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	Prealgebra Math 050 to Fall 2006	Introductory Algebra Math 107 Summer and Fall 2006	Math 112	ACCUPLACER Tests
ACCUPLACER TESTS: Arithmetic = ARIT.pro; Elementary Algebra = ELAGLG.pro; College Level Math = CLM.pro
STRAND 1: QUANTITATIVE LITERACY AND LOGIC (L)
“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.
STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS 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 representations.					ARIT.pro
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.					ARIT.pro
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.					ARIT.pro ELAGLG.pro
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 .					ARIT.pro ELAGLG.pro
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.					ARIT.pro ELAGLG.pro CLM.pro
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 .					CLM.pro
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.					CLM.pro
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.					ELAGLG.pro
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 media					ARIT.pro ELAGLG.pro
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 due.”