7th Math TIA Pacing Guide

Document Sample

```					                                                                                          Northwest Arkansas Instructional Alignment                                                                                 WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                        Objective                                             Task Analysis                                                    Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
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?
C.7.2                  NO.3.7.2                                                 Solve with and without appropriate technology, multi-   with and without appropriate technology:                  mental computation
Solve, with and without appropriate technology, multi-   step problems using a variety of methods and tools      *represent multi-step problems using manipulatives        technology
step problems using a variety of methods and tools       Ex.                                                     (including 2 or more steps)                               Distributive Property
Ex.                                                      objects, mental computation, paper and pencil           *solve problems mentally                                  rational numbers
objects, mental computation, paper and pencil                                                                    *solve multi-step problems with paper and pencil          like terms
problem solving strategy

FIRST NINE WEEKS
1. Enduring Understanding - Real numbers are either rational or irrational.
1a. Essential Question - What kinds of numbers make up the set of real numbers?
F.7.3                  NO.1.7.6                                                 Identify subsets of the real number system (natural,    *demonstrate that natural numbers are counting            real number system
Recognize subsets of the real number system              whole, integers, rational, and irrational numbers)      numbers beginning with 1 and that they build on one       natural numbers
(natural, whole, integers, rational, and irrational                                                              another                                                   whole numbers
numbers)                                                                                                         *identify whole numbers as numbers whose value            integers
includes zero and all natural numbers                     rational numbers
*integers are all whole numbers and their opposites       irrational numbers
*apply the definition of a rational number (any number    perfect square
that can be written as a/b where a is any integer and b   square root
is any integer except 0. Including any terminating        undefined fraction
decimals, repeating decimals and perfect squares)
*recognize that a fraction whose denominator is zero
is undefined
*identify irrational numbers as numbers that have
infinite but non-repeating decimal representations (Ex.
π; any square root that is not a perfect square)
*identify subsets of the real number system

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Northwest Arkansas Instructional Alignment                                                                                WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                      Objective                                            Task Analysis                                                   Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess a set of core ways ofthat support numbers. problem solving is important,
2. Enduring Understanding - Exponential and scientific notation are efficient beliefs expressing their work:
takes significant time and repeated efforts, and exponents?
2a. Essential Question - What is the purpose of requires reflection.
F.7.3                  NO.1.7.2                                                A. Demonstrate, with and without appropriate          with and without appropriate technology:                scientific notation
Demonstrate, with and without appropriate technology,   technology, an understanding of place value using     *write the number in expanded notation Ex. 103 =        exponents
an understanding of place value using powers of 10      powers of 10                                          10×10×10                                                place value
and write numbers greater than one in scientific        B. Write numbers greater than one in scientific       *multiply and divide by multiples of 10                 expanded notation
notation                                                notation                                              *demonstrate the value of a decimal when dividing or    power
multiplying by a power (multiple) of 10                 base
*demonstrate that exponents are repeated
multiplication
*identify the whole number of a scientific notation
number as a value ≥ 1 and < 10
F.7.3           1      NO.1.7.3                                                Convert between scientific notation and standard      *multiply and divide by powers of ten to convert        scientific notation
Convert between scientific notation and standard        notation using numbers greater than one               between standard and scientific notation                standard notation
notation using numbers greater than one                                                                                                                               powers of ten

3. Enduring Understanding - Fractions, decimals, and percents can be used interchangeably.
3a. Essential Question - What determines an appropriate representation for a number?
F.7.3                  NO.1.7.5                                                Compare and represent integers, fractions, decimals   *locate integers on a number line                      integers
Compare and represent integers, fractions, decimals     and mixed numbers and find their approximate          *locate fractions on a number line                     number line
and mixed numbers and find their approximate            location on a number line                             *locate decimals on a number line
location on a number line                                                                                     *locate mixed numbers on a number line
*locate and compare the values of integers, fractions,
decimals and mixed numbers on a number line

F.7.1                  M.13.7.6                                                A. Find the distance between two points on a number *plot two points on a number line                         distance
Find the distance between two points on a number        line                                                *find the distance between two points                     midpoint
line and locate the midpoint                            B. Locate the midpoint                              *average two numbers on a number line to locate the       number line
midpoint
F.7.1                  NO.1.7.4                                                A. Find decimals for mixed numbers & explain why      *explain how a part relates to a whole                  decimal
Find decimal and percent equivalents for mixed          they represent the same value                         *restate a mixed number as a whole number + fraction    percent
numbers and explain why they represent the same         B. Find percent equivalents of mixed numbers &        *convert fractions by dividing denominator into         equivalents
value                                                   explain why they represent the same value             numerator                                               convert
*write a decimal as a mixed number
*express mixed numbers as percents > 100
*demonstrate that the percent can be found by finding
the fraction-to-decimal equivalent and then multiply
the decimal by 100

2 of 18
Northwest Arkansas Instructional Alignment                                                                                  WORK IN PROGRESS
NCTM Focal    # of                AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                   Objective                                           Task Analysis                                                          Materials/Resources
*teacher word
Connector   Tested                     Expectations (SLE)
F.7.1           1      Enduring Understanding - Successful problem solvers possessthe set *explain how beliefs that whole and vice versa
NO.1.7.1                                           A. Show with and without models and pictures a         of core a part relates to a support their                      part-to-part
work: problem solving is important,
Relate, with and without models and pictures,      concept of ratio including ratios <1 and >100         *match decimals and percents of the same value                   part-to-whole
takes significant time and including B. Show with and requires reflection. *represent percents out of 100
