Superlesson
Project 1-2
Geometry
Chapter 1, Visual Thinking and Mathematical
Models
Logic and reasoning are important skills in mathematics and in life. Knowing how to reason will help you to find the answers to many questions, even if you don't have all the information you need to figure out the answer directly. Learn how scientists use logic and reasoning on the Internet.
Part A, Inductive Reasoning
1. Learn how bacteria grow at the Cells alive site.
a. According to the site, how long does it take for one cell to split into 2 cells?
b. If you start with two cells, make a table showing the number of cells you will have after 0, 20, 40, 60, 80, 100, 120, and 140 minutes.
c. Use inductive reasoning to determine the number of cells after 4 hours.
d. Find a formula that relates n, the number of cells, to t, the number of 20-minute time periods that have passed.
e. Do you think this growth can continue indefinitely? Explain why or give some potential problems with it.
Part B, The Language of Logic
2. Learn how penicillin kills bacteria at the Cells alive site.
a. Complete the statement below:
All bacteria are killed by __________.
b. Describe a counter example to your statement in a.c. For the statement "All X are Y," if you find only one X that is not Y, have you proved the statement to be false?
d. If not all bacteria were killed by penicillin, how could you rewrite the statement in a to make it true?
3. Read about some of the different places that bacteria and other organisms have been found in the Why Files. Use the information you find here to write three statements using the terms all, some, and none.