Using Patterning to Explore Powers and Exponents | Free Math Lessons
Do your kids always confuse all the exponent rules? Do they multiply the exponents when they are supposed to add them? Do your students stumble over rational or negative exponents? Is scientific notation a chore because of a lack of exponent understanding? If so, then you need to use patterning to help students create understanding around exponents! Check out my FREE math lessons that I used with my students in both Math 8 and Algebra 1. Note: Some of the lessons around fractional exponents have moved to Algebra 2 in some states.
All of these lessons featured in this post can be found in MS Word and PDF formats on my K-8 Math Lessons and High School Math Lessons pages. Be sure to subscribe to get more fantastic lesson ideas sent straight to your inbox.
Math Practice Standards
Investigations are a great way to incorporate the math practice standards into your classroom. The investigations in this blog post align to the following Standards of Mathematical Practice:
- SMP.2 Reason abstractly and quantitatively.
- SMP.3 Construct viable arguments and critique the reasoning of others.
- SMP.7 Look for and make use of structure.
- SMP.8 Look for and express regularity in repeated reasoning.
Math Standards
These lessons work well with Grade 8, Algebra 1, and Algebra 2 students. Ideally, they can be used as a first-time introduction, but they can also be used as a review. Additionally, some of these ideas are foundational for understanding scientific notation in 8.EE.4. They align to the following Common Core Math Standards:
- 8.EE.1 Understand, explain, and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.
- A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
- A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
- N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
- N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Free Math Lessons
All of these lessons featured in this post can be found in MS Word and PDF formats on my K-8 Math Lessons and High School Math Lessons pages. Be sure to subscribe to get more fantastic lesson ideas sent straight to your inbox.
Exponent Exploration #1
Students use patterns to explore positive and negative exponents including raising a number to the 0th power. Students have to create their own rules and justify their reasoning. (Skip this lesson exploration if you don’t want to investigate negative exponents. However, it is really useful in helping students understand scientific notation!)
Exponent Exploration #2
In this exploration students discover that when multiplying two powers with the same base, you add the exponents.
Exponent Exploration #3
This activity explores raising a power to a power.
Exponent Exploration #4
Do you students struggle with simplifying rational expressions with exponents For example, (5y3z6d4)/ (25yz8d3)? If so, this is the activity they need! Although, this concept might seem hard initially, most 8th graders can solve these types of problems if they are presented it using patterns.
Exponent Exploration #5-Rational Exponents and Radicals
Rational exponents don’t have to be terrifying for your students! Use patterns and connect rational exponents to factors and radicals. Although not necessarily intuitive to those of us who were taught the rules, it’s actually a common sense way to teach rational exponents that makes sense to students!
Fractional Exponent Warm-up
This is a short warm-up or exit ticket that confronts student misconceptions about negative exponents and rational exponents.
Integer Exponent Operations Worksheet
Students can practice the laws of exponents using this worksheet.
Ohio’s Model Curriculum with Instructional Supports
Have you seen Ohio’s Model Curriculum with Instructional Supports? It’s a wonderful document with example, tips, and resources for Ohio standards that mostly aligns with the Common Core. I would encourage you to check it out! Here is the Grade 8 and Algebra 1 documents.
Conclusion
Kids and teens learn best and retain more information when they create their own understanding. It’s our responsibility as educators to provide these opportunities for them. But time is a factor, and it’s hard to find engaging lessons that promote deep thinking and the Standards of Mathematical Practice. That’s why I want to share my resources with you! All of these lessons mentioned in this post and other lessons can be found in MS Word and PDF formats on my K-8 Math Lessons and High School Math Lessons pages. Subscribe if you want more lesson ideas delivered straight to your inbox. Share this post with your other math teacher friends or department chair.
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