Parameters of TEXMAT and the MMT Program

I. Field Axioms - Exercises pp. 33-34 (Algebraic Structures)

This first section of the course focuses on the Real Number System and the Complex Number System. In our first several classes, we examine the general laws of behaviors or axioms for real numbers. The axioms are given in three sets; 1) the Field Axioms; 2) The Order Axioms; 3) The Completeness Axioms.

The first section focuses on the field axioms (6 in number) from which we can deduce all familiar properties of real numbers that depend ONLY upon addition and multiplication.


I. Field Axioms


Exercises

1. Prove that if a, b is an element of R and b not equal 0, then -a/b = a/-b = -(a/b).
2. Let a, b be nonzero real numbers. Show that (ab)-1 = a-1/b-1.
3. Let a, b elements of R and b not equal to zero. Prove: if x is a nonzero real number, then ax/bx = a/b.
4. Let a,b,c,d be an element of R where b is not equal to zero and d is not equal to zero.
Prove that a/b times c/d = ac/bd.
5. Verify that a/b = c/d if and only if ad = bc.
6. Assuming b is not equal to 0, verify the following:
a) a/b + c/b = (a+ c)/b b) a/b - c/b = (a-c)/b

I. Field Axioms - Exercises pp. 31-32 (Algebraic Structures)

This first section of the course focuses on the Real Number System and the Complex Number System. In our first several classes, we examine the general laws of behaviors or axioms for real numbers. The axioms are given in three sets; 1) the Field Axioms; 2) The Order Axioms; 3) The Completeness Axioms. The first section focuses on the field axioms (6 in number) from which we can deduce all familiar properties of real numbers that depend ONLY upon addition and multiplication.


Exercises

1. Use the technique of Theorem 12 to prove that (-a)(b = a(-b) = - (ab).
2. Prove that (-a)(-b) = ab. Hence deduce (-1)(-1) = 1.
3. Prove that -0 = 0.
4. Verify the following: i) -(a + b) = -a - b; ii) -(a-b) = -a + b; iii) -(-a+b) = a-b.

NCTM Assessment Principles

The NCTM Assessment Principle(s)

TEKS Discussion (MMT Journal)

Differentiated Instructional Strategies - One Size Doesn't Fit All

By Your Own Design CD--The First Five Star Structure

Read the following Articles and respond to the discussion/reflection questions in your MMT Journal.

1. Dreaming all that We Might Realize
2. Revisioning Professional Development: What Learner-Centered Professional Development Looks Like
3. Six Ways To Immediately Improve Professional Development
4. Ideas That Work: Mathematics Professional Development
5. A Look Within

HMC Calculus Tutorials

Visual Calculus

MacTutor History of Mathematics Archives