Math 210 Course Outline  

Numeration, Place Value and Arithmetic Operations
Roman numerals

Place value in base ten

Expanded form of a number

Meanings of the four arithmetic operations for whole numbers, including:

        a)  Interpretations for subtraction:

                Part-whole (missing addend)

                Take-away

                Comparison

        b)  Definition of division and the Quotient-Remainder Theorem

        c)  Interpretations for division:

                Partitive

                Measurement

Basic properties of operations:  commutative, associative, distributive properties, additive identity, multiplicative identity

Mental Math and Estimation
Mental math techniques:  compensation, using compatible numbers, using the distributive property

Standard Algorithms of Arithmetic

Addition, Subtraction, Multiplication and Division algorithms

Understanding why the standard algorithms work and fluency in their use

Using chip models, base ten blocks, bundles or monetary units to illustrate the algorithms 

Pre-algebra and Algebra

Interpreting and evaluating algebraic expressions

Algebraic identities

Word problems

      Solutions via Bar/strip diagrams

       Solutions via algebra

       Teacher Solutions

Laws of integer exponents 

Number Theory

Properties and definitions of prime and composite numbers

Factor trees

Divisibility tests for 2, 3, 4, 5, 6, 8, 9, 10, 11, 12

Sieve of Eratosthenes

Test for Primeness 

Fundamental Theorem of Arithmetic

GCF and LCM 

        Finding using prime factorizations

        Finding using Euclidean Algorithm

        Relationship between GCF and LCM

Proof of infinitely many primes

Fractions

Form, meaning and representation of fractions (common fractions, aka positive rational numbers)

Equivalence of fractions

Ordering fractions

Multiplicative inverse

Mixed numbers

Fluency with arithmetic operations 

Bar diagrams illustrating addition and subtraction

Area models illustrating products

Word problems

Decimals, Ratios, Rates and Percentages

Definition of decimals in terms of place value, expanded form

Understanding of and fluency with arithmetic operations

Ratios, Proportions, Rates, Speed-Distance-Time 

Percents

Word problems

Real numbers:  Integers, Irrational and Rational Numbers

Integers:  Absolute Value, Additive inverse, Arithmetic operations

Properties of inequalities

Decimal characterizations of rational and irrational numbers

Scientific notation

Real numbers

Density of rationals, of irrationals

Classifying real numbers as rational or irrational

Proof of the irrationality of the square root of 2 

Common Final Exam

Spring Semester 2013 Common Final Exam Date:  Saturday, May 11, 2013, 11:30am - 1:30pm.  

All students enrolled in Math 210 take the common final in classrooms to be announced late in the semester.  Under certain circumstances (e.g. religious prohibition),  exceptions may be made by prior permission of the instructor, to take the final exam during the departmental make-up sessions.

Practice Problems for the Math 210 Final Exam (pdf file).  

The problems on this practice demonstrate the breadth and level of difficulty of the final exam.  

Solutions are posted here by section:

Section A
Section B
Section C
Section D
Section E
Section F
Section G
Section H

Course Resources

Free tutoring for Math 210 students is available in the Math Tutoring Center in LO1319, starting the second week of semester.

Introduction to Base 5 explains how to convert from base 5 numerals to base 10 numerals and vice versa.

Integer Arithmetic  An alternative to the development of integer arithmetic in Chapter 8 of Elementary Mathematics for Teachers, by Thomas H. Parker and Scott Baldridge

Supplemental Resources

A requirement for entrance into the CSU is completion of Algebra I, Geometry, and Algebra II.  Students who would benefit from a review of basic algebra are encouraged to enroll in Math 102 or to purchase ALEKS before enrolling in Math 210 or Math 310.  ALEKS is a self-paced, computer tutoring program that reviews and provides practice in basic algebra.  A free trial on ALEKS is available.   Use this link if you would like to purchase access to ALEKS:  ALEKS  

Student Practice Problems for grades 1 to 8 (Algebra I) California Math Standards

Overhead Slides from The Winning Equation  An in-service program for Grade 4-7 teachers

Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in
Grade 4–6 Texts Used in Singapore by Sybilla Beckmann