MATH 108 - Mathematical Concepts for Elementary School Teachers-Number Systems
MATH 108
Mathematical Concepts for Elementary School Teachers-Number Systems
Disciplines
Mathematics (Masters Required)
4.000
0 - May not be repeated
Recommended for prospective and in-service elementary school teachers. Mathematical investigations and problem solving involving sets, number sense, integers, and rational and real numbers.
64.000-72.000 Total Hours
Total Hours
128.000-144.000 Total Hours
64.000-72.000 Total Hours
Prerequisite: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures. Prerequisite or Corequisite: None Concurrent Corequisite: None Course Advisories: None Limitation on Enrollment: None
Course Objectives:
Use a variety of problem-solving strategies, including inductive and deductive reasoning, to solve non-routine problems.
Solve problems relating to sets and their elements.
Operate with place value systems, including bases other than 10.
Recognize and use various models for addition, subtraction, multiplication, and division of whole numbers, integers, fractions, and decimals.
Evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances
Analyze the structure and properties of whole, rational, and real number systems.
Recognize and use prime and composite numbers.
Find factors and multiples, use divisibility tests, analyze LCMs and GCFs and their role in standard algorithms.
Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations and justify their equivalence; explain the concept of irrational numbers; illustrate the use of a number line representation; recognize and use ratios and proportions in problem-solving situations.
Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communications, connections, modeling, reasoning, and representation.
Develop activities implementing national and state curriculum standards, in particular common core standards.
Student Learning Outcomes
MATH108 SLO1 - Use a variety of problem-solving strategies to solve non-routine problems.
MATH108 SLO2 - Use at least two different approaches including traditional algorithms, mental math, estimation, and physical models to solve problems involving operations on whole numbers, integers, and rational numbers.
MATH108 SLO3 - Evaluate, compare, and contrast mathematical and logical techniques and concepts.
MATH108 SLO4 - Develop real-world problems for all contexts of the basic number operations of addition, subtraction, multiplication, and division using whole numbers, integers, and rational numbers.
Problem Solving.
Critical thinking and inductive reasoning.
Patterns.
Problem solving strategies.
Problem solving using calculators or computers.
Communication, connections, modeling, reasoning, and representation.
Set Theory, Relations and Functions.
Set notation.
Describing sets.
Set operations.
Relations and Functions.
Numeration.
History of numeration systems.
Using exponents.
Whole numbers.
Algorithms for whole number operations.
Mental math and estimation strategies.
Computation in different bases.
Integers.
Operations (addition, subtraction, multiplication and division).
Equations and Inequalities.
Divisibility.
Prime and Composite Numbers.
Prime Factorization of Integers.
Greatest Common Divisor and Least Common Multiple.
Modular Arithmetic.
Rational Numbers.
Symbols and definitions.
Location of rational numbers on the number line.
Operations (addition, subtraction, multiplication and division).
Fractions, decimals, percents and scientific notation.
Ratios and proportions.
Real Numbers.
Irrational Numbers vs. Rational Numbers.
Decimal representation of a real number.
Number Line Representation
Operations (addition, subtraction, multiplication and division).
National and State Standards
All topics will be connected to national and state curriculum standards for elementary school math including Common Core State Standards.
Methods of Instruction
Directed Study
Discussion
Lecture
Projects
Lecture is the primary activity to be used, along with in-class student problem-solving. Students are expected to work outside of class on assigned exercises as well as on supplementary reading from the text.
Please show all work, diagrams, charts, graphs, anything you come up with on the blue paper provided.
1. The school cafeteria is ready to serve two kinds of sandwiches, tuna and ham, and two kinds of pizza, pepperoni and vegetarian. There are 48 servings of pizza prepared. There are 8 more tuna sandwiches prepared than there are servings of pepperoni pizza. There are 4 fewer ham sandwiches prepared than there are servings of vegetarian pizza. Altogether, how many sandwiches are prepared?
a. List 8 quantities involved in this problem.
b. Sketch a diagram to show the relevant sums and differences in this situation.
c. Solve the problem.
2. Consider the following problem:
Two trains leave from different stations and travel toward each other on parallel tracks. They leave at the same time. The stations are 217 miles apart. One train travels at 65 mph and the other travels at 72 mph. How long after they leave their stations do they meet each other?
List six quantities in the problem (DO NOT solve the problem). If a value is given, write it next to the quantity. If no value is given, write an appropriate unit of measure.
3. A. Add 24five + 33five in base five. (The numbers are already written in base five, so there should be no conversions done.)
B. How would you illustrate this with the base five blocks using drawings and showing the intermediate steps?
4. 1012five = ______________ in base ten.
5. 29ten = ___ in base three
6. 203.6ten = ____________five
7. A. If you are counting in base five, what would be the next six numerals after 2314five?
B. If you have been counting in base five, what would the five numerals before 2314five have been?
A. Appropriate Readings: Students are required to read assigned chapters in texts. Outside readings are generally not required.
B. Writing Assignments: Students must work on assignments to demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to their problems.
C. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.
D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. Critical thinking will also be emphasized through numerous treatments of word problems and applications. Students will be expected to explain, compare and evaluate algorithms.
Three one-hour exams
Comprehensive final examination
Quizzes
Written homework assignments
Mathematics for Elementary Teachers: A Contemporary ApproachMusser, Peterson, Burger, Wiley, 2013Reconceptualizing Mathematics: Courseware for Elementary and Middle Grade Teachers-Number and Number Sense ModulesSan Diego State University, Center for Research in Mathematics and Science Education, 2014