# Final 7th grade Map 7 13 10

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```					                                                                               Curriculum Map -- Grade 7 -- Mathematics
First Quarter
Big Idea: Scientific Notation
1. Enduring       1. Essential Question: When are exponents or scientific notation used?
Understanding:             Skills                                                           Learning Plan                                                            ELP (SLE)
Exponential and         (Student
Objective(s)      Assessment     Instructional       Materials/         Essential
scientific notation      Learning                                                                                                     Level 1              Level 2                Level 3                 Level 4
are efficient ways    Expectations)                                         Strategies       Resources          Vocabulary
of expressing     NO.1.7.2          *I will                                             2-2; Lab 2A        *scientific                N/A                   N/A                    N/A                     N/A
numbers.        Demonstrate,      demonstrate                                                            notation
with and without understanding of                                                        *exponents
appropriate       place value using                                                      *place value
technology, an    powers of 10.                                                          *standard
understanding of *I will write                                                           notation
place value using numbers greater                                                        *power
powers of 10 and than one in                                                             *base
write numbers     scientific notation.
greater than one
in scientific
notation.

NO.1.7.3              *I will convert                                    2-2                *scientific        Identify the value   Identify the place     Write numbers          Write numbers
Convert between       between scientific                                                    notation           of a digit in a      value of a digit in    greater than 1 in      from 0 to 1 in
scientific notation   notation and                                                          *standard          number being         numbers greater        standard and           standard and
and standard          standard notation.                                                    notation           represented in       than 1 being           scientific notation,   scientific notation,
notation using                                                                              *powers of ten     standard form by     represented in         with assistance        with assistance
numbers greater                                                                                                pointing, with       standard and
than one.                                                                                                      teacher              scientific notation,
assistance           with teacher
assistance

ELPNO.1.6-8.6 Convert between standard and scientific notation, using numbers greater than zero
NO.3.7.5          *I will write and                                      2-1; 2-2; 8-7      *absolute value           N/A                   N/A                    N/A                     N/A
Represent and     solve problems                                                            *exponents
solve problem     using exponents.                                                          *square roots
situations that   *I will write and                                                         *perfect squares
can be modeled solve problems
by and solved     using square
using concepts    roots.
and absolute
value, exponents
and square roots
(for perfect
squares) with and
without
appropriate
technology.

July 13, 2010                                                                       Page 1 of 55
Big Idea: Order of Operations
2. Enduring         2. Essential Question: Why are mathematical rules necessary?
Understanding:                Skills                                                        Learning Plan                                                              ELP (SLE)
To achieve the             (Student        Objective(s)    Assessment     Instructional       Materials/        Essential
unique and correct                                                                                                                         Level 1            Level 2             Level 3              Level 4
Learning                                          Strategies        Resources        Vocabulary
solution, the        Expectations) *I will apply the
NO.2.7.3                                                             2-3              *order of                      N/A                 N/A                 N/A                  N/A
conventions for      Apply rules        rules for order of                                                 operations
order of operation    (conventions) for operations.                                                         *positive rational
must be          order of operation                                                                    numbers
universally applied.   to integers and                                                                       *exponents
positive rational                                                                     *grouping
numbers                                                                               symbols
including                                                                             (brackets,
parentheses,                                                                          parentheses)
brackets or
exponents.

NO.3.7.1            *I will solve real                                   Problem Solving *positive rational   Compute              Compute            Compute             Compute
Compute, with       world problems                                       Handbook (xxviii- numbers            accurately and       accurately and     accurately and      accurately and
and without         involving integers.                                  xxix); pg. 248    *absolute value    use simple           use simple         use simple          explain strategies
appropriate                                                                                *integers          estimation           estimation         estimation          for estimation in
technology, with                                                                                              strategies, with     strategies with    strategies for      problem solving
integers and                                                                                                  teacher              peer and teacher   simple problems     involving simple
positive rational                                                                                             assistance (e.g.,    assistance with    involving           fractions, decimals,
numbers using                                                                                                 pointing to          and without        fractions,          and percents with
real world                                                                                                    location to round)   technology         decimals and        and without
situations to solve                                                                                           with and without                        percents with and   technology
problems.                                                                                                     technology                              without
technology

ELPNO.1.6-8.4 Compute accurately and make reasonable estimates in different contexts, with and without technology

July 13, 2010                                                                          Page 2 of 55
Big Idea: Factoriing - Primes, LCM, GCF
3. Enduring       3. Essential Question: Why are LCM and GCF important?
Understanding:             Skills                                                       Learning Plan                                                               ELP (SLE)
LCM, GCF, and           (Student       Objective(s)   Assessment     Instructional       Materials/         Essential
prime numbers are                                                                                                                          Level 1         Level 2             Level 3               Level 4
Learning                                       Strategies       Resources          Vocabulary
necessary for the     Expectations) *I will apply
NO.3.7.4                                                          2-4; 2-5; 2-6      *prime numbers              Find all the    Find common         Apply                Use prime
computation of     Apply            factorization,                                                      *composite                  factors of      factors and         factorization to     factorization (e.g.,
problems involving   factorization,   LCM, and GCF to                                                     numbers                     numbers less    multiples of two    determine            tree diagrams) to
fractions.      LCM, and GCF to solve problems.                                                      *prime                      than 25, with   given numbers,      greatest common      determine greatest
solve problems                                                                       factorization               assistance      with assistance     factor and least     common factor and
using more than                                                                      *LCM                                                            common multiple,     least common
two numbers and                                                                      *GCF                                                            with assistance      multiple of
explain the                                                                                                                                                               composite numbers
solution.                                                                                                                                                                 less than 100, with
assistance

ELPNO.1.6-8.5 Apply methods of factorization to find greatest common factor (GCF) and least common multiple (LCM)
Big Idea: Integers
4. Enduring    4. Essential Question: How do operations with integers compare to operations with whole numbers?
Understanding:          Skills                                                               Learning Plan                                                          ELP (SLE)
Integers are the      (Student         Objective(s)     Assessment          Instructional       Materials/           Essential
set of whole        Learning                                                                                                        Level 1             Level 2             Level 3               Level 4
Strategies      Resources             Vocabulary
numbers and their NO.2.7.4
Expectations) *I will model                                             3-3;                 *integers       Identify the         Model, using        Model, using         Model, using
opposites.    Model and          addition,                                              3-3 Lab;             *absolute value numeric operation    manipulatives,      manipulatives,       manipulatives, and
subtraction,       multiplication, and                                    4 Lab;          3-5 *inverse         term (e.g.,          subtraction,        subtraction,         subtraction,
multiplication and division of                                                                 operations      pointing to an       multiplication of   multiplication and   multiplication and
division of        integers.                                                                                   item or picture      decimals, with      division of          division algorithms
integers.                                                                                                      when given the       assistance          fractions and        for rational
term)                                    decimals, with       numbers, with
assistance           assistance

ELPNO.1.6-8.1 Understand the meaning of add, subtract, multiply, and divide and their relationships with rational numbers

July 13, 2010                                                                           Page 3 of 55
(continued)       NO.3.7.5            *I will write and                                         3-1                *absolute value         N/A                 N/A                 N/A                  N/A
4. Enduring        Represent and       solve problems
Understanding:       solve problem       using the concept
Integers are the     situations that     of absolute value.
set of whole       can be modeled
numbers and their     by and solved
opposites.       using concepts
and absolute
value, exponents
and square roots
(for perfect
squares) with and
without
appropriate
technology.

Big Idea: One-Step Equations
5. Enduring         5. Essential Question: Why are equations useful?
Understanding:              Skills                                                                  Learning Plan                                                         ELP (SLE)
One-step              (Student          Objective(s)     Assessment          Instructional         Materials/          Essential
equations are the                                                                                                                            Level 1             Level 2             Level 3              Level 4
Learning                                                 Strategies          Resources          Vocabulary
building blocks for      Expectations) *I will apply
NO.2.7.2                                                                      2-11; 2-12;        *equations        Identify the        Solve simple one-   Solve simple one-   Solve grade-
all algebraic      Apply the           properties of                                             3-6                *integers         numeric operation   step equations      step equations      appropriate, one-
manipulations.      addition,           equality to solving                                                          *properties of    when given a        with whole          with whole          step and two-step
subtraction,        one-step                                                                     equality          term (e.g.,         numbers, with       numbers,            equations, showing
multiplication and equations with                                                                *inverse          pointing to an      teacher or peer     fractions,          all steps, with or
division properties integers.                                                                    operations        item or picture     assistance          decimals, and       without assistance
of equality to one-                                                                              *one-step         when given the                          integers, with
step equations                                                                                   equations         term)                                   teacher or peer
with integers,                                                                                                                                             assistance
fractions, and
decimals.

