Unit Plan / Lesson Plan / Project Plan

Doing, assessing and designing a math project

Group Member: Darshan, Prem, Rong The project we have chosen from the “Mathematical Magic” book is a variation of the Fibonacci sequence. As we all know, Fibonacci sequence has a lot of amazing properties. This game is a generalization of one of Fibonacci sequence’s property. In this game, some seemly unrelated numbers are actually related. By using mathematical analysis, we can find out the reason behind the magic. Students will be surprised that we can use just one number to predict the sum of the ten numbers. Students will benefit from the game by witness the power of math. However, this game has a lot of addition calculation, which we think is both strength and a weakness. We say it is strength because this gives students a lot of practice in doing addition fast and accurately. The weakness is that if students make only one small mistake, the result will not match the magician’s prediction. Therefore, we think it might be better for the students to play in groups of two. Each student picks one number to play. Luckily, this game can be modified for two students to play at the same time as it needs two numbers to start playing. When they are doing the calculation, one can do the addition and the other can check the calculation result. This will reduce the calculation mistakes to minimum and ensure the game to play smoothly. Another problem to this game is that the calculation time and accuracy will highly depend on the students’ math calculation skills. Therefore, for lower grade or less competent students, it might be better to allow them to use calculators if the game takes too long. The “Read Your Mind” Game The project we have created is for Grade 9 students. A major problem for many grade 9 students is that they regard math as a hard and boring subject. The project is intended to arouse students’ interest in learning math. Math can be challenging. Math can also be fun. In order to understand the theory behind the game, they have to understand polynomial addition, which is closely related to the topic of Ch 5 in “Math Links 9”. Therefore, this game is also a good activity for students to get a deeper understanding of polynomial addition. The detailed activities are described step by step on the poster. We create this game by ourselves. We also reference to the “Math Links 9” textbook and “Mathematical Magic”. The length of the game will take about 10-15 minutes. Students are required to create a key from the chosen number. During the game, the students are needed to take out their pens and paper. They need follow the magician’s guide to produce a key from each chosen secret number. Because this is supposed to be a fun activity for the students to participate, the students will not be marked on their performance. However, for those students who are actively participating in the game and solving the mystery behind it, some bonus marks will be given as a reward.

Solving the Black Friday Problem

My Two Most Memorable Practicum Experience

Biog 11: I did my short practicum at Langley Secondary School. The teachers were very friendly and helpful even if they were not my sponsor teachers. I had a chance to listen to various classes such as drama, home economy, etc. On class that I was especially impressed with was Biology 11. I thought it might be a boring class because students just needed to memorize a lot of stuff to do well. The class was talking about mitosis. After the initial introduction to the topic, the teacher told one interesting story after another in between the lecture. Some of them were related to the Pro-D day he just attended. He talked about the new biological discovery and researches at UBC. He also talked about H1N1 pandemic which was the hot topic. When he went to the sideway of the class, every student turned around. Clearly, everyone was interested. The class finished before I realized it. Math 9: I taught one Math 9 lesson on polynomial addition and subtraction. As I observed the same class before, I notice that the young kids were very active and talkative. How can I use this high energy to my favour? I decided to use a game to gain students interest. The game was called “Guess your Secret Number”, which could be explained by polynomial addition. It asked each student wrote down a number that no one else knew. Then after a few calculations on the secret number, students would tell me their calculation result. By pondering over the result, I would guess what their secret numbers were. After the game started, the students actively participated. At one period of time, the classroom was so quiet because the students were all doing the calculation and trying to play the game.

Comment on Freewriting

By writing on a set period of time freely and continuously, free writing allows me to break all the rules and thinks outside the box. Sometimes, I am amazed at what I have written down, which normally I would not think about or would not dare to try. My conscious mind always guides me “This is not right. That is not the way to go”. It shoots down many ideas before new thoughts being fully developed. Especially during the brain storming stage, I am stuck with ideas I don’t like too much. Hence, free writing is a very useful tool for me to use. However, free writing will inevitably produce a lot of useless information. Sometimes, after pages of writing, I realized I cannot use any of them. Therefore, we need to balance between these two sides of free writing in order to make good use of it.

Division by Zero

Math is The art of rigorous prove The practice of predictability Zero is The origin of undefined outcomes The start of abstraction Ancient people Have one finger to represent 1 Have nine fingers to represent 9 Yet No finger to represent 0 We cannot show 0 by any object in real world Furthermore Any number times 0 The result is an ambiguous 0 Therefore Division by 0 Any result is possible Zero is The defiance of math’s predictability Result? Math cannot let zero do whatever it wants Hence the rule No division by zero

Micro Teaching Reflection

For our teaching of the Pythagorean Theorem, I feel it goes on well over all. It also needs improvement on many areas. We start with a real life application (ladder problem) and ask the students to think about how to solve it. Most feedbacks show that they like the intro/bridge. Some students hope the topic to be more clear and suggested writing the topic on the board after the introduction. Good idea! Then we use visual prop to prove the theorem geometrically. Students, especially visual learners, like it this way because they can see why this theorem is true by themselves. Some students feel the proving part is a little bit rushed. They wish it was discussed more thoroughly. Most students like the game we provided. But some students do not have a chance to fully participate in because we only have one sheet for each group. Next time we need to provide more. Some students notice the discrepancy of policies among three of us: allow using the ruler to measure the triangle or not. We need more communication among us beforehand. We wrap up the teaching with the solution to the ladder problem and summary. Students like the way we finish it. However, they do mention that terms like “orthogonal” needs some explanations.