Creating an algebraic expression through patterns

In today's class we learned about using different algebraic expressions to describe patterns. When I was in school I had never been taught that we could use algebraic expressions to model rules for patterns and vice versa--I never knew there was a relationship between the too! After today's lesson, I was really in awe that by drawing out patterns I would be able to not only create an algebraic expression, but also understand algebraic expression. Often times when we see an expression such as this: 3x+2; many students are taken aback and if given numbers can actually come up with an answer. However, many students may not be able to explain what each number stands for and how it applies to real life. The same thing can be said about patterns; most students are able to recognize patterns, but may not know that patterns are connected to other mathematical concepts or real life. After discovering that there is in fact a relation between patterns and algebraic expression I decided to create a math problem that can demonstrate this relation.

Problem: Zola is baking cookies for a school bake sale. Now, Zola has never made cookies so, for her first batch she starts off with 3 cookies and then after seeing that they turned out AMAZING! She continues adding cookies to each of her batches. If Zola's 1st batch is 3 cookies, how many cookies will she have on her 25th batch? Formulate an algebraic expression using this model or develop another way to solve.

Questions to consider: How many cookies remain consistent? How many cookies does each batch increase by?

                                                                       Potential Algebraic Expression

25th batch= n+2

                 =25 +2

                 =27 cookies 

Now after her 25th batch, Zola is realizing that the process she has chosen is taking her twice as long to create enough cookies for her class. She needs to make at least 2,000 cookies for her school!!! So, she decided to change her system, she decided that for her first batch she would increase the amount of trays she puts in the oven--instead of 1 she will put 3. Each tray can hold up to 12 cookies. How many batches would Zola have to go through to get to 2,000 cookies?

Questions to consider: How many cookies do all trays have together? (12+12+12=36)

So first batch will have 36 cookies.

Batch	Number of Cookies
1	36
2	72
3	108
4	?

Potential algebraic expression: 36 + n 

So each batch of cookies increased by 36 cookies. 

Concluding thoughts: 

I have concluded from the lesson and through creating my own problem that visualizing algebraic expressions is very important for students because by doing this students are better able to understand  not only the components of an algebraic expression, but it allows students to understand patterns and allow students to extend their algebraic reasoning skills.