Assignment 4 - Unit Plan

EDCP342A  2010

Unit Planning Assignment (Assignment 4) Introduction

Due Fri. Dec. 10, 2010 (hand in electronically on your blog)

Donna Braaten

The overview of the unit topic (Sequences and Series - Math 12) is included below.  The links for the Unit Chart Overview, 3 Lessons (tabbed in an Excel spreadsheet) and Project Description are listed at the bottom of this post. 

Topic of the Unit

     The topic of the unit is Sequences and Series.  This topic is included in the curriculum as series are used throughout physics and in business calculations.  Understanding sequences is a prerequisite to understanding series.  Sequences and series are found throughout nature and help to predict what will happen in the future.  The learning I hope for my students is to understand and appreciate the inclusion of patterns and sequences in nature, music and business.  My hope is that they find it rewarding to recognize a pattern, express the pattern and then use it to predict what will happen next.  I also want for them to learn about several famous sequences and series, their discoverers, origins and uses such as Fibonacci Sequence, Harmonic and Taylor Series.  I think what makes this topic so interesting is its mystery, such as really considering what an infinite series really means or how recursion goes on and on.  It is mysterious but is also used to predict very concrete, practical numbers such as calculating the payments on a loan or the profit on an investment.  Discovering patterns is a way to make sense of the world.

Breakdown of Unit into Lessons and Projects

     I will start the Unit by introducing the students to patterns and rules.  They will learn and practice how to recognize a pattern in a list of items.  As it could be difficult to get lost in the topic, I will provide a roadmap to the unit in the first lesson.  This will provide navigation to the students to understand what they have learned and what is coming next.  The actual list of ten lessons will consist of:

1.     Getting Started with Patterns

2.     Sequences

3.     Arithmetic Sequences & Series

4.     Geometric Sequences

5.     Compound Interest

6.     Geometric Series

7.     Project Presentations Day

8.     Infinite Geometric Series

9.     Other Infinite Series

10.  Technology

     After understanding the importance and enjoying the satisfaction of recognizing patterns, the students will learn about famous sequences and series and their significance in many areas of life such as nature, business and music.

I will then focus on Arithmetic Sequences and Series followed by Geometric Sequence and Series.  Once they understand Geometric Sequences, I will have them apply this to calculating compound interest for loans and investments using current bank rates.

     We will then learn about more famous sequences and series though peer presentations.  I will follow this up with the introduction to Infinite Series and have them ponder such complex terms as zero and infinity.  I will end the unit with a focus on technology to show how spreadsheet applications can help detect, manage and manipulate series.

Pedagogy of the Unit

     In order to encourage students’ active participation, I will keep the momentum throughout the unit by employing interesting hooks as well as applying Daily Points.  Daily Points are a quick review exercise that not only reinforces the topic but also lets the students see the immediate benefit of doing the assigned homework.

     The introduction of a project will also help the students connect complex topics to actual people (the discoverers) and practical examples.  The created posters will remain on the wall as a constant reminder that there are people and applications behind patterns and formulae.  I will introduce financial terms as part of understanding compound interest to appeal to those who are more business oriented.  I will also express patterns found in nature and/or music for those who are more interested in the nature and the arts.  Lastly, I will utilize technology as many concepts can be reinforced through the use of a spreadsheet application.

Assessment and Evaluation

     In order to obtain a well-rounded assessment, many forms of review will be used which are both formative and summative. Formative assessment for this lesson will consist of the following:

· Teacher Observation during the introduction exercises to see if students are getting the main concepts and to understand where the trouble spots may be.

· Use Open-Response questions during the start of any new topic during the Teacher-directed instruction.

· Check student work during the in class activity to check student progress.

     Summative/End of Lesson Assessment will be based on:

·  Teacher Observation during the introduction exercises to see if students are getting the main concepts and to understand where the trouble spots may be.

·  Formal-Written evaluation - students will demonstrate their knowledge by successfully completing a unit test after all lessons in the unit are completed.

·  Authentic Assessment - students will demonstrate their connection to real world context by successfully completing a math project based on a prescribed rubric.

     Lastly as a mixture of both formative and summative, I will introduce the concept of Daily Points in which I will ask the students to complete 3-5 problems at the start of each class that is reflective of the homework.  One of the problems will be directly from the homework and they will be able to use their notes.  This will allow me to see how well they are grasping the new concepts while letting the students know that doing their homework is valued.

Additional files:

Unit Plan Chart: 
https://docs.google.com/document/d/1gqYIaoiYCsL-w0_JiQzUNzCjZaosN165B6rMWRYgNSk/edit?hl=en&authkey=CIzj8vsF

3 Lesson Plans (sheets are tabbed at bottom):
https://spreadsheets.google.com/ccc?key=0AnL6aYoFt33fdDQ1NW9HZkxIQVg3V1FNQ2dKRTRRZ1E&hl=en&authkey=CPzinvYO

Project Plan:
https://docs.google.com/document/d/1yMI0siWsEL_H7cwHgw1fwg3QVqzN6DNw5Of5uG_RcA4/edit?hl=en&authkey=CKeMnfIK


Unit Plan Overview (posted here):
https://docs.google.com/document/d/1QFuF-E5oKIXo8jnbUwxb5xX9RTccFWrpL9OYmWHZVAI/edit?hl=en&authkey=CKTNjvIK