Contact Information
Coordinator: Kayla Heacock
Textbook
Mathematics for Elementary Teachers with Activities, 6 th Edition (ISBN: 9780136937609)
Additional Textbook Information
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Course Description
Elementary Topics in Mathematics I and II is a sequence for majors in elementary education and related fields. The purpose of the course sequence is develop mathematical topics usually taught in grades pre-K-5 to a depth required for future elementary educators (and related fields) to establish professional expertise. The courses are taught through an inquiry approach that focuses on problem solving and discussion. Math 1101 focuses on the development of arithmetic and number systems, including whole numbers, integers, and rational numbers; and foundations of number theory. Math 1102 focuses on statistics and probability; ratios and proportional reasoning; algebraic reasoning; measurement; and properties of two-dimensional and three-dimensional objects.
Key themes include
- explaining and justifying standard and nonstandard algorithms for basic arithmetic operations learned in grades preK-5;
- students' construction and critique of their own ideas and others' ideas; and
- using manipulatives to represent and justify algorithms.
Satisfies Tier I requirement for elementary education majors only. Does not apply to Arts & Sciences natural science requirements.
MATH 1101 Topics, Beckmann 2021
Chapter 1 - Numbers and the Base-Ten System
1.1 The Counting Numbers
1.2 Decimals and Negative Numbers
1.3 Reasoning to Compare Numbers in Base Ten
1.4 Reasoning about Rounding
Chapter 2 - Fractions and Problem Solving
2.1 Defining and Reasoning About Fractions
2.2 Reasoning About Equivalent Fractions
2.3 Reasoning to Compare Fractions
2.4 Reasoning About Percent
Chapter 3 - Addition and Subtraction
3.1 Interpretations of Addition and Subtraction
3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts
3.3 Why the Standard Algorithms for Addition and Subtraction in Base Ten Work
3.4 Reasoning About Fraction Addition and Subtraction
3.5 Why We Add and Subtract Negative Numbers the Way We Do
Chapter 4 - Multiplication
4.1 Interpretations of Multiplication
4.2 Why Multiplying by 10 is Special in Base Ten
4.3 The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes
4.4 The Distributive Property
4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts
4.6 Why the Standard Algorithm for Multiplying Whole Numbers Works
Chapter 5 - Multiplication of fractions, decimals (negative numbers are omitted)
5.1 Making Sense of Fraction Multiplication
5.2 Making Sense of Decimal Multiplication
Chapter 6 - Division
6.1 Interpretations of Division
6.2 Division and Fractions and Division with Remainder
6.3 Why Division Algorithms Work
6.4 Fraction Division from the How-Many-Groups Perspective
6.5 Fraction Division from the How-Many-Units-in-1-Group Perspective
6.6 Dividing decimals
Chapter 8 - Number Theory
8.1 Factors and Multiples
8.2 Even and Odd
8.3 Divisibility Tests
8.4 Prime Numbers
8.5 Greatest Common Factor and Least Common Multiple
8.6 Rational and Irrational Numbers
MATH 1102 Topics, Beckmann 2021
Chapter 7 - Ratio and Proportional Reasoning
7.1 Motivating and Defining Ratio and Proportional Relationships
7.2 Solving Proportion Problems by Reasoning With Multiplication and Division
7.3 The Values of a Ratio: Unit Rates and Multipliers
7.4 Proportional Relationships
7.5 Proportional Relationships Versus Inversely Proportional Relationships
7.6 Percent Revisited: Percent Increase and Decrease
Chapter 9 - Algebra
9.1 Numerical Expressions
9.2 Expressions With Variables
9.3 Equations
9.4 Solving Algebra Word Problems With Strip Diagrams and With Algebra
9.5 Sequences
9.6 Functions
9.7 Linear and Other Relationships
Chapter 10 - Geometry
10.1 Lines and Angles
10.3 Circles and Spheres
10.4 Triangles, Quadrilaterals, and Other Polygons
Chapter 11 - Measurement
11.1 Concepts of Measurement
11.2 Length, Area, Volume, and Dimension
11.4 Converting From One Unit of Measurement to Another
Chapter 12 - Area of Shapes
12.1 Areas of Rectangles Revisited
12.2 Moving and Additivity Principles of Area
12.3 Areas of Triangles
12.4 Areas of Parallelograms and Other Polygons
12.6 Area and Circumference of Circles and the Number
12.8 Contrasting and Relating Perimeter and Area of Shapes
12.9 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem
Chapter 13 - Solid Shapes and Their Volume and Surface Area
13.1 Polyhedra and Other Solid Shapes
13.2 Patterns and Surface Area
13.3 Volumes of Solid Shapes
Chapter 14 - Geometry of Motion and Change
14.1 Reflections, Translations, and Rotations
14.2 Symmetry
14.3 Congruence
14.5 Similarity
Chapter 15 - Statistics
15.1 Formulating Statistical Questions, Gathering Data, and Using Samples
15.2 Displaying Data and Interpreting Data
15.3 The Center of Data: Mean, Median, and Mode
15.4 Summarizing, Describing, and Comparing Data Distributions
Chapter 16 - Probability
16.1 Basic Principles of Probability
16.2 Counting the Number of Outcomes
16.3 Calculating Probabilities of Compound Events