Lesson 1


LESSON 1.  The Need for Mathematics


Objective: Students look at how observations can lead to classic mathematical formulas




Teacher Notes:


Equations are important in solving problems in science and engineering.  We solve formulas all the time without realizing it from figuring out interest on money in the bank to figuring how much money you have left after purchasing items from a store.   Use the following examples to find a formula with your students. 


There are 2 meters of water in a pond before the beginning of the rainy season.  The pond is connected to the storm drain system and adds 3 cm per hour in a normal storm.  Can you create an equation to help determine the depth of the water after 6 hours? 


First you need to make sure all the units are the same, so convert 2 meters to 200 cm.  The equations would look like: y=3x +200

(y is the final depth; x = number of hours of rain and 200 refers to 200 initial depth)  for 6 hours: y=3(6) + 200 = 218 cm after the first 6 hours


Now discuss with students what is wrong with the formula.  It does not take into consideration that the amount of rainfall changes.  It is very unlikely that the amount of rain per hour would be the same.  But then, it is a good guess.  In order to make simple formulas to work you have to assume constant rates.  Life however, does not work that way, and scientists and mathematicians then have to add all the other variations to make a formula true. 

Students should read the text and then answer the questions on the worksheet.  You may want to have a discussion of whether math was invented or discovered.  There is really no correct answer, just how students justify their answer.  This unit is for students to think about math as dynamic and changing.





1. Formulas are developed from data that mathematicians, scientists or engineers called; they find a pattern   2.  up to the students remarks;  3.  rules and properties;  4.  the followers of the philosophy of Pythagoras;  5.  a2+b2= c2 (Pythagorean Theorem) 6. flat world vs spherical world;  7.    8.  Nonlinear i.e. calculus; 9. disordered10. 



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