ELPNO.1.6-8.3 Apply the addition, subtraction, multiplication, and division property of equality in equations

July 13, 2010                                                                               Page 4 of 55
Big Idea: Central Tendencies
6. Enduring        6. Essential Question: Why are multiple central tendencies needed?
Understanding:              Skills                                                           Learning Plan                                                         ELP (SLE)
Statistical           (Student        Objective(s)    Assessment       Instructional        Materials/        Essential
measures                                                                                                                          Level 1            Level 2            Level 3             Level 4
Learning                                           Strategies         Resources        Vocabulary
influence          Expectations) *I will analyze
DAP.15.7.2                                                             1-2              *central            Organize data     Determine           Determine the       Determine
interpretations and   Analyze, with and central                                                               tendencies          from least to     measures of         measures of         measures of central
predictions about    without           tendencies by                                                         *mean               greatest, with    range and mode,     mean, median,       tendency and
data.          appropriate       comparing and                                                         *average            assistance        with assistance     mode, and range     measures of
technology, a set contrasting range,                                                    *median                                                   of a given set of   spread, with and
of data by using mean, median                                                           *mode                                                     whole number        without appropriate
and comparing     and mode.                                                             *range                                                    data, using         technology, with
measures of                                                                             *quartile                                                 appropriate         assistance
central                                                                                 *interquartile                                            technology, with
tendencies                                                                              range                                                     assistance
(mean, median,
mode) and
measures of
quartile,
interquartile
range).

ELPDAP.5.6-8.2 Analyze measures of central tendency and measures of spread, with and without appropriate technology, and explain what each indicates about the set of data
Big Idea: Interpret and Construct Graphs
7. Enduring      7. Essential Question: How can the results of statistical investigations be used to support an argument?
Understanding:            Skills                                                              Learning Plan                                                     ELP (SLE)
Graphical           (Student         Objective(s)   Assessment         Instructional        Materials/        Essential
representations                                                                                                                      Level 1           Level 2            Level 3             Level 4
Learning                                              Strategies         Resources        Vocabulary
influence        Expectations) *I will identify
DAP.14.7.1                                                               1-1               *sample           Collect simple    Collect and        Collect and         Collect, organize,
interpretations and Identify different different ways of                                                       *population       data, with        organize simple organize simple graph, and interpret
predictions about ways of selecting selecting                                                                 *random sample assistance (e.g., data using tally      data using tally    simple data
data.        samples and        samples.                                                                *survey           favorite color,   marks and          marks and           samples (e.g., bar,
compose                                                                                    *response         food or drink,    frequency tables, frequency tables, line, stem-and-leaf,
appropriate                                                                                *representative   number of         with assistance    and graph (e.g., circle graphs,
questions (Ex.                                                                             sample            siblings)                            bar, line, stem-    scatter plots), as
Survey response,                                                                                                                                  and-leaf) the       grade level
random sample,                                                                                                                                    data, with          appropriate, with
representative                                                                                                                                    assistance          assistance
sample and
convenience
sample).

ELPDAP.5.6-8.1 Collect, organize, graph, and interpret a variety of data samples

July 13, 2010                                                                            Page 5 of 55
(continued)       DAP.14.7.2           *I will identify that                                   Supplement           *line graph        Collect simple      Collect and         Collect and         Collect, organize,
7. Enduring        Explain which        line graphs are                                                              *circle graph      data, with          organize simple     organize simple     graph, and interpret
Understanding:       types of display     used to graph                                                                *part-to-whole     assistance (e.g.,   data using tally    data using tally    simple data
Graphical        are appropriate      change over time.                                                            comparison         favorite color,     marks and           marks and           samples (e.g., bar,
representations     for various data     *I will identify that                                                        *scatter plot      food or drink,      frequency tables,   frequency tables,   line, stem-and-leaf,
influence        sets (Ex. Line       circle graphs are                                                            *trends            number of           with assistance     and graph (e.g.,    circle graphs,
interpretations and   graph for change     used to graph                                                                                   siblings)                               bar, line, stem-    scatter plots), as
data.          graph for part-to-   comparisons.                                                                                                                            data, with          appropriate, with
whole                *I will identify that                                                                                                                   assistance          assistance
comparison,          scatter plots are
scatter plot for     used to graph
trends).             trends.

ELPDAP.5.6-8.1 Collect, organize, graph, and interpret a variety of data samples
DAP.14.7.3        *I will construct                                         1-4; 1-5;             *box-and-whisker          N/A                 N/A                 N/A                  N/A
Construct and     and interpret box-                                        1-6; 1-7;             plots
interpret circle  and-whisker plots.                                        1-8; 1-9              *histograms
graphs, box-and- *I will construct                                          cstl.syr.edu/fipse/   *scatter plots
whisker plots,    and interpret                                             TabBar/BldCirc/B      *double line
histograms,       histograms.                                               UILDCIR.HTM           graphs
scatter plots and *I will construct                                                               *circle graphs
double line       and interpret
graphs with and scatter plots.
without           *I will construct
appropriate       and interpret
technology.       double line
graphs.             *I
will interpret circle
graphs.

July 13, 2010                                                                              Page 6 of 55
(continued)       DAP.15.7.1          *I will analyze                                       1-9                 *misleading                N/A                 N/A                 N/A                  N/A
7. Enduring        Analyze data        graphs by                                                                 scale
Understanding:       displays,           distinguishing                                                            *intervals
Graphical        including ways      between accurate                                                          *central
representations     that they can be    and misleading                                                            tendencies
interpretations and
data.
DAP.16.7.1         *I will evaluate                                       1-8; Supplement     *conjectures        Make predictions     Identify the        Compare the         Compare and
Make, with and     scatter plot and                                       http://www.regent   *scatter plot       using simple data    maximum             maximum             contrast the
without            the line of best fit.                                  sprep.org/Regent    *line of best fit   sets, with teacher   (highest) and       (highest) and       maximum (highest)
appropriate                                                               s/math/ALGEBRA      *relationship       or peer              minimum (lowest)    minimum (lowest)    and minimum
technology,                                                               /AD4/linefit.htm                        assistance           value of the data   value of data       (lowest) value of
conjectures of                                                            and                                                          points from         points from         data points from
possible                                                                  http://www.regent                                            simple data         simple data         simple data tables
relationships in a                                                        sprep.org/Regent                                             tables or graphs,   tables or graphs,   or graphs, with
scatter plot and                                                          s/math/ALGEBRA                                               with teacher or     with teacher or     teacher or peer
approximate the                                                           /AD4/scatter.htm                                             peer assistance     peer assistance     assistance
line of best fit
(trend line).

ELPDAP.5.6-8.3 Make inferences and predictions, and justify conclusions, based on data, with and without technology

July 13, 2010                                                                           Page 7 of 55
Big Idea: Probability
8. Enduring        8. Essential Question: How are experimental and theoretical probability related?
Understanding:              Skills                                                           Learning Plan                                                             ELP (SLE)
Changes in             (Student         Objective(s)  Assessment       Instructional        Materials/        Essential
experimental                                                                                                                           Level 1             Level 2             Level 3               Level 4
Learning                                          Strategies         Resources        Vocabulary
probability of an      Expectations) *I will understand
DAP.17.7.1                                                            10-1; 10-2; 10-4 *probability            Participate in an   Participate in an   Conduct              Identify the
event are not      Understand that that the value of a                                                     *certain               experiment to       experiment and      experiments and      theoretical
dependent upon       probability can    probability must                                                     *impossible            determine the       determine the       calculate            probability of
the theoretical     take any value     be between 0 and                                                     outcome                probability of an   fairness of the     probability, and     events within an
probability of the   between 0 and 1 1.                                                                      *most likely           event occurring,    experiment          complete a           experiment
same event.        (events that are                                                                        *least likely          using nonverbal     (game), with        frequency table or
not going to occur                                                                      *equally likely        responses           assistance          chart using the
have probability                                                                                                                                       data set
0, events certain
to occur have
probability 1).

DAP.17.7.2           *I will create                                       10-2; 10-4        *theoretical
Design, with and     understanding of                                                       probability
without              theoretical                                                            *experimental
appropriate          probability by                                                         probability
technology, an       designing an
experiment to test   experiment.
a theoretical
probability and
explain how the
results may vary
(Ex. Suggested
materials for
simulations are:
two-color
counters, a
number cube,
and spinners).

