This post is the sequence of instruction with work examples from a STEM Santa FE Camp held on January 28, 2021. The students are 7th and 8th graders enrolled in a summer program following a year of primarily on-line instruction.
The Answer is 4. This activity is a great introduction and also will give an instructor some idea of the student’s experience with translating math problems into different formats. The students will be asked to provide 3 kinds of representations, number, picture and word.:
1) Write a mathematics statement that gives the answer. 2) Draw a picture. 3) Write some words.
These student examples are hard to see because they are written on paper towels, but they show great work nonetheless.
We can several ways to get 4 in each, a picture and a word problem. Students share out their ideas setting a process we will use several times over the course of the lesson.
Engage: Observe a pooled test demonstration where 3 samples are put into two pools which are then tested. Draw a diagram of the pooled test:
Explore: Students use their diagrams to repeat the test. Students practiced with the pipettes and water, finally loading two vials with water and closing the tops. We gave them a vinegar vial and they mixed the three so that they did not know which was which. After making the pools, students test them with pH strips.
Next we discussed the results of the lab work – in our experiments which pools were positive? What are all the possible outcomes with one positive among the 3? (see left slide below). Now lets consider what pools we could get if we didn’t know how many positives in the group so they could range from 0 to 3. Students then got to do the experiment one more time when they did not know how many positives were in the group. Following the experiments, we looked at the range of possible sample conditions and pools. (see slide on right)
An interesting strategy mentioned by a student when he and his partner got 2 positive pools when the number of positive samples is unknown. He said that he and his partner wanted to test the middle sample first. If it was water, they would know that the left and right samples were vinegar because the two pools were vinegar.
With all this experience we reviewed the history of pooled testing and watched a speeded up video we made of the Dorfman method where 25 samples are tested for 10 pH strips. Students asked to watch this a second time.
With not much time left we looked at a slide that shows a line backed up at a lab. The final inquiry was open ended. We are a group of 16 people. If we want to test our group or one of similar size what could be a good strategy? Put one or two positives in the group. We were really impressed with the student work at the end. All the teams wanted to present their ideas. Examples below.