1.8.1
Read, write, add, subtract,
multiply, and divide real numbers in various forms including radicals,
exponential, and scientific notation; convert a standard number to scientific
notation and vice versa.
1.8.2
Compute with rational and
irrational numbers to solve a variety of problems including rates, recipes,
unit cost, and percents (e.g., discounts, interest, sale price, commissions,
taxes).
Word Problems and Number
Theory (I)
1.8.3
Explain and apply concepts of
number theory and properties of real numbers to solve problems.
Comparison and Ordering
1.8.6
Compare and order rational
numbers.
1.8.7
(E)
Estimate in problem-solving
situations and in practical applications; determine the reasonableness of the
answer and verify the results.
1.8.9
Explain the relationship
between fractions, decimals, and percents and translate among various
representations of equal numbers (e.g., from fractions to decimals to percents,
various forms of ³1² such as 3/3 or 16/16) to solve problems efficiently.
2.8.1
Use inductive reasoning to
find the missing term in number and geometric patterns and to generalize basic
patterns to the nth term, with and without calculators; use written, oral, and
symbolic language to identify and describe patterns, sequences, and functions.
2.8.2
Translate among verbal
descriptions and graphic, tabular, and algebraic representations of
mathematical situations.
Variables (unknowns) (E)
2.8.3
Identify, model, describe, and
evaluate relationships, including functions, using a variety of methods with
and without technology.
2.8.3a Calculate an unknown quantity
given a formula and the other quantities.
Number sentences and
Equations (I)
2.8.4
Add and subtract binomials
describing the connection between the algebraic process and the arithmetic
process.
2.8.5
Describe how a change in one
variable of a mathematical relationship affects the remaining variables using
various tools and methods.
2.8.6
Model, identify, and solve
linear equations and inequalities, using formal and informal methods, and
relate this process to the order of operations.
2.8.7
Solve simple linear equations
and connect that process to the order of operations.
Comparison and Ordering
3.8.1 (E)
Solve problems which require
comparison and conversion of units of measure for length, weight/mass, and
volume within the same measurement system (customary and metric); estimate
conversions between like units of the two systems to solve problems.
3.8.2
Demonstrate an understanding
of precision, error and tolerance in measurement using the appropriate
measurement tool to the required degree of accuracy.
3.8.3
Select and apply appropriate
formulas to solve problems; identify the relationship between changes in area
and volume and changes in linear measures of figures.
3.8.5
Apply ratios and proportions
to calculate rates and as a method of indirect measure (e.g., miles per hour,
cost per unit).
4.8.1
Construct regular and irregular
polygons such as triangles, quadrilaterals, pentagons, hexagons, and octagons.
Congruence, similarity, and
transformations (E)
4.8.2
Apply the properties of
equality and proportionality to solve problems involving congruent or similar
shapes (e.g., create scale drawings, perspective drawings).
Coordinate geometry and line
of symmetry (W)
4.8.3
Use coordinate geometry and
models to change scale (enlarge and reduce).
Line slopes and linear
equations (I)
4.8.5
Use coordinate geometry to
represent and interpret relationships defined by equations and formulas
(including distance, midpoint, and slope) with and without technology.
4.8.5a Apply coordinate geometry skills
to real world situations such as map grids.
Lines, angles, and geometric
figures (I)
4.8.6
Form generalizations and
validate conclusions about properties of geometric shapes including parallel
lines, perpendicular lines,
bisectors, triangles, and quadrilaterals.
4.8.7
Verify and explain the
Pythagorean Theorem with various methods (e.g., using grid paper, applying it
to a missing side of a right triangle); determine missing sides and angles of
triangles based on properties of their sides and angles.
4.8.8
Use hand tools, technology,
and models to construct figures and bisect angles and line segments;
distinguish among constructions, sketches and drawings.
Data collection and
organization (E)
5.8.1
Organize, display, read, and
analyze data with and without technology using a variety of displays
including box and whisker plots.
5.8.2
Find the theoretical
probability of an event using different counting methods (e.g., tree diagrams,
sample spaces, and organized lists) and compare those results with actual
(experimental) results, differentiating between the probability of an event and
the odds of an event.
5.8.2a Identify the uses of probability
in the real world.
5.8.3
Solve real-life problems by
finding the number of combinations possible in given situations using a variety
of counting methods.
5.8.5
Evaluate arguments that are
based on data analysis for accuracy and validity; analyze the effect a change
of scale or a change of format will have on statistical charts and graphs.
5.8.6
Formulate accurate inferences
and projections based on interpolations (filling in) and extrapolations
(extending) of data to solve problems.
6.1
Select modify, develop, and
apply strategies to solve a variety of mathematical and practical problems and
to investigate and understand mathematical concepts.
6.2 (E)
Apply previous experience and
knowledge to new problem-solving situations.
6.3 (E)
Formulate own problems; use
various approaches to investigate and solve problems.
6.4 (E)
Explain and verify results
with respect to the original problem.
