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| MCHCS
Standards Checklist - Mathematics
- Eighth Grade |
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| K
| 1st | 2nd
| 3rd | 4th
| 5th | 6th
| 7th | 8th |
| The
content standards express what all students can and need
to learn in mathematics to prepare them for the study
of advanced mathematics, for science and technical careers
and for post-secondary study in all content areas. |
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Algebra |
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Use properties of numbers to demonstrate whether
assertions are true or false.
Students solve equations and inequalities
involving absolute values.
Solve linear equations and inequalities in
one variable, solve literal equations (formulas)
for a given variable and apply these skills.
Add, subtract, and multiply polynomials and
divide polynomials with monomial binomial
divisors.
Simplify rational algebraic expressions by
combining like terms and by addition, subtraction,
multiplication, and division of the polynomial
components of these expressions.
Factor completely binomials and trinomials.
Determine the slope of a line when given an
equation of the line, the graph of the line
or two points on the line.
Describe slope as a rate of change and identify
slopes as positive, negative, zero, or undefined.
Use the Pythagorean Theorem and its converse
to find distance measure in the special case
of right triangles.
Determine the domain and range of a relation
given a set of ordered pairs, a graph, or
a function rule, and will identify the relations
that are and are not functions.
Analyze a given set of data for the existence
of a pattern, represent the pattern algebraically
and graphically, if possible, and determine
if the relation is a function. |
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Geometry |
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Use measures expressed as rates (e.g., speed,
density) and measures expressed as products
(e.g., person-days) to solve problems.
Estimate and compute the area of more complex
or irregular two- and three-dimensional figures
by breaking the figures down into more basic
geometric objects.
Know the five major "existence"
postulates about points, lines, and planes:
A line contains at least two points, a plane
contains at least three points not all on
one line, and a space contains at least four
points not all on one plane.
There is exactly one line through two points.
There is exactly one plane through three points
not on one line.
If two points lie in a plane, then the line
joining them lies in that plane.
If two planes intersect, their intersection
is a line.
Use pictorial representations and coordinate
methods to solve problems involving symmetry
and transformation.
Understand the meaning of "locus"
and describe and draw the locus of points
satisfying a given condition; solve locus
problems using constructions.
Use the properties of angles, arcs, and chords
to solve problems involving circles.
Identify and give examples of undefined terms,
axioms, theorems, and inductive and deductive
reasoning.
Judge the validity of a logical argument.
Prove basic theorems involving congruence
and similarity.
Determine how changes in dimensions affect
the perimeter, area, and volume of common
geometric figures and solids.
Solve practical problems involving complementary,
supplementary, and congruent angles that include
vertical angles, angles formed when parallel
lines are cut by a transversal, and angles
in polygons.
Know and use the Exterior Angle Theorem to
find angle measures in triangles.
Use formulas for surface area and volume of
three-dimensional objects to solve practical
problems.
Use proportional reasoning to solve practical
problems, given similar geometric objects. |
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Probability
and Statistics |
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Know the definitions of the notion of independent
events and us the rules for addition, multiplication,
and complementation to solve for probabilities
of particular events in finite sample spaces.
Organize and describe distributions of data
by using a number of different methods, including
frequency tables, histograms, standard line
and bargraphs, stem-and-leaf displays, scatterplots,
and box-and-whisker plots.
Understand that the probability of either
of two disjoint events occurring is the sum
of the two individual probabilities and that
the probability of one event following another,
in independent trials, is the product of the
two probabilities.
Understand the meaning of, and compute, the
minimum, the lower quartile, the median, the
upper quartile, and maximum of a data set. |
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Mathematical
Reasoning |
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Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information,
identifying missing information, sequencing
and prioritizing information, and observing
patterns.
Formulate and justify mathematical conjectures
based on a general description of the mathematical
question or problem posed.
Use estimation to verify the reasonableness
of calculated results.
Apply strategies and results from simpler
problems to more complex problems.
Estimate unknown quantities graphically and
solve for them by using logical reasoning
and arithmetic and algebraic techniques.
Make and test conjectures by using both inductive
and deductive reasoning.
Use a variety of methods, such as words, numbers,
symbols, charts, graphs, tables, diagrams,
and models, to explain mathematical reasoning.
Express the solution clearly and logically
by using the appropriate mathematical notation
and terms and clear language; support solutions
with evidence in both verbal and symbolic
work.
Indicate the relative advantages of exact
and approximate solutions to problems and
give answers to a specified degree of accuracy.
Make precise calculations and check the validity
of the results from the context of the problem.
Evaluate the reasonableness of the solution
in the context of the original problem.
Note the method of deriving the solution and
demonstrate a conceptual understanding of
the derivation by solving similar problems.
Develop generalizations of the results obtained
and the strategies used and apply them to
new problem situations.
Use various forms of displays to compare two
sets of data.
Understand the meaning of, and compute the
minimum, the lower quartile, the median, the
upper quartile, and the maximum of a data
set. |
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