Group Micro-Teaching: Lesson Plan

Topic: Graphing Relations
Grade: 10
Partners: Arshbir, Sissi 

Objective/Goals: Students will be able to describe a possible situation for a given graph and sketch a possible graph for a given situation.

Time: 15 minutes

Strategies to help learn: Class is set in groups to allow students to work together. Also, it is inquiry based learning; students will develop critical thinking and collaborative skills

Hook: Kahoot quiz serves as a hook

Materials required: Computer, colorful envelopes (group activity), large paper for the group activity, markers

Assessment: The group activity will act as formative assessment of their knowledge, and the kahoot will serve as a check of prior knowledge.

Assumed prior knowledge: It is assumed that students will know the axes of a graph, as well as the coordinates of a graph, and be able to plot a graