Mathematics for Elementary Teachers

Format:

Book

Conference/Event

Author/Creator:

Manes, Michelle, author.

Conference Name:

Michelle Manes

Language:

English

Subjects (All):

Education--Textbooks.

Education.

General education--Textbooks.

General education.

Education, Elementary--Textbooks.

Education, Elementary.

Physical Description:

1 online resource

Place of Publication:

[Place of publication not identified] University of Hawaii Manoa [2017]

Language Note:

In English.

Summary:

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

Contents:

I. Problem Solving

Introduction

Problem or Exercise?

Problem Solving Strategies

Beware of Patterns!

Problem Bank

Careful Use of Language in Mathematics

Explaning Your Work

The Last Step

II. Place Value

Dots and Boxes

Other Rules

Binary Numbers

Other Bases

Number Systems

Even Numbers

Exploration

III. Number and Operations

Addition: Dots and Boxes

Subtration: Dots and Boxes

Multiplication: Dots and Boxes

Division: Dots and Boxes

Number Line Model

Area Model for Multiplication

Properties of Operations

Division Explorations

IV. Fractions

What is a Fraction?

The Key Fraction Rule

Adding and Subtracting Fractions

What is a Fraction? Revisited

Multiplying Fractions

Dividing Fractions: Meaning

Dividing Fractions: Invert and Multiply

Dividing Fractions: Problems

Fractions involving zero

Egyptian Fractions

Algebra Connections

What is a Fraction? Part 3

V. Patterns and Algebraic Thinking

Borders on a Square

Careful Use of Language in Mathematics: =

Growing Patterns

Matching Game

Structural and Procedural Algebra

VI. Place Value and Decimals

Review of Dots & Boxes Model

Decimals

x-mals

Division and Decimals

More x -mals

Terminating or Repeating?

Operations on Decimals

Orders of Magnitude

VII. Geometry

Tangrams

Triangles and Quadrilaterals

Polygons

Platonic Solids

Painted Cubes

Symmetry

Geometry in Art and Science

VIII. Voyaging on Hokule?a

Hokule?a

Worldwide Voyage

Navigation

Notes:

Description based on print resource