Math 210 Mathematics for K-8 Teachers

OPTIONAL TEXT A Problem Solving Approach to Mathematics for Elementary School Teachers
by Billstein, Libeskind, and Lott (8th Ed).

REQUIRED READING You must download chapters in PDF format (free!). They are required reading and will guide
the mathematical content covered in the course. The chapters contain the educational goals determined by standards
linked to the curriculum, sample problems from K-8 textbooks, and Released Items. This combination helps you answer
the questions “What do we need to know?” and “Why do we need to know this?” The posted chapters also contain the
homework problems.

SUPPLIES Portable whiteboard, eraser, and whiteboard markers.

BRIEF COURSE DESCRIPTION This course is an intensive exploration of mathematical concepts and content
commonly taught in grades K-8: problem-solving strategies; sets; functions; logic (quantifiers, conditional and
biconditional statements); numeration systems; addition, subtraction, multiplication, and division of whole numbers;
integers; greatest common divisor and least common multiple; addition, subtraction, multiplication, and division of
rational numbers; integer and exponents; decimals and operations on decimals; percents; and algebraic thinking. See
chapter highlights for more information …

In this course we will focus on the math concepts and content for grades K-8:
• reconceptualize mathematics you think you already know
• learn mathematics at a much deeper level
• experience various types of reasoning
• learn problem solving strategies
• make connections among mathematical topics
• enjoy and appreciate mathematics

LECTURE NOTES Lecture notes will be posted the evening before class. Please bring your copy of the notes to class.

CLASS ACTIVITIES Some class meetings includes structured cooperative learning activities to reinforce
fundamental mathematical concepts, to learn from others, to increase willingness to try new problems, and to improve
frequency of success in problem solving. Cooperative learning activities represent opportunities to meet other students
in the class to form study groups to work on the homework and prepare for the exams . Cooperative learning activities
also help the class to maintain a positive classroom environment. The problems contained in the activities summarize
the key concepts for the material covered. The problems we solve together meet educational goals determined by
standards established by the National Council of Teachers of Mathematics (NCTM).

HOMEWORK ASSIGNMENTS

• Grading selected problems. Only selected problems in the assigned homework will be graded, but all the assigned
problems must be worked for credit and to prepare for the exams. Each homework assignment is worth 20 points,
with 10 points maximum for “effort” reflected in the submitted homework and 10 points maximum for
“correctness” of the graded problems. Sloppy, careless, slipshod, disheveled, dowdy, shabby, unconcerned, frowzy,
or neglectful handwriting and improper use of mathematical notation typically results in less points for “effort,”
therefore homework assignments should be written carefully and concisely.

• Incomplete homework. 1 point will be deducted for each assigned problem that is skipped, ignored, overlooked,
omitted, disregarded, or forgotten, which can lead to low scores .

• Show your work (SYW). You must show your work (SYW) to homework questions for credit. Partial credit will be
given as generously as appropriate.

• Link between homework assignments and your course grade. There is a remarkable, noticeable, prominent,
outstanding, conspicuous, striking correlation between your grade on the homework assignments and your course
grade, so please give the homework assignments the attention they deserve.

• Help! Many of the problems we solve in class will resemble the homework problems you have been assigned. You
can work with other students, you can use my office hours, or you can see me after class for additional help . You
can also receive free walk-in tutoring from the CSUSM Math Lab, located in 1104 Kellog Library.

• Homework assignments and the writing requirement. The 2500 word writing requirement will be exceeded by
these homework assignments.

• Solutions. Detailed answers to the assignments will be made available after the due date.

• Late Homework. Late homework will not be accepted, without exception (e.g., car trouble, illness, emergency, …).
But your two lowest homework scores will be dropped. You can scan it and submit by email as a single PDF file.

EXAMS The date of the exams will be announced one week in advance. You should study each weekend to avoid
cramming, which often causes confusion, frustration, disorder, chaos, agitation, disarray, jumble, tangles, disturbances,
and hullabaloo.

GRADING Assigned homework, two exams, and a final exam will be used to determine the final course grade.
These components have different relative importance:

Letter grades are assigned according to the following rule: 100-90 = A, 89-80 = B, 79 – 65 = C, 64 – 50 = D, 49 – 0 = F

EXPECTATIONS In this course, you will be expected to
• Communicate ideas orally and in writing.
• Represent mathematical concepts using words, diagrams, algebra, manipulatives, and contextualized situations.
• Learn problem solving strategies.
• Independently solve problems.

