LAP 1- You Be the Teacher Project

Group 1 – This group was tasked with discovering and teaching the quotient rule. They did a fantastic job throughout the project, consistently working hard and taking the task of teaching their classmates very seriously. For example, they decided to not include non-examples in their lesson because they thought that non-examples were more confusing than helpful. They also wrote out scripts for themselves of what to say when teaching. Group 1 – Quotient Rule Lesson Plan and Discovery Sheet 

Group 2 – While I originally grouped students in pairs, one of the students in this group was absent almost the entire week so Student A worked by himself the entire time. Student A is a very smart student, but can be very stubborn at times. From the very beginning of the project, he decided that he did not want to do it. After a negative attitude for the first day and a half, I realized that his prolonged negativity was partially caused by the fact that he has confused about his exponent rule. I worked with him for extended periods of time on two different days of the project to ensure that he understood the material, which turned his attitude mostly around.  Although he did not write much on this discovery sheet of lesson plan, he spent a long time thinking about how to write his exponent rule algebraically, which was not an easy task because of the negatives: Group 2 – Negative Exponents. He ended up doing great presentations for both groups of students (see him teach at 6:44 in this video). In his daily progress check-in sheet, he barely wrote anything on the first day, but he started writing more on the second and third days after I had worked with him and he understood more: Daily Progress Check-in.

Here are seven different project reflections from my students that show the range of student responses to this project. In response to the question “Would you like to do an activity like this again?” three of the students said yes, two said maybe, and two said no. I also noted that many students said that doing the worksheets was their favorite part, which was no surprise since my students always asked me for worksheets. I was glad that I got them to make the worksheets this time, instead of me! Project Reflections

LAP 2 – Practicing Exponents with Worksheets

Student A did a great job showing her work as she completed a tier 1 worksheet. I consistently pushed my students to show their thinking, and I was happy to see that many of them increasingly did that as the year progressed. Because Student A showed her work, I was able to see that she didn’t understand that you could have a negative exponent, so she switched any answer that would be negative to positive. A lot of my students found working with negative exponents difficult. Tier 1 – Student A

I chose to include Student B’s work because he was a student who came to Claremont from Life Skills (a full-time special education resource room) at the start of the second quarter. He was several grade levels behind in math and lacked basic number sense. However, he exhibited an impressive capacity for learning which really shone through in this exponent unit. Throughout the mini-lessons he consistently advocated for himself and asked his classmates for help until he understood the rules. His successful completion of this sheet, with some guidance from me and his classmates, is a great testament to his growth. Tier 1 – Student B

As students completed their tiered worksheets, I realized that many of them were struggling with negative exponents. I also wanted them to understand the difference between negative exponents and negative bases, so I had them complete a worksheet that differentiated between those different scenarios: Negative Exponents vs. Negative Bases.

After completing that activity in class, I gave my students a homework assignment to reinforce the material. In the first student’s work, you can see that he got a bit confused with raising a negative number to a negative power, which understandably is a confusing idea. In the second student’s work, her biggest mistake was forgetting how to cube a number, for which this unit provided good review. Negative Exponents HW. After these two activities, I saw much less confusion amongst my students about simplifying exponential expressions when there were negatives involved.

LAP 3 – Equivalent Exponential Expressions

After playing card games that dealt with equivalent exponential expressions, students completed an exit slip that asked them to create their own set of equivalent expressions using each exponent rule. The first student needed more of a challenge, so I gave him a starting expression that included a negative exponent. The second student did not need as high a challenge, so his starting expression had a positive exponent. In his exit slip, his only mistake was with the product rule: he added both bases together instead of multiplying them. This was a very intelligent mistake, however, for it showed that he knew he had to add the exponents together (and the exponents he chose did indeed add to the correct number), he just forgot that that happens when you multiply the bases. Exit Slips

LAP 4 – Converting Between Scientific Notation and Standard Notation

The confusion with negatives reappeared in Student A’s work, for he forgot to include negatives in all of this scientific notation expressions that represented numbers less than 0. Conversion – Student A

Student B demonstrated a clear understanding of converting numbers from scientific notation to standard notation. It is worth noting that in this activity, students swapped papers and checked each other’s work. Whoever checked Student B’s work mistakenly marked #28 and #30 as correct and incorrect, respectively. This revealed common mistakes with scientific notation and exponents. In #28, there is an invisible decimal point at the end of the whole number that many students forgot about, and for #30, a few students forgot that any number raised to the zero power equals 1. Conversion – Student B

LAP 5 – Comparing (i.e. dividing) Numbers in Scientific Notation

After doing some great thinking during the starter, my students did really well with comparing numbers in scientific notation. In this student’s work, his understanding of the quotient rule helps him more easily compare the numbers. This activity helped my students see the usefulness of the exponent rules. Comparing Numbers 

When comparing real-world quantities in scientific notation, Student A wrote all of her numbers in scientific notation without the decimal point in the standard position. Her exponents were correct, though, which shows that her thinking was correct, she just forgot to put the decimal on her paper. In her comparisons, she identifies which quantity is bigger, which shows her attention to the real-world aspect of the activity. Student A

Student B took the time to convert some of his answers from scientific notation to standard notation. I saw a few students doing this, for it helped them understand how big or small the quantities actually were. Again, this student used the quotient rule to make his comparisons. Student B

After the first day of class, one of my student’s came up with an alternative method of comparing numbers in scientific notation by writing them in standard notation and crossing out the zeroes. This student rarely wanted to share his thinking with the class, but was so excited about his method that he solved several problems on the board for his classmates. To positively reenforce his contribution, I created a starter for the next day in which my students compared the quotient rule method with his method: Different Method Starter

LAP 6 – Multiplying Numbers in Scientific Notation

Because of their work dividing numbers in scientific notation, students caught on quickly to the multiplying numbers in scientific notation by rearranging the factors using the product rule: Multiplication Practice

LAP 7 – Looking at PARCC Problems

In both of these examples of student work, students struggled on #11 to place the number 0.00074 in the correct range of numbers, first choosing option C before we corrected it as a class to option D. This led to a good class discussion about number sense centered about the following question: How could we tell how big or small a number is when it’s less than zero? We determined that the number of zeroes and places after the decimal point is a good marker, since the more zeroes there are the further away the number is from zero, which means it’s smaller. Students used this understanding to correctly answer the next problem. PARCC Problems Involving Scientific Notation