Exponents with Coefficients

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SWBAT apply rules of exponents with expressions that include leading coefficients.

Big Idea

Simplifying exponential expressions becomes a bit more challenging when we add leading coefficients. This lesson will help students tackle this shift in rigor.

Warm Up

7 minutes

For today's Warm Up assignment, I have provided two review problems from the previous day's lesson in addition to one fluency-building question called a magic square. The magic square requires students to think flexibly about integers and find the missing number in the square that, when found, will add with the other three numbers to total the number below the square. Because my students continue to struggle with integer operations, I continue to include these type problems on the Warm Up assignment so they will have constant exposure and additional time to help ideas "click" for them.

Once the timer sounds after 5 minutes, I invite volunteers to share their answers. I then ask for the class to signal thumbs up or thumbs down as to whether they agree with the volunteer or not. If no one disagrees, we move on to the next problem. I a student does disagree, I ask that student to give her answer and explain why it is correct. I then poll the class to see if that student has convinced others she is correct.

Let's Review

7 minutes

Because middle schoolers commonly use and confuse rules in mathematics, I wanted to provide an opportunity to review what we have already seen in class the previous few days. If students are unsure about an answer, I encourage them to look back at their exponents foldable we created where they recorded, in their own words, how exponents are treated when multiplied, divided, or taken as a power. Taking time to review helps build student confidence with their skills before adding additional ones later in the lesson.

To keep the class moving, I call on student volunteers that I select from my cup of name sticks to simplify each equation. If the selected student is reluctant to answer, I encourage them to "phone a friend" (ask someone at their table for help). This helps to lower the anxiety level and allows the student to focus on the problem at hand. Once all six problems have been simplified, we move to today's learning objective.

Learning Objective

1 minutes

Today's Learning Objective builds upon the work we have been doing previously and adds another level of complexity by introducing coefficients. Most students are not familiar with the term 'coefficient' so I introduce it as key vocabulary before moving on.

Key Vocbulary

3 minutes

I introduce 'coefficient' as key vocabulary because students will likely see and hear this word for years to come in mathematics. I want them to be very comfortable using the correct term for "the big number in front of the variable". Students enter the word in their journal's glossary along with the definition in their own words and a visual of the word. We also add the word to our word wall for future reference during games and lessons that focus on academic vocabulary.

Sample Analysis

4 minutes

Once students have an understanding of the word coefficient, I explain that I am going to show them some samples of math problems with coefficients and I want them to analyze those samples to see if they can figure out how they are treated when combined with variables and exponents.

I reveal two samples that model multiplication. I give students 15 seconds to analyze. Then I ask them to 'turn and talk' with their table partner about what they see. I eavesdrop on conversations and make a mental note of a student who can articulate well what they see happening. I call the class back to listen to my pre-selected "volunteer". I ask the students to agree or disagree with a thumbs-up or down signal. I then encourage students to write a brief statement in their journals about how to treat coefficients.

Once they have written in their journals, I ask them to predict how they think coefficients are treated when being divided. I then show them samples and ask if their predictions were correct. I encourage them to modify what they have already written to include division. We then move to applying these ideas to practice problems.

Let's Practice!

8 minutes

To make sure students have a clear understanding of how to simplify problems that include coefficients as well as variables and exponents, I reveal five practice problems. I ask students to record the problems and the solutions in their journals. We then review each one as a class for consensus.

Work Time

10 minutes

For Work Time, I distribute a half page worksheet, Simplifying Equations with Coefficients and Exponents, to students. This includes 15 problems for students to simplify using both rules of exponents and coefficients. I encourage students to think about what operation is occurring with each problem so that they apply the appropriate exponent rule. I then set the timer for 10 minutes and begin moving through the room redirecting student as needed to finish. Once the timer sounds, I tell students to turn their paper over.

Ticket Out the Door

5 minutes

Once the timer sounds, I reveal the day's Ticket Out the Door prompt which students will answer on the back of their Work Time paper. I have created a prompt that asks students to analyze the work of Mei and decide if she has done the work correctly or not. If they decide she has done the work correctly, I ask that they explain how they know. If they decide she is incorrect, I ask them to fix her work. When students analyze another student's work for errors, they are employing MP 3 and gaining a deeper experience with the math that will hopefully assist them in learning at higher levels.

When the bell rings ending class, I instruct students to bring me their work, which I will later review and sort to make adjustments to my subsequent lessons and grouping strategies.