Chapter 3 Chapter Three:

3.1 Objectives of Chapter Three:

By the end of this day, participants will be able to:

  • Understand some problems used to detect talented and gifted students.
  • Use several strategies for generalization and teaching across setting, individuals, and stimuli.
  • Know learning styles for exceptional students.
  • Apply individual education plan (IEP).
  • Use multiple-intelligence for Gardener for dealing with gifted and talented students and students with certain disabilities.

3.2 German Mathematician: Carl Friedrich Gauss:

the famous German mathematician (Carl Friedrich Gauss) (1777-1855) used special formula to very quickly compute the sum of the integers from 1 to 100. What is remarkable about this is that Gauss was only 7 years old at the time! His schoolteacher gave his class, as an exercise, the assignment to calculate:

1+2+3+—+99+100,

figuring that it would take the students many minutes. The teacher was quite surprised when young Gauss came up with the answer almost immediately! Gauss, even at age 7, recognized that there was a quick way to add consecutive integers, and used the same process that we used to prove.

3.3 Activity 1:

Problem:

  1. Compute the sum l + 2 + 3 + 4 of the first 4 positive integers.

  2. Compute the sum 1 + 2 + 3 + 4 + 5 of the first 5 positive integers.

  3. Compute the sum 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 of the first 10 positive integers.

  4. Find a formula for the sum of the first (n) positive integers. Make sure your formula gives you the sums that you computed in parts (a)-(c).

  5. Compute the sum 1 + 2 + 3 +…………..+ 100 of the first 100 positive integers.

3.4 Activity 2:

Problem:

  1. How can you calculate √2, and what is the meaning of it?

3.5 Activity 3:

Problem:

How can you prove that 𝜋= (3.14) 𝑜𝑟 𝜋= (22/7), and what is the meaning of it?