Extending the Use of Exponents Part I
Lesson 9 of 10
Objective: SWBAT extend their understanding of previously learned rules of exponents by completing a real-world task.
As is typical for a Wednesday, the usual 5 minute warm-up activity is replaced by a 15 minute CI (Continuous Improvement) Quiz #5 (See my Strategies Folder for a full explanation). The quiz, which includes 10 questions over random standards that will be taught over the year, helps students see academic progress each week as we plot our performance and reflect on our learning.
Once the fifteen minutes allotted for the CI Quiz has elapsed, I collect the answer sheets from students and quickly go over the answers. While some teachers allow students to grade their own quizzes, I find I get much more accurate data if I do it. However, I do want students to know what they missed, so I take the time to gov over each question and answer. I then distribute the previous week's graded answer sheets to students so they can graph the results from Week#4 in their CI data folders.
The unit lessons to this point have been scaffolded to prepare students for this task from Illustrative Mathematics. The task requires students to look for and apply patterns in bacterial growth over time.
Because the majority of my students have had little or no experience with performance tasks, I felt the need to preview the activity in preparation for the work that would come the following day. To do so, I shared, via the smartboard, the activity's scenario and revealed the table students would be using.
I wanted to ensure students understood the scenario, so I showed a brief (1:47) video about growing bacteria (How To Grow Bacteria.mp4). This video provided essential visual cues for my English language learners as well as for any of my students who may not have had previous experience from which to draw.
After the video, we returned to the scenario. Making connections to the video, I guided students to complete the table entries for 1, 2, 3 and 4 hours. I asked what patterns they noticed. I then asked students to talk in their groups about how many bacteria would have been in the petri dish an hour before the experiment began. I selected one group to give their answer and explain their thinking. Their spokesperson was able to explain that if the bacteria doubled every hour, then an hour before, there would have been half as many bacteria.
I asked how we should represent this data in the table. One student suggested using -1 for the time since it was an hour before the experiment began. I then asked what number would we use to represent the number of bacteria. Another student answered, "1000". This was a misconception I expected, so I asked, "So I will write 1000 under the -1 in the table?" The student immediately saw his mistake (since the table was scaled in thousands) and said, "No, just write a 1."
I then asked, "How will we represent the number of bacteria two hours before the experiment started?" Several students responded, "One-half." I asked one of them to explain their thinking. She explained, "There would be 500, since half of 1000 is 500. But since the table is in thousands, you have to use a fraction." I asked students to give a "thumbs up"if they understood and agreed with their peer's thinking. The majority of students showed agreement, so I was confident I had provided enough support for students to work on the full task the following day.
In closing, I explained to students that they would be completing the activity with their tablemates the following day. For practice halving numbers, I orally gave each student a number and asked him/her to halve it in order to leave the room. For struggling students, I gave round, even numbers like 800. For my more adept students, I gave messier numbers like 246 and 99.