Day 21: Flipping the Inequality Sign

Regular Math Lesson Objective: Multiply two different exponents with the same base; simplify division exponential expressions by factoring

Regular Math Standard: 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. 

Regular Math Lesson Sequence:

1. Chart with the base of 3 for a warm up
2. Review the homework and pepper
3. Students worked on an exploration to match the objective of dividing exponential expressions by factoring. It was really helpful to see students write the word factor as part of their reasoning to the first question on the exploration about how to simple 8/12 and 2/3. Interestingly many students claimed that 2 to the 7th power over 2 to the 5th power in expanded form could be simplified because the numerator and denominator shared a common factor of 4. When they said this, I crossed out a 2 times 2 on the top and bottom. It became more apparent that we could cross out more. 
4. Passed out progress reports for students to have signed 
5. Exit ticket to assess student knowledge of the lesson and the previous lessons. 

The above image is the first of three questions I asked of students on the exit ticket. Overall, I was pleased with the work that students showed. This is the fourth different base that they have seen in four days (base 2, base 10, and base 3) so I think it's clear that the repetition is making an impact. As the picture above illustrates, students were not writing 1/4x4 in expanded form, so I put the feedback directly on the exit ticket for these students. 

This was the second question that I assessed. The top error is something that I did not see a whole bunch of times, but I thought the misconception was worth showing here. My writing is the red ink for the student who added the exponents. The lower picture is a great reason for why students can find simplifying these expressions valuable. It saves a tremendous amount of labor.

The last question pictured above is going to be covered by the next day's lesson, but many students put together quality answers. I had several state that 3 to the second power to the fourth power was 81 squared. I also had students do what was done above. It's amazing how when one thing is taught to them all day that they become fixated on that being the pathway to solve all problems. It's this type of thinking that  is forcing me to be less willing to give answers immediately to students this school year instead of letting them explore first.

Honors Math Objective:

Honors Math Standard: A1-REI-D12 Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Honors Math Lesson Sequence:

1. Open Middle - Creating an inequality using the integers -4 to 4 to get x > 2/3. I was a little disappointed with the class on this problem. They immediately expressed frustration and became defeated just at the site of the task. Only two of the seven or so groups in the room made an honest effort to attack the problem. And while I will freely admit that this problem is a challenging problem, it is also a seventh grade standard being taught to eighth grade students. It could be that student confidence is low in this class after the most recent quiz and that is having an impact. I think the kids got the message when I asked how many students had bothered to write the integers from negative four to positive four in a list. Only three out of twenty-six hands went up to indicate they had done this. The kids had no objection when I said that even if they had no clue how to solve this they should have at least taken this step of writing what they do know. I would one hundred percent use this problem again in the future - to not use it would be watering down the class.
2. Passed out progress as students worked on the warm up problem to be signed.
3. I had the students do addition and subtraction inequalities in their groups while I circumvented the room. I have basically ditched the concept of taking notes this year and find that student engagement is higher and that I can clarify issues better in this way. Students are also doing more thinking. To save me some aggravation, I had the students repeat after me that it was not homework (since it said it at the top). 
4. I assigned a similar homework to the sheet above to ensure that students were getting independent practice to what they had peer assistance for during class.