| Form A: Math Alignment Table |
| Alignment to Math High School
Content Expectations |
| Math High School Content Expectations |
Prealgebra
Math 050 to
Summer 2006 |
Prealgebra
Math 050 to
Fall 2006 |
Introductory
Algebra
Math 107
Summer and
Fall 2006 |
Math 112 |
ACCUPLACER
Tests |
STANDARD L2: CALCULATION, ALGORITHMS,
AND ESTIMATION
Students calculate fluently, estimate proficiently, and
describe and use algorithms in appropriate situations
(e.g., approximating solutions to equations .) They
understand the basic ideas of ite ration and
algorithms . |
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L2.1 Calculation Using Real and Complex
Numbers |
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L2.1.1 Explain the meaning and uses of weighted
averages (e.g., GNP, consumer price index, grade
point average). |
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L2.1.2 Calculate fluently with numerical
expressions
involving exponents; use the rules of exponents ;
evaluate numerical expressions involving rational
and negative exponents; transition easily between
roots and exponents |
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ELAGLG.pro
CLM.pro |
L2.1.3 Explain the exponential relationship
between
a number and its base 10 logarithm, and use it to
relate rules of logarithms to those of exponents in
expressions involving numbers. |
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L2.1.4 Know that the complex number i is one of
two
solutions to x2 = -1. |
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CLM.pro |
L2.1.5 Add, subtract , and multiply complex
numbers;
use conjugates to simplify quotients of complex
numbers. |
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CLM.pro |
L2.1.6 Recognize when exact answers aren’t always
possible or practical; use appropriate algorithms to
approximate solutions to equations (e.g., to
approximate square roots). |
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| L2.2 Sequences and Iteration |
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L2.2.1 Find the nth term in arithmetic,
geometric, or
other simple sequences. |
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CLM.pro |
L2.2.2 Compute sums of finite arithmetic and
geometric sequences. |
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ELAGLG.pro |
L2.2.3 Use iterative processes in such examples
as
computing compound interest or applying
approximation procedures. |
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| STANDARD L3: MEASUREMENT AND |
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ARIT.pro |
PRECISION Students apply measurement units
and
calculations, and understand the concept of error. |
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L3.1 Measurement Units, Calculations, and
Scales |
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L3.1.1 Convert units of measurement within and
between systems; explain how arithmetic operations
on measurements affect units, and carry units
through calculations correctly. |
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ARIT.pro |
L3.1.2 Describe and interpret logarithmic
relationships in such contexts as the Richter scale,
the pH scale, or decibel measurements (e.g., explain
why a small change in the scale can represent a
large change in intensity); solve applied problems. |
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| L3.2 Understanding Error |
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L3.2.1 Determine what degree of accuracy is
reasonable for measurements in a given situation;
express accuracy through use of significant digits,
error tolerance, or percent of error; describe how
errors in measurements are magnified by
computation; recognize accumulated error in applied
situations. |
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L3.2.2 Describe and explain round-off error,
rounding, and truncating. |
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L3.2.3 Know the meaning of and interpret
statistical
significance, margin of error, and confidence level. |
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STANDARD L4: MATHEMATICAL REASONING,
LOGIC, AND PROOF
Students understand mathematical reasoning as
being grounded in logic and proof and can
distinguish mathematical arguments from other types
of arguments. They can interpret arguments made
about quantitative situations in the popular media.
Students know the language and laws of logic and
can apply them in both mathematical and everyday
settings. They write proofs using direct and indirect
methods and use counterexamples appropriately to
show that statements are false. |
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| L4.1 Mathematical Reasoning |
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L4.1.1 Distinguish between inductive and
deductive
reasoning, identifying and providing examples of
each. |
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L4.1.2 Differentiate between statistical
arguments
(statements verified empirically using examples or
data) and logical arguments based on the rules of
logic. |
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L4.1.3 Define and explain the roles of axioms
(postulates), definitions, theorems, counterexamples,
and proofs in the logical structure of mathematics;
identify and give examples of each. |
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| L4.2 Language and Laws of Logic |
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L4.2.1 Know and use the terms of basic logic
(e.g.,
proposition, negation, truth and falsity, implication, if
and only if, contrapositive, and converse). |
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L4.2.2 Use the connectives “NOT,” “AND,” “OR,”
and
“IF…,THEN,” in mathematical and everyday settings.
Know the truth table of each connective and how to
logically negate statements involving these
connectives. |
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L4.2.3 Use the quantifiers “THERE EXISTS” and
“ALL” in mathematical and everyday settings and
know how to logically negate statements involving
them. |
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L4.2.4 Write the converse, inverse, and
contrapositive of an “If…, then…” statement; use the
fact, in mathematical and everyday settings, that the
contrapositive is logically equivalent to the original
while the inverse and converse are not. |
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| L4.3 Proof |
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L4.3.1 Know the basic structure for the proof of
an
“If…, then…” statement (assuming the hypothesis
and ending with the conclusion) and know that
proving the contrapositive is equivalen |
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L4.3.2 Construct proofs by contradiction; use
counterexamples, when appropriate, to disprove a
statement. |
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L4.3.3 Explain the difference between a necessary
and a sufficient condition within the statement of a
theorem; determine the correct conclusions based on
interpreting a theorem in which necessary or
sufficient conditions in the theorem or hypothesis are
satisfied. |
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| RECOMMENDED: |
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*L1.2.5 Read and interpret representations from
various technological sources, such as contour or
isobar diagrams. |
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*L2.1.7 Understand the mathematical bases for the
differences among voting procedures. |
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*L2.2.4 Compute sums of infinite geometric
sequences. |
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| STRAND 2: ALEGEBRA AND FUNCTIONS
(A) |
In the middle grades, students see
the progressive generalization of arithmetic to algebra. They learn
symbolic manipulation skills and use them to solve
equations. They study simple forms of elementary polynomial functions
such as linear , quadratic, and power functions as represented by tables,
graphs,
symbols, and verbal descriptions.
In high school, students continue to develop their “symbol sense” by
examining expressions, equations, and functions, and applying algebraic
properties to
solve equations. They construct a conceptual framework for analyzing any
function and, using this framework, they revisit the functions they have
studied
before in greater depth. By the end of high school, their catalog of
functions will encompass linear, quadratic, polynomial, rational, power,
exponential,
logarithmic, and trigonometric functions . They will be able to reason
about functions and their properties and solve multi- step problems that
involve both
functions and equation-solving. Students will use deductive reasoning to
justify algebraic processes as they solve equations and inequalities , as
well as when
transforming expressions.
This rich learning experience in Algebra will provide opportunities for
students to understand both its structure and its applicability to
solving real-world
problems. Students will view algebra as a tool for analyzing and
describing mathematical relationships, and for modeling problems that
come from the
workplace, the sciences, technology, engineering, and mathematics. |
STANDARD A1: EXPRESSIONS, EQUATIONS,
AND INEQUALITIES. Students recognize,
construct, interpret, and evaluate expressions. They
fluently transform symbolic expressions into
equivalent forms. They determine appropriate
techniques for solving each type of equation,
inequality, or system of equations, apply the
techniques correctly to solve, justify the steps in the
solutions, and draw conclusions from the solutions.
They know and apply common formulas. |
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