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```					                                                      8th Grade Math Curriculum

Posted: October 10, 2001
Last Updated: May 3, 2006

Rationale

The eighth grade mathematics curriculum is designed to expose and facilitate learning of the basic mathematical
concepts, knowledge, and skills necessary for the successful participation and application in the secondary level
math classes.

Course Description

The eighth grade student's mathematics course is designed to review and acquire a solid foundation, which includes
the knowledge of numerical operations, mathematical systems, geometry, number theory, probability and statistics,
measurements, and algebraic expressions.

Duration: 1 Year

Performance Required            Alignment to               Instructional Strategies                   Assessment                       Level of
Show-Me Standards                                                                                    Performance
Required
General Objective # NO,1,A      Performance   Content
and compare numbers                 3.3
MA 5
1. Specific Objectives:
The student will:               MA, NO, 1,                 In cooperative learning groups students    Students will complete a
A. compare and order            A, 8                       will discuss the values of rationals and   constructed response
rationals and percents                                     percents and plot them on a number         question taken from the
including finding their                                    line.                                      Assessment Annotations for
approximate location on a                                                                             the Curriculum
number line.                                               Real Numbers by Richard Powers             Frameworks.p.195
Benchmark B problem #2
Ordering Rational Numbers by Richard
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Powers

General Objective #NO, 1, B   Performance   Content

The student will represent        3.4
and use rational numbers.                    MA 1
2. Specific Objectives:
The student will:             MA, NO, 1,              Discuss methods of fractional              Students will create a
B, 8                    representation and computation             performance event in the
1. use fractions to solve                             including shortcuts. Practice with         form of a take home
problems.                                             selected response quizzes.                 test(including an answer
key) that compares the cost
MAP Released Items by Richard              of items from several
Powers                                     stores. The performance
event will include topics
such as fraction off,
percentage off, sales tax,
etc.
2. use decimals to solve      MA, NO, 1,              Discuss methods of decimal                 Students will create a
problems.                     B, 8                    representation and computation             performance event in the
including shortcuts. Practice with         form of a take home
selected response quizzes.                 test(including an answer
key) that compares the cost
of items from several
stores. The performance
event will include topics
such as fraction off,
percentage off, sales tax,
etc.
3. use percents to solve      MA, NO, 1,              Analyze the use of proportions and         Students will create a
problems.                     B, 8                    equations calculating percents including   performance event in the
but not limited to Commission,             form of a take home
Discount/Sale Price, and Percent of a      test(including an answer
number. Practice with selected response    key) that compares the cost
quizzes.                                   of items from several
stores. The performance
event will include topics
such as fraction off,
percentage off, sales tax,
etc.
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General Objective # NO, 1,      Performance   Content
C
The student will compose            3.6        MA 1
and decompose numbers.
3. Specific Objectives:
The student will:               MA, NO, 1,              Interpret among the equivalent              Students will take a free
1. make conversions among       C, 8                    representations of fractions, decimals     and constructed response
fractions, decimals,and                                 and percents, and make conversions.        exam.
percents.
2. make conversions among       MA, NO, 1,              Re-introduce students to expanded          Students will take a free
expanded notation, scientific   C, 8                    notation and exponential notation. Also,   and constructed response
notation and standard form.                             engage the students in the actual          exam.
multiplication of large and small
numbers and promote the discovery of
patterns to aid in the computation.
General Objective # NO, 1,      Performance   Content
D
The student will classify and       1.10       MA 5
describe numeric
relationships.
4. Specific Objectives:
The student will:               MA, NO, 1,              Analyze the rules of divisibility and      Students will complete a
1. use factors and multiples    D, 8                    apply them in the evaluation of the        selected response quiz.
to describe relationships                               LCM and GCF.
between and among numbers
including but not limited to                            MAP Released Items by Richard
LCM, GCF, and divisibility                              Powers
rules.
2. use factors and multiples    MA, NO, 1,              Using multiple methods, provide            Students will complete a
to justify characteristics of   D, 8                    extensive examples of how to create the    selected response quiz.
numbers including but not                               factorization using only prime numbers
limited to prime and                                    after facilitating a conversation on the
composite numbers, and                                  nature of prime and composite numbers.
prime factorization.
MAP Released Items by Richard
Powers
General Objective # NO,2,B      Performance   Content
The student will describe
effects of operations             3.4, 4.1     MA 1
5. Specific Objectives:
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The student will:             MA, NO, 2,              Using a variety of techniques such as         Given problems with errors
1. describe the effects of    B, 8                    rules, money, temperature, etc., students     the student will be expected
multiplication and division                           will calculate and analyze products and       to find the error and
on integers.                                          quotients.                                    describe the effect the
solution.
General Objective # NO, 2,    Performance   Content
C
The student will apply          1.6, 1.10    MA 5
properties of operations.
6. Specific Objectives:
The student will:             MA, NO, 2,              Review the order of operations for            Students will complete a
1. apply properties of        C, 8                    rational numbers, and design problems         selected response quiz. The
operations to rational                                to solve including problems with              quiz will contain problems
numbers, including order of                           inverse operations.                           including order of
operations and inverse                                                                              operations and inverse
operations.                                           Order of Operations by Richard Powers         operations.

