About this text:
Summary:
This is a print blog post by a group of students from IIT Madras (the Indian Institute of Technology Madras – a public engineering and research institution in India) working under the NSSIITM (a group working on projects dedicated to the education and service of others). They present and explain numerous sequences and series that are some of the most wellknown number sets in mathematics. They begin explaining what the Fibonacci numbers are (the most famous set of the list presented). They then discuss where we see terms of this number sequence in nature and its connections to the Golden Ratio. They also mention some of the interesting mathematical properties the Fibonacci Numbers display. The next sequences they explain are the Figurate Number Sequences, Lazy Caterer’s Sequence, Magic Square Series, Catalan Number Series, and the Look and Say Sequence. They end mentioning some special series in other fields outside of mathematics; however, they do not explain these at all.
Complexity:
First, this text is at about an eleventh grade reading level. Second, the writing style of this text is more relaxed and informal. It is not written in a narrative format, but it is written towards high school students. There are pictures or diagrams to represent the number sequence being explained which helps bring the complexity of the text down. Also, the writers always write out the sequence along with showing the summation notation for the series, also keeping the complexity down. The series are shown in two different ways. Also, the structure of the text makes it very easy to follow. The different sequences and series are clearly separated and the introduction paragraph sets the reader up nicely for the text to follow. There is also a lot of white space so the reading isn’t so dense and difficult to read. All of these things bring the complexity down. Third, the reader does have to have a decent amount of prior knowledge to understand this text. They must understand sequences and series, what they are and how they are set up/shown, and some general areas of study in math. This definitely makes the text more complex. The topics covered are very interesting though and something students can easily see so their motivation to read the text and curiosity will be high making the complexity low.
Citation:
IIT Madras. “Famous Mathematical Sequences and Series.” Web blog post. EduBlog. NSSIITM, 16 Apr. 2013. Web. 24 July 2014. <http://edublognss.wordpress.com/2013/04/16/famousmathematicalsequencesandseries/>.
Context to use this text in:
This text would be used for high school algebra I or II students. Therefore, depending on the student, the reader could be anywhere from a ninth through twelfth grade student.
Within the curriculum of algebra, there is always a chapter or part of a chapter devoted to learning sequences and series. Textbooks typically cover what they are, the different mathematical representations of them, how to go between these different representations, and some simple, justscratchingthesurface real world examples. This text would then be explored at the end of this chapter or sections within the chapter, possibly even after the formal assessment on the entire chapter. Hypothetically, I would devote a day to wrap up this concept and make sense of why it is included in our curriculum because it always seemed to me as if it were an afterthought or even “filler” concept. We would take a day as a class to explore the applications and importance of sequences and series outside of the classroom and in the real world. The day following reading this text would include any last comments or questions on this topic and we would begin our next chapter or unit of exploration in the curriculum.
Guiding questions to establish purpose for this text:
What are the sets of numbers being discussed? What is the rule between terms for each of these sets of numbers? Why are they, and sequences and series in general, important?
Lesson plan for this text:

What teachers do … 
What students do … 
Before Reading Text 
Introduce TED talk video Click here to view this video!


Play TED talk video 
Students will observe the TED talk video and write down three places they’ve observed the Fibonacci Sequence (two can be from the video). Be specific! 

Introduce “Nature by Numbers” Click here to view this video!



Play “Nature by Numbers” video 
Students will observe “Nature by Numbers” thinking about the magnitude of this sequence of numbers. There is no real activity here. It is more of a “wow” moment for the students. 

Introduce Vocabulary Activity



Circulate the room while the students are working, looking for large ideas the students are missing, misconceptions, or if they have questions. 


Lead the class in a whole class discussion on any last questions or concepts they are unsure about. The objective is for all students to have some understanding now of all the terms by pooling everyone’s knowledge. 
Students will ask questions about the last terms that were still confusing to the students even after their group conversations. 

Introduce the Text

Students will preview the reading and guide with the teacher. 

While Reading Text 
Circulate the room while students are reading looking for large ideas students are missing in the reading and so students can ask questions if they have them quietly. 
Students will read the text while filling in the reading chart. 
After Reading Text 
Circulate the room while discussing with partners listening for large misconceptions and answering student’s questions when needed. 
Students will discuss the chart with a partner focusing on the following two questions:

Have a couple students share out their responses as one large group (the whole class) and clear up any misconceptions or questions. 
Students will share out to the whole class their responses to the pair and share. 

Give Admit Slip for the next day


Possible Extension: Have students create their own sequence based on a pattern they encounter on a regular basis. Describe the pattern and where it is found. Then, represent this pattern as a sequence of numbers and describe the rule governing the sequence.
Citations:
Benjamin, Arthur. “The magic of Fibonacci numbers.” TEDGlobal 2013. TED Conferences, LLC. June 2013. Conference Presentation.
IIT Madras. “Famous Mathematical Sequences and Series.” Web blog post. EduBlog. NSSIITM, 16 Apr. 2013. Web. 24 July 2014. <http://edublognss.wordpress.com/2013/04/16/famousmathematicalsequencesandseries/>.
Vila, Cristobal. Eterea. Web. 30 July, 2014.