LOOSE ENDS
• Students who miss class are still responsible for announcements or changes regarding the course outline, homework
assignments, due dates, and exam dates.
• Check your email regularly for announcements regarding this class.
• If you need to leave early, please inform me before class.
• You will need a password (TBA) to access posted material.
• Do not “cross-talk” during the lecture—it’s rude, disruptive, and disrespectful to everyone.
• Please put your electronic gadgets in “silent mode” or “manner mode” before class begins.
• Late homework will not be accepted.
• Extra-credit work will be given inclusively beyond the course requirements. Stay tuned!
• Everyone shares the responsibility in making this class an enjoyable place to learn useful mathematics, make
inevitable mistakes, and share constructive ideas. Please help me create such an environment.

FINAL EXAM:
MW 9am-10:15am → Mon, May 14 from 9:15am-11:15am
MW 4pm-5:15pm → Mon, May 14 from 4pm-6pm

CHAPTER HIGHLIGHTS

Chapter 1 Problem Solving and Reasoning Inductive reasoning is introduced as a way to make conclusions or
generalizations. Patterns are described, extended, and generalized. Tables are used to organize and see patterns. Algebra
is used to generalize some patterns. Polya’s four phases of problem solving process are discussed, and problem solving
strategies are illustrated with a variety of word problems. The roles of variables are discussed, along with the
correspondence between word phrases and algebraic expressions . Additive and multiplicative reasoning are introduced.
An introduction to the language of logic (statements, quantifiers, …) is given. Euler diagrams and truth tables are used
to represent and analyze arguments.

Chapter 2 Sets, Place Value, Addition and Subtraction with Whole Numbers Sets, operations with sets, and Venn
diagrams are introduced. Place value, expanded form , positional enumeration systems, counting, word forms, rounding,
estimation, and number sense are discussed. Models of addition and subtraction are discussed, and additive reasoning is
reinforced. The Singaporean math model is used to represent and solve problems. Properties are used to promote
number sense and some algebraic reasoning. Fact families help prove basic interesting algebraic relationships. Base-10
models are used to develop addition and subtraction algorithms. The partial sums method and partial differences
method are used, along with a variety of other addition and subtraction algorithms. Estimation is also discussed. Basefive
and base-twelve addition and subtraction are also discussed.

Chapter 3 Multiplication and Division with Whole Numbers Multiplication is defined as combining equal-sized
groups, as recommended in the literature. The various models of multiplication and division are discussed, along with
the types of word problems that have multiplicative structure. The Singaporean math model is used to represent and
solve problems. Properties of multiplication, which promote algebraic understanding and proficiency, are explored
using inductive, deductive, and algebraic reasoning. The three uses of the Division Algorithm are also addressed. The
partial products method and partial quotients method are used to develop the traditional multiplication and division
algorithms. Mental arithmetic, adjustments, compatible numbers, and estimation are also discussed.

Chapter 4 Number Theory and Integers The equivalent meanings of the symbol a|b are given, and divisibility tests
are addressed. The Sieve of Eratosthenes, Fundamental Theorem of Arithmetic, LCM, GCF, and Euclidean Algorithm
are discussed. A number theory result is included to give a sense of the distribution of prime numbers. Clock and
modular arithmetic are discussed. Models are used to help define addition and subtraction with integers. Inductive
reasoning is used to extend many whole number properties. Patterns are used to motivate the rule for signs with
integers .

Chapter 5 Fractions and Rational Numbers Models of fractions, nomenclature, symbolic notation, and various
interpretations of fractions are discussed. Division models are used to show that a fraction is a quotient. The
Singaporean math model is used to represent and solve problems. Inductive reasoning is used to establish the concept of
equivalent fractions. Common fractions, rounding, estimation, benchmarks for comparing fractions , cross product rule,
and the density property of fractions are also addressed. Whole number operations are extended to fractions in a natural
way using diagrams. Additive and multiplicative reasoning are extended to fractions. The Singaporean math model is
used to represent and solve problems. Algebraic properties of fraction are used to solve equations.

Chapter 6 Decimals, Proportional Reasoning, and Real Numbers The expanded form of a decimal is emphasized
in the nomenclature for decimals. Comparing decimals, rounding decimals, the similarities and differences between 4.3
and 4.30, terminating decimals, scientific notation, operations with decimals, and estimation are discussed. Additive
and multiplicative reasoning are reinforced. Equivalent ratios and the value of a ratio are emphasized. Proportional
reasoning is introduced and distinguished from additive reasoning. Tables and fractions are used to proportions
involving “missing value” problems. Proportional reasoning is described algebraically and graphically . Percent is used
to make comparisons between two quantities. The three types of percent problems and representational tools are
discussed. Relationships between rational numbers and decimals are discussed. Relationships between irrational
numbers and decimals are discussed. The real number line is discussed .