concepts of ratio, proportion, and percent, repeated efforts, and without models and pictures the                                                                         ratio
percents less than 1 and greater than 100          concept of percent including percents <1 and >100     *describe a situation in which a percent might be                proportion
C. Show with and without models & pictures            between 1 & 100                                                  percent
proportion including proportions <1 and >100          *draw a picture or model a number as a decimal and
D. Relate with and without models and pictures        percent
concepts of ratio, percent, and proportions including
percents <1 and >100

F.7.3                  NO.3.7.4                                             A. Apply factorization to solve problems using more          *find multiples and factors of given numbers            prime numbers
Apply factorization, LCM, and GCF to solve problems than two numbers and explain the solution                     *find the prime factorization of a number (Ex. tree     composite numbers
using more than two numbers and explain the solution B. Apply LCM to solve problems using more than two           diagram)                                                prime factorization
numbers and explain the solution                             *identify numbers as prime or composite                 LCM
C. Apply GCF to solve problems using more than two           *find the LCM and GCF of more than two numbers          GCF
numbers and explain the solution                             *apply and explain solutions

F.7.1         MC-1     NO.3.7.6                                                 Solve, with and without technology, real-world percent   with and without appropriate technology:                technology
OR-1     Solve, with and without technology, real-world percent   problems                                                 * Solve percent problems                                percent
problems                                                 Ex.                                                      Ex.                                                     interest
Ex.                                                      I=PRT                                                    What number is 50% of 80?                               principal
I=PRT                                                                                                             80 is what percent of 50?                               rate
80 is 50% of what number?                               time
*use fractions, decimals and percents interchangeably
* Apply knowledge of percent to real-world situations
Ex.
I = PRT

4. Enduring Understanding - Integers have magnitude and direction.
4a. Essential Question - How do operations with integers compare to operations with whole numbers?
F.7.3                  NO.2.7.4                                                A. Model and develop addition and subtraction of          *model addition and subtraction of positive and         integers
Model and develop addition, subtraction, multiplication integers                                                  negative numbers using manipulatives                    absolute value
and division of integers                                B. Model and develop multiplication and division of       *model multiplication and division of positive and      opposites
integers                                                  negative numbers using manipulatives                    inverse operations

3 of 18
Northwest Arkansas Instructional Alignment                                                                                      WORK IN PROGRESS
NCTM Focal    # of                AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                     Objective                                            Task Analysis                                                               Materials/Resources
*teacher word
Connector   Tested                    Expectations (SLE)
F.7.3           2      Enduring Understanding - Successful problem solversorder of operationsset *solve problems with integers using order of their
NO.2.7.3                                             A. Apply rules (conventions) for possess a to of core beliefs that support                                                order of operations
work: problem solving is important,
Apply rules (conventions) for order of operations to integers including parentheses, brackets or exponents operations                                                          integers
takes significant time and repeated efforts, and requires reflection.to *solve problems with positive rational numbers using
integers and positive rational numbers including     B. Apply rules (conventions) for order of operations                                                                      rational numbers
parentheses, brackets or exponents                   positive rational numbers including parentheses,      order of operations                                                 exponents
brackets or exponents                                 *use rules for order of operations including:                       grouping symbols (brackets,
•grouping symbols ( ), [ ]                                          parentheses)
•fraction bar
•exponents
•multiplication & division left to right
•addition & subtraction left to right

F.7.3                  NO.2.7.1                                                 A. Apply the Distributive Property of multiplication over   *solve using Distributive Property to simplify            Distributive Property
Apply the Distributive Property of multiplication over   addition or subtraction to simplify computations with       computations with addition or subtractions of integers    integers
addition or subtraction to simplify computations with    integers                                                    5(2+3)         5(2+3)                                     solve
integers, fractions and decimals                         B. Apply the Distributive Property of multiplication over    5(5)        5(2)+5(3)                                    simplify
addition or subtraction to simplify computations with         25          10 + 15                                     evaluate
fractions                                                                   25                                        decompose
C. Apply the Distributive Property of multiplication over
addition or subtraction to simplify computations with         5(3-2)        5(3-2)
decimals                                                    5(3)-5(2)        5(1)
15-10           5
5
*solve using Distributive Property to simplify
computations with addition or subtraction to solve
problems with fractions
2(5 + 1/2)      2(5 - 1/2)
10 + 1          10 - 1
11             9
*solve using Distributive Property to simplify
computations with addition or subtraction to solve
problems with decimals
5.03 (3)
5(3) + .03(3)
15 + .09
15.09

*use subtraction to make multiplication of decimals
easier (mental math)
5(10.98)       5(11) - 5(.02)
50+4.90          55 - .10
54.9            54.9

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Northwest Arkansas Instructional Alignment                                                                                 WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                       Objective                                               Task Analysis                                                   Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important,
5. Enduring Understanding - Algebraic representations generalize patterns and relationships.
takes significant time and repeated efforts, andrules necessary?
5a. Essential Question - Why are mathematical requires reflection.
F.7.3           1      NO.3.7.1                                                Compute, with and without appropriate technology,         with and without appropriate technology:                technology
Compute, with and without appropriate technology,       with integers and positive rational numbers using real-   *solve word problems using addition of positive         integers
with integers and positive rational numbers using real- world situations to solve problems                        integers, decimals, and fractions (including mixed      positive rational numbers
world situations to solve problems                                                                                numbers)                                                absolute value
*solve word problems using subtraction of positive
integers, decimals, and fractions (including mixed
numbers)
*solve word problems using multiplication of positive
integers, decimals, and fractions (including mixed
numbers)
*solve word problems using division of positive
integers, decimals, and fractions (including mixed
numbers)
*explain solution

6. Enduring Understanding - Computational estimations produce approximate results.
6a. Essential Question - What determines a reasonable estimation for a given situation?
F.7.3           1      NO.3.7.3                                                A. Determine when an estimate is sufficient               *determine when an estimate is sufficient               estimate
Determine when an estimate is sufficient and use        B. Use estimation to decide whether answers are           *use estimation strategies to check for                 estimation
estimation to decide whether answers are reasonable     reasonable in problems including fractions and            reasonableness of solutions                             reasonable
in problems including fractions and decimals            decimals

7. Enduring Understanding - Powers and roots are related.
7a. Essential question - How are powers and roots related?
F.7.3                  NO.3.7.5                                                A. Represent and solve problem situations that can be     with and without appropriate technology:                absolute value
Represent and solve problem situations that can be      modeled by and solved using concepts of absolute          *write and solve problems using the concept of          exponents
modeled by and solved using concepts of absolute        value with and without appropriate technology             absolute value                                          square roots
value, exponents and square roots (for perfect          B. Represent and solve problem situations that can be     *write and solve problems using exponents               perfect squares
squares) with and without appropriate technology        modeled by and solved using concepts of exponents         *write and solve problems using square roots            technology
with and without appropriate technology
C. Represent and solve problem situations that can be
modeled by and solved using concepts of square
roots (for perfect squares) with and without
appropriate technology

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Northwest Arkansas Instructional Alignment                                                                                   WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                          Objective                                               Task Analysis                                                    Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important,
SECOND NINE WEEKS
takes significant time and repeated efforts, and requirescan be expressed graphically, numerically, symbolically, and verbally.
1. Enduring Understanding - Patterns and relationships reflection.
1a. Essential Question - What can be learned from an identified pattern/function?
F.7.3         MC-2     A.4.7.2                                                   Identify and extend patterns in real-world situations      *use skills in A.4.7.1                                   patterns
OR-1     Identify and extend patterns in real-world situations                                                                *find missing terms and numbers in a pattern or a        term
function table                                           arithmetic sequence
*predict patterns in real-world situations               geometric sequence
*write a rule to extend a pattern to the nth term
F.7.3                  A.4.7.3                                                   Interpret and write a rule for a two-operation function    *A.4.6.2                                                  function table
Interpret and write a rule for a two operation function   table                                                      *interpret and write the algebraic rule for one- and two-
table                                                     Ex.                                                        operation function tables
Ex.                                                       multiply by 2, add 1
F.7.3                  A.4.7.1                                                   Create and complete a function table (input/output)        *identify (x-value) as input and (y-value) as output     function table
Create and complete a function table (input/output)       using a given rule with two operations                     *apply a given rule with two operations to create and    input/output
using a given rule with two operations                                                                               complete a function table

F.7.3                  A.6.7.3                                                   Create and complete a function table (input/output)        *create and complete a function table using a given      function table
Create and complete a function table (input/output)       using a given rule with two operations in real-world       rule with two operations in real-world situations        input/output
using a given rule with two operations in real-world      situations
situations
F.7.1                  A.7.7.1                                                   Use, with and without appropriate technology, tables       *use tables to identify situations with constant or      technology
Use, with and without appropriate technology, tables      and graphs to compare and identify situations with         varying rates of change (Ex.. d=rt)                      rates
and graphs to compare and identify situations with        constant or varying rates of change                        *use graphs to identify situations with constant or      constant rate of change
constant or varying rates of change                                                                                  varying rates of change                                  varying rates of change

2. Enduring Understanding - Functional relationships can be expressed verbally, graphically, numerically, and symbolically and are
used to solve real-world problems.
2a. Essential Question - How can a function be identified?
F.7.3                  A.6.7.1                                                   A. Use tables to represent linear equations by plotting,   *use tables to represent the relationship in a linear    linear equations
Use tables and graphs to represent linear equations       with and without appropriate technology, points in a       equation, with and without appropriate technology        technology
by plotting, with and without appropriate technology,     coordinate plane                                           *use graphs to represent the relationship in a linear    coordinate plane
points in a coordinate plane                              B. Graph linear equations by plotting, with and without    equation on a coordinate plane, with and without         x-axis
appropriate technology, points in a coordinate plane       appropriate technology                                   y-axis
ordered pairs
origin

6 of 18
Northwest Arkansas Instructional Alignment                                                                                     WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                         Objective                                               Task Analysis                                                      Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
2b. Essential Question - - Successful problem solvers possess a set of
Enduring UnderstandingWhat can be learned from studying functions? core beliefs that support their work: problem solving is important,
F.7.3           1                                                       A. Solve simple linear equations using integers
A.5.7.2 significant time and repeated efforts, and requires reflection.
takes                                                                                                   *solve linear equations                                                 linear equations
Solve simple linear equations using integers and B. Graph simple linear equations in a coordinate plane *graph solution points on a coordinate plane using a T-                 integers
graph on a coordinate plane                                                                             chart                                                                   coordinate plane
use a T chart                                                                                                                                                                   x-axis
y-axis
origin
F.7.1                  G.10.7.1                                                  Plot points in the coordinate plane                      *identify four quadrants on coordinate plane                 coordinate plane
Plot points in the coordinate plane                                                                                *identify x and y axis                                       x-axis
*use ordered pairs to plot points on coordinate plane        y-axis
ordered pairs
origin
F.7.3           1      A.6.7.2                                                   Represent, with and without appropriate technology,     *same as A.6.7.1 with real-world applications                 technology
Represent, with and without appropriate technology,       linear equations by plotting and graphing points in the                                                               linear equations
linear equations by plotting and graphing points in the   coordinate plane using all four quadrants given data in                                                               coordinate plane
coordinate plane using all four quadrants given data in   a table from a real-world situation                                                                                   quadrants
a table from a real-world situation                                                                                                                                             origin
x-axis
y-axis

3. Enduring Understanding - Algebraic representations generalize patterns and relationships.
3a. Essential Question - Why are equations and inequalities useful?
