Math Blog 7: Patterning and Algebraic Thinking

What is Algebra?

Algebra involves a generalized thinking about relationships and number change. According to our understanding this becomes a natural process when students are ready to move from pattering to algebra. In general is said to be more about determining any terms or variables.

What is a variable?

The idea is that we teach our students to represent the mathematical relationships, and analyze the change thats occurred within them. Symbols are used to represent the unknown as specified in the video above, and students must learn to interpret expressions, and formulas. A formula is a special algebraic equation that shows a relationship between two, or more different quantities.
IE 3n+7n=10n

How to approach teaching these sorts of questions came up in the classroom and a set of helpful hints were given:

•  Use soft language:  Find two fractions that are almost but not quite equal to each other 
• Ask true or false questions: Mike says 1/3 is halfway between 1/4 and 1/2 because 3 is halfway between 2 and 4 is Mike right? 
• Ask effective questions
• Make them real
• Use open ended questions 
• Set the stage ( orient students to understand and provide the opportunity to reveal their ideas. Orient them to deal with the process and the math context 
• Encourage collaborative work by not providing all the anwsers 
• Collaborating what they've learn't, and how they got the results 

I enjoyed learning about setting up proposed questions I think this layout will be useful throughout my teaching block. Open ended questions push students further to explore the proposed problem and understand the experience further. In most cases they can begin at a level they feel comfortable addressing the variables they believe they need to solve the equation given.

With this in mind I enjoyed Adri's math lesson as it provided multi outlets for understanding the basic principles of algebra. If the student didn't quite graph the ideas of using the letter variables like "n," they also had to opportunity to recreate the pattern with the Q-tips provided. This tactical element is really useful when working with students who exhibit learning disabilities, or are visual learners.

The link below is also a great resource I used to further explain algebraic thinking. I enjoy it because it addresses all grade levels, and its very visual for those visual learners. 

http://thinkmath.edc.org/resource/algebraic-thinking