Microteaching !!

Applications of Quadratic Functions

Subject: Math

Grade level: 11

Duration: 15 minutes

Prescribed Learning Outcomes:

 It is expected that students will be able to:

-C4: Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph, including: vertex and to solve problems

-C5. Solve problems that involve quadratic equations

Objectives:

Students will be able to:

-Learn how to analyze and solve real-life problems involving quadratic functions

-Identify the relationships between maximum/minimum problems and quadratic functions

Materials/Resources:

-white boards in the classroom

-Handouts of the word problems

  

Lesson Plan
Introduction	5 minutes	-Divide the class into groups of three -Handout the “hook” question to each group and encourage the students to come up with the dimensions that would enclose the largest area without using algebra A rancher has 800m of fencing to enclose a rectangular cattle pen along a river bank. There is no fencing needed along the river bank. Can you guess which dimensions would enclose the largest area? (HINT: the dimensions are integers)
Entry	5 minutes	-Go over the rancher question on the board, using algebraic method Ask one or two students to  come to the board and present their solutions. Encourage those students that think they've made mistakes. This is to promote mathematical thinking and that mistakes are part of the learning process.
Development	~4 minutes	-Ask the students to work on a similar problem individually You are trying to build a rectangular dog fence in your backyard using 600cm of fencing material. Since your dog is relatively big, you goal is to make a fence with the largest area possible using the given material. What should the dimensions of the fence be?
Closing	1 minute	-Go over the solution together.

Adaptations and Modifications:

-Allow students to work in groups

-Provide more time for work if needed

Assessment/Evaluation:

-Go around the classroom while the students solve the problems together in groups on the board to check their understanding

-Observe the students while they work independently and identify what the most commonly made mistakes are

2-Column Puzzle

Exit Slip - Mon, Nov 23

The video we watched reminds me of Silent Way, one of the methods used to teach pronunciation. It doesn't make sense when we first think about it, as pronunciation is teaching sounds, segmentals, and suprasegmentals that are to be taught by modeling and getting students exposed to the correct models, but it makes perfect sense when we begin to think beyond the surface. I made this link between Math and teaching English pronunciation via Silent Way, as I found the video did exactly that, i.e. the students were well engaged and actively participated without the typical and traditional pencil/paper approach. I look forward to using this approach with slight modifications depending on the topic/subject of course in my classroom.

Moreover, the video demonstrated long pauses when the teacher posed a question. This is something that I think all educators should consider to allow enough thinking time for students to get their cognitive processes working. 

Arbitrary vs. Necessary in the Math Curriculum

This article allows its readers to think about things that we generally tend to ignore under the umbrella of ‘that’s the way it is”, or ‘that’s the convention’, or even ‘true-because-teacher-says-so’. My question if what if I let the students break the convention. For example, what if I let them write the y-coordinate before they write the x-coordinate. Would it be looked upon as breaking the rules, or would it give the students some power or control over Math, I wonder. Moreover, I wouldn’t want to answer ‘the-why’ questions from the students via ‘that’s the convention’. I would like to support their curiosity and get them explore ‘why that’s the way it is’. However, there is a fine line between satisfying curiosity, and exploring for purpose and getting confused, i.e. as an educator, I’d need to be careful for not getting the students confused by sharing too much information and getting them exposed to it without support.

One of the ways for defining arbitrary and necessary is by considering what can/cannot be solved. In other words, ‘arbitrary’ is information (or “received wisdom”) that may not be be worked out and is in the "realm of memory", whereas ‘necessary’ includes the properties and relationships that are in the "realm of awareness", and can be worked out, as described in the article. The decision of what’s arbitrary and what's necessary can vary from topic to topic. The question of what arbitrary and necessary are under a given topic can be responded to by considering the answers. For instance, the aspects of the lesson that can be summarized as “symbols, notation, and convention” are arbitrary, and the properties and relationships that carry good explanation to satifsy the ‘why’ are necessary. However, if one excels at explaining the ‘why’, what’s arbitrary can become necessary, as Hewitt outlines why New York is New York.

Furthermore, the differentiation between arbitrary and necessary of course influences the lesson plans, as this decision would greatly impact how much time should be spent on what and why. As teachers, we don’t want to spent too much time to what's arbitrary. Instead, our focus should be on problem based and inquiry based learning within the given topic. It's related to what's we talked about previously regarding regarding instrumental and relational thinking. We want to teach the students to think mathematically under the given topic.

SNAP Math Fair Field Trip - Exit Slip

Firstly, thanks so much Susan for giving us the incredible opportunity to work with kids outside the classroom setting where the kids are the experts, and we’re the guests. Secondly, I’m more happy than surprised to see the expected outcomes of SNAP Math Fair becoming a reality. For instance, the students delivered and communicated their projects in such a professional way; they were confident, ready, and well-prepared and having fun at the same time.

Thirdly, I love the connections educators are establishing to make Math more relevant and fun. I personally never thought of anthropology as a source of creating Math fun problems/puzzles to solve. Me and my group members (Jordan and Mandeep) had a chance to ask the students where they got the ideas from for the problem/puzzle they were presenting. The ideas of course originated from the artifacts/displays at the Museum of Anthropology, but the connections the students made with Math was fascinating!

I’m glad to be part of the profession where there’s so much room for creativity and inquiry. However, making creativity and inquiry part of the Mathematics education for the general public to appreciate is yet to be achieved.

SNAP Math Fair

I’d absolutely love to organize the SNAP Math Fair. However, I’m not sure if I can organize it during my extended practicum, as surviving the long practicum is a challenge on its own, I think.

Nevertheless, once I officially become an educator/teacher, I’ll definitely incorporate such activities/fairs into my teaching. I have a few ideas that are discussed below.

One of the ideas is to get two schools involved in the Fair. It can either mean that students from both schools present/display the problems the same day one after the other or collaboratively, or it can be broken down into two days, i.e. students from school A display their problems and are the hosts, whereas the students from school B are the guests and they come and solve the problem and vice versa. The both streams have pros and cons. For instance, having students from 2 schools at one place requires more space/organization, etc. On the other hand, having 2 schools work on it collaboratively can help strengthen connections between educators and students, hence the community.

Another challenge could be convincing other Math teachers or principal/administration to organize the Math Fair in the first place. For this to work out, we can’t afford to leave gaps and have to be on top of things in terms of organization and preparatory work required for the fair.