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MATH 1101, 1102 Elementary Topics in Math I, II

Contact Information

Coordinator: Allyson Hallman-Thrasher


Mathematics for Elementary Teachers with Activities, Loose-Leaf Version

Online Textbook Resources

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. Math 1102 focuses on ratios and proportional reasoning; foundations of number theory; algebraic reasoning; measurement; and properties of two-dimensional and three-dimensional objects. 

Key themes include

  1. explaining and justifying standard and nonstandard algorithms for basic arithmetic operations learned in grades preK-5;
  2. students' construction and critique of their own ideas and others' ideas; and
  3. 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 2018

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 Solving Problems and Explaining Solutions

2.2 Defining and Reasoning About Fractions

2.3 Reasoning About Equivalent Fractions

2.4 Reasoning to Compare Fractions

2.5 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

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

MATH 1102 Topics and Coverage, Beckmann 2018

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 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

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

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

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