ELPDAP.5.6-8.4 Understand the difference between theoretical and experimental probability, and explain how the results may vary

July 13, 2010                                                                          Page 8 of 55
Curriculum Map -- Grade 7 -- Mathematics
Second Quarter

Big Idea: Fractions, Decimals, Percents, and Integers
9. Enduring     9. Essential Question: What determines an appropriate representation for a number?
Understanding:           Skills                                                          Learning Plan                                                         ELP (SLE)
Fractions,         (Student         Objective(s)  Assessment        Instructional       Materials/      Essential
decimals, and                                                                                                                    Level 1            Level 2              Level 3              Level 4
Learning                                            Strategies       Resources       Vocabulary
percents can be     Expectations) *I will
NO.1.7.1                                                              6-1; 6-3        *percent                    N/A                N/A                  N/A                  N/A
used        Relate, with and demonstrate                                                          *numerator
interchangeably   without models     understanding of                                                   *denominator
and pictures,      fractions and                                                      *common
concepts of ratio, percents by                                                        denominator
proportion, and    representing                                                       *proportion *ratio
percent, including numbers in each
percents less      of these forms.
than 1 and
greater than 100.

NO.1.7.4             *I will                                            3-9; 6-1        *decimal                  N/A                N/A                  N/A                  N/A
Find decimal and     demonstrate                                                        *percent
percent              understanding of                                                   *equivalents
equivalents for      fractions and                                                      *convert
mixed numbers        decimals by                                                        *mixed numbers
and explain why      representing
they represent the   percent
same value.          equivalents for
mixed numbers.

NO.1.7.5             *I will analyze                                    3-1 (Int)       *integers          Identify a number   Match models of     Identify the        Compare and order
Compare and          numbers by                                                         *number line       as a fraction,      whole numbers,      location of a       fractions, decimals,
represent            comparing                                                          *greater than      decimal, or         fractions, and      whole number,       and percents, with
integers,            fractions,                                                         *less than         percent (e.g.,      decimals to         fraction, and       assistance or
fractions,           decimals and                                                                          pointing to an      equivalent words    decimal on a        without assistance
decimals and         integers on a                                                                         item or picture     with assistance     number line, with
mixed numbers        number line.                                                                          when given the      (e.g., ½, 1/3, ¼,   or without
and find their                                                                                             term)               50%, 25%, 100%)     assistance
approximate
location on a
number line

ELPNO.1.6-8.2 Convert, compare, and order fractions, decimals and percents

July 13, 2010                                                                       Page 9 of 55
(continued)     NO.1.7.6              *I will recognize    3Ext (p. 178) Irr;   *natural            N/A   N/A   N/A   N/A
9. Enduring      Recognize             the subsets of the   http://www.studyz    *whole
Understanding:     subsets of the        real number          one.org/mtestpre     *integers
Fractions,     real number           system.              p/math8/a/numbe      *rational numbers
decimals, and    system (natural,                           r_subsets7l.cfm      *irrational
percents can be    whole, integers,                                                numbers
used         rational, and
interchangeably.   irrational
numbers)

NO.2.7.1              *I will apply the    Supplement           *distributive       N/A   N/A   N/A   N/A
Apply the             distributive                              property
distributive          property to
property of           simplify
multiplication over   computations.
subtraction to
simplify
computations with
integers,
fractions, and
decimals.

July 13, 2010                                         Page 10 of 55
Big Idea: Compare and Estimate Real Numbers
10. Enduring     10. Essential Question: What determines a reasonable estimation for a given situation?
Understanding:            Skills                                                          Learning Plan                                                            ELP (SLE)
Computational          (Student        Objective(s)   Assessment       Instructional       Materials/         Essential
estimations are                                                                                                                       Level 1           Level 2             Level 3              Level 4
Learning                                          Strategies        Resources        Vocabulary
helpful when       Expectations) *I will find the
M.13.7.6                                                             Supplement        *midpoint                     N/A                N/A                 N/A                  N/A
determining     Find the distance distance and                                       http://www.imacc. *distance
reasonableness.    between two       midpoint between                                   org/standards/ex0
points on a       two points on a                                    2.html
number line and number line.
locate the
midpoint.

NO.3.7.3            *I will determine                                    4-1 (dec);   4-   *real numbers     Compute              Compute            Compute             Compute
Determine when when an estimate                                          9(frac)           *estimation       accurately and       accurately and     accurately and      accurately and
an estimate is      is reasonable.                                                                           use simple           use simple         use simple          explain strategies
sufficient and use                                                                                           estimation           estimation         estimation          for estimation in
estimation to                                                                                                strategies, with     strategies with    strategies for      problem solving
decide whether                                                                                               teacher              peer and teacher   simple problems     involving simple
answers are                                                                                                  assistance (e.g.,    assistance with    involving           fractions, decimals,
reasonable in                                                                                                pointing to          and without        fractions,          and percents with
problems                                                                                                     location to round)   technology         decimals and        and without
including fractions                                                                                          with and without                        percents with and   technology
and decimals.                                                                                                technology                              without
technology

ELPNO.1.6-8.4 Compute accurately and make reasonable estimates in different contexts, with and without technology

July 13, 2010                                                                       Page 11 of 55
Big Idea: Ratio and Proportion
11. Enduring      11. Essential Question: How can properties of triangles be applied to solve problems?
Understanding:            Skills                                                            Learning Plan                                        ELP (SLE)
Relationships exist      (Student         Objective(s)  Assessment         Instructional        Materials/        Essential
among angles,                                                                                                               Level 1   Level 2           Level 3   Level 4
Learning                                             Strategies        Resources        Vocabulary
sides and         Expectations) *I will represent
NO.1.7.1                                                                5-1, 5-2, 5-3    *ratio            N/A       N/A                  N/A    N/A
triangles.      Relate, with and proportions as                                                          *proportion
without models     fractions and
and pictures,      percents.
concepts of ratio,
proportion, and
percent, including
percents less
than 1 and
greater than 100.

G.8.7.6.              *I will apply                                     5-5; 5-6          *similarity        N/A       N/A                  N/A    N/A
Develop the           proportions to                                                      *congruent
properties of         determine
similar figures       similarity.
(Ex. ratio of sides
and congruent
angles)

M.13.7.5              *I will apply                                      5-6              *angle             N/A       N/A                  N/A    N/A
Apply properties      proportion to                                                       *measurement
(scale factors,       solve for missing
ratio, and            measurement in
proportion) of        similar figures.
congruent or
similar triangles
to solve problems
involving missing
lengths and angle
measures.

July 13, 2010                                                                     Page 12 of 55
Big Idea: One-Step Equations
12. Enduring     12. Essential Question: When are equations useful?
Understanding:            Skills                                                                Learning Plan                                                       ELP (SLE)
Algebraic           (Student          Objective(s)  Assessment           Instructional        Materials/         Essential
representations                                                                                                                      Level 1             Level 2             Level 3              Level 4
Learning                                               Strategies         Resources         Vocabulary
generalize patterns NO.2.7.2
Expectations) *I will apply                                              4-6; 4-12         *properties of   Identify the        Solve simple one-   Solve simple one-   Solve grade-
and relationships. Apply the           properties of                                                             equality         numeric operation   step equations      step equations      appropriate, one-
addition,           equality by                                                                                when given a        with whole          with whole          step and two-step
subtraction,        solving one-step                                                                           term (e.g.,         numbers, with       numbers,            equations, showing
multiplication and equations with                                                                              pointing to an      teacher or peer     fractions,          all steps, with or
division properties fractions and                                                                              item or picture     assistance          decimals, and       without assistance
of equality to one- decimals.                                                                                  when given the                          integers, with
step equations                                                                                                 term)                                   teacher or peer
with integers,                                                                                                                                         assistance
fractions, and
decimals.

ELPNO.1.6-8.3 Apply the addition, subtraction, multiplication, and division property of equality in equations
A.5.7.3           *I will translate                                           2-7, 2-8, 2-9, 2-10 *expressions         N/A                 N/A                 N/A                  N/A
Translate phrases words into                                                                      *like terms
and sentences     algebraic                                                                       *equation
into algebraic    expressions or
expressions and sentences.
equations         *I will combine
including         like terms.
parentheses and
positive and
rational numbers
and simplify
algebraic
expressions by
combining like
terms.