General Objective # NO, 2,    Performance   Content
D
The student will apply          1.6, 3.4
operations on real numbers.                  MA 5
7. Specific Objectives:
The student will:             MA, NO, 2,              Given a list of perfect squares and     Via a selected response
1. apply the relationship     D, 8                                                            exam students will evaluate
square roots, the teacher will facilitate a
between squares and square                            discussion and provide examples of how  squares and square roots of
roots to solve a problem.                             to approximate the values of nonperfect perfect squares and
squares.                                approximate the values of
square roots of non perfect
Squares, Square Root, Cubes , and Cube squares, and solve problems
Roots by Richard Powers                 involving them.
2. apply the relationship     MA, NO, 2,              Given a list of perfect cubes and cube  Via a selected response
between cubes and cube        D, 8                    roots, the teacher will facilitate a    exam students will evaluate
roots to solve a problem.                             discussion and provide examples of how cube and cube roots of
to approximate the values of nonperfect perfect squares and
squares.                                approximate the values of
cube roots of non-perfect
Squares, Square Root, Cubes , and Cube cubes, and solve problems
Roots by Richard Powers                 involving them.

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General Objective # NO, 3,       Performance   Content
C
The student will compute           1.10, 3.3    MA 1
problems.
8. Specific Objectives:
The student will:                MA, NO, 3,              Using manipulatives the students will       Students will complete a
1. apply all operations on       C, 8                    discover the rules of operations on all     selected response test over
rational numbers.                                        rational numbers and make applications      the applications of all
with this knowledge.                        operations on rational
numbers.

General Objective # NO, 3,     Performance     Content
D
The student will estimate and     3.3, 4.1
justify solutions.                              MA 1
9. Specific Objectives:
The student will:              MA, NO, 3,                Based on previously answered questions      Given problems in a
D, 8                      the students will be presented with         selected response format
1. estimate the results of all                           estimation strategies that help them find   students will determine the
operations on rational                                   the reasonableness of an answer.            solution through estimation.
numbers and percents.
2. justify the results of all  MA, NO, 3,                Based on estimates the students will        Students will pick a
operations on rational         D, 8                      defend the estimates and provide three      problem and its solution
numbers and percents.                                    reasons.                                    and defend the
reasonableness of the
solution.
General Objective #NO, 3, E      Performance   Content
The student will use
proportional reasoning.              3.3
MA 1
10. Specific Objectives:
The student will:                MA, NO, 3,              Facilitate a discussion on rates and         Students will be able to
1. solve problems involving      E,8                     provide example of how to convert rates     determine a rate based on a
rates                                                    into unit rates including unit pricing.     table or graph, and use this
rate to calculate an amount.
2. solve problems involving      MA, NO, 3,              Assist students in measuring on a scale     Using a variety of
proportions, such as scaling     E,8                     drawing and making conversions, as          assessments (selected and
and finding equivalent ratios.                           well as using proportions to solve for a    closed ended constructed
missing value.                              response), the students will
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solve problems using
proportions including but
not limited to scale
drawing.
General Objective # AR,1,B      Performance   Content
The student will create and
analyze patterns.                 1.6, 3.6     MA 4
11. Specific Objectives:
The student will:               MA, AR, 1,              Teacher will model the use of patterns       Students will design and
B, 8                    and how to determine the next terms in      justify pictorial and
1. generalize patterns                                  a numerical pattern as well as              graphical representations of
represented graphically using                           discovering the rule to determine the nth   patterns including writing
words or symbolic rules,                                term.                                       algebraic expressions or
including recursive notation.                                                                       number sentences.
Patterns and Sequences by Richard
Powers

