# Calculate and find approximations of square roots with

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```							    8th Grade Math

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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
*apply the identity properties

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

rev. 05-2009                                                                                                                                                                             4 of 24

Northwest Arkansas Instructional Alignment
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
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

Northwest Arkansas Instructional Alignment
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
*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

Northwest Arkansas Instructional Alignment
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
multiplication and division properties
of equality to one-step equations with
integers
multiplication and division properties
of equality to one-step equations with
fractions
multiplication and division properties
of equality to one-step equations with
decimals

rev. 05-2009                                                                                                                                                                              7 of 24

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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
multiplication and division, squaring
and square roots) to solve two-step
equation

rev. 05-2009                                                                                                                                                                               9 of 24

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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,

rev. 05-2009                                                                                                                                                                    12 of 24

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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:
(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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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-

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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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

Northwest Arkansas Instructional Alignment
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
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

Northwest Arkansas Instructional Alignment
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

rev. 05-2009                                                                                                                                                                             21 of 24

Northwest Arkansas Instructional Alignment
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
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

Northwest Arkansas Instructional Alignment
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

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

Northwest Arkansas Instructional Alignment
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
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

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