July 13, 2010                                                                          Page 13 of 55
(continued)       A.5.7.4             *I will evaluate                                     4-6, 4-12          *rational numbers Select an         Identify and            Combine like          Write and evaluate
12. Enduring       Write and           algebraic                                                                                 algebraic         combine like            terms of algebraic    simple algebraic
Understanding:       evaluate            expressions using                                                                         expression from a terms of simple         expressions and       expressions, with
Algebraic        algebraic           positive rational                                                                         given sample,     algebraic               evaluate an           assistance
representations     expressions using   numbers.                                                                                  with assistance   expressions, with       algebraic
generalize patterns   positive rational                                                                                                               assistance              expression given
and relationships.   numbers.                                                                                                                                                the replacement
set, with
assistance

ELPA.2.6-8.1 Write and evaluate simple algebraic expressions
A.6.7.1            *I will represent                                     12-1, 12-4         *coordinate plane Participate in a      Collect data from   Collect data from     Use data to
Use tables and     linear equations                                                         *linear equation  real-world activity   a real-world        a real-world          complete a table,
graphs to          by plotting points                                                       *point            and identify the      activity and        activity, record      graph results, and
represent linear   on the coordinate                                                                          data, with teacher    record results on   results on a table,   write a simple
equations by       plane.                                                                                     assistance            a table, with       and graph the         equation, with and
plotting, with and                                                                                                                  assistance          results on grid       without technology,
without                                                                                                                                                 paper, with           with assistance
appropriate                                                                                                                                             assistance
technology,
points in a
coordinate plane.

ELPA.2.6-8.4 Develop and apply mathematical models to represent and understand quantitative relationships, with and without technology
A.6.7.2            *I will represent                                    12-1 Word          *quadrant                  N/A                  N/A                 N/A                    N/A
Represent, with    linear equations                                    Problems
and without        by plotting points
appropriate        on the coordinate
technology, linear plane given data
equations by       from real world
plotting and       applications.
graphing points in
the coordinate
plane using all
given data in a
table from a real
world situation.

July 13, 2010                                                                          Page 14 of 55
Big Idea: Coordinate Plane
13. Enduring    13. Essential Question: What is the benefit of demonstrating figures and functions on the coordinate plane?
Understanding:           Skills                                                           Learning Plan                                                            ELP (SLE)
Figures and         (Student           Objective(s)  Assessment      Instructional        Materials/        Essential
functions can be                                                                                                                     Level 1             Level 2              Level 3                Level 4
Learning                                           Strategies        Resources         Vocabulary
represented on the G.9.7.1
Expectations) *I will identify                                      7-10; 7-11       *symmetry                    N/A                 N/A                   N/A                   N/A
coordinate plane. Examine the          congruence and                                                     *rotational
congruence,          similarity in                                                      symmetry
similarity, and line relationship to                                                    *line symmetry
or rotational        transformations.
symmetry of
objects using
transformations.
G.9.7.2             *I will perform                                      7-10               *translation              N/A                 N/A                   N/A                   N/A
Perform             translations and                                                        *reflection
translations and reflections.
reflections of two-
dimensional
figures using a
variety of
methods (paper
folding, tracing,
graph paper).

G.10.7.1               *I will apply                                     3-2                *coordinate plane Identify the parts   Draw a               Describe the          Plot ordered pairs
Plot points in the     concepts of the                                                                        of the coordinate    coordinate plane,    location of points    on a coordinate
coordinate plane       coordinate plane                                                                       plane, given a       number the lines     on a coordinate       plane to form a
by plotting points.                                                                    term and a grid      correctly, label     plane in relation     geometric figure,
(e.g., teacher       the x- and y-axis,   to the origin, with   with assistance
says origin,         and name the         assistance
G.10.7.2               *I will construct                                 3-2 #27-30         *vertices         to a picture of a    with assistance
Plot points that       geometric figures                                                                      origin)
form the vertices      in the coordinate
of a geometric         plane.
figure and draw,
identify and
classify the figure.

ELPG.3.6-8.4 Use coordinate geometry system to plot ordered pairs and to form geometric figures

July 13, 2010                                                                      Page 15 of 55
Big Idea: Linear Equations
14. Enduring   14. Essential Question: What can be learned from studying linear equations?
Understanding:          Skills                                                           Learning Plan                                                                      ELP (SLE)
Linear equations      (Student         Objective(s)   Assessment       Instructional        Materials/        Essential
graphically and                                                                                                                           Level 1                Level 2             Level 3             Level 4
Learning                                           Strategies        Resources         Vocabulary
numerically.    Expectations) *I will solve and
A.5.7.1                                                                11-5; 11-6; 12-4 *linear equations            Represent a            Use simple          Write simple       Write and graph
Solve and graph graph linear                                                            *inequalities                simple equation        equations and       equations and      simple equations
one-step linear    equations.                                                                                        using manipula-        inequalities to     inequalities to    and inequalities to
equations and      *I will solve and                                                                                 tives, with            model real-world    model real-world   model real-world
inequalities using graph                                                                                             assistance             situations using    situations using   situations using
a variety of       inequalities.                                                                                                            manipulatives,      manipulatives,     manipula-tives, with
methods (i.e.,                                                                                                                              with assistance     with assistance    assistance
hands-on, inverse
operations,
symbolic) with
real world
application with
and without
technology

ELPA.2.6-8.3 Write, solve, and graph equations and inequalities to model real-world situations, using manipulatives
A.5.7.2           *I will solve and                                         12-4                *T-chart                  N/A                   N/A                 N/A                 N/A
Solve simple      graph equations
linear equations with integers.
using integers
and graph on a
coordinate plane

Big Idea: Patterns and Functions
15. Enduring      15. Essential Question: What can be learned from an identified pattern or function?
Understanding:             Skills                                                            Learning Plan                                                                  ELP (SLE)
Patterns and           (Student         Objective(s)   Assessment       Instructional        Materials/       Essential
relationships can                                                                                                                          Level 1                Level 2             Level 3             Level 4
Learning                                           Strategies         Resources       Vocabulary
be expressed         Expectations) *I will construct a
A.4.7.1                                                                 12-1            *function table           Identify terms in      Identify the next   Complete a         Create and
graphically,     Create and         function table                                                                                 simple mathema-        term in a           simple function    complete a simple
numerically, and    complete a         using two                                                                                      tical patterns, with   mathematical        table by finding   function table,
verbally.      function table     operations.                                                                                    assistance             pattern, when       missing terms,     using a given rule,
(input/output)                                                                                                                           given a visual      with assistance    with one or two
using a given rule                                                                                                                       prompt, with                           operations, with
with two                                                                                                                                 assistance                             assistance
operations.

A.4.7.2            *I will extend                                           12-2; 12-2         *patterns
Identify and       patterns in real                                         Problem Solving
extend patterns in world situations.
real world
situations.

ELPA.2.6-8.2 Create and complete a function table, using a given rule

July 13, 2010                                                                           Page 16 of 55
(continued)      A.4.7.3               *I will write a rule                     12-2            *function          Select an         Identify and        Combine like         Write and evaluate
15. Enduring      Interpret and write   for a two-                                                                  algebraic         combine like        terms of algebraic   simple algebraic
Understanding:      a rule for a two-     operation function                                                          expression from a terms of simple     expressions and      expressions, with
Patterns and      operation function    table.                                                                      given sample,     algebraic           evaluate an          assistance
relationships can   table (Ex. multiply                                                                               with assistance   expressions, with   algebraic
be expressed      by 2, add 1).                                                                                                       assistance          expression given
graphically,                                                                                                                                             the replacement
numerically, and                                                                                                                                            set, with
verbally.                                                                                                                                              assistance

ELPA.2.6-8.1 Write and evaluate simple algebraic expressions
A.6.7.3            *I will construct a                         12-1 Word       *function table           N/A               N/A                 N/A                  N/A
Create and         function table                              Problems
complete a         using two
function table     operations in real
(input/output)     world situations.
using a given rule
with two
operations in real
world situations.

A.7.7.1               *I will identify                         12-7            *rates of change          N/A               N/A                 N/A                  N/A
Use, with and         constant and
without               varying rates of
appropriate           change.
technology,
tables and graphs
to compare and
identify situations
with constant or
varying rates of
change.