General Objective # AR, 1,      Performance   Content
C
The student will classify           1.6
objects and representations.                   MA 4
12. Specific Objectives:
The student will:               MA, AR, 1,              Given multiple representations of           Students will compare and
1. compare and contrast         C, 8                    patterns students will analyze the          contrast patterns based on
various forms of                                        similarities and differences.               data given in multiple
representations of patterns.                                                                        formats such as tables,
graphs etc.
General Objective # AR, 1,D     Performance   Content
The student will identify and
compare functions.                1.6, 3.6     MA 4
13. Specific Objectives:
The student will:               MA, AR, 1,              Facilitate a discussion on the definition   Using tables, graphs and
1. compare properties of        D, 8                    and characteristics of linear functions.    equations, the student will
linear functions between or                                                                         verify whether a linear
among tables, graphs, and                                                                           function is represented. The
equations.                                                                                          student will also compare
intercepts, slopes, etc.
General Objective # AR, 2,      Performance   Content
A
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The student will represent       1.6, 3.1     MA 4
mathematical situations.
14. Specific Objectives:
The student will:              MA, AR, 2,              Analyze patterns represented in various     The student will complete
1. use symbolic algebra to     A, 8                    forms, and discuss the development of a    a constructed response quiz
represent and solve problems                           symbolic rule to find any term in the      in which he/she will
that involve linear                                    pattern.                                   generate patterns and their
relationships including                                                                           symbolic rule.
recursive relationships.                               Understanding and Writing Equations
by Richard Powers

MAP Released Items by Richard
Powers

General Objective # AR, 2,B    Performance   Content

The student will describe and     3.6         MA 4
use mathematical
manipulation.
15. Specific Objectives:
The student will:             MA, AR, 2,               Based on previously learned skills         Students will complete an
1. generate equivalent forms B, 8                      students will create and simplify linear   exam in which they
for linear expressions.                                expressions by applying properties of      simplify expressions and
operations and combining like terms.       solve equations including
but not limited to changing
between slope intercept and
standard form
General Objective #AR, 3, A Performance      Content
The student will use
mathematical models.            1.6, 3.6      MA 4
16. Specific Objectives:
The student will:            MA, AR, 3,                Teacher will model different ways to       Students will choose
1. model and solve problems, A,8                       represent and solve problems.              another appropriate
using multiple                                                                                    representation of a problem
representations such as                                                                           as well as solve, and
graphs, tables, equations or                                                                      analyze the process,
inequalities.                                                                                     solution and graph of an
equation and inequality.
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General Objective #AR, 4, A     Performance   Content
The student will analyze
change.                           1.6, 4.1     MA 2,
MA 4
17. Specific Objectives:
The student will:               MA, AR, 4,              Teacher will facilitate a discussion that    Students will analyze the
1. analyze the nature of        A,8                     analyzes the nature of change in linear      result of changes in slope
changes (including slope and                            relationships.                               and intercepts including
intercepts) in quantities in                                                                         negative slope, and rate of
linear relationships.                                                                                change.
General Objective #GSR, 1,      Performance   Content
A
1.6, 3.6     MA 2
The student will describe and
use geometric relationships.
18. Specific Objectives:
The student will:               MA, GSR, 1,             Using concept circles students will          Students will take a series
1. describe, classify and       A, 8                    analyze triangles and their relationships.   of selected and constructed
generate relationships                                  Also students will solve problems by         response questions.
between and among triangles                             writing and solving equations including
using their defining                                    Pythagorean Theorem.
properties including                                    Classifying Polygons by Richard
Pythagorean theorem.                                    Powers
2. describe, classify and       MA, GSR, 1,             Using concept circles students will          Students will take a series
generate relationships          A, 8                    analyze quadrilaterals and their             of selected and constructed
between and among                                       relationships. Also students will solve      response questions.
quadrilaterals using their                              problems by writing and solving
defining properties.                                    equations
Classifying Polygons by Richard
Powers

