, scatter plots, frequency plots, frequency tables or double-line calculating percents, measures of horizontal bar graph
tables or double line graphs graphs central tendency, range, fractional line plots
parts, probability) in order to solve outlier
real-world problems pie chart
population sample
possible outcome
predictions
quartile
scatter plot
stem-and-leaf plot
infer
relationship
measures of central
tendencies
measures of spread
rev. 05-2009 21 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
2. Enduring Understanding - Sampling affects the relationship between experimental and theoretical
probability.
2a. Essential Question - How are experimental and theoretical probability related?
FP.8.3 3 DAP.17.8.2 A. Predict theoretical probabilities *explore, identify, and use dependent events
Make predictions based on theoretical B. Design and conduct an experiment to appropriate sampling methods for independent events
probabilities, design and conduct an test the predictions experimental trials fair
experiment to test the predictions, compare C. Compare actual results to predicted *identify, use and design appropriate biased
actual results to predicted results, and results and explain differences survey tools for experimental trials favorable outcome
explain differences *identify and discuss sampling odds against
methods odds in favor
*compare and contrast the validity of simulation
data sets with different size random numbers
populations random
*compare and contrast the reliability equally likely
of data sets with different size most likely
populations least likely
*determine conjectures about the theoretical
population from a given data set and probability
validate conclusions experimental
*estimate the probability of an event probability
*use a simulated model of a real-life validity of the
situation to apply experimental sampling
techniques reliability of the
*explain the differences between sampling
theoretical and experimental prediction/conjecture
probability
rev. 05-2009 22 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
2b. Essential Question - How can data representation influence conclusions?
FP.8.3 DAP.15.8.2 Interpret, with and without appropriate with and without appropriate variability
Analyze, with and without appropriate technology, graphs by comparing technology: variants
technology, graphs by comparing measures measures of central tendencies and *determine measures of central outlier
of central tendencies and measures of measures of spread tendency mode
spread *compare measures of central median
tendency mean
*analyze the relationship of range
measures of spread in data sets (i.e. conclusion
range, quartiles, outliers) measures of central
tendency
compute
average
quartiles
measures of spread
FP.8.3 DAP.15.8.4 Describe how the inclusion of outliers *determine how the inclusion of mean
Describe how the inclusion of outliers affects those measures of central outliers affect the measures of measures of central
affects those measures of central tendency central tendency tendency
tendency *determine how the exclusion of median
outliers affect the measures of mode
central tendency outlier
*compare and contrast the measures
of central tendency for the same data
set when outliers are included or
excluded
FP.8.3 DAP.15.8.1 Compare and contrast the reliability of *identify biased samples sample
Compare and contrast the reliability of data sets with different size populations *identify and discuss sampling stratified sample
data sets with different size populations Ex. methods systematic sample
Ex. 40/80 vs. 40/800 *compare the validity of data sets random sample
40/80 vs. 40/800 with different size populations biased sample
*contrast the reliability of data sets population
with different size population
FP.8.3 DAP.15.8.3 Given at least one of the measures of *create a data set when given any mean
Given at least one of the measures of central tendency create a data set one of the three measures of central measures of central
central tendency create a data set tendency (mean, median, and mode) tendency
median
mode
average
rev. 05-2009 23 of 24
8th Grade Math
Northwest Arkansas Instructional Alignment
Eighth Grade Mathematics
AR Department of Education
NCTM Focal # of CONTENT STANDARD/ Essential
Materials/Resources &
Point or Times Student Learning Expectations (SLE) Objective Task Analysis Vocabulary
Reteaching Concepts
Connector Tested *teacher word
FP.8.3 DAP.16.8.1 Use observations about differences *define measures of central tendency conjecture
Use observations about differences between sets of data to make *identify biased samples fair
between sets of data to make conjectures conjectures about the populations from *identify and discuss sampling predictions
about the populations from which the which the data was taken methods infer
data was taken *compare the validity of data sets conclude
with different size populations sampling
*contrast the reliability of data sets validity
with different size populations reliability
*determine conjectures about the
populations from given data sets and
validate conclusions
3. Enduring Understanding - The relationship among events affects probability.
3a. Essential Question - How do compound events affect probability?
FP.8.3 DAP.17.8.1 Compute, with and without appropriate with and without appropriate combination
Compute, with and without appropriate technology, probabilities of compound technology: compound
technology, probabilities of compound events using organized lists, tree *use data from organized list (i.e. probability
events, using organized lists, tree diagrams diagrams and logic grids stem-and-leaf plots and frequency odds against
and logic grid tables) odds in favor
*classify events as independent or permutation
dependent probability
*use data from tree diagrams and simple probability
logic grids tree diagram
*find the probability of independent logic grid
events random
*find the probability of dependent outcomes
events independent event
*compute simple and compound dependent event
probabilities
rev. 05-2009 24 of 24