July 13, 2010                                                              Page 17 of 55
Curriculum Map -- Grade 7 -- Mathematics
Third Quarter

Big Idea: Measurement
16. Enduring       16. Essential Question: How do you determine when metric or customary units should be used?
Understanding:             Skills                                                         Learning Plan                                                                ELP (SLE)
Selection standard        (Student       Objective(s)    Assessment     Instructional         Materials/       Essential
measurement tools                                                                                                                        Level 1              Level 2             Level 3              Level 4
Learning                                        Strategies         Resources        Vocabulary
and units depends      Expectations) I will select and
M.12.7.1                                                            8-1;              *customary units         Select               Identify measure-   Draw and            Explain, using
on real-world      Understand,      use appropriate                                    http://www.coe.uh *metric units            appropriate tools    ment tools from     measure distance    simple phrases,
situations.      select and use   measurement                                        .edu/archive/scie *length                  for measuring        pictures and        to the nearest      how to use
the appropriate  tools.                                             nce/science_less *weight                   real-world objects   objects and state   mm and 1/16 of      measurement in
units and tools                                                     ons/scienceles3/ *mass                     or figures (e.g.,    the uses, with      an inch with        real-world
(metric and                                                         measure/index.ht *capacity                 height, weight),     assistance          accuracy, as        situations (e.g.,
customary) to                                                       ml                *volume                  using words                              grade               construction,
measure length,                                                                                                and/or gestures,                         appropriate, with   architecture,
weight, mass and                                                                                               with assistance                          assistance          cartography)
volume to the
required degree
of accuracy for
real world
problems.

ELPM.4.6-8.1 Determine which unit of measure or measurement tool matches the context for a problem situation
M.12.7.2         *I will compare                                      8-1;                 *conversion         Identify and         Identify and        Identify and use    Make comparisons
Understand       units within the                                                                              compare various      compare various     basic units of      of standard units of
relationships    same system.                                                                                  measurement          measurement         length, weight,     measure-ment in
among units                                                                                                    units using          units using         capacity, and       real-world problems
within the same                                                                                                models, with         models, with peer   time related to
system.                                                                                                        teacher              assistance          real-world
assistance                               objects, using
simple phrases,
with assistance
(e.g., word wall,
peer, teacher)

ELPM.4.6-8.2 Make comparisons and conversions of standard units of measurement in real-world problems

July 13, 2010                                                                        Page 18 of 55
(continued)       M.13.7.1           *I will solve real                                http://www.su *elapsed time              N/A       N/A                  N/A    N/A
16. Enduring       Solve real world   world elapsed                                     perteacherwor
Understanding:      problems           time problems.
Selection standard   involving two or
ksheets.com/
measurement tools    more elapsed                                                         elapsed-
and units depends    times, counting                                                      time/elapsed-
on real-world      forward and                                                          time-story-
situations.      backward (Ex.
problems2.pdf
calendar and
clock).

M.13.7.2           *I will draw and                                  Lab 8A; 8-2          *accuracy           N/A       N/A                  N/A    N/A
Draw and           measure distance
measure distance   to the nearest
to the nearest     mm and 1/16
mm and 1/16 inch   inch.
accurately.

Big Idea: Percent
17. Enduring     17. Essential Question: How are percents used in the real world?
Understanding:           Skills                                                           Learning Plan                                              ELP (SLE)
Percents can be        (Student         Objective(s)   Assessment        Instructional       Materials/            Essential
used as fractions                                                                                                                Level 1   Level 2           Level 3   Level 4
Learning                                             Strategies       Resources            Vocabulary
and decimals.      Expectations) *I will solve real
NO.3.7.6                                                               6-3; 6-4; 6-5; 6-6   *simple interest    N/A       N/A                  N/A    N/A
Solve, with and    world percent                                                            *rate
without            problems.                                                                *principal
technology, real                                                                            *sales tax
world percent                                                                               *percent of
problems      (Ex.                                                                          change
I=PRT)

July 13, 2010                                                                    Page 19 of 55
Big Idea: Multi-Step Problems
18. Enduring        18. Essential Question: What are the specific strategies that have wide application in attacking problems and can help in problem solving?
Understanding:               Skills                                                            Learning Plan                                                      ELP (SLE)
Problem solving is          (Student          Objective(s)  Assessment        Instructional       Materials/        Essential
important, takes                                                                                                                      Level 1            Level 2            Level 3                    Level 4
Learning                                            Strategies        Resources        Vocabulary
significant time       Expectations) *I will solve multi-
NO.3.7.2                                                               Use Problem                        Compute            Compute            Compute                    Compute
and repeated        Solve, with and     step problems.                                     Solving pages                      accurately and     accurately and     accurately and             accurately and
efforts, and       without                                                                throughout text                    use simple         use simple         use simple                 explain strategies
requires reflection.   appropriate                                                                                               estimation         estimation         estimation                 for estimation in
technology, multi-                                                                                        strategies, with   strategies with    strategies for             problem solving
step problems                                                                                             teacher            peer and teacher simple problems              involving simple
using a variety of                                                                                        assistance (e.g., assistance with     involving                  fractions, decimals,
methods and                                                                                               pointing to        and without        fractions,                 and percents with
tools (Ex. objects,                                                                                       location to round) technology         decimals and               and without
mental                                                                                                    with and without                      percents with and          technology
computation,                                                                                              technology                            without
paper and pencil).                                                                                                                              technology

ELPNO.1.6-8.4 Compute accurately and make reasonable estimates in different contexts, with and without technology
Big Idea: 2-D Geometry
19. Enduring         19a. Essential Question: How are triangles used to determine the sum of the interior angles of polygons?
Understanding:               Skills                                                             Learning Plan                                                          ELP (SLE)
Relationships exist         (Student        Objective(s)     Assessment       Instructional        Materials/          Essential
among the angles                                                                                                                           Level 1            Level 2               Level 3             Level 4
Learning                                            Strategies        Resources           Vocabulary
and sides of          Expectations) *I will identify,
G.8.7.1                                                                 7-5; 7-6; 7-7      *two-dimensional Identify a figure,    Select proper         Sort and identify Identify and draw
geometric figures.     Identify, draw,   draw, classify and                                                       *regular polygons given the term       geometric shape,      geometric          two- and three-
classify and      compare                                                                  *irregular         (e.g., teacher      given the             shapes, using two- dimensional
compare           geometric figures.                                                       polygons           says circle,        character-istics of   and three-         geometric shapes,
geometric figures                                                                          *vertex            student can point   the shape, with       dimensional        using isometric dot
using models and                                                                                              to a picture of a   assistance            models, with       paper, with
real world                                                                                                    circle)                                   assistance         assistance
examples

G.8.7.2               *I will compare                                     7-5; 7-6;    7-7; *concave
Investigate           and contrast the                                    http://www.sparkn *convex
geometric             characteristics of                                  otes.com/math/ge
properties and        one-, two- and                                      ometry1/polygons
their relationships   three-dimensional                                   /section2.rhtml
in one, two and       models.
three dimensions      *I will compare
models, including     convex and
convex and            concave
concave polygons      polygons.

ELPG.3.6-8.1 Classify and identify key properties of two- and three-dimensional geometric shapes

July 13, 2010                                                                           Page 20 of 55
(continued)        G.8.7.4              *I will determine                                      7-8; 7-9            *interior angles          N/A                   N/A                   N/A                    N/A
19. Enduring        Use paper or         the sum of the
Understanding:       physical models      measures of
Relationships exist   to determine the     interior angles
among the angles      sum of the           triangles and
and sides of       measures of          quadrilaterals.
geometric figures.    interior angles of
triangles and

19b. Essential Question: How do angles formed by parallel lines and transversals relate to one another?
G.8.7.3             *I will recognize                                  7-2; 7-3; Lab 7A; *perpendicular            Identify basic        Investigate          Identify angles in     Classify the pairs of
Recognize the       pairs of angles                                    http://www.icoach *parallel                 geometric             properties of        relation to parallel   angles formed
pairs of angles     formed by parallel                                 math.com/SiteMa *transversal                vocabulary and        parallel lines and   lines and a            between two
formed and the      lines and a                                        p/LinearPair.html *interior angles          properties (i.e.,     transversals         transversal using      intersecting lines
relationship        transversal.                                                         *exterior angles          teacher uses a        using models,        models, with           and parallel lines
between the                                                                              *corresponding            picture for student   with assistance      assistance             cut by a transversal
angles including                                                                         angles                    to identify)                                                      with assistance
two intersecting                                                                         *vertical angles
lines and parallel                                                                       *skew lines
lines cut by a
transversal (Ex.
vertical,
supplementary,
complementary,
corresponding,
alternate interior,
alternate exterior
angles and linear
pair).

