PLANNING
I teach a food protection course for Intermediate/Advanced ESOL students who want to be food handlers. I prepare them by teaching food protection vocabulary used for the course. I also teach them English language reading, writing, speaking, and listening. At the end of the term, food protection instructors from Kingsborough Community College train my students for about one week, then students take the food protection certification examinations. If they pass, they get the food protection license which allows them to start a food business in New York or work as supervisors/managers in food establishments. One of our students’ goals is to pass the certification test. They can also choose to continue with their studies and take High School Equivalency preparation classes.
With this problem, I wanted to integrate math instruction with food safety. The math problem is about Escherichia coli (E. coli), a type of bacteria, which is one of the topics covered in the Food Handler Course my students are taking. The presence of microorganisms in foods has caused many to be sick. Students taking the Food Handler Course are taught how to protect their customers from eating foods contaminated by microorganisms. In this problem, my students saw firsthand how the E. Coli bacteria multiplies. They noted reasons why a food worker does his or her best to prevent the multiplication of bacteria in the food we eat.
ANTICIPATING STUDENT RESPONSES
I expected that students might confuse the minutes place with the second place 00:00:00 – hour:minute:second. I had to clarify that the population of E. coli, during binary fusion, doubles every 20 minutes instead of every 20 seconds. We see the minutes and hours change and the seconds remain static.
I also anticipated conversion problems. As the multiplication time for E. coli accumulates, when do you round off to the hour? I explained that once the minute column gets up to 60 minutes (example: 00:40:00 + 20 minutes), it rounds off to one hour. I advised students to eave nothing in the minute column and write 1 (one) in the hour column. They should have in mind that 60 minutes equals 1 hour. Instead of writing 60 minutes, they should write 1 hour in the hour column.
HOW I SOLVED THE PROBLEM
I drew a line down the middle of a piece of paper and doubled E. coli bacteria numbers in increments of 20 minutes. I continued in that pattern until I got to 5 hours.
| TIME INCREMENT | NUMBER OF E. COLI |
| 00:00:00 | 1 |
| 00:20:00 | 1 x 2 = 2 |
| 00:40:00 | 2 x 2 = 4 |
| 01:00:00 | 4 x 2 = 8 |
| 01:20:00 | 8 x 2 = 16 |
| 01:40:00 | 16 x 2 = 32 |
| 02:00:00 | 32 x 2 = 64 |
| 02:20:00 | 64 x 2 = 128 |
| 02:40:00 | 128 x 2 = 256 |
| 03:00:00 | 256 x 2 = 512 |
| 03:20:00 | 512 x 2 = 1,024 |
| 03:40:00 | 1,024 x 2 = 2,048 |
| 04:00:00 | 2,048 x 2 = 4,096 |
| 04:20:00 | 4,096 x 2 = 8,192 |
| 04:40:00 | 8,192 x 2 = 16,384 |
| 05:00:00 | 16,384 x 2 = 32,768 |
INTRODUCING THE PROBLEM
To introduce the problem, I showed students a picture of how E. coli grows and I asked students what they noticed and what questions they had.
Notice/Wonder
Among other things, my students noticed that the number of E. coli bacteria doubles every 20 minutes and that the number of increases grows as when their numbers increase.
Sketch the next image
I then asked students to imagine taking a photo after another 20 minutes. What would they see?
Here are some examples of the sketches students made:
Pose the question
After students noticed, wondered, and drew the next photo, I posed the following question to the group:
Looking at the picture of E. coli growth, how many can you count after 5 hours?
In solving the problem, I wanted my students to show how they got their answers. I expected to see different methods of arriving at the answers.
STUDENT WORK
Hibah’s Approach
Hibah approached the question by orderly writing out the multiplication of E. coli in the increments of 20 minutes. Her starting point was 00:00:00 with one E. coli. As minutes increased, the number of E. coli doubled.
Omima’s Approach
At the far left of Omima’s work, she was just writing the 20 minutes increment as the same figure 20:00. She doubled the numbers of E. coli every 20 minutes before arriving at her answer.
Yris’ Approach
Yris noted that at 00:00:00, there is only one E. coli. She noted the doubling of E. Coli after every 20 minutes, then she multiplied by 2 to get the next number of E. coli. It landed her at the right figure.
READING FOR MORE INFORMATION
After they solved the math problem, I gave students a WebMD article on E. coli bacteria with reading comprehension questions. By reading the article, students familiarized themselves with E. coli bacteria and how they reproduce by multiplying.
LESSON PLAN
The materials used in the lesson were from the following lesson plan, written by Eric Appleton:
Bacteria population growth lesson plan
The lesson includes the notice/wonder and other handouts, links to readings, and a practice test question, among other resources.
POSTSCRIPT
Omima Ali, whose was a student in this class, was featured in the New York Times on October 13, 2022 in the story, With Job Skills Support, ‘I Feel Like I Want to Fly.’
