1. Alpha and Number MATH 112
Course Title Math for Elementary Teachers II
(Math Elem Teach II)
Credits 3
Date of Outline October 2004 (Revised October 2006)
Course Description Demonstrates operations and develops the properties of the natural numbers, integers, rational numbers, and real numbers. Explores the use of mathematical operations to solve problems including geometry, probability, and physical rates
2.
Contact Hours/Type 3 hours lecture per week
MATH 111 with at least a C. 4. Prerequisites
Corequisites
Recommended
None
At least 11th grade reading skills.
Preparation
Approved by _____________________________________ Date________________

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5. General Course Objectives
Maui Community College Standards:
Outcome 1.1
– Use writing to discover and articulate ideas.
Outcome 2.1
- Apply numeric, graphic, and symbolic skills and other forms of quantitative reasoning accurately and appropriately.
Outcome 2.2
- Demonstrate mastery of mathematical concepts, skills, and applications, using technology when appropriate.
Outcome 2.3
- Communicate clearly and concisely the methods and results of quantitative problem solving.
Outcome 2.4
- Formulate and test hypotheses using numerical experimentation.
Outcome 2.5
- Define quantitative issues and problems, gather relevant information, analyze that information, and present results.
Outcome 5.1 – Identify and state problems, issues, arguments and questions contained in a body of information.
Outcome 5.2 – Identify and analyze assumptions and underlying points of view relating to an issue or problem.
University of Hawaii Manoa Symbolic Reasoning Hallmarks (By System agreement, this course is designed to satisfy the following Foundations Symbolic Reasoning criteria for the University of Manoa)
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Expose students to the beauty, power, clarity and precision of formal systems
Help students understand the concept of proof as a chain of inferences
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Teach students how to apply formal rules or algorithms
Require students to use appropriate symbolic techniques in the context of problem solving, and in the presentation and critical evaluation of evidence
Not focus solely on computational skills
Build a bridge from theory to practice and show students how to traverse this bridge
6.
Specific Course Objectives, Competencies, and Student Learning Outcomes
For assessment purposes, these are linked to #7. Recommended Course Content.
On successful completion of this course, students will be able to a.
interpret arithmetic operations using set theory and counting; b.
model and interpret the relationship between adding and subtracting; c.
model and interpret the relationship between multiplication and division; d.
connect multiplication to repeated addition as well as area of rectangles;

3 e.
connect division to repeated subtractions as well as portioning of a set into subsets with the same number of elements; f.
represent operations of addition and multiplication using translations along a line and composition of translations; g.
model new functions created by magnification and reflection; h.
connect primes and their relation to composite numbers; i.
connect the concept of unit and rational in different contexts; j.
apply a rational as a ratio when connected to probabilities; k.
apply various rates including speed and averages; l.
apply dimensional analysis to help solve a problem; m.
describe an irrational number and the significance of specific irrational numbers such as pi; n.
describe the geometry of the real number line from studying translations, reflections and dilations of the real number line; o.
connect the addition of the reals with the composition of translations while preserving the distance of two points; p.
connect the multiplication of the reals with the composition of dilations while multiplying the distance between two points. q.
represent and interpret data on graphs r.
determine appropriate statistical measures s.
use appropriate statistical terms and their interpretations t.
connect counting theory with probability theory and interpret results u.
solve problems using geometric theory v.
solve problems using different units of measurement
7. Recommended Course Content and Approximate Time Spent on Each Topic
Linked to #6. Specific Course Objectives, Competencies, and Student Learning
Outcomes.
3 weeks
Introduction to the course syllabus along with a discussion of what will be expected throughout the semester.
Algebraic Reasoning and Representation
Functions and Graphing
(a,b,c,d,e,f,g,h,i,k,l,m)
4 weeks
Statistics
Graphical Representation of Data
Measures of Central Tendency and Variation
Statistical Inference
Probability
Empirical Probability
Principles of Counting

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4 weeks
Theoretical Probability
(a,q,r,s,t)
Geometric Figures
Measurement
Measurement process
Area and Perimeter
Pythagorean Theorem
Surface area and volume
(a,i,l,u,v)
4 weeks
Transformations, Symmetries and Tilings
Translations
Rotations
Reflections
Glide Reflections
Congruence, Constructions and Similarity
Congruent Triangles
Constructing Geometric Figures
Similar Triangles
(n,o,p)
8.
Text and Materials, Reference Materials, Auxiliary Materials and Content
Appropriate text(s) and materials will be chosen at the time the course is offered.
By University of Hawaii System-wide agreement on September 18, 2004, campuses agreed to use materials created by Joel Weiner with support of Neil
Pateman, Instructor for ITE 324, 325 (Elementary Mathematics I, II) College of
Education. MCC supports this agreement to facilitate system-wide articulation of
MATH 112. Additional materials such as Thomas Sonnabend Mathematics for
Teachers or Longs Mathematical Reasoning for Elementary Teachers will be used for reference materials.
Internet searches
9.
Recommended Course Requirements and Evaluation
Specific course requirements are at the discretion of the instructor at the time the course is being offered.
55%-90% Written – in-class exams
5%- 25% Out of class work (including take home exams and homework)
0%-30% In-class exercises and group work
10%-25% Written reflective papers

10.
Methods of Instruction
Instructional methods will vary considerably with instructors. Specific methods will be at the discretion of the instructor teaching the course and the method by which the course is taught. These might include but are not limited to a.
exams and papers with feedback and discussion b.
lectures (kept to a minimum) and class discussion c.
problem solving d.
Power Point presentations (kept to a minimum) e.
videos, DVDs, CD-ROMs with detailed viewing guide and discussion questions f.
group activities g.
oral reports and other student presentations h.
games and simulations i.
web-based assignments and activities j.
reflective journals or papers k.
group and/or individual research projects with reports or poster presentations l.
study logs and study groups m.
other contemporary learning techniques (such as problem-based learning, investigative case-based learning) n.
homework assignments
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