F.7.3                  A.5.7.4                                                   A. Write algebraic expressions using positive rational   *write and solve algebraic expressions with one or           algebraic expressions
Write and evaluate algebraic expressions using            numbers                                                  more variables using positive rational numbers               rational numbers
positive rational numbers                                 B. Evaluate algebraic expressions using positive                                                                      variables
rational numbers
F.7.3           4      A.5.7.3                                                   A. Translate phrases into algebraic expressions          *express word phrases using variables, positive              algebraic expressions
Translate phrases and sentences into algebraic            B. Translate sentences into equations including          numbers, rational numbers, and operations                    equations
expressions and equations including parentheses and       parentheses, positive numbers and rational numbers       *explain use of the Distributive Property to simplify like   rational numbers
positive and rational numbers and simplify algebraic      C. Simplify algebraic by combining like terms            terms                                                        coefficient
expressions by combining like terms                                                                                *simplify algebraic expressions by combining like            constant
terms                                                        variable

7 of 18
Northwest Arkansas Instructional Alignment                                                                                  WORK IN PROGRESS
NCTM Focal    # of                 AR Department of Education
Essential Vocabulary
Point or   Times          CONTENT STANDARD/ Student Learning                                     Objective                                           Task Analysis                                                       Materials/Resources
*teacher word
Connector   Tested                     Expectations (SLE)
F.7.3                  Enduring Understanding - Successful problem one-step linear equations using a *identify phrases that indicate inequalities in real-world linear equations
A.5.7.1                                                A. Solve and graph solvers possess a set of core beliefs that support their work: problem solving                                            is important,
Solve and graph one-step linear equations and          variety of methods (Ex. hands-on, inverse operations, situations                                              inequalities
takes significant time and repeated efforts, real-world application with and without *solve one-step linear equations and inequalities, with inverse operations
inequalities using a variety of methods (Ex. hands-on, symbolic) with and requires reflection.
inverse operations, symbolic) with real-world          technology                                             and without appropriate technology, using a variety of technology
application, with and without technology               B. Solve and graph one-step linear inequalities using methods                                                 variables
a variety of methods (Ex. hands-on, inverse            *graph one-step equations and inequalities on a
operations, symbolic) with real-world application with number line
and without technology
F.7.3           1      NO.2.7.2                                                A. Apply the addition, subtraction, multiplication and   *know the properties of equality for addition,           equations
Apply the addition, subtraction, multiplication and     division properties of equality to one-step equations    subtraction, multiplication, and division and apply to   integers
division properties of equality to one-step equations   with integers                                            one-step equations using integers                        properties of equality
with integers, fractions, and decimals                  B. Apply the addition, subtraction, multiplication and   *know the properties of equality for addition,           inverse operations
division properties of equality to one-step equations    subtraction, multiplication, and division and apply to   one-step equations
with fractions                                           one-step equations using fractions
C. Apply the addition, subtraction, multiplication and   *know the properties of equality for addition,
division properties of equality to one-step equations    subtraction, multiplication, and division and apply to
with decimals                                            one-step equations using decimals

8 of 18
Northwest Arkansas Instructional Alignment                                                                                      WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                         Objective                                              Task Analysis                                                      Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important,
THIRD NINE WEEKS
takes significant time and repeated efforts, and requires reflection.
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?
F.7.1           2      DAP.14.7.1                                                Identify different ways of selecting samples and         *develop appropriate questions for surveys                 sample vs population
Identify different ways of selecting samples and          compose appropriate questions                            *identify survey response, random sample,                  random sample
compose appropriate questions                             Ex.                                                      representative sample & convenience sample                 survey response
Ex.                                                       survey response, random sample, representative                                                                      representative sample
survey response, random sample, representative            sample and convenience sample                                                                                       convenience sample
sample and convenience sample
F.7.1                  DAP.14.7.2                                                A. Explain that line graphs are appropriate for          *identify that line graphs are used to graph change        line graph
Explain which types of display are appropriate for        graphing change over time                                over time                                                  circle graph
various data sets (line graph for change over time,       B. Explain that circle graphs are appropriate for        *identify that circle graphs are used to graph part-to-    part-to-whole comparison
circle graph for part-to-whole comparison, scatter plot   graphing part-to-whole comparisons                       whole comparisons                                          scatter plot
for trends)                                               C. Explain that scatter plots are appropriate graphing   *identify that scatter plots are used to graph trends      trends
trends
F.7.3           1      DAP.15.7.2                                                A. Analyze, with and without appropriate technology, a   with and without appropriate technology:                   technology
Analyze, with and without appropriate technology, a       set of data by using and comparing measures of           *find the mean, median and mode for a set of data          central tendencies
set of data by using and comparing measures of            central tendencies (mean, median, mode)                  *compare the mean, median, mode for a set of data          mean
central tendencies (mean, median, mode) and               B. Analyze, with and without appropriate technology, a   *find measures of spread (range, quartile, interquartile   average
measures of spread (range, quartile, interquartile        set of data by using and comparing measures of           range) for a set of data                                   median
range)                                                    spread (range, quartile, interquartile range)            *compare measures of spread using a box-and-               mode
*analyze measures of central tendency and measures         range
of spread (including outliers) for a set of data           quartile
interquartile range
outliers

F.7.1           1      DAP.15.7.1                                             Analyze data displays, including ways that they can be *identify data display composition:                             misleading
Analyze data displays, including ways that they can be misleading                                             •scale                                                          scale
misleading                                                                                                    •data sample population techniques                              intervals
•misuse of central tendencies                                   central tendencies

9 of 18
Northwest Arkansas Instructional Alignment                                                                              WORK IN PROGRESS
NCTM Focal    # of                 AR Department of Education
Essential Vocabulary
Point or   Times          CONTENT STANDARD/ Student Learning                                     Objective                                             Task Analysis                                               Materials/Resources
*teacher word
Connector   Tested                    Expectations (SLE)
F.7.1         MC-3     Enduring Understanding - Successful problem solvers graphs with anda set with and without appropriate technology: their
DAP.14.7.3                                             A. Construct and interpret circle possess               of core beliefs that support                         double problem
work: bar graphs solving is important,
OR-1     Construct and interpret circle graphs, box-and-whisker without appropriate technology                         *circle                                               circle graphs
takes significant time double line                     B. Construct and requires reflection.