3. describe, classify and       MA, GSR, 1,             Using concept circles students will          .Students will take a series
generate relationships          A, 8                    analyze polygons and their                   of selected and constructed
between and among                                       relationships. Also students will solve      response questions.
polygons using their defining                           problems by writing and solving
properties.                                             equations
Classifying Polygons by Richard
Powers
4. describe, classify and       MA, GSR, 1,             Using concept circles students will          Students will take a series
generate relationships          A, 8                    analyze 3-dimensional objects and their      of selected and constructed
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between and among types of                               relationships.                              response questions
3-dimensional objects using
their defining properties                                Cross sections by Richard Powers
including a)Pythagorean
Theorem b) cross section of
a 3-dimensional object
results in what 2-
dimensional shape.
General Objective #GSR, 1,       Performance   Content
B
1.6, 3.6     MA 2
The student will apply
geometric relationships.
19. Specific Objectives:
The student will:                MA, GSR, 1,             Students will create, analyze and solve     Students will take a series
1. apply relationships           B, 8                    problems using similar polygons             of selected and constructed
between corresponding sides                              including solving for a missing side or     response questions
and corresponding areas of                               angle.
similar polygons to solve
problems.
General Objective #GSR, 2,       Performance   Content
A
3.6        MA 2
The student will use
coordinate systems.
20. Specific Objectives:
The student will:                MA, GSR, 2,             Students will create similar triangles      Students will participate in
1. use coordinate geometry       A, 8                    and put in vertices to make right           a performance event in
to analyze properties of right                           triangles when given the hypotenuse.        which they will graph the
triangles.                                               Also students will calculate area.          missing vertex to form a
right triangle, and solve for
The Coordinate System by Richard            the missing side and/or
Powers                                      perimeter and area.

2. use coordinate geometry       MA, GSR, 2,             Students will graph points and
to analyze properties of         A, 8                    determine which quadrilateral results.
quadrilaterals.                                          Also students will discuss attributes and
calculate areas.

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Area and Perimeter of Rectangles by
Richard Powers

General Objective #GSR, 3,      Performance   Content
A
3.6        MA 2
The student will use
transformations on objects.
21. Specific Objectives:
The student will:               MA, GSR, 3,             Following teacher led discussion and         Students will take a series
1. reposition shapes under      A, 8                    examples; students will complete             of selected and constructed
formal transformations such                             guided and independent practice.             response questions
as reflection, rotation, and                            Students will also analyze
translation.                                            transformations and identify which has
occurred in an example.

Transformations by Richard Powers

General Objective #GSR, 3,      Performance   Content
B
3.6        MA 2
The student will use
transformations on functions.
22. Specific Objectives:
The student will:               MA, GSR, 3,             After completing dilations students will     Students will take a series
1. describe the relationship    B, 8                    hypothesize about and evaluate the           of selected and constructed
between the scale factor and                            areas based on scale factor including the    response questions
the areas of the image using                            use of a table of values for linear, area,
a dilation                                              and volume.
(stretching/shrinking).
Transformations by Richard Powers
General Objective #GSR, 3,      Performance   Content
C
1.6        MA 2
The student will use
symmetry.
23. Specific Objectives:
The student will:               MA, GSR, 3,             Students will determine if a regular         Students will take a series
1. identify the number of       C, 8                    polygon has rotational symmetry and          of selected and constructed
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rotational symmetries of                                describe the symmetry.                      response questions
regular polygons.
Rotational Symmetry by Richard
Powers
General Objective #GSR, 4,     Performance    Content
A
3.3        MA 2
The student will recognize
and draw 3-dimensional
representations.
24. Specific Objectives:
The student will:              MA, GSR, 4,              Students will compare an isometric          Students will create an
1. create isometric drawings   A, 8                     drawing with a mat plan.                    isometric drawing from a
from a given mat plan.                                                                              given mat plan.
Isometric Drawings and Mat Plans by
Richard Powers
General Objective #GSR, 4,     Performance    Content
B
3.1        MA 2
The student will draw and
use visual modes.
25. Specific Objectives:
The student will:              MA, GSR, 4,              Teacher will model the use of perimeter     Students will manipulate
1. draw or use visual models   B, 8                     and area of complex polygons with           shapes to create a new
to represent and solve                                  manipulatives and discuss the               shape or change perimeter
problems.                                               similarities and differences.               or area. Also students will
view a visual model and
pick the corresponding
result. (tent or cube)
General Objective #M, 1, B     Performance    Content

The student will identify           1.6        MA 2
equivalent measures.
26. Specific Objectives:
The student will:              MA, M, 1, B,             Students will convert within cubic units    Students will take a quiz of
1. identify the equivalent     8                        including but not limited to yd to ft and   selected and constructed
volume of measures within a                             m to cm.                                    response questions.
system of measurement (m ³
to cm ³)

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General Objective #M, 2, B      Performance    Content

The student will use angle         1.4, 3.2     MA 2
measurement.
27. Specific Objectives:
The student will:               MA, M, 2, B,             Based on discussion of reflex angles        Students will perform
1. use tools to determine the   8                        and prior knowledge of protractors,         measurements of reflex
measure of reflex angles to                              students will measure angles that are       angles.
the nearest degree.                                      greater than 180 degrees

Angle Measure by Richard Powers
General Objective #M, 2, C      Performance    Content

