Arithmetic Sequences
2020.09.30 10:57 am - 11:40 am
Teaching point: How do we use the term formula for an arithmetic sequence?
Agenda
Agenda
Do now (5 minutes)
Do now (5 minutes)
Intro to Sequences Mini Lesson (15-20 minutes)
Intro to Sequences Mini Lesson (15-20 minutes)
TOK Connection (10 minutes)
TOK Connection (10 minutes)
Exit Ticket (5 minutes)
Exit Ticket (5 minutes)
Intro to Sequences
Intro to Sequences
Patterns are everywhere in the world around you – in the distribution of petals on a flower, the position of cracks in dried mud, or the wind-shaped crests of sand on the beach. Patterns are powerful because they allow for prediction and are visually beautiful.
Patterns are everywhere in the world around you – in the distribution of petals on a flower, the position of cracks in dried mud, or the wind-shaped crests of sand on the beach. Patterns are powerful because they allow for prediction and are visually beautiful.
A sequence is a list of numbers that follows a pattern. It may be as simple as a list of positive integers
A sequence is a list of numbers that follows a pattern. It may be as simple as a list of positive integers
1,2,3,4,5,… or more complex such as 0,1,1,2,3,5,8,13,21,34,…
1,2,3,4,5,… or more complex such as 0,1,1,2,3,5,8,13,21,34,…
The second sequence is a well-known sequence called the Fibonacci sequence, which is related to the Golden Ratio and models the patterns of the spirals in the nautilus shells.
The second sequence is a well-known sequence called the Fibonacci sequence, which is related to the Golden Ratio and models the patterns of the spirals in the nautilus shells.
TOK Connection
TOK Connection
As seen in the magnificent video by ViHart, the Fibonacci sequence is frequently occurring in nature. Observations like this have led to the knowledge question, ‘Does mathematics exist independent of human construction?’
As seen in the magnificent video by ViHart, the Fibonacci sequence is frequently occurring in nature. Observations like this have led to the knowledge question, ‘Does mathematics exist independent of human construction?’
In short, is mathematics ‘out there’ serving as the foundational fabric holding together our very elegant universe? Or alternatively, is mathematics created by humans in the same way that we have created language?
In short, is mathematics ‘out there’ serving as the foundational fabric holding together our very elegant universe? Or alternatively, is mathematics created by humans in the same way that we have created language?
These two competing views are referred to as, Platonism – the belief that mathematics exists independent of humanity and Formalism – the belief that mathematics is created by humanity.
These two competing views are referred to as, Platonism – the belief that mathematics exists independent of humanity and Formalism – the belief that mathematics is created by humanity.
Discuss arguments in favor of both Formalism and Platonism.
Discuss arguments in favor of both Formalism and Platonism.
Exit Ticket
Exit Ticket
Click below for your exit ticket. It must be finished before you leave. It will not be available after class.