MAT 107  Mathematics for Elementary School Teachers: Real Numbers, Section 01, # 20077, Spring 2006


Class meets MW 11:30-12:45 in SBS B209.


Instructor: Serban Raianu, office: NSM A-123, office phone number: (310) 243-3139,

e-mail address:, , URL:; office hours: Monday, Wednesday 1:00-2:30, Friday: 11:00-12:00,  or by appointment.


Course Description: This course is designed for prospective elementary school teachers.

Sets and set theoretic operations as related to counting numbers and rational numbers and arithmetic operations. Real number system and its origin, development, structure and use. Special emphasis on problem solving and the development and application of algorithms.


Text: Mathematics for Elementary Teachers: A Contemporary Approach (7th edition), by Gary Musser, William Burger, and Blake Peterson.

After completing MAT 107 the student should be able to

  • successfully engage in mathematical problem-solving and algebraic thinking
  • understand basic properties of numbers: the commutative, associative and distributive laws, etc. and their use in elementary arithmetic.
  • understand place value and its relationship to whole number and decimal number algorithms
  • exhibit a conceptual understanding of standard algorithms for adding, subtracting, multiplying, dividing, and raising to a power rational numbers, decimals and integers
  • understand exponents and the laws of exponents
  • understand ratios and proportions and their applications and engage in proportional reasoning
  • understand percentages as proportions and as decimals and apply them in practical problems
  • understand prime numbers and composites, divisibility, least common multiples and greatest common factors , and their applications in arithmetic and elementary problem solving
  • understand basic concepts of algebra, functions, and set theory
  • demonstrate skill in computing and solving problems accurately
  • demonstrate skill in mathematical reasoning, in explaining mathematical procedures and results.


Prerequisites: Students must have satisfied the ELM requirement before enrolling in MAT 107.



Grades: Grades will be based on three in‑class full‑period examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, and other assignments (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will be collected three times, on the days of the three exams, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every Monday, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q. There are also 5 points awarded for attendance and class participation, this portion of the grade is denoted by A. The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F. 

To determine your final grade  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

        A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

        C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.


Makeup’s: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with your instructor, who may then substitute the relevant score from your final examination for the missing grade.


Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see their instructor as soon as possible.


Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)



Tentative schedule: 

M 1/23: 1.1 The Problem Solving Process: Problems 1,4,7,10,13,16,19

W 1/25: 1.2 Additional Strategies: Problems 1,4,7,10,13,16

M 1/30: 2.1 Sets and Whole Numbers: Exercises 1,5,9,13,17,21 Problems 27,33,34

W 2/1: 2.2 Whole Numbers and Numeration: Exercises 1,5,9,13 Problems 15,18,20

M 2/6: 2.3 Hindu-Arabic and Other Number Systems: Exercises 1,5,9,13,17 Problems 19,20,21

W 2/8: 2.4 Functions: Exercises 1,5,9,13 Problems 16,19,25

M 2/13: Exam I  

W 2/15: 3.1 Addition and Subtraction: Exercises 1,4,5,6,10,12 Problems 14,17,19  

M 2/20: Presidents’ Day

W 2/22: 3.2 Multiplication and Division:  Exercises 1,5,6,9,11,13,14 Problems 16,19,25

M 2/27: 3.3 Ordering and Exponents: Exercises 1,3,5,7,9,10,11 Problems 12,15,17

W 3/1: 4.1 Mental Math, Estimation and Calculators: Exercises 1,4,5,9,13,17,21 Problems 25,28,34

M 3/6: 4.2 Written Algorithms for Whole Number Operations: Exercises 1,3,5,10,11,14,15,16,18,20,22 Problems 23,26,32

W 3/8: 5.1 Primes, Composites, and Tests for Divisibility: Exercises 1,5,9 Problems 13,16,22

M 3/13: 5.2 Counting Factors, Greatest Common Factor, and Least Common Multiple: Exercises 1,4,5,7,9 Problems 16,22,23

W 3/15: Exam II

M 3/20: 6.1 The Set of Fractions: Exercises 1,5,6,7,9,11 Problems 13,16,22

W 3/22: 6.2 Operations on Fractions both conceptually, and algorithmically – Addition and Subtraction: Exercises 1,3,4,6,7,8,10,14 Problems 16,19,25

M 3/27: Spring Recess

W 3/29: Spring Recess

M 4/3: 6.3 Operations on Fractions both conceptually, and algorithmically – Multiplication and Division: Exercises 1,4,5,7,8,9,10,13,14,17 Problems 22,28,29

W 4/5: 7.1 Decimals: 1,2,3,4(a,b),5,7(a,b,e),8,9,10(a,b,c),11(a,c,e),12(d),13,16(a,b),17 Problems 18,19

M 4/10: 7.2 Operations with Decimals: Exercises 1,2,3(a,b),5,6(a),7(a),8(a),9,10(a,b),11(a),12(a,b) Problems 13,16,22

W 4/12: 7.3 Ratio and Proportion: Exercises 1,5,7,8(c),9,10,11(a) Problems 12,15,21

M 4/17: 7.4 Percent: Exercises 1,2(a),3(a),4(a,c),5,6(a),7(a,b,c)(Use method ii only, use a proportion),9,10(a) Problems 11,14,20

W 4/19: 8.1 Concepts and algorithms – Addition and Subtraction: Exercises 1,2,4(a,b,c),5,6,7,9,11,12,13,14(a,b),16(a,b),17 Problems 19,22,24

M 4/24: 8.2 Concepts and algorithms –Multiplication and Division, and Order: Exercises 1,2(a(i)),3,4,5,6,7,9,11(a,b),12(a,b),13,15,16(a),17,18(a,e),20(a,b),21 Problems 22,25,31

W 4/26: Exam III

M 5/1: 9.1 Rational Numbers: Exercises 1,2,5,6(a),7,8(a),9,10(a),11(a),13,15,16(a),17,18(a),19(a),21 Problems 24,27,29

W 5/3: 9.2 Real Numbers: Exercises1,3,5,6,7(a),9,11,13,14(a),15(a,c,d,f),16(a),17,18(a), 19(a,d),20(a),21 Problems 23,24,25,31

M 5/8: 9.3 Functions and their Graphs: Exercises 1,3,4,5,8,9,10,16,18 Problems 19,20,21

W 5/10: Review

Final exam: Wednesday, May 17, 11:30 a.m. - 1:30 p.m.