This book is an activity-based, discussion-based, problem-based, manipulative-based laboratory manual that can be used in a mathematic course in number and operations for elementary and middle school preservice teachers. In our course, this mathematics laboratory manual is used as the primary text along with minimal use of a booklet on fraction concepts linked ot Common Core fraction standards in grades one to seven. Our introductory course in numbers and operations is considered a mathematics "content" course. However, all the activities are modeled with methods that would be appropriate for teaching young learners, and the activities are based on incorporating the Mathematical Practices of the Common Core and mathematics content standards for grades K to 8. Although there are some activities in the book that do not explicitly fit within key strands of a K to 8 curriculum, most activities are organized around the key areas of early number, base-ten and place value, problem solving, mental arithmetic,and an extensive focus on fraction concepts and operations. Many of the labs have a PowerPoint presentation designed to accompany the questions in the lab so that instructors who may not have used the class activity extensively have some guidance for developing the key concepts of the lab. There are also prepared videos to introduce key ideas prior to working on them in class, so that the students have enough preliminary exposure that deeper discussion occurs as students work through the questions during the in-class activity. This laboratory manual is designed as loose leaf with hole punches so that students can easily organize their mathematical explorations into a notebook that is a detailed record of what has ben done in class along with any supplemental materials. This expected organization is integral to our approach of requiring significant depth of understanding on assessments. Further since we also focus explicitly on the child's perspective, the questions in each activity and on the assessments are meant to elicit responses that would match the language of teachers as they are interacting with a child in that mathematical/social context or match the language that a child with deep understanding would use.

Online Modules for a Course in Number and Operations

Big Ideas

Number Talks

Bell-Ringer Problems

Problem Solving: Gaussian Addition

Common Core Mathematical Practices

Handshake Problem

Polya’s Fourth Step in Problem Solving

Candies and Desks

The Oldest Has RED HAIR!

Bob & Ann (Part Two)

Early Number Development

Addition of Whole Numbers (Basic Facts Strategies)

Whole Number Subtraction (Subtraction Problem Types)

Whole Number Multiplication (Models of Multiplication)

Division of Whole Numbers

Division by Zero

Patterns

Number Sense

More Number Sense

Examining Base Ten

Examining Alternative Algorithms

Operations in Other Bases

Transition from Whole Numbers to Fractions

Reading about Fractions Is FUN!

Number Line Representations of Fractions (Fraction Strips)

Iterating Unit Fractions

Iterating Unit Fractions to Estimate and Count on the Number Line

How Far Did She Walk?

Whoa! I Got Six! Give Me the Pencil!!!

Where Is One on the Number Line?

Whole Unit to Fraction/Fraction to Whole Unit

Equivalent Fractions

Strategies for Comparing Fractions

More Reading about Fractions Is FUN!

Fractions (Intro to Models)

Searching for Structure

The Structure of Arithmetic Operations (Linking to Fraction Models)

Fraction Concepts and Operations

Fraction Word Problems

Modeling Fraction Operations

Identifying Models of Fraction Operations

Mental Arithmetic (Decomposition)

Mental Arithmetic (Difference of Squares)

Mental Arithmetic (Multiplying or Dividing by 5)

Mental Arithmetic (Halving and Doubling)

Mental Arithmetic (Factoring)

Mental Arithmetic (Other Strategies)

Mental Arithmetic Review (Hands-up Cards Activity)

Mental Arithmetic Practice

Computational Estimation Preliminary Skills Worksheet

Computational Estimation

Prime Numbers

Generating Prime Numbers

Even and Odd Worksheet

Number Theory (Lab A)

Number Theory (Lab B)

Real Number Explorations

**Appendix A: **Comparison Anchor Responses

**Appendix B:** Comparing Fractions and Modeling Conclusions

**Appendix C:** Cut-out Cards for Fraction Comparisons Strategies

**Appendix D:** Fraction Operation Assignments

**Appendix E:** Fraction Comparison Key

**Appendix F:** Number Strings