The Knowre Data Insights series was launched to identify and help teachers address the math skills that students struggle with the most. To identify these skills, we looked to Knowre’s data. Specifically, the Knowre practice questions with the highest number of incorrect answer attempts. After connecting these incorrectly answered questions with the core math concepts being tested, we identified the categories of skills that students, on a national level, struggle with most frequently.

The first category we identified, linear graphing, was addressed in the inaugural edition of the series. In this second installment, we’ll be addressing the properties of exponents. As exponents make appearances in all levels of algebra, understanding them is integral to continued math success.

**The Rules**

The study of exponents is grounded in the learning and understanding of “the rules.” Often, students are able to successfully learn and practice each of the rules separately. However, when given problems where a combination of the rules must be used, they struggle. This is seen in the below Knowre exponent questions.

Question A has an 84% incorrect answer rate, question B, 83.6%, and question C, 82.2%.

**The Knowre Equivalency Challenge**

Though exponents are integrally connected to much of what students have already been learning in class, they are often perceived by students as totally new. Taking the time to emphasize the connection between exponents and student’s prior knowledge will go along way in supporting student success on this topic. One quick way to do this is with the Knowre Equivalency Challenge, a team competition designed to get students thinking about the many different ways they can express the same number.

Download Equivalency Challenge Rules

**Exponent Worksheet and Activity**

Another way to support student success with exponents is to focus on developing a more conceptual understanding of what exponents represent. One way to achieve this is through a comparison exercise. The process of comparing forces students to think about how different expressions relate to one another. Student work on this type of activity will also reveal common misunderstandings that will be helpful in retargeting and reteaching. Download the worksheet below to bring this activity into your classroom.

Download Exponent Worksheet and Answer Key

Extend the impact of the exponent comparison activity by having students explain their problem solving process to the rest of the class. This can be done by going through each and every question, or by choosing to highlight the items that the majority of students got wrong.

Pre-select a student who got each problem correct and ask them to explain to the rest of the class how they determined their answer and why that answer is correct. Facilitate class

conversation to dive more deeply into each question.

**Knowre Lessons to Review Before Teaching Exponents**

Pre-Algebra:

Lesson 1-3 (Factors)

Lesson 1-4 (Prime/Composite Numbers and Exponents)

Lesson 2-4 (Order of Operations with Integers)

Lesson 3-1 (Variable Expressions)

Lesson 3-2 (Adding and Subtracting Variable Expressions)

**Knowre Lessons on Exponents**

Pre-Algebra: Lesson 3-4

Algebra 1: Chapter 6

Algebra 2: Lessons 5-1, 5-2, 5-8, 11-1, 11-2, 11-6

**More Resources**

Want more ideas for teaching exponents? Here are three additional resources that we recommend:

- Mistakes, Radicals, Rational Exponents, and Partitioning?,
*Reason and Wonder*. The author explores reasons why his students who struggle with exponents have no trouble with square and cube roots in radical form. - Ms. Hagan’s Book of Exponent Rules,
*Math Equals Love*. Sarah chronicles how she cut down her exponent rules unit from two weeks to three days. She also gives suggestions for what activities to do on each of the three days. - Exponent Rules Unit,
*Don’t Panic, the Answer is 42*. More worksheets, games, and quizzes!