plots, histograms, scatter plots and and repeated efforts,and interpret box-and-whisker plots with •explain part-to-whole correlation                               box-and-whisker plots
graphs, with and without appropriate technology        and without appropriate technology                     •demonstrate taking numbers from fractions to         histograms
C. Construct and interpret histograms with and without decimals to percents to degrees                       scatter plots
appropriate technology                                 •use a protractor to create angles                    double line graphs
D. Construct and interpret scatter plots with and      •construct circle graph                               technology
without appropriate technology                         •interpret data                                       correlation
E. Construct and interpret double line graphs with and *box-and-whisker plots                                trend line
without appropriate technology                         •represent each quartile as 25%                       line of best fit
•analyze and record the spread                             stem-and-leaf plots
•interpret central tendencies                              Venn diagrams
•find medians and extremes
•construct box-and-whisker plot & identify outliers, if
any
*histogram
•create a frequency table, place the frequency of
occurency on y-axis & intervals of continuous data on
x-axis
•construct histogram (similar to a bar graph except
bars touch)
•compare independent variables to dependent
variables
•interpret data
*scatter plot
•determine dependent (y) variable & independent (x)
variable
•plot points (x,y)
•decide the overall correlation
•interpret data
*double line graphs
•determine dependent (y) & independent (x) variable
•identify the data sets (2 or more)
•plot points & connect data set independently
•evaluate and compare changes over time
*title, label & key all graphs appropriately

10 of 18
Northwest Arkansas Instructional Alignment                                                                                      WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                           Objective                                               Task Analysis                                                      Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
2. Enduring Understanding - Sampling affects solvers possess a set of core beliefs and theoretical probability.
Enduring Understanding - Successful problemthe relationship between experimentalthat support their work: problem solving is important,
takes significant time and repeated efforts, andand theoretical probability related?
2a. Essential Question - How are experimental requires reflection.
F.7.1           1      DAP.17.7.1                                                 Demonstrate that probability can take any value            *describe events that will not occur as probability 0       probability
Understand that probability can take any value             between 0 and 1(events that are not going to occur         *describe events that will certainly occur as probability   certainty
between 0 and 1 (events that are not going to occur        have probability 0, events certain to occur have           of 1                                                        outcome
have probability 0, events certain to occur have           probability 1)                                             *create situations in which the probability falls           most likely
probability 1)                                                                                                        between 0 & 1                                               least likely
equally likely
F.7.1                  DAP.17.7.2                                                 Design, with and without appropriate technology, an        with and without appropriate technology:                    technology
Design, with and without appropriate technology, an        experiment to test a theoretical probability and explain   *create theoretical probabilities and test them             theoretical probability
experiment to test a theoretical probability and explain   how the results may vary                                   (experiment)                                                experimental probability
how the results may vary                                   Ex.                                                        *explain how results vary
Ex.                                                        suggested materials for simulations are two-color          *formulate reasons why theoretical and experimental
suggested materials for simulations are: two-color         counters, a number cube, and spinners                      results vary
counters, a number cube, and spinners

3. Enduring Understanding - Linear relationships are characterized by a constant rate of change.
3a. Essential Question - Why are linear functions useful?
F.7.1           1      DAP.16.7.1                                                 A. Make, with and without appropriate technology,          *given a scatter plot determine a relationship between      technology
Make, with and without appropriate technology,             conjectures of possible relationships in a scatter plot    the dependent and independent variables                     conjectures
conjectures of possible relationships in a scatter plot    B. Approximate the line of best fit (trend line)           *make a conjecture about possible relationships             scatter plot
and approximate the line of best fit (trend line)                                                                     between variables                                           line of best fit
*construct a line of best fit to most appropriately         trend line
represent the "average" relationship between                dependent variable
dependent and independent variables                         independent variable
relationship

11 of 18
Northwest Arkansas Instructional Alignment                                                                             WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                     Objective                                         Task Analysis                                                      Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess atools and units depends on real-world situations.
4. Enduring Understanding - Selection of standard measurement set of core beliefs that support their work: problem solving is important,
4a. Essential question - Why are scientific and and tools used to measure different attributes?
takes significant time and repeated efforts,units requires reflection.
