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STANDARDS
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BENCHMARKS
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| Demonstrate
knowledge and use of numbers and their representations
in a broad range of theoretical and practical settings. |
6.A.3 Represent fractions,
decimals, percentages, exponents and scientific notation
in equivalent forms. |
| Investigate,
represent and solve problems using number facts, operations
(addition, subtraction, multiplication, division) and
their properties, algorithms and relationships. |
6.B.3a Solve practical
computation problems involving whole numbers, integers
and rational numbers. |
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6.B.3b Apply primes,
factors, divisors, multiples and common factors and
common multiples in solving problems. |
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6.B.3c Identify and
apply properties of real numbers including pi, squares,
and square roots. |
| Compute and
estimate using mental mathematics, paper-and-pencil
methods, calculators and computers. |
6.C.3a Select computational
procedures and solve problems with whole numbers, fractions,
decimals, percents and proportions. |
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6.C.3b Show evidence
that computational results using whole numbers, fractions,
decimals, percents and proportions are correct and
/or that estimates are reasonable. |
| Solve problems
using comparison of quantities, ratios, proportions
and percents. |
6.D.3 Apply ratios
and proportions to solve pratical problems. |
| Measure and
compare quantities using appropriate units, instruments
and methods. |
7.A.3a Measure length,
capacity, weight/mass and angles using sophisticated
instruments (e.g., compass, protractor, trundle wheel). |
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7.A.3b Apply concepts
and attributes of length, capacity, weight/mass, perimeter,
area, volume, time, temperature and angle measures
in practical situations. |
| Estimate measurements
and determine acceptable levels of accuracy. |
7.B.3 Select and
apply instruments including rulers and protactors and
units of measure to the degree of accuracy required. |
| Select and
use appropriate technology, instruments and formulas
to solve problems, interpret results and communicate
findings. |
7.C.3a Construct
a simple scale drawing for a given situation. |
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7.C.3b Use concrete
and graphic models and appropriate formulas to find
perimeters, areas, surface areas and volumes of two-
and three- dimensional regions. |
| Describe numerical
relationships using variables and patterns. |
8.A.3a Apply the
basic properties of commutative, associative, distributive,
transitive, inverse, identity, zero, equality and order
of operations to solve problems. |
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8.A.3b Solve problems
using linear expressions, equations and inequalities. |
| Interpret and
describe numerical relationships using tables, graphs
and symbols. |
8.B.3 Use graphing
technology and algebraic methods to analyze and predict
linear relationships and make generalizations from
linear patterns. |
| Solve problems
using systems of numbers and their properties. |
8.C.3 Apply the properties
of numbers and operations including inverses in algebraic
settings derived from economics, business and the sciences. |
| Use algebraic
concepts and procedures to represent and solve problems. |
8.D.3a Solve problems
using numeric, graphic or symbolic representations
of variables, expressions, equations and inequalities. |
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8.D.3b Propose and
solve problems using proportions, formulas and linear
functions. |
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8.D.3c Apply properties
of powers, perfect squares and square roots. |
| Demonstrate
and apply geometric concepts involving points, lines,
planes and space. |
9.A.3a Draw or construct
two- and three- dimensional geometric figures including
prisms, pyramids, cylinders and cones. |
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9.A.3b Draw transformation
images of figures, with and without the use of technology. |
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9.A.3c Use concepts
of symmetry, congruency, similiarity, scale, perspective,
and angles to describe and analyze two -and three-dimensional
shapes found in practical applications (e.g., geodesic
domes, A-frame houses, basketball courts, inclined
planes, art forms, blueprints). |
| Identify, describe,
classify and compare relationships using points, lines,
planes and solids. |
9.B.3 Identify, describe,
classify and compare two- and three-dimensional geometric
figures and models according to their properties. |
| Construct convincing
arguments and proofs to solve problems. |
9.C.3a Construct,
develop and communicate logical arguments (informal
proofs) about geometric figures and patterns. |
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9.C.3b Develop and
solve problems using geometric relationships and models,
with and without the use of technology. |
| Use trigonometric
ratios and circular functions to solve problems. |
9.D.3 Compute distances,
lengths and measures of angles using proportions, the
Pythagorean theorem and its converse. |
| Organize, describe
and make predictions from existing data. |
10.A.3a Construct,
read and interpret tables, graphs (including circle
graphs) and charts to organize and represent data. |
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10.A.3b Compare the
mean, median, mode and range, with and without the
use of technology. |
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10.A.3c Test the
reasonableness of an argument based on data and communicate
their findings. |
| Formulate questions,
design data collection methods, gather and analyze
data and communicate findings. |
10.B.3. Formulate
questions(e.g., relationships between car age and mileage,
average incomes and years of schooling), devise and
conduct experiments or simulations, gather data, draw
conclusions and communicate results to an audience
using traditional methods and contemporary technologies. |
| Determine, describe
and apply the probabilities of events. |
10.C.3a Determine
the probability and odds of events using fundamental
counting principles. |
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10.C.3b Analyze problem
situations (e.g., board games, grading scales) and
make predictions about results. |
