Unit Plan - Math 9: Polynomials

Unit Plan

Lesson Plan 1

Lesson Plan 2

Lesson Plan 3

Project

Write up

Reflection on Group Micro-Teaching

I found this lesson to be a really relaxing and enjoyable experience. I went in with nothing but a piece of string; I had no notes to rely on and I felt more confident than I had before any other presentation or teaching experience, which was interesting and surprising to me. The lesson went well, included a mix of history, applications and technology as well as theory, and I didn't forget anything!

The feedback we received was, on the whole, very positive. The major concern that people had was that there was not enough time for the peer lessons and many would have preferred to learn all the mini lessons first-hand. There seemed to be a general feeling of being left out. I thus propose the following changes: Firstly, more time would be allowed at each station. Secondly, each student would rotate through all three stations, I would thus change the work to be done in the triads. Each triad member would take turns to share three things they learned during the lesson with their two peers, each student must share different things than already mentioned by their peers.

This was a successful lesson which, with some modifications, I would definitely use in my future classroom.

Review of a "bad" Word Problem

"Mrs. Phillpott is a cook for the Thornberry family. She usually makes a 5 pound roast for dinner on Thursdays. She knows that it takes 2 1/2 hours to cook this roast. Her boss is having a dinner party and she needs to make more food. She decides that she needs 15 pounds of meat. The problem is that she only has one oven and it will not hold a roast bigger than 10 pounds. How could she solve this problem? Answer in paragraph form."

http://fi.edu/school/math2/nov.html

I have a few issues with this problem. Firstly it is not very relatable, how many student's families will have cooks?! It also implies the Thornberry family is of a certain social class. They have a 5 pound roast every week and host a dinner party for which they require 15 pounds of meat. This may be upsetting for students whose parents struggle financially. 

I also find the wording of this problem terrible for a math problem. It is worded in such a way that no math is necessary. "She cooks her normal 5 pound roast and goes to the grocery store and buys 10 pounds of cold roast" would be a perfectly correct answer based on what is given. The problem states that she requires more "food" and she decides she needs "15 pounds of meat", at no point does it specify the oven must be used or that the meat must be a roast, which would make for a more interesting and mathematical problem.

Answering in words rather than numbers and equations is good to get students thinking more deeply but it is not effective when the solution could well be "she goes to the store and buys 15 pounds of tinned meat"!

Presentation of Old & New Projects

This blog post is related to an earlier post entitled "Review of math 9 polyhedra project created by Susan Gerofsky"

Power Point Presentation

New Project - Design a Ski Hill

Reflection on Article - "Creativity, flexibility, adaptivity, and strategy use in mathematics"

This article seems to bring forward more questions than answers. The thing that struck me most upon reading this is how much research still needs to be done. I was shocked that this paper was published only last year and that research in this area is pretty new.

I very much agree that there are discrepancies in the meaning of an 'appropriate method', different methods will be appropriate when different criteria is taken into account. Personally I feel that individual characteristics is an important element to consider. We are all individuals who learn differently and our methods should be appropriate for us first and foremost. I was thus surprised that the problem solving approach led to such a high instance of incorrect answers. I also agree that whatever strategy is used, the path to success always starts with having a full understanding of the problem.

A remark in this article which stood out to me was regarding intentions. The best of intentions can lead to bad, and unexpected results. As teachers we have to realise the great effect we have on students and to take as many factors into account before making decisions, we have to be especially careful not to pass on any bad habits!

Finally, it is clear that if a general consensus is ever reached as to the best approach, it needs to be implemented in a students' education as early as possible as prior knowledge definitely has an impact.

Review of a math 9 polyhedra project created by Susan Gerofsky

Experience:

Researching the four topics was very interesting although obtaining information for part one was difficult. Also the mathematics involved for some parts is too complicated for a grade nine to understand. No guidance as to the weighting of parts a, b, and c is given which could lead to some groups putting emphasis on the biography and others on the mathematical ideas. Making the origami model was fun for those of us who enjoy art projects; however this task is frustrating for those who do not.

Overall we found this project interesting but dated. There was no relationship with today’s world and we question the value this project has beyond providing interesting facts.

Benefits:

• Students will learn interesting facts through research and from peers rather than their teacher
• History is incorporated into the classroom, enriching the learning experience
• Students will see how mathematical ideas can extend into the arts and architecture, making mathematics seem less isolated as a subject
• Learning about mathematicians, connecting math to real people can spark interest and provide comfort to those who may see the subject as alien
• Allowing students to create and thus touch and experience in real life the Platonic solids allows them to realise their simplicity 

Weaknesses:

• It is unclear as to why some people work with partners and some alone to write the paper
• There are no specifics on whether each person writes about a different part or all contribute to every part, writing an essay with someone else is not easy
• Each person has to make an origami model, time consuming & some students may struggle with this, not beneficial, there needs to be more of a point to making them
• Other than introducing polyhedra and some history the intended learning outcomes of this project are not obvious
• No specifics for what the presentation should look like
• Students may not connect with mathematicians from the past
• The math involved in some sections is too complex for the grade level
• No connections to the lives of the students
• Group work, especially of this nature, is very time consuming

Uses:

• Introducing the class to polyhedra, good start to 3D geometry
• Can be incorporated into volume, or surface area units
• Allowing the class to experience group work and obtain skills in researching
• Incorporating history into the math classroom

Modifications & Extensions:

• Only one student per group makes an origami model, the teacher can bring in the fifth one. They show the template to the other group members before gluing so that all students can see how it is constructed and benefit
• All students should be involved in the research, then two can work together to produce the written work, one can present and one can make the model so that everyone contributes, if they want to change that they can but they must inform the teacher of their roles
• Find modern day uses for polyhedral, compare with historical
• Research more than one of the areas or people then groups can compare
• Presentation only, no essay
• Using paper templates students can cut out all kinds of regular polygons with the same side length, then try to create all kinds of regular 3D objects by gluing the regular polygons together
• Find patterns in the construction of the solids
• Use Geomag for constructing the solids (stick magnets with iron balls, easier and more fun to use than paper and glue)

Cycling Digits

''I have in mind a number which when you remove the units digit and place it at the front, gives the same result as multiplying the original number by 2. Am I telling the truth?''

                                                                                     Thinking Mathematically pg 165