ELPG.3.6-8.2 Identify the pairs of angles formed between two intersecting lines and parallel lines cut by a transversal and discuss the relationship between the angles, as grade appropriate

July 13, 2010                                                                             Page 21 of 55
Big Idea: Area, Perimeter, and Circumference
20. Enduring     20. Essential Question: How are the area, perimeter and circumference of polygons and circles related?
Understanding:           Skills                                                           Learning Plan                                                                ELP (SLE)
Area is defined by      (Student         Objective(s)    Assessment      Instructional       Materials/         Essential
the boundaries of                                                                                                                       Level 1               Level 2               Level 3               Level 4
Learning                                           Strategies        Resources         Vocabulary
the object.       Expectations) *I will discover the
G.8.7.5                                                                8-3              *radius                Identify the           Label the radius,     Draw and label       Model and develop
Model and          relationship                                                         *diameter              radius, diameter,      diameter, center,     the radius,          the concept that pi
develop the        between diameter                                                     *circumference         center, chord,         chord, and            diameter, and the    (p) is the ratio of
concept that pi is and                                                                  *pi                    and circumfer-         circumfer-ence of     center of a circle   the circumfer-ence
the ratio of the   circumference.                                                       *ratio                 ence of a circle,      a circle, using a     and determine        to the diameter of
circumference to                                                                                               from a diagram,        word bank, with       the relation-ships   any circle
the diameter of                                                                                                with assistance        assistance            to the
any circle.                                                                                                                                                 circumference,
with assistance

ELPG.3.6-8.5 Identify and describe the characteristics of circles
M.12.7.3          *I will find                                             8-3; 8-4; 8-5;   *perimeter          Demonstrate            Find the              Use formulas to      Use formulas to
Find different    different areas for                                      www.regentsprep                      perimeter using        perimeter of the      find perimeter       find perimeter and
areas for a given a given perimeter.                                       .org/Regents/mat                     manipulatives          figure by             and area of          area of polygons
perimeter and     *I will find                                             h/fperim/Tperim.                     (e.g., paper clips,    measuring the         parallelograms       and volume and
find a different  different a                                              htm                                  craft sticks, grids)   length of the         and volume of        surface area of
perimeter for a   perimeter for a                                                                               and                    sides, find the       rectangular          prisms, cylinders,
given area.       given area.                                                                                   measurement            area of an            prisms, cylinders,   pyramids, and
tools (e.g.,           enclosed region       and cones, as        cones in real-world
area of an             squares and half      appropriate, with    appropriate, with
enclosed region        squares on a grid,    and without          and without
by covering it with    and find the          appropriate          appropriate
squares, and find      volume by filling a   technology, with     technology, with
volume by filling a    rectangular prism     assistance,          assistance
rectangular prism      with cubes, with
with cubes, with       assistance
assistance
M.13.7.3            *I will find the                                       8-3; 8-5; 8-6      *trapezoid
Develop and use     area of a
strategies to       trapezoid.
solve problems      *I will find area
involving area of   and
a trapezoid and     circumference
circumference       of circles.
and area of a
circle

ELPM.4.6-8.3 Select and apply formulas to solve problems involving perimeter, area, surface area, and volume of geometric figures, with and without appropriate technology

July 13, 2010                                                                        Page 22 of 55
(continued)       M.13.7.7           *I will find area of                                 8 Ext (p. 456)     *irregular figures    N/A       N/A                  N/A    N/A
20. Enduring       Estimate and       irregular shapes.
Understanding:      compute the area
Area is defined by   of more complex
the boundaries of    or irregular two-
the object.      dimensional
shapes by
dividing them into
more basic
shapes

Big Idea: Circle Graphs
21. Enduring     21. Essential Question: How is raw data translated into percents to be used to construct a circle graph?
Understanding:            Skills                                                              Learning Plan                                             ELP (SLE)
Circle graphs         (Student        Objective(s)    Assessment         Instructional        Materials/           Essential
represent the parts                                                                                                                  Level 1   Level 2           Level 3   Level 4
Learning                                             Strategies         Resources           Vocabulary
of data to the     Expectations) *I will construct
DAP.14.7.3                                                               Lab 7D (p.335);      *sector             N/A       N/A                  N/A    N/A
whole.       Construct and     circle graphs.                                         http://cstl.syr.edu/ *central angle
interpret circle                                                         fipse/TabBar/Bld
graphs, box-and-                                                         Circ/BUILDCIR.H
whisker plots,                                                           TM
histograms,
scatter plots and
double line
graphs with and
without
appropriate
technology.

July 13, 2010                                                                        Page 23 of 55
Big Idea: 3-D Geometry
22. Enduring     22. Essential Question: How are geometric properties used in constructions?
Understanding:           Skills                                                            Learning Plan                                                      ELP (SLE)
Constructions are       (Student        Objective(s)  Assessment         Instructional        Materials/       Essential
based on                                                                                                                    Level 1              Level 2              Level 3             Level 4
Learning                                           Strategies        Resources        Vocabulary
properties of      Expectations) *I will draw and
G.8.7.1                                                                9-1             *face            Identify a figure,   Select proper        Sort and identify Identify and draw
geometric figures. Identify, draw,   classify three                                                       *base            given the term       geometric shape,     geometric          two- and three-
classify and      dimensional                                                          *edge            (e.g., teacher       given the            shapes, using two- dimensional
compare           figures.                                                             *vertex          says circle,         characteristics of   and three-         geometric shapes,
geometric figures                                                                      *polyhedron      student can point    the shape, with      dimensional        using isometric dot
using models and                                                                       *prism           to a picture of a    assistance           models, with       paper, with
real world                                                                             *pyramid         circle)                                   assistance         assistance
examples.                                                                              *cylinder
*cone
*sphere
*hemisphere

ELPG.3.6-8.1 Classify and identify key properties of two- and three-dimensional geometric shapes
G.11.7.1         *I will build three-                                       Use                  *net    Identify a figure,   Select proper        Sort and identify Identify and draw
Build three-     dimensional                                                Manipulatives and            given the term       geometric shape,     geometric          two- and three-
dimensional      figures from two-                                          http://illuminations         (e.g., teacher       given the            shapes, using two- dimensional
solids from two- dimensional                                                .nctm.org/Lesson             says circle,         characteristics of   and three-         geometric shapes,
dimensional      patterns.                                                  Detail.aspx?id=L5            student can point    the shape, with      dimensional        using isometric dot
patterns (Ex.                                                               70                           to a picture of a    assistance           models, with       paper, with
nets).                                                                                                   circle)                                   assistance         assistance

ELPG.3.6-8.1 Classify and identify key properties of two- and three-dimensional geometric shapes
G.11.7.2           *I will create three                                     http://illuminations                N/A                  N/A                  N/A                 N/A
Construct a        dimensional                                              .nctm.org/Lesson
building out of    solids from two-                                         Detail.aspx?id=L6
cubes from a set dimensional                                                10 and
of views (Ex.      illustrations.                                           http://www.fi.uu.nl
front, top, side).                                                          /toepassingen/02
015/toepassing_w
isweb.en.html

July 13, 2010                                                                           Page 24 of 55
Curriculum Map -- Grade 7 -- Mathematics
Fourth Quarter
BEFORE BENCHMARK
Big Idea: Volume andSurface Area
23. Enduring     23. Essential Question: How do the dimensions of a geometric figure affect area, surface area, and volume?
Understanding:             Skills                                                         Learning Plan                                                             ELP (SLE)
Volume is defined         (Student        Objective(s)   Assessment      Instructional        Materials/        Essential
by the boundaries                                                                                                                  Level 1                 Level 2               Level 3               Level 4
Learning                                         Strategies        Resources         Vocabulary
of the surface area M.13.7.4
Expectations) *I will use                                           9-2; 9-4          *surface area    Demon-strata             Find the              Use formulas to      Use formulas to
of a polyhedron. Derive and use       formulas for                                                         *volume          perimeter using          perimeter of the      find perimeter       find perimeter and
formulas for       surface area of                                                                       manipulatives            figure by             and area of          area of polygons
surface area and prisms and                                                                              (e.g., paper clips,      measuring the         parallelo-grams      and volume and
volume of prisms cylinders.                                                                              craft sticks, grids)     length of the         and volume of        surface area of
and cylinders and *I will use                                                                            and measure-             sides, find the       rectangular          prisms, cylinders,
justify them using formulas for                                                                          ment tools (e.g.,        area of an            prisms, cylinders,   pyramids, and
geometric models volume of prisms                                                                        rulers), find the        enclosed region       and cones, as        cones in real-world
and common         and cylinders.                                                                        area of an               by counting           grade                problems, as grade
materials                                                                                                enclosed region          squares and half      appropriate, with    appropriate, with
by covering it with      squares on a grid,    and without          and without
squares, and find        and find the          appropriate          appropriate
volume by filling a      volume by filling a   technology, with     technology, with
rectangular prism        rectangular prism     assistance,          assistance
with cubes, with         with cubes, with
assistance               assistance

