Contextualization

Notable identities are part of an essential group of mathematical concepts, more precisely in Algebra. These tools are mostly used in the simplification of algebraic expressions, that is, they allow faster calculating involving operations with polynomials. The mastery of those techniques is essential in order to face situations including second degree equations, factorization and polynomials developments, which are frequently used in different mathematical branches and which we will need even more as we progress into more complex levels of the discipline.

This project focuses specifically in notable identities regarding Sum, Difference Squares and the Sum, Difference Cubes. The first concept involves simplifying (a+b)² and (a-b)² type expressions while the second is a formula to develop (a+b)³ and (a-b)³ types of expressions. It is crucial to master those techniques because they are commonly seen in different and more complex problems and mathematics concepts.

As a way to initiate a more flowing knowledge construction, bringing the students practical applications for those concepts is a good strategy. It may be done linking those concepts either to everyday life or to another disciplines. Notable Identities are commonly seen when we need to find out the surface of geometrical figures. Let us think that one needs to paint one's bedroom wall, it will be essential to find out how much paint will be necessary for the task at hand. We have here a simple instance on how Notable Identities may be used very practically.

Additionally, these identities are tightly related to physics, in specific, in what refers to kinetics and dynamic studies. When studying about acceleration for instance, the use of identities allows for a more simplified reading of those equations. Those applications become more evident once the students fully understand those concepts, which will enlarge the possible applications.

To further help students deepen the comprehension of the subject, there are some tools they may use, such as the ones shown in the list below:

1. Khan Academy
2. JustMath
3. Math Planet
4. YouTube – Matematica Zup

Practical Activity

Activity Title: Unveiling the Notable Identities - How about solving a mystery?

Project Goals:

• Comprehending and implementing Notable Identity in order to problem solve in real situations.
• Acquiring socio emotional capabilities, including team work, trouble shooting and time managing.

In-depth Project Description:

The Project will be focused in finding the answer for a “math word puzzle.” Each team will get to see a series of riddles that will need them to understand and implement notable Identities. The solution of each riddle is a step that takes you to the final resolution to this mystery.

The riddles have been created so that the application of notable identity concepts is essential in order to find the answer to each of those puzzles. The way the riddles show themselves, it also sparks the student critical thinking and encourages teamwork.

Required materials:

• Notebook to jot down the calculations and other notes
• Pencil and Eraser.
• List containing riddles
• Calculator (if desired)

In-depth step-by-step Activity Description:

1. Setting Teams Create 3 to 5 members for each of them
2. Beforehand study: Previous to the riddle session, make a revision about Notable Identity Concepts, (difference, Sum Squares and Sum, Difference Cubed) Using the suggested material from this project introduction to further understand them .
3. Riddle Time: The solving for this proposed riddles shall begin, using notable Identities as needed
4. Record Keeping: Each time a riddle has been successfully solved, all that was used in order to get the right response shall be properly written. The act of documenting is paramount for future concept revision, plus it helps when time to make final report arrives. .
5. Mystery Solution Each one the riddles solved leads you closer to solving the mystery. The teams must work and talk to one another so they may reach the ultimate resolution
6. Reporting the findings: The team, now that the mystery is solved shall write an in depth report of how it was solved

Project Submission Details:

• Each Riddle’s Solution each time one riddle gets solved the process must get properly written, with no skipping steps, and well organized .

• Mystery Resolution: Once all of the riddles have been answered correctly, then it's time to show how the mystery got solved.

• Report: This will consist of the report submitted as the project final deliverable. It shall have the following sections:

  1. Introduction: Insert here the Context concerning the Notable identities. How the use of such Identities when it came to solving the puzzles was used. .
  2. Developing the subject : In here the activity must be detailed, meaning, the solving of riddles explained. Also how the group worked together. The obstacles faced, the ways to solve or get around the issues and how it all was done.
  3. Wrapping-up: The team shall report what was learnt regarding both the concept of the notables identities as the set of capabilities acquired in the socio, emotional aspects. It is of paramount significance to state the manner how teamwork was essential for the solving of the puzzle
  4. Bibliography: The team should insert a listing for every single resource used for the understanding the Notable Identity concept. Additionally the resources used in the process of finding a solution for those riddles.