The student will apply             3.4, 4.1     MA 2
geometric measurements.
28. Specific Objectives:
The student will:               MA, M, 2, C,             Teacher will demonstrate the use of         Student will pick a three-
1. describe how to solve        8                        formulas and how to evaluate them to        dimensional object and
problems involving surface                               find surface area, volume, or any part of   explain how to find surface
area and/or volume of a                                  the formula including finding errors of     area and volume.
rectangular or triangular                                computation.
prism, or cylinder.
Surface Area by Richard Powers
General Objective #M, 2, D      Performance    Content

The student will analyze           1.7, 3.8     MA 2
precision.
29. Specific Objectives:
The student will:               MA, M, 2, D,             Following a discussion on the precision     Students will have to
1. analyze precision and        8                        (rounding to the smallest place), the       choose the most precise
accuracy in measurement                                  students will determine the number of       measurement and determine
situations and determine                                 significant digits.                         the number of significant
number of significant digits.                                                                        digits.
Using Significant Digits by Richard
Powers

General Objective #M, 2, E      Performance    Content

The student will use              1.6, 1.10     MA 2
relationships within a
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measurement system.
30. Specific Objectives:
The student will:               MA, M, 2, E,              Students will make conversion               Students will take a quiz of
1. convert square or cubic      8                         including but not limited to ft to yd       selected and constructed
units to equivalent square or                             squared.                                    response questions.
cubic units within the same
system of measurement.
General Objective #DP, 1, A     Performance     Content

The student will formulate           1.2         MA 3
questions.
31. Specific Objectives:
The student will:               MA, DP, 1,                Students will create and analyze a          Teacher observation of
1. formulate questions,         A, 8                      survey and determine if it is biased or     survey the student created
design studies, and collect                               not.                                        and analyzed.(Social
Displaying Data by Richard Powers
General Objective #DP, 1, C     Performance     Content

The student will represent         1.8, 3.6      MA 3
and interpret data.
32. Specific Objectives:
The student will:               MA, DP, 1, C,             Students will use provided data to          Students will take an exam
1. select, create, and use      8                         choose and create a representation          of selected and constructed
appropriate graphical                                     including but not limited to all types of   response questions.
representation of data                                    graphs, stem and leaf, histogram, Venn
(including scatter plots).                                diagram with which the students will
create 5 questions that can be answered
by using the representation.

Displaying Data by Richard Powers
General Objective #DP, 2, A     Performance     Content

The student will describe and      3.4           MA 3
analyze data.
33. Specific Objectives:
The student will:             MA, DP, 2,                  Using appropriate data representations      Students will take an exam
1. find, use and interpret    A, 8                        such as box and whisker, students will      of selected and constructed
measures of center, outliers,                             find, use and interpret values including    response questions.
and spread, including range                               mean without outliers, median, mode,
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and inter quartile range.                                  spread, outliers, and most typical.

Displaying Data by Richard Powers

MAP Released Items by Richard
Powers
General Objective #DP, 2, B      Performance     Content

The student will compare              3.6         MA 3
data representations.
34. Specific Objectives:
The student will:                MA, DP, 2, B,             Determine the best choice for              Given a set of data the
1. compare different             8                         representing data and which                students will choose and
representations of the same                                representation is misleading.              construct an approprite
data and evaluate how well                                                                            representation along with a
each representation shows                                  Displaying Data by Richard Powers          representation that is
important aspects of the data.                                                                        misleading.
General Objective #DP, 3, A      Performance     Content

The student will develop and          3.5         MA 3
evaluate inferences.
35. Specific Objectives:
The student will:                MA, DP, 3,                Determine whether a correlation is         Students will graph two sets
1. make conjectures about        A, 8                      positive, negative, or none. Also          of data and determine the
possible relationships                                     students will approximate a fitted line.   correlation. If appropriate
between 2 characteristics of                                                                          the students will put in a
a sample on the basis of                                   Displaying Data by Richard Powers          fitted line and make
scatter plots of the data and                                                                         predictions.
approximate lines of fit.
General Objective #DP, 4, A      Performance     Content

The student will apply basic          3.5         MA 3
concepts of probability.
36. Specific Objectives:
The student will:                MA, DP, 4,                Students will describe how theoretical      Students will take a quiz of
1. make conjectures (based       A, 8                      and experimental probability are           selected and constructed
on theoretical probability)                                different as well as how they can work     response questions.
about the results of                                       together to help us find the solution to
experiments.                                               problems. These problems range from
simple probability to dependent events
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to finding the probability of an
experiment based on theoretical
probability.

Experimental and Theoretical
Probability by Richard Powers

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