LESSON PLAN – INTRODUCTION TO SEQUENCES
Lesson Overview
This microteaching session is designed to introduce the concept of sequences in mathematics and its possible applications.
Duration
15 minutes
Materials and Equipment Needed for this Lesson
White board, markers & TCs’ cell phone(s)
Lesson Stages
1. Warm-up (2 minutes)
- Background
- In-real life examples: paychecks; as you work more hours, you get paid more.
- Brief Introduction
- Definitions and differences between set, sequence, and series
- Set is a collection of numbers
- Sequence is a set, but with order
- Series is the summation of all the terms in a sequence
- Today we are focused on arithmetic sequences/series
- Arithmetic sequence is a sequence where the difference between consecutive terms is constant
- Arithmetic series is the summation of a finite arithmetic sequence
2. Presentation (3 minutes)
- General Form
- an=a1+d(n-1)
- an=ak+d(n-k)
- Examples
- 2, 5, 8, 11, …:
an=2+3(n-1) - 31, 26, 21, 16, …:
an=31+(-5)(n-1) - Applications
- Linear relations
- Fibonacci sequence
- 1,1,2,3,5,8,13,...
- an=an-1+an-2
3. Extension (5 minutes)
- Extension: arithmetic sum
- History of Gauss
- Computing the sum from 1 to 100 for a punishment in primary school.
- General form:
Sn=n(a1+an)2
Sn=n(2a1+(n-1)d)2 - Orange equation is used when we know the total number of terms, first term, and the last term.
- Green equation is used when we know the total number of terms, first term and the common difference of successive members.
- Extension: averages: μ=Snn= a1+an2
4. In-class activity (5 minutes)
- Fibonacci sequence “mathic”
- Ask a volunteer to pick two numbers between 100 to 200
- Once he/she list their own Fibonacci sequence up until 10th term, allow him/her to use a cellphone to find the sum.
- While he/she types all the numbers on the phone, find the sum quickly before him/her.
- Compare answers!
- If time allows, ask another volunteer.
- Explain the trick!
5. Evaluation (5 minutes)
Hi David, Hugo and Jackson. Thanks for this lesson plan for today's micro teaching! Here are some comments that you will want to consider either before or after today's lesson (depending on your timetable today):
ReplyDelete(1) You should include a number of facts you've left out: a) who is in your teaching group, b) what grade and course is this for, c) what are the connections to the BC secondary math curriculum (competencies, big ideas, objectives, etc.) These are expected for every lesson plan, certainly including those you share with your SA on practicum!
(2) The presentation seems to be simply 'giving' students a bunch of equations without much meaning attached, and asking them to plug in numbers. The extension has more exploration, story and perhaps a bit of inquiry involved.
I HIGHLY suggest switching these two sections -- starting with the 'extension' activities, and then (if still necessary) going to the 'presentation'. Note that simply giving a list of 'plug-and-chug' equations without students having any sense what they signify is not recommended as a way to promote understanding; with good short-term memory, people can memorize the formulas, but they are not a long-lasting, meaningful kind of learning in themselves. Giving priority to meaning-making is generally a good idea, and if you are going to start by giving formulas (to promote computational fluency, for example), don't wait too long before you offer learning activities to help kids make sense of them.
I'm interested to see how the Fibonacci activity works out!
Cheers
Susan