LAGUARDIA COMMUNITY COLLEGE
CITY UNIVERSITY OF NEW YORK
DEPARTMENT OF MATHEMATICS, ENGINEERING and COMPUTER SCIENCE
MAT 103 — EARLY CONCEPTS OF MATH FOR CHILDREN
3 class hours, 3 credits
Catalog Description
This course combines theory with practical aspects of how children learn mathematics.
Students learn how to help young children to develop numerical relationships and
geometric patterns. This course is of particular value to Childhood Education majors,
students interested in child psychology, and parents and others who teach mathematics
informally in homes and community settings.
Instructional Objectives
1.
To increase students’ ability to explain basic mathematical concepts in simple
terminology.
2.
To provide a background for understanding the skills of arithmetic and the
structure of the number system.
3.
To introduce mathematical activities, games, and manipulative aids as tools to be
used with children.
4.
To increase students’ confidence in their own mathematical knowledge and ability
to teach mathematics.
Performance Objectives
The student will be able to:
1.
Demonstrate the use of mathematical activities, games, and manipulatives for
teaching mathematics to children.
2.
Describe the relationships between different types of numbers (counting numbers,
negative numbers, fractions, decimal numbers).
3.
Describe models for understanding and using basic arithmetic operations.
4.
Explain strategies suitable for children in learning basic facts and doing
calculations.
5.
Use concrete models to teach the base ten place-value system.
6.
Describe models for teaching fractions for young children’s comprehension and
computation.
7.
Explain her or his mathematical ideas clearly and simply as needed in teaching
children.
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1
Textbook
Mathematics for Elementary Teachers with Activity Manual Volume 1
Third Edition (Custom Edition for LaGuardia Community College)
Author: Sybilla Beckmann
Publisher: Pearson, 2011
Class Activities
The manual activities are carefully integrated into the course and the manual is located at
the back of Chapter Nine. Please bring your textbook to class so you can participate in
these important activities.
Grading
Your grade in this course will be determined as follows.
Test I
Test II
Project
Final Examination
20%
20%
30%
30%
Project
Your project involves an observation in a classroom followed by two pieces of writing
based on what you observe. You’ll write an observation report and a lesson plan.
Here’s how the project will work.
First, you’ll need to set up your observation:
1. Choose a school you would like to visit and give the name of the school to your
instructor so that he/she can write a letter of introduction for you.
2. Take your letter to the school and present it to the principal.
3. The principal will then assign you to a particular teacher.
4. Contact the teacher to set up a date and time for your observation. Make sure the
teacher knows that you need to observe a mathematics lesson!
During the observation, write down all you can about what’s going on. You can
handwrite your notes or use a tablet or whatever lets you get down the most information.
You’ll use your notes to write an observation report. Your observation report should
include the following elements.
 State the school and the grade level you visited. Indicate anything special about the
class — bilingual program, “gifted and talented” students, special-needs children, etc.
 Describe the classroom setting — how many students, the type of room, how the seats
are arranged, what’s on the walls, etc.
 State the mathematics topic that was covered. Describe all the teaching strategies
used during the lesson. Include a description of any worksheets, books,
manipulatives, visual aids, electronic devices, and other materials that were used.
 Give examples of problems, questions, and activities that the teacher demonstrated
and the children worked on.
 Give examples of students’ oral and written responses on the work they did.
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



Describe how the students behaved during the lesson — both overall and the behavior
of particular students.
Describe the homework assigned as a follow-up. Give your opinion on how well the
homework reinforces this lesson and leads into the next one.
Talk about how good a lesson you think this is for teaching mathematical skills.
Talk about how good a lesson you think this is for helping children to understand
mathematics.
The last component of the project is the lesson plan. You have two choices.
 If you believe that you can make major improvements to the lesson you observed,
then write a new lesson plan for the topic.
OR
 If you’d teach the topic pretty much the same way the teacher did, then write a plan
for a lesson following up on the one you observed.