F.7.2           1      M.12.7.1                                              For real-world problems to the required degree of   *state the common standard units                         customary measurement
Understand, select and use the appropriate units and  accuracy:                                           *apply the prefixes of the metric system                 hours to minutes
tools (metric and customary) to measure length,       A. Select and use the appropriate units and tools   *select the appropriate tool to measure in applicable    feet to inches
weight, mass and volume to the required degree of     (metric and customary) to measure length            units (Ex. ruler, meter stick, gallon, liter, grams,     quarts to gallons
accuracy for real-world problems                      B. Select and use the appropriate units and tools   pound, tons, protractor, degrees, etc.)                  benchmark prefixes: milli-,
(metric and customary) to measure weight            *apply the appropriate tool to measure length, weight,   centi-, kilo-
Note: Use the appropriate tool to measure degrees of C. Select and use the appropriate units and tools    mass, and volume of a variety of real-world objects      length
angles. Students are given a protractor to use on the (metric and customary) to measure mass              *use a variety of measurement tools (graduated           weight
Benchmark test. There have been test questions        D. Select and use the appropriate units and tools   cylinder, triple beam balance, meter stick, protractor   mass
concerning the use of the protractor.                 (metric and customary) to measure volume            and others)                                              volume
E. Select and use the appropriate tool to measure                                                            degree
angle degrees (protractor)                                                                                   metric units
gram/liter/meter
pounds
gallons
yards
capacity
protractor

C.7.1                  M.13.7.2                                               A. Draw and measure distance to the nearest 1/16   *know measuring begins with the first tic mark           accurately
Draw and measure distance to the nearest mm and        inch accurately                                    *be able to record distance to the nearest 1/16 inch     precision
1/16 inch accurately.                                  B. Draw and measure distance to the nearest mm     *be able to draw a line to the nearest 1/16 inch         tic mark/origin
accurately                                         *be able to record distance to the nearest mm
*be able to draw a line to the nearest mm

F.7.1           2      M.12.7.2                                             Compare units within the same system                 *compare standard units
seconds↔minutes↔hours↔d
Understand relationships among units within the same                                                      *compare metric units
ays
system
inches↔feet↔yards↔miles
ounces↔cups↔pints↔
quarts↔gallons
benchmark prefixes
kilo-↔deci-↔centi-↔milli-
grams
liters
meters

12 of 18
Northwest Arkansas Instructional Alignment                                                                                 WORK IN PROGRESS
NCTM Focal    # of                AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                Objective                                        Task Analysis                                                                Materials/Resources
*teacher word
Connector   Tested                    Expectations (SLE)
C.7.1                  Enduring Understanding - Successful problem problems involving two or moreset *explain timebeliefs(clock and calendar; Ex.
M.13.7.1                                        A. Solve real-world solvers possess a               of core concepts that support their                                 elapsed time
work: problem solving is important,
Solve real-world problems involving two or more elapsed times, counting forward and backward on a  number of days in each month) in the context of
takes significant time and repeated efforts, and requires reflection. counting forward and backward
elapsed times, counting forward and backward    calendar
(calendar and clock)                            B. Solve real-world problems involving two or more *solve real-world situations involving two or more
elapsed times, counting forward and backward on a  elapsed times
clock

5. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, areas, and volumes of geometric figures.
5a. Essential Question - How are interior angles and the number of sides of the polygon related?
C.7.1         OR-1     G.8.7.4                                              A. Use paper or physical models to determine the sum       *fold/cut paper to make physical models of                interior angles
Use paper or physical models to determine the sum of of the measures of interior angles of triangles            quadrilaterals & triangles                                quadrilaterals
the measures of interior angles of triangles and     B. Use paper or physical models to determine the sum       *demonstrate that the measures of the sum of the          triangles
*demonstrate that the measures of the sum of the          overlapping
interior angles of triangles is 180º                      diagonals
*find a missing angle given two angles in a triangle
*find a missing angle given three angles in a

6. Enduring Understanding - Geometric figures can change position and maintain the same attributes on a coordinate plane.
6a. Essential Question - How does the movement of a geometric figure affect its attributes?
F.7.1                  G.10.7.2                                                 Plot points that form the vertices of a geometric figure *identify vertices of polygons                         vertices
Plot points that form the vertices of a geometric figure and draw, identify and classify the figure               *replicate (draw) polygons on a coordinate plane using faces
and draw, identify and classify the figure                                                                        ordered pairs                                          edges
*classify figures according to number of vertices
C.7.1           1      G.9.7.2                                                 A. Perform translations of two-dimensional figures      *fold/cut paper to perform translations of 2-             rotation
Perform translations and reflections of two-            using a variety of methods (paper folding, tracing,     dimensional figures                                       translation
dimensional figures using a variety of methods (paper   graph paper)                                            *trace to perform translations of 2-dimensional figures   reflection
folding, tracing, graph paper)                          B. Perform reflections of two-dimensional figures       *use graph paper to perform translations of 2-            two-dimensional figure
using a variety of methods (paper folding, tracing,     dimensional figures
graph paper)                                            *fold/cut paper to perform reflections of 2-dimensional
figures
*trace to perform reflections of 2-dimensional figures
*use graph paper to perform reflections of 2-
dimensional figures

13 of 18
Northwest Arkansas Instructional Alignment                                                                                    WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                          Objective                                              Task Analysis                                                     Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess sides of core beliefs that support their work: problem solving is important,
7. Enduring Understanding - Relationships exist among angles, a set and triangles.
takes significant time and repeated efforts, and requiresbe applied to solve problems?