6.5 (E)
Verify, interpret, and
evaluate results with respect to the original problem situation, determining an
efficient strategy for the given situation.
6.6 (E)
Try more than one strategy
when the first strategy proves to be unproductive.
6.7 (E)
Apply multi-step, integrated,
mathematical problem-solving strategies, persisting until a solution is found
or until it is clear that no solution exists.
6.8 (E)
Apply solutions and strategies
from earlier problems to new problem situations.
6.9 (E)
Generalize solutions and
strategies from earlier problems to new problem situations.
6.10 (E)
Interpret and solve a variety
of mathematical problems by paraphrasing, identifying necessary and extraneous
information, selecting and justifying efficient methods and/or strategies, and
ensuring the answer is reasonable.
6.11 (E)
Apply combinations of proven
strategies and previous knowledge to solve non-routine problems.
6.12 (I)
Use technology, including
calculators and/or computers to understand quantitative relationships, e.g.,
for skip counting and pattern exploration.
6.13 (E)
Use technology , including
calculators and/or computers to solve problems and verify solutions.
6.14 (E)
Use technology, including
calculators and/or computers, to investigate, define, and describe quantitative
relationships such as patterns and functions.
7.1 (E)
Discuss and exchange ideas
about mathematics as a part of learning.
7.2 (E)
Use inquiry techniques (e.g.
discussion, questioning, research, data gathering, reading, writing, and active
listening) to solve and develop understanding of mathematical problems.
7.3 (I)
Read expository text to learn
about mathematics.
7.4 (E)
Use pictorial representations
to identify mathematical operations and concepts.
7.5 (I)
Identify and translate key
words and phrases that imply mathematical operations.
7.6 (E)
Interpret and solve word
problems without the necessity of key words or phrases.
7.7 (E)
Use physical materials,
models, discussions, pictures, or writing to represent and communicate
mathematical ideas.
7.8 (E)
Use physical material,
diagrams, and tables to represent and then communicate mathematical ideas
through oral, verbal, and written formats.
7.9 (E)
Model and explain mathematical
relationships using manipulatives, oral, written, pictorial, graphical, and
algebraic methods.
7.10 (W)
Evaluate the effectiveness of
written and oral presentation of mathematics.
7.11 (I)
Make conjectures and present
arguments in discussions of mathematical ideas.
7.12 (I)
Explain and justify thinking
about mathematical ideas and solutions.
7.13 (E)
Explain and evaluate thinking
about mathematical ideas and solutions; discuss the validity of simple
arguments.
7.14 (I)
Explain and evaluate
thinking about mathematical ideas and solutions based on the role of
definitions, properties, common rules, and symbols in solving problems.
7.15 (E)
Use everyday language to
explain thinking about strategies and solutions to mathematical problems.
7.16 (E)
Express mathematical ideas
and use them to define, compare, and solve problems orally and in writing.
7.17 (E)
Use mathematical notation
to communicate and explain mathematical situations.
8.1 (I)
Justify and explain the
solutions to problems using manipulative and physical models.
8.2 (E)
Justify answers and the steps
taken to solve problems with and without manipulative and physical models.
8.3 (I)
Construct, justify, and defend mathematical conclusions using logical
arguments, in situations related to mathematics, science, and technology.
8.4 (E)
Use patterns and relationships
to analyze mathematical situations; draw logical conclusions about mathematical
problems.
8.5 (E)
Follow a logical argument and
judge its validity.
Follow a logical argument and
judge its validity, including the use of if-then statements (syllogisms) and
the connectors ³and² and ³or².
8.6
Apply deductive and inductive
reasoning in mathematical situations to extend logical reasoning.
8.7
Recognize and apply deductive
and inductive reasoning in both concrete and abstract contexts.
8.8 (E)
Ask questions to reflect on,
clarify, and extend thinking.
8.9 (I)
Review and refine the
assumption and steps used to drive conclusions in mathematical arguments.
8.10 (I)
Construct valid arguments;
make and test and defend conjectures about algebraic and geometric properties
based on mathematical principles.
8.11 (E)
Determine relevant,
irrelevant, and/or sufficient information to solve mathematical problems,
including consumer problems.
9.1 (E)
Link new concepts to prior
knowledge.
9.2 (E)
Use mathematical ideas from
one area of mathematics to explain an idea from another area of mathematics.
9.3 (E)
Use models to explain the
relationship of concepts to procedures as they apply to problems in real life.
9.4 (I)
Use the connections among
mathematical topics to develop multiple approaches to problems.
9.5 (I)
Identify practical
applications of mathematical principles that can be applied to other
disciplines.
9.6 (I)
Use and analyze the
connections between mathematics and other disciplines.
9.7 (E)
Apply mathematical thinking
and modeling to solve problems that arise in other disciplines (e.g. rhythm in
music and motion in science).
9.8 (E)
Identify, explain, and use
mathematics in everyday life.
9.9
Recall and accurately record numerical, alphabetical, symbolic and factual sequential data transmitted either verbally or in writing.