Math 103. Theory of Arithmetic

Course Description: Analyses of the mathematical issues and methodology underlying elementary mathematics in grades K-5. Topics include sets, arithmetic algorithms, elementary number theory, rational and irrational numbers, measurement, and probability. There is an emphasis on problem solving. Priority registration will be given to students enrolled in teacher education programs leading to certification in elementary or childhood education. Prerequisite: MATH 012 or equivalent. Credit: 4 hours. This course satisfies the General Education Criteria for a Quant Reasoning I course.

Required Materials:

• Mathematics for Elementary School Teachers, Billstein, et.al. 8th edition. 2004. (note: the text is required in both Math 103 and Math 117, and is packaged with Geometer's Sketchpad software, required for Math 117)
• Learning Mathematics in Elementary and Middle Schools, Cathcart, et.al. 4th edition. 2006
• Calculator: Use of a calculator is encouraged during class, on homework and on exams. Note: the TI-83 plus or TI-84 can be used in both Math 103 and Math 117.
• Manipulatives Kit: Purchase the ETA/Cuisenaire "Start With Manipulatives" kit either from the bookstore or order by mail using the order form in the Cathcart text.
• Class Notes: Purchase "MATH 103 notes" packet at TIS
• 3-ring binder, 2 or 3 inch, and dividers for binder
• metric/English Ruler
• scissors

UNIT 1

Lab #1: ISAT Rubric Training

Lecture #2: Sets, Venn diagrams, Conceptual Models for + - × ÷ of whole numbers
* Read sections 2-1, 2-2, 2-3, 2-4 in the Billstein text
* Read chapters 5 , 7, & 8 in the Cathcart text

Lab #2: Pattern Blocks

Lecture #3: Numeration Systems, Bases, Mental Math, Estimation
* Read chapter 3 in the Billstein text
* Read chapters 6 & 9 in the Cathcart text

Lab #3: Base Ten Blocks Lecture #4: Integer Ops with Signed Numbers, Divisibility & Primes, LCD, GCF
* Read chapter 4 in the Billstein text
* Read chapter 10 in the Cathcart text

Lab #4: Two Color Counters

Lecture #5: Real, Rational & Irrational Numbers, + - × ÷ Rational Nos., Proportions
* Read chapter 5 in the Billstein text
* Read chapters 11 & 13 in the Cathcart text

Lab #5: Fraction Circles

Lecture #6: Decimals, Percents
* Read chapter 6 in the Billstein text
* Read chapter 12 in the Cathcart text

Lab #6: Cuisenaire Rods

Lecture #7: Unit 1 Test: Bring your calculator.

Lab #7: Spinners

UNIT 2

Lab #8: Dice

Lecture #9: Descriptive Statistics
* Read chapter 8 in the Billstein text
* Read chapter 16 in the Cathcart text

Lab #9: Tangrams

Lecture #10: Intro to Geometry, Polygons, Areas, Angles, Networks
* Read chapter 9 in the Billstein text
* Read chapter 14 in the Cathcart text

Lab #10: Geoboards

Lecture #11: Constructions, Congruence, Similarity
* Read chapter 10 in the Billstein text

Lab #11: Myras and Mirrors

Lecture #12: Tessellations, Measurement & metric system, Exact vs. Approximate, Precision
* Read chapters 11& 12 in the Billstein text
* Read chapter 15 in the Cathcart text

Lab #12: Color Cubes

Lecture #13: Unit 2 Test: Bring calculator & ruler.

Lab #13: Grocery Store Math; "Sir Cumference"

Lecture #14: Algebraic thinking, Functions, math video

Lab #14: Transparent Color Chips

Lecture #15: Review for Final

Department of Mathematics University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Telephone: (217) 333-3350    Fax (217) 333-9576 office@math.uiuc.edu

Last modified March 15, 2006