Weekly Outline
Possible Exercises
(instructors will
give the actual
assignments)
Week Topics
Sections Pages
1
Chapter 1
1.1
1.2
1.3
1.4
Chapter 2
2.1
2.2
2.3
2.4
2.5
2.6
Chapter 3
3.1
3.2
1
2-11
11-25
25-32
32-35
38
39-48
48-53
53-57
58-68
68-78
78-89
92
93-100
100-110
3.3
111-120
pp. 118-120, 1-15
3.4
3.5
Chapter 4
4.1
4.2
121-132
132-137
140
140-146
147-149
pp. 130-132, 1-26
p. 137, 1-4
4.3
150-163
pp. 159-163, 1-26
4.4
163-172
pp. 171-172, 1-18
2
3
4
Numbers and the Decimal System
The Counting Numbers
Decimals and Negative Numbers
Comparing Numbers in the Decimal System
Rounding Numbers
Fractions
The Meaning of Fractions
Interlude: Solving Problems and Explaining Solutions
Fractions as Numbers
Equivalent Fractions
Comparing Fractions
Percent
Addition and Subtraction
Interpretations of Addition and Subtraction
The Commutative and Associative Properties
of Addition, Mental Math, and Single-Digit Facts
Why the Common Algorithms for Adding and
Subtracting Numbers in the Decimal System Work
Adding and Subtracting Fractions
Adding and Subtracting Negative Numbers
Multiplication
Interpretations of Multiplication
Why Multiplying Numbers by 10 is Easy in the
Decimal System
The Commutative and Associative Properties of
Multiplication
The Distributive Property
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p. 11, 1-8
pp. 23-25, 1-15
pp. 31-32, 1-16
p. 35, 1-7
pp. 45-48, 1-22
None
p. 57, 1-8
pp. 65-68, 1-26
pp. 76-78, 1-20
pp. 88-89, 1-23
pp. 99-100, 1-6
pp. 109-110, 1-13
p. 146, 1-8
p. 149, 1-5
5
6
7
8
9
10
11
12
Properties of Arithmetic, Mental Math, and
Single-Digit Multiplication Facts
Why the Common Algorithm for Multiplying
Whole Numbers Works
Review for Test I
Test I
Multiplication of Fractions, Decimals, and
Negative Numbers
Multiplying Fractions
Multiplying Decimals
Multiplying Negative Numbers
Powers and Scientific Notation
Division
Interpretations of Division
Division and Fractions; Division with Remainder
Division
Why the Common Long-Division Algorithm Works
Fraction Division from the “How Many Groups?”
Perspective
Fraction Division from the “How Many In One
Group?” Perspective
Dividing Decimals
Combining Multiplication and Division:
Proportional Reasoning
The Meanings of Ratio, Rate, and Proportion
Solving Proportion Problems by Reasoning with
Multiplication and Division
Connecting Ratios and Fractions
When You Can Use a Proportion and When You
Cannot
Percent Revisited: Percent Increase and Decrease
Number Theory
Factors and Multiples
Greatest Common Factor (GCF) and Least Common
Multiple (LCM)
Prime Numbers
Even and Odd Numbers
Divisibility Tests
Number Theory
Rational and Irrational Numbers
Looking Back at the Number Systems
Review for Test II
Test II
Algebra
Mathematical Expressions and Formulas
Equations
Solving Equations
Review for Final Examination
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4.5
173-182
pp. 179-182, 1-18
4.6
182-191
pp. 189-191, 1-13
Chapter 5 194
5.1
5.2
5.3
5.4
Chapter 6
6.1
6.2
194-202
203-207
207-210
210-217
219
219-226
226-234
pp. 200-202, 1-22
pp. 206-207, 1-12
p. 210, 1-3
pp. 216-217, 1-12
6.3
6.4
234-250
250-258
pp. 246-250, 1-27
pp. 256-258, 1-16
6.5
258-266
pp. 264-266, 1-14
6.6
266-274
Chapter 7 277
pp. 272-274, 1-16
7.1
278-284
pp. 283-284, 1-8
7.2
7.3
7.4
284-295
295-299
299-301
pp. 292-295, 1-25
pp. 298-299, 1-5
pp. 300-301, 1-8
7.5
301-312
Chapter 8 314
8.1
314-318
pp. 309-312, 1-27
8.2
8.3
8.4
8.5
318-325
325-330
331-334
334-338
pp. 323-325, 1-20
p. 330, 1-7
pp. 333-334, 1-12
pp. 337-338, 1-15
8.6
8.7
338-351
352-353
pp. 349-351, 1-20
p. 353, 1-2
Chapter 9
9.1
9.2
9.3
356
357-366
367-375
375-380
pp. 363-366, 1-25
pp. 372-375, 1-17
pp. 379-380, 1-7
p. 226, 1-8
pp. 232-234, 1-16
pp. 317-318, 1-9