ELPM.4.6-8.3 Select and apply formulas to solve problems involving perimeter, area, surface area, and volume of geometric figures, with and without appropriate technology

July 13, 2010                                                                        Page 25 of 55
AFTER BENCHMARK
Big Idea: Pythagorean Theorem
24. Enduring     24. Essential Question: How can you use the relationships of right triangles to solve problems in the real world?
Understanding:            Skills                                                            Learning Plan                                                                    ELP (SLE)
Pythagorean          (Student
Theorem uses                            Objective(s)      Assessment   Instructional        Materials/         Essential
Learning                                                                                                   Level 1                         Level 2             Level 3              Level 4
relationships of    Expectations)                                         Strategies         Resources        Vocabulary
right triangles to
G.8.8.3             *I will identify the                                8-8              *leg                     N/A                             N/A                 N/A                  N/A
solve problems.
Determine           usage of                                                             *hypotenuse
appropriate         congruency within
application of      problems.
geometric ideas *I will the usage
and relationships, of similarity within
such as             problems.
congruence,         *I will identify the
similarity, and the usage of
Pythagorean         Pythagorean
theorem, with and Theorem
without
appropriate
technology.

M.13.8.4            *I will apply the                                         8-8                *coordinate plane         N/A                 N/A                 N/A                  N/A
Find the distance   Pythagorean
between two         Theorem to find
points on a         the distance
coordinate plane    between two
using with the      points.
Pythagorean
theorem.

Big Idea: Multi-Step Problems
25. Enduring         25. Essential Question: How are properties of one-step equations used to solve multi-step equations?
Understanding:               Skills                                                            Learning Plan                                                                 ELP (SLE)
The ability to solve        (Student          Objective(s)   Assessment       Instructional       Materials/        Essential
multi-step                                                                                                                                  Level 1             Level 2             Level 3              Level 4
Learning                                            Strategies        Resources        Vocabulary
equations leads to       Expectations) *I will apply
NO.2.8.1                                                               11-1; 11-2; 11-3                              Identify the        Solve simple one-   Solve simple one-   Solve grade-
the ability to solve   Apply the           properties of                                                                                    numeric operation   step equations      step equations      appropriate, one-
more difficult      addition,           equality to solve                                                                                when given a        with whole          with whole          step and two-step
equations.         subtraction,        two-step                                                                                         term (e.g.,         numbers, with       numbers,            equations, showing
multiplication and equations.                                                                                        pointing to an      teacher or peer     fractions,          all steps, with or
division properties                                                                                                  item or picture     assistance          decimals, and       without assistance
of equality to two-                                                                                                  when given the                          integers, with
step equations.                                                                                                      term)                                   teacher or peer
assistance

ELPNO.1.6-8.3 Apply the addition, subtraction, multiplication, and division property of equality in equations

July 13, 2010                                                                              Page 26 of 55
(continued)       25.   A.5.8.1               *I will solve and                                       11-1; 11-2; 11-3   *inequality      Represent a         Use simple          Write simple        Write and graph
Enduring           Solve and graph       graph two-step                                                                              simple equation     equations and       equations and       simple equations
Understanding:        two-step              equations.                                                                                  using manipula-     inequalities to     inequalities to     and inequalities to
The ability to solve    equations and         *I will solve and                                                                           tives, with         model real-world    model real-world    model            real-
multi-step         inequalities with     graphing                                                                                    assistance          situations using    situations using    world situations
equations leads to      one variable and      inequalities.                                                                                                   manipula-tives,     manipula-tives,     using manipula-
the ability to solve   verify the            *I will verify the                                                                                              with assistance     with assistance     tives, with
more difficult      reasonableness        reasonableness                                                                                                                                          assistance
equations.         of the result with    of an equation or
real world            inequality.
application with
and without
technology

ELPA.2.6-8.3 Write, solve, and graph equations and inequalities to model real-world situations, using manipulatives
REVIEW
NO.1.7.1              *I will                                                      Review                               N/A                  N/A                 N/A                  N/A
Relate, with and      demonstrate
without models        understanding of
and pictures,         fractions and
concepts of ratio,    percents by
proportion, and       representing
percent, including    numbers in each
percents less         of these forms.
than 1 and
greater than 100.

NO.2.7.2              *I will apply                                                Review                         Identify the        Solve simple one-   Solve simple one-   Solve grade-
Apply the             properties of                                                                               numeric operation   step equations      step equations      appropriate, one-
addition,             equality to solving                                                                         when given a        with whole          with whole          step and two-step
subtraction,          one-step                                                                                    term (e.g.,         numbers, with       numbers,            equations, showing
multiplication and    equations with                                                                              pointing to an      teacher or peer     fractions,          all steps, with or
division properties   integers.                                                                                   item or picture     assistance          decimals, and       without assistance
of equality to one-                                                                                               when given the                          integers, with
step equations                                                                                                    term)                                   teacher or peer
with integers,                                                                                                                                            assistance
fractions, and
decimals.

ELPNO.1.6-8.3 Apply the addition, subtraction, multiplication, and division property of equality in equations

July 13, 2010                                                                               Page 27 of 55
NO.3.7.1            *I will solve real                                        Review                          Compute              Compute            Compute             Compute
Compute, with       world problems                                                                            accurately and       accurately and     accurately and      accurately and
and without         involving integers.                                                                       use simple           use simple         use simple          explain strategies
appropriate                                                                                                   estimation           estimation         estimation          for estimation in
technology, with                                                                                              strategies, with     strategies with    strategies for      problem solving
integers and                                                                                                  teacher              peer and teacher   simple problems     involving simple
positive rational                                                                                             assistance (e.g.,    assistance with    involving           fractions, decimals,
numbers using                                                                                                 pointing to          and without        fractions,          and percents with
real-world                                                                                                    location to round)   technology         decimals and        and without
situations to solve                                                                                           with and without                        percents with and   technology
problems.                                                                                                     technology                              without
technology

NO.3.7.2            *I will solve multi-                                      Review
Solve, with and     step problems.
without
appropriate
technology, multi-
step problems
using a variety of
methods and
tools (Ex. objects,
mental
computation,
paper and pencil).

ELPNO.1.6-8.4 Compute accurately and make reasonable estimates in different contexts, with and without technology
NO.3.7.4        I will apply                                                 Review                           Find all the         Find common        Apply               Use prime
Apply           factorization,                                                                                factors of           factors and        factorization to    factorization (e.g.,
factorization,  LCM, and GCF to                                                                               numbers less         multiples of two   determine           tree diagrams) to
LCM, and GCF to solve problems.                                                                               than 25, with        given numbers,     greatest common     determine greatest
solve problems                                                                                                assistance           with assistance    factor and least    common factor and
using more than                                                                                                                                       common multiple,    least common
two numbers and                                                                                                                                       with assistance     multiple of
explain the                                                                                                                                                               composite numbers
solution.                                                                                                                                                                 less than 100, with
assistance

ELPNO.1.6-8.5 Apply methods of factorization to find greatest common factor (GCF) and least common multiple (LCM)

July 13, 2010                                                                    Page 28 of 55
NO.3.7.6             *I will solve real                                    Review              N/A                  N/A                 N/A                 N/A
Solve, with and      world percent
without              problems.
technology, real
world percent
problems
(Ex. I=PRT)

A.4.7.1              *I will construct a                                   Review       Identify terms in    Identify the next   Complete a         Create and
Create and           function table                                                     simple math-         term in a           simple function    complete a simple
complete a           using two                                                          ematical patterns,   mathematical        table by finding   function table,
function table       operations.                                                        with assistance      pattern, when       missing terms,     using a given rule,
(input/output)                                                                                               given a visual      with assistance    with one or two
using a given rule                                                                                           prompt, with                           operations, with
with two                                                                                                     assistance                             assistance
operations
A.4.7.2            *I will extend                                          Review
Identify and       patterns in real
extend patterns in world situations.
real world
situations

ELPA.2.6-8.2 Create and complete a function table, using a given rule
A.5.7.3           *I will translate                                        Review              N/A                  N/A                 N/A                 N/A
Translate phrases words into
and sentences     algebraic
into algebraic    expressions or
expressions and sentences.
equations         *I will combine
including         like terms.
parentheses and
positive and
rational numbers
and simplify
algebraic
expressions by
combining like
terms

July 13, 2010                                                                   Page 29 of 55
G.8.7.1              *I will                                                                  Review                                Identify a figure,     Select proper         Sort and identify Identify and draw
Identify, draw,      identify,draw,                                                                                                 given the term         geometric shape,      geometric          two- and three-
classify and         classify and                                                                                                   (e.g., teacher         given the             shapes, using two- dimensional
compare              compare                                                                                                        says circle,           character-istics of   and three-         geometric shapes,
geometric figures    geometric figures.                                                                                             student can point      the shape, with       dimensional        using isometric dot
using models and                                                                                                                    to a picture of a      assistance            models, with       paper, with
real world                                                                                                                          circle)                                      assistance         assistance
examples.

