Updates on TJ Admission – 2018

Appendix A

Sample Mathematical/Scientific thinking questions.

1. A scientific team is interested in conducting a study on whether eating jelly beans causes pimples. You are invited to participate in how the study is designed. What would you suggest? Be sure to indicate what data you would collect. Why do you think the data you collect will allow the scientific team to assess the role of jelly beans in the formation of acne?

2. A group of scientists travels to a recently discovered isolated island where there are some strange mammals that eat different amounts according to the weather. They acquire the following data:

(enter a table of data including how much they ate of bananas, grass, and tree nuts and the weather, every day for 30 days… The data would vary in interesting ways, not always consistently)

Do you think that weather is impacting the food patterns in predictable ways? What steps would you take to validate your belief?

(Note: this could be interpreted to be mathematical, i.e. do something with the data, or scientific, i.e. maybe someone would collect more data and explain how).

3. A child doodles the following crazy figure, and then asks you to calculate its area. How would you try to approximate it?

(enter a figure that has lots of rounded parts, i.e. not something that could easily be seen to be a circle or something, but would require some approximation by other figures. The figure could also contain some repeated pieces that get smaller and smaller, to see if a student thinks iteratively).

4. A strong medication for a new and dangerous disease has some side effects: too low a dose makes the medication not very effective against the disease, and too strong a dose makes the medication effective but patients risk severe side effects. Twenty adult, male patients with similar weights were included in a study intended to find the ideal dose, and their results are recorded below. How would you go about studying the ideal dose of the medication using mathematics?

(Students could be provided with some data about disease measurements and side- effect measurements, or some charts of data, and see if the kids are able to come up with models using quadratic functions, or estimate using local linear estimators…. kids may do quite creative things!)