Multiplying and Dividing Exponents: To Add or Not to Add

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SWBAT interpret complex expressions and apply algebraic properties to simplify and evaluate expressions involving exponents .

Big Idea

This lesson helps students make the connection between performing operations with real numbers and exponents.

Entry Ticket: To Add or Not to Add

15 minutes

The purpose of the Entry Ticket: Exponents is to activate students’ prior knowledge about working with exponents and expressions. I start by having students work on the Entry Ticket as soon as they enter the class – as the year has progressed it has become more and more automatic that students take out their binders and get to work on the Entry Ticket rather than milling around or socializing. This also frees up a couple of quick minutes for me to take care of housekeeping (attendance, etc.) and not waste valuable instructional time.

I typically give students a 2 minute warning so they know we will be talking as a group soon. About 5 minutes into class, I ask students to talk and turn to a partner about the Entry Ticket, specifically to converse about how they solved the problem and to identify the rules used to solve each problem. We then review the Entry Ticket as a class and ask groups to share out any discrepancies/errors and how to correct them.

I then turn my attention to the agenda board which has the lesson and language objectives, agenda and homework written on it. We review the objective as a class, and I talk about how this lesson’s objective fits into the bigger objectives of the unit (to support students who have difficulty seeing the big picture and/or shifting back and forth between the gestalt and the details of lessons and units). I typically have students write down the homework assignment during this time and hand out copies of the homework, but have students file the homework in their binders (I have also had classes where having the homework was too much of a distraction – in these cases I handed the homework out at the end of class).  

The lesson objective is referred to with verbal and non-verbal cues throughout the lesson to contextualize the lesson for students. I ask students what they think they will need to do in order to be successful and meet the day’s objective. The reason for this is to scaffold and model metacognitive strategies in the hopes of students learning these skills and using them with increasing independence. After the day’s agenda has been reviewed, the class shifts to the middle of the lesson.

●       Extensions and Scaffolds: I like to add in peer editing and feedback for the writing portion of this lesson ideally for all students, but often there is not enough time. So, adding the peer reflection piece as an extension for students who have completed the written response can be a quick and easy way to keep all students engaged in learning and on relevant material that is still tied to the objective of the lesson.

●       Environment for this lesson: This lesson is taught as a 90 minute block. I like having students seated in groups of 2 or 4, mainly to provide more opportunities for students to have academic conversations with each other.

●       Tools and Instructional Technology or Software:

SmartBoard, Khan Academy, Calculator, Word Processor (optional, for written responses) 



Explicit Instruction and Active Note-taking

20 minutes

To begin this section of class, I cue students to make sure they all have their binders and something to write with. I also explicitly tell students they need to take notes on the video we are about to watch (I recently have realized that I have a deeply engrained assumption that most students know when I want them to take notes, but in reality the majority of my 9th graders need explicit instruction of not only when to take notes, but how to take notes. I recommend to students that they take notes in two-column format, with the term or example on the left column and notes, definitions work on the right column. In addition the top of the notes should always have a clear topic, which I try to provide each class and the date. At the conclusion of the note-taking, I have students write a “Elevator Ride” statement at the end of their notes to support them in paraphrasing/identifying the main idea(s) of the session.

Once students are all set up with their notes I write the topic for the day “Multiplying and Dividing Exponents” on the board and ask them to be sure to have that as their topic for their notes. I then let students know we will be watching a video on the topic and that they should be taking notes and that I will be asking questions throughout the video.

I show the Khan Academy video on “Exponent Rules Part 1” 


Reviewing Notes: After showing the video for part 1, I ask students to complete the following protocol: 2 minutes to add more details to their notes, 3 minutes sharing their notes with a partner (during this time the partner adds to/revises their notes), and 3 minutes flipping roles (the partner who initially revised now reviews their notes while the other partner now revises their notes). The intent of this protocol is to engage students in academic conversations with each other, but perhaps more importantly is to provide students with an immediate and different perspective on the important aspects of the video and the mathematics behind it.

I ask students if they have any additional questions, including if they would like to review one of the examples from the video or review an additional practice problem similar to the ones on the video on the SmartBoard as a class.

Guided Practice

20 minutes

For the next section of class, students work on a problem set in small groups. I like to give problems that are a mix of similar to those in the focus lesson/explicit instruction section as well as problems that have  anew or different twist to them.

For example, the Regents Exam Prep Center has a nice set of Practice Problems that students can practice. The problems can be projected on the white board, or students can work on the problems individually or in pairs online if there is access to technology (laptop, ipad, iphone, etc.) and the internet in the classroom.

I want students to be pushed to apply what they know to new situations and not simply be able to show they can follow the mathematical rules in isolation. 


Additional Support/Instruction: sometime teach a second section of explicit instruction utilizing Khan Academy as a technology resource. 2nd Chunk - Kahn Academy Video, Part 2 (10 minutes) and Reviewing Notes (10 minutes)I then show the Khan Academy video “Exponent Rules Part 2 

 Reviewing Notes:  have students follow the same protocol from the first video to check each other’s notes in pairs (2 minutes to silently review their own notes, and then 3 minutes sharing while the partner revises, and 3 minutes with roles reversed).

Independent Practice: Quiz

20 minutes

For independent practice, students complete a short quiz (Quiz: Multiplying and Dividing Exponents) that is aligned to the day's learning objectives. 

If students complete the quiz early, I provide an answer key and have them self-correct the quiz and also try to identify where in the process they made mistakes and how to correct them. I also like to review the answers at the close of the class and take a quick poll to identify the 1 or 2 problems that a. students did well on (to celebrate) and b. the class struggled with and then re-teach right then and there to provide some immediate and constructive feedback.


Exit Ticket: Summarazing and Pre-Writing Activity

15 minutes

In this activity students are asked to engage in the all important task of paraphrasing and summarizing information. To accomplish this task, students are asked to complete the Exit Ticket: Focus on Summarizing in partners in response to the prompt: “Summarize the key ideas in class today. Provide examples to back up your claims.”

Students are expected to write out a 1-2 paragraph response based on the Idea Organizer they completed earlier for homework. The intent is to get students to use the content reviewed in class in multiple language domains, including listening, speaking, reading and writing. Of all the tasks, writing is the most difficult for many students because it is not something that is automatically learned and something that requires a great deal of cognitive energy.