Components
|
8-10
Benchmark |
Number
Sense |
- Understand
and use properties and symbolic representations of rational numbers,
powers, and roots.
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- Compare
and order rational numbers, powers, and roots.
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- Understand
concepts of and use processes involving prime and composite numbers,
factors and multiples, and divisibility.
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- Understand
and apply the concepts of ratio and both direct and inverse proportion.
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- Understand
operations on rational numbers, powers, and roots.
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- Compute
with rational numbers, powers, and roots.
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- Use
mental arithmetic, pencil and paper, calculator, or computer as appropriate
to the task involving real numbers.
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- Identify
situations involving rational numbers, powers, and roots in which estimation
is sufficient and computation is not required.
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- Use
estimation to predict computation results and to determine the reasonableness
of answers involving real numbers, for example, estimating the interest
on a loan.
|
Measurement
|
- Understand
how changes in dimension affect perimeter, area, and volume.
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|
- Measure
objects and events directly or use indirect methods such as finding
the volume of a cone given its height and diameter.
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- Calculate
rate and other derived and indirect measurements.
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- Understand
that the precision and accuracy of measurement are affected by the measurement
tools and calculating procedures.
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- Know
when to estimate and use estimation to obtain reasonable approximations,
for example, estimating how much paint is needed to paint the walls
of a classroom.
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- Understand
the benefits of standard units of measurement and the advantages of
the metric system.
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- Compare,
contrast, and use both the U.S. system and metric system.
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- Select
and use tools that will provide an appropriate degree of precision and
accuracy for the situation, for example, using kilometers vs. light
years.
|
Geometric
Sense |
- Use
geometric properties and relationships to compare, contrast, describe,
and classify 2- and 3- dimensional geometric figures.
|
|
- Construct
geometric models and scale drawings using tools as appropriate, for
example, building a model of a bridge.
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- Understand
and use properties of symmetry, congruence, and similarity.
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- Perform
complex geometric constructions using a variety of tools and technologies,
such as paper folding, computer software, straightedge, compass.
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- Understand
and use coordinate grids.
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- Understand
and apply multiple geometric transformations using combinations of translations,
reflections, and/or rotations.
|
Probability
and Statistics |
- Understand
the properties of dependent and independent events.
|
- Understand
and use appropriate counting procedures to determine probabilities.
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|
- Use
both experimental and theoretical methods to determine probabilities.
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- Collect
data using appropriate methods and technology.
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- Organize
and display data in appropriate forms, such as tables, graphs, scatter
plots, and box and whisker plots.
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|
- Calculate
and use the different measures of central tendency, variability, and
range as appropriate to describe data.
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- Use
statistics to support different points of view, for example, in a debate
or a position paper.
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- Predict
outcomes and design and conduct experiments to verify or disprove predictions.
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- Understand
and make inferences based on the analysis of experimental results, statistical
data, and graphical representations.
|
Algebraic
Sense |
- Recognize,
extend, and create complex patterns and sequences.
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- Generalize
and express rules describing patterns and sequences.
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- Translate
among tabular, symbolic, and graphical representations of relations
using =, ?, >, <, ³ ,
=
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- Use
variables to write expressions, equations, and inequalities.
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- Simplify
and evaluate expressions and formulas.
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- Solve
equations and inequalities.
|
Components
|
8-10
Benchmark |
Investigate
situations |
- Investigate
complex situations that involve more than one step or variable in order
to reach a solution.
|
|
- Develop,
use, and explain a variety of strategies and approaches (e.g. work backwards,
draw diagrams, make charts, graphs, and tables, use formulas and technology).
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- Recognize
when a problem can't be solved and state the needed information in order
to solve it.
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- Recognize
when an approach is unproductive and try a new approach.
|
Formulate
questions and define the problem |
- Define
problems and determine which questions need to be answered in complex
situations.
|
- Identify
the unknowns in complex, open-ended problem situations.
|
Construct
solutions |
- Determine
which materials, information, strategies, and variables could be used
to solve complex, open-ended problems.
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- Select
and use tools that are appropriate to solve a complex problem.
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- Organize
relevant information in a manner consistent with solving problems.
|
Components
|
8-10
Benchmark |
Relate
concepts and procedures within mathematics |
- Relate
and use conceptual and procedural understandings among multiple mathematical
content areas (e.g. shift geometric probability problems from a diagram
to coordinate grid and then use algebra to solve the problems).
|
- Demonstrate
the relationships between ideas in mathematics using equivalent mathematical
models and representations (e.g. direct variation, slope, tangent).
|
Relate
mathematical concepts and procedures to other disciplines |
- Apply
mathematical approaches to solve quantitative, spatial, or data-based
problems in other content areas.
|
- Analyze
and discuss the contributions of men, women, and members of other cultures
to mathematics.
|
Related
mathematical concepts and procedures to real life situations |
- Identify
situations in which mathematics can be used to solve problems with local,
national, or international implications such as calculating resources
necessary for interstate highway maintenance.
|
- Investigate
the mathematical knowledge and training requirements for occupational/career
areas of interest.
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