# Equivalence

## 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

## Building a Foundation for Learning Algebra in the Elementary Grades

The research summarized in this Volume of In Brief focuses on the ability of elementary students to reason algebraically. The articles can be used with CTS Section IV.

## Balancing Act: The Truth behind the Equals Sign

This article illustrates the misconceptions that students have when using the equals sign and describes an activity used with students to develop the foundation for an accurate conception of equivalency. The author states that developing an accurate understanding of the equal sign is the basis for comprehending equations and inequalities. This article could be used to supplement the readings from sections II and IV.