# Properties of Operations

## Uncovering Student Thinking in Mathematics- 25 K-12 Formative Assessment Probes

The 10 assessment probes in the "Number and Operations" section of this book can be used as a CTS application to examine student thinking after conducting a CTS. Additionally, the teacher background notes provide valuable information on instructional implications (CTS Section II) and research on learning (CTS Section III). For example, the "Comparing FRactions" probe can be used with the "Fractions" CTS to examine student work related to part-whole relationships when comparing fractions.

- Addition and Subtraction
- Addition and Subtraction of Whole Numbers
- Assessment Task
- Comparing and Ordering Numbers
- Computation and Operations
- Counting
- Decimals
- Equivalence
- Estimation
- Exponents
- Facts
- Fractions
- Fractions, Decimals, and Percents
- Large and Small Numbers
- Mathematics Education Book
- Multiplication and Division
- Multiplication and Division of Whole Numbers
- Numbers and Operations
- Percent
- Place Value
- Properties of Operations
- Ratio and Proportion
- Rational Numbers

## The Young Mathematician at Work: Multiplication and Division (2nd in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

## The Young Mathematician at Work: Fractions, Decimals and Perent (3rd in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

## Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.

Description: A summary of the structures used by students for adding and subtracting mulitdigit numbers. The article identifies and describes categories of methods devised by students to sovle the problems as well as typical errors that may arise with each method. This article can be used to supplement sections II and IV.