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Mathematics Content Expectations

Project Contents:

*Introductory Comments and Recommendations
*Math Overview of Content Expectations Taught in LCC Courses
*Individual Course Syllabus/Resources Aligned to Mathematics Expectations
*Alignment of ACCUPLACER Tests to High School Expectations

The process used for this alignment project was as follows:

• The state expectations were studied, converted to a Microsoft Word document, and copied into a table format to be used for
the alignment form.

• Expectations were aligned with each individual course syllabus. When a matching syllabus item was not clear, the textbooks
used in the courses were checked to identify alignment.

• An expectation was marked as aligned if it was probable and foreseeable that a significant portion of the expectation was met.

• The completed data was given to the department chair for review and input.

• The ACCUPLACER manual was reviewed, math tests completed and items aligned with high school expectations.

Recommendation: I would recommend that this document be a “working document” –- that instructors use it throughout the term
while teaching the course – and collaboratively it be edited, updated, expanded , and used as a starting point to assist LCC staff and
students in the alignment process of the K-16 educational program desired by the state of Michigan.

Form A: Math Alignment Table
Alignment to Math High School Content Expectations
Math High School Content Expectations Prealgebra
Math 050 to
Summer 2006
Math 050 to
Fall 2006
Math 107
Summer and
ACCUPLACER TESTS: Arithmetic =; Elementary Algebra =; College Level Math =
“In an increasingly complex world , adults are challenged to apply sophisticated quantitative knowledge and reasoning in their professional and
personal lives. The technological demands of the workplace, the abundance of data in the political and public policy context, and the array of
information involved in making personal and family decisions of all types necessitate an unprecedented facility not only with fundamental
mathematical, statistical, and computing ideas and processes, but with higher- order abilities to apply and integrate those ideas and processes in a
range of areas.”

The Michigan Grade Level Content Expectations in Mathematics for grades K-8 prescribe a thorough treatment of number, including strong emphasis
on computational fluency and understanding of number concepts, to be completed largely by the sixth grade. The expectations in this Quantitative
Literacy and Logic strand provide a definition of secondary school quantitative literacy for all students and emphasize the importance of logic as part
of mathematics and in everyday life. They assume fluency (that is, efficiency and accuracy) in calculation with the basic number operations involving
rational numbers in all forms (including percentages and decimals), without calculators.

Mathematical reasoning and logic are at the heart of the study of mathematics. As students progress through elementary and middle school, they
increasingly are asked to explain and justify the thinking underlying their work. In high school, students peel away the contexts and study the
language and thought patterns of formal mathematical reasoning. By learning logic and by constructing arguments and proofs, students will
strengthen not only their knowledge and facility with mathematics, but also their ways of thinking in other areas of study and in their daily lives.

Connections and applications of number ideas and logic to other areas of mathematics, such as algebra, geometry, and statistics, are emphasized in
this strand. Number representations and properties extend from the rational numbers into the real and complex numbers, as well as to other systems
that students will encounter both in the workplace and in more advanced mathematics. The expectations for calculation, algorithms and estimation
reflect important uses of number in a range of real-life situations. Ideas about measurement and precision tie closely to geometry.

1 Estry, D., & Ferrini-Mundy, J. (January, 2005). Quantitative Literacy Task Force Final Report and Recommendations. East Lansing: Michigan State University.

Based on their knowledge of the properties of arithmetic
students understand and reason about numbers, number
systems, and the relationships between them. They
represent quantitative relationships using mathematica
symbols, and interpret relationships from those
L1.1 Number Systems and Number Sense          
L1.1.1 Know the different properties that hold in
different number systems, and recognize that the
applicable properties change in the transition from
the positive integers, to all integers, to the rational
numbers, and to the real numbers.
L1.1.2 Explain why the multiplicative inverse of a
number has the same sign as the number, while the
additive inverse of a number has the opposite sign.
L1.1.3 Explain how the properties of associativity,
commutativity, and distributivity, as well as identity
and inverse elements, are used in arithmetic and
algebraic calculations .
L1.1.4 Describe the reasons for the different effects
of multiplication by, or exponentiation of, a positive
number by a number less than 0, a number between
0 and 1, and a number greater than 1.
L1.1.5 Justify numerical relationships (e.g., show that
the sum of even integers is even; that every integer
can be written as 3m+k, where k is 0, 1, or 2, and m
is an integer; or that the sum of the first n positive
integers is n (n+1)/2).
L1.1.6 Explain the importance of the irrational
numbers and in basic right triangle trigonometry ; the
importance of π because of its role in circle
relationships; and the role of e in applications such
as continuously compounded interest .
L1.2 Representations and Relationships          
L1.2.1 Use mathematical symbols (e.g., interval
notation, set notation, summation notation) to
represent quantitative relationships and situations.
L1.2.2 Interpret representations that reflect absolute
value relationships (e.g. l x - a l ≤ b, or a ± b) in such
contexts as error tolerance.
L1.2.3 Use vectors to represent quantities that have
magnitude and direction; interpret direction and
magnitude of a vector numerically, and calculate the
sum and difference of two vectors.
L1.2.4 Organize and summarize a data set in a table,
plot , chart, or spreadsheet; find patterns in a display
of data; understand and critique data displays in the
L1.3 Counting and Probabilistic Reasoning          
L1.3.1 Describe, explain, and apply various counting
techniques (e.g., finding the number of different 4-
letter passwords; permutations; and combinations);
relate combinations to Pascal’s triangle; know when
to use each technique.
to use each technique.
L1.3.2 Define and interpret commonly used
expressions of probability (e.g., chances of an event,
likelihood , odds).
L1.3.3 Recognize and explain common probability
misconceptions such as “hot streaks” and “being
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