ELPG.3.6-8.1 Classify and identify key properties of two- and three-dimensional geometric shapes
G.8.7.3             *I will recognize                                            Review                                             Identify basic         Investigate           Identify angles in     Classify the pairs of
Recognize the       pairs of angles                                                                                                 geometric              properties of         relation to parallel   angles formed
pairs of angles     formed by parallel                                                                                              vocabulary and         parallel lines and    lines and a            between two
formed and the      lines and a                                                                                                     properties (i.e.,      transversals          transversal using      intersecting lines
relationship        transversal.                                                                                                    teacher uses a         using models,         models, with           and parallel lines
between the                                                                                                                         picture for student    with assistance       assistance             cut by a transversal
angles including                                                                                                                    to identify)                                                        with assistance
two intersecting
lines and parallel
lines cut by a
transversal (Ex.
vertical,
supplementary,
complementary,
corresponding,
alternate interior,
alternate exterior
angles and linear
pair).

ELPG.3.6-8.2 Identify the pairs of angles formed between two intersecting lines and parallel lines cut by a transversal and discuss the relationship between the angles, as grade appropriate
G.8.7.4              *I will determine                                                        Review                                         N/A                   N/A                    N/A                   N/A
Use paper or         the sum of the
physical models      measures of
to determine the     interior angles
sum of the           triangles and
interior angles of
triangles and

July 13, 2010                                                                                   Page 30 of 55
G.8.7.6               *I will apply                                            Review                     N/A                  N/A                  N/A                 N/A
Develop the           proportions to
properties of         determine
similar figures       similarity.
(Ex. ratio of sides
and congruent
angles).

G.9.7.2             *I will perform                                            Review                     N/A                  N/A                  N/A                 N/A
Perform             translations and
translations and reflections.
reflections of two-
dimensional
figures using a
variety of
methods (paper
folding, tracing,
graph paper).

G.11.7.1              *I will build three-                                     Review              Identify a figure,   Select proper        Sort and identify Identify and draw
Build three-          dimensional                                                                  given the term       geometric shape,     geometric          two- and three-
dimensional           figures from two-                                                            (e.g., teacher       given the            shapes, using two- dimensional
solids from two-      dimensional                                                                  says circle,         characteristics of   and three-         geometric shapes,
dimensional           patterns.                                                                    student can point    the shape, with      dimensional        using isometric dot
patterns (Ex.                                                                                      to a picture of a    assistance           models, with       paper, with
nets).                                                                                             circle)                                   assistance         assistance

ELPG.3.6-8.1 Classify and identify key properties of two- and three-dimensional geometric shapes
M.13.7.1         *I will solve real                                              Review                   N/A                  N/A                  N/A                 N/A
Solve real world world elapsed
problems         time problems.
involving two or
more elapsed
times, counting
forward and
backward (Ex.
calendar and
clock).

July 13, 2010                                                                      Page 31 of 55
M.13.7.3             *I will find the                                           Review                          Demonstrate            Find the              Use formulas to      Use formulas to
Develop and use      area of a                                                                                  perimeter using        perimeter of the      find perimeter       find perimeter and
strategies to        trapezoid.                                                                                 manipulatives          figure by             and area of          area of polygons
solve problems       *I will find area                                                                          (e.g., paper clips,    measuring the         parallelo-grams      and volume and
involving area of    and                                                                                        craft sticks, grids)   length of the         and volume of        surface area of
a trapezoid and      circumference of                                                                           and measure-           sides, find the       rectangular          prisms, cylinders,
circumference        circles.                                                                                   ment tools (e.g.,      area of an            prisms, cylinders,   pyramids, and
and area of a                                                                                                   rulers), find the      enclosed region       and cones, as        cones in real-world
enclosed region        squares and half      appropriate, with    appropriate, with
by covering it with    squares on a grid,    and without          and without
squares, and find      and find the          appropriate          appropriate
volume by filling a    volume by filling a   technology, with     technology, with
rectangular prism      rectangular prism     assistance,          assistance
with cubes, with       with cubes, with
assistance             assistance

ELPM.4.6-8.3 Select and apply formulas to solve problems involving perimeter, area, surface area, and volume of geometric figures, with and without appropriate technology
M.13.7.7           *I will find area of                                         Review                                N/A                  N/A                N/A                         N/A
Estimate and       irregular shapes.
compute the area
of more complex
or irregular two-
dimensional
shapes by
dividing them into
more basic
shapes

DAP.14.7.2           *I will identify that                                      Review        line graph,       Collect simple         Collect and           Collect and          Collect, organize,
Explain which        line graphs are                                                          circle graph,     data, with             organize simple       organize simple      graph, and interpret
types of display     used to graph                                                            part-to-whole     assistance (e.g.,      data using tally      data using tally     simple data
are appropriate      change over time.                                                        comparison,       favorite color,        marks and             marks and            samples (e.g., bar,
for various data     *I will identify that                                                    scatter plot,     food or drink,         frequency tables,     frequency tables,    line, stem-and-leaf,
sets (Ex. line       circle graphs are                                                        trends            number of              with assistance       and graph (e.g.,     circle graphs,
graph for change     used to graph                                                                              siblings)                                    bar, line, stem-     scatter plots), as
over time, circle    part-to-whole                                                                                                                           and-leaf) the        grade level
graph for part-to-   comparisons.                                                                                                                            data, with           appropriate, with
whole                *I will identify that                                                                                                                   assistance           assistance
comparison,          scatter plots are
scatter plot for     used to graph
trends)              trends.

July 13, 2010                                                                      Page 32 of 55
ELPDAP.5.6-8.1 Collect, organize, graph, and interpret a variety of data samples
DAP.16.7.1         *I will evaluate                                         Review        1- conjectures,        Make predictions     Identify the        Compare the          Compare and
Make, with and     scatter plot and                                         8                scatter plot,       using simple data    maximum             maximum              contrast the
without            the line of best fit.                                                     line of best fit,   sets, with teacher   (highest) and       (highest) and        maximum (highest)
appropriate                                                                                  relationship        or peer              minimum (lowest)    minimum (lowest)     and minimum
technology,                                                                                                      assistance           value of the data   value of data        (lowest) value of
conjectures of                                                                                                                        points from         points from          data points from
possible                                                                                                                              simple data         simple data          simple data tables
relationships in a                                                                                                                    tables or graphs,   tables or graphs,    or graphs, with
scatter plot and                                                                                                                      with teacher or     with teacher or      teacher or peer
approximate the                                                                                                                       peer assistance     peer assistance      assistance
line of best fit
(trend line)

ELPDAP.5.6-8.3 Make inferences and predictions, and justify conclusions, based on data, with and without technology
DAP.17.7.1         *I will understand                                          Review        probability,       Participate in an     Participate in an   Conduct              Identify the
Understand that that the value of a                                                          certain,           experiment to         experiment and      experiments and      theoretical
probability can    probability must                                                          impossible         determine the         determine the       calculate            probability of
take any value     be between 0 and                                                          outcome,           probability of an     fairness of the     probability, and     events within an
between 0 and 1 1                                                                            most likely,       event occurring,      experiment          complete a           experiment
(events that are                                                                             least likely,      using nonverbal       (game), with        frequency table or
not going to occur                                                                           equally likely     responses             assistance          chart using the
have probability                                                                                                                                          data set
0, events certain
to occur have
probability 1)

ELPDAP.5.6-8.4 Understand the difference between theoretical and experimental probability, and explain how the results may vary

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