7a. Essential question - How can properties of triangles reflection.
F.7.1                  G.8.7.6 Develop the properties of similar figures (ratio Develop the properties of similar figures (ratio of sides *categorize shapes                                          similar figures
of sides and congruent angles)                           and congruent angles)                                     *explain the concept of similarity and scale                congruent angles
*identify similar figures according to properties of        ratio
sides and angles                                            scale
F.7.1         MC-1     M.13.7.5                                                  Apply properties (scale factors, ratio, and proportion)   *identify corresponding parts of triangles                 scale factors
OR-1     Apply properties (scale factors, ratio, and proportion)   of congruent or similar triangles to solve problems       *set up proportion formulas (scale factors, ratios)        ratio
of congruent or similar triangles to solve problems       involving missing lengths and angle measures              using variables to find a missing length of a triangle     proportion
involving missing lengths and angle measures                                                                        *apply correlation properties to find a missing angle of   congruent
a triangle                                                 similar
correlation

14 of 18
Northwest Arkansas Instructional Alignment                                                                                WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                     Objective                                              Task Analysis                                                        Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: problem solving is important,
FOURTH NINE WEEKS
requires properties
takes significant time and repeated efforts, and based onreflection. of geometric figures.
1. Enduring Understanding - Constructions are
1a. Essential Question - How are geometric properties used in constructions?
F.7.2           2      G.8.7.1                                                A. Identify, draw, classify and compare 2-D geometric   *identify and model 2-dimensional geometric figures     regular polygon
Identify, draw, classify and compare geometric figures figures using models and real-world examples            including regular and irregular polygons                irregular polygon
using models and real-world examples                   B. Identify, draw, classify and compare 3-D geometric   *classify 2-dimensional geometric figures               two-dimensional figures
figures using models and real-world examples            *compare 2-dimensional geometric figures using real-    three-dimensional figures
world examples                                          (pyramid, cone, sphere,
*draw 2-dimensional geometric figures                   cylinder, cube, prism)
*identify and model 3-dimensional figures               quadrilaterals (rectangle,
*classify geometric 3-dimensional figures               square, parallelogram,
*compare geometric 3-dimensional figures using real-    trapezoid, rhombus)
world examples                                          circle
*draw 3-dimensional geometric figures                   ellipse
triangles (scalene, isosceles,
equilateral, right, acute,
obtuse)
pentagons, hexagons,
octagon, decagon, n-gon

F.7.2           3      G.8.7.2                                               Investigate geometric properties and their               *draw convex and concave polygons                       one-dimensional model
Investigate geometric properties and their            relationships in one-, two-, and three-dimensional       *compare and contrast the characteristics of one-, two- two-dimensional model
relationships in one-, two-, and three-dimensional    models, including convex and concave polygons            , and three-dimensional models to see relationships     three-dimensional model
models, including convex and concave polygons                                                                  among them                                              angles
convex polygon
concave polygon
classification of polygons by
sides
classification of polygons by
angles

15 of 18
Northwest Arkansas Instructional Alignment                                                                              WORK IN PROGRESS
NCTM Focal    # of                 AR Department of Education
Essential Vocabulary
Point or   Times          CONTENT STANDARD/ Student Learning                                       Objective                                              Task Analysis                                                 Materials/Resources
*teacher word
Connector   Tested                     Expectations (SLE)
F.7.2                  Enduring Understanding - Successful problem of angles formed and the a set *identify vertical angles and know that they are
G.8.7.3                                               A. Identify the pairs solvers possess                                                                            angles
of core beliefs that support their work: problem solving                          is important,
Recognize the pairs of angles formed and the          relationship between the angles of two intersecting       congruent                                              right angle
lines (vertical, adjacent, linear pair, reflection.
takes significant time and repeated efforts, and requires supplementary, *identify supplementary angles and know that they are acute angle
relationship between the angles including two
intersecting lines and parallel lines cut by a        perpendicular)                                            congruent to 180º                                      obtuse angle
transversal (vertical, supplementary, complementary, B. Identify the pairs of angles formed and the             *identify complementary angles and know that they      intersecting lines
corresponding, alternate interior, alternate exterior relationship between parallel lines cut by a transversal are congruent to 90º                                    transversal
angles and linear pair)                               (vertical, supplementary, corresponding, alternate        *identify corresponding angles and know that they are vertical angles
interior, alternate exterior angles and linear pair)      congruent                                              supplementary angles
C. Identify the pairs of angles and the relationship that *identify alternate interior angles/alternate exterior complementary angles
exists to form complementary angles                       angles and know that they are congruent                corresponding angles
*identify linear pairs and adjacent angles             alternate interior angles
*identify the relationship of the angles formed by a   alternate exterior angles
transversal and parallel lines                         linear pair
alternate pair
parallel lines
interior
exterior
congruent

2. Enduring Understanding - Relationships exist among the angles, sides, lengths, perimeters, and areas of two-dimensional.
2a. Essential Question - How are the areas of rectangles, parallelograms, triangles, trapezoids, and circles related?
F.7.2                  M.13.7.3                                                A. Develop and use strategies to solve problems   *use a variety of strategies to solve for area of a          trapezoid
Develop and use strategies to solve problems            involving area of a trapezoid                     trapezoid                                                    altitude/height
involving area of a trapezoid and circumference and     B. Develop and use strategies to solve problems   *apply formula for area of trapezoid                         base 1, base 2
area of a circle                                        involving circumference of a circle               *use a variety of strategies to solve for finding the        circumference
C. Develop and use strategies to solve problems   circumference of a circle                                    area of a circle
involving area of a circle                        *apply the formula for circumference of a circle             radius
*use a variety of strategies to solve for finding the area   pi (π)
of a circle
*apply the formula for area of a circle

F.7.3                  M.12.7.3                                                A. Find different areas for a given perimeter     *given a perimeter, solve for area of various shapes         linear units
Find different areas for a given perimeter and find a   B. Find a different perimeter for a given area    *label using appropriate units                               volume
different perimeter for a given area                                                                      *given an area, identify all perimeter combinations          perimeter
using whole numbers                                          area
*label using appropriate units                               square units

3. Enduring Understanding - Generalizations can be made to represent the relationship between area and volume.
3a. Essential Question - How do the dimensions of a geometric figure affect area, surface area, and volume?

16 of 18
Northwest Arkansas Instructional Alignment                                                                                WORK IN PROGRESS
NCTM Focal    # of               AR Department of Education
Essential Vocabulary
Point or   Times          CONTENT STANDARD/ Student Learning                                    Objective                                          Task Analysis                                                           Materials/Resources
*teacher word
Connector   Tested                   Expectations (SLE)
F.7.2           2      Enduring Understanding - Successful problem solvers possess prisms *use core beliefs that support their work: area
M.13.7.4                                            A. Derive and use formulas for surface area of a set of the formulas for finding the areas of common          surface problem solving             is important,
Derive and use formulas for surface area and volume and justify them using geometric models and common shapes: circles, squares, triangles and rectangles         volume
takes and cylinders and justify and repeated efforts, and requires reflection. *draw nets and use them to find the formula for the prisms
of prisms significant time them using               materials
geometric models and common materials               B. Derive and use formulas for surface area of        surface area of a prism                                 cylinders
cylinders and justify them using geometric models and *use the formula to find the surface area of a prism    nets
common materials                                      *use real world items to compare to nets                derived formula
C. Derive and use formulas for volume of prisms and *apply appropriate units to surface area
justify them using geometric models and common        *draw nets and use them to find the formula for the
materials                                             surface area of a cylinder
D. Derive and use formulas for volume of cylinders    *use the formula to find the surface area of a cylinder
and justify them using geometric models and common *use manipulatives to find a formula for the volume of
materials                                             rectangular prisms
*apply the derived formula of volume to a variety of
rectangular prisms (including common item i.e.,
matchbox, tissue box, shoebox, etc.)
*identify the surface area parts of a cylinder as a
rectangle attached to two circles at each end
*use manipulatives to find a formula for the volume of
cylinders
*apply the derived formula of volume to a variety of
cylinders (paper towel roll, soup can, etc.)

3b. Essential Question - How can formulas be developed using models?
F.7.2                  M.13.7.7                                               Estimate and compute the area of more complex or           *apply the formulas for finding the areas of basic      regular two-dimensional
Estimate and compute the area of more complex or       irregular two-dimensional shapes by dividing them into     shapes: circles, quadrilateral, triangles               shapes
irregular two-dimensional shapes by dividing them into more basic shapes                                          *divide irregular/complex figures into basic 2-         irregular two-dimensional
more basic shapes                                                                                                 dimensional shapes                                      shapes
*find the area of basic shapes and combine these        area
areas to find the area of the irregular figure          complex

F.7.2                  G.8.7.5                                                  Model and develop the concept that pi (π) is the ratio   *measure the radius and diameter                        pi (π)
Model and develop the concept that pi (π) is the ratio   of the circumference to the diameter of any circle       *measure the circumference of circle                    ratio
of the circumference to the diameter of any circle                                                                *discover a relationship between the diameter and       circumference
circumference (known as pi)                             diameter
*apply the formula for finding the circumference of a   radius
circle                                                  chord

17 of 18
Northwest Arkansas Instructional Alignment                                                                               WORK IN PROGRESS
NCTM Focal    # of             AR Department of Education
Essential Vocabulary
Point or   Times         CONTENT STANDARD/ Student Learning                                       Objective                                             Task Analysis                                                    Materials/Resources
*teacher word
Connector   Tested                Expectations (SLE)
4. Enduring Understanding - Geometric relationships exist between two-dimensional and three-dimensional problem
Enduring Understanding - Successful problem solvers possess a set of core beliefs that support their work: figures. solving is important,
takes significant time and repeated efforts, and requires reflection.
4a. Essential Question - How are two-dimensional and three-dimensional figures related?
F.7.2           1      G.11.7.1                                                Build three-dimensional solids from two-dimensional     *match 2-dimensional patterns to 3-dimensional solids rectangular prism
Build three-dimensional solids from two-dimensional     patterns (nets)                                         *build 3-dimensional solids from a given 2-           pyramids
patterns (nets)                                                                                                 dimensional pattern (net)                             cylinders
cones
3-dimensional solids
2-dimensional patterns
nets
F.7.2           1      G.11.7.2                                                Construct a building out of cubes from a set of views   *practice visualization skills using sets of cubes (front, cubes
Construct a building out of cubes from a set of views   (front, top, side)                                      back, right side, left side and top)
(front, top, side)                                                                                              *construct buildings using cubes
F.7.1           1      G.9.7.1                                                 Examine the congruence, similarity, and line or         *describe transformations-translations, reflections,     congruence
Examine the congruence, similarity, and line or         rotational symmetry of objects using transformations    and rotations                                            similarity
rotational symmetry of objects using transformations                                                            *identify symmetrical objects using transformations      line symmetry
*identify congruence/similarity in relationship to       rotational symmetry
transformations                                          transformations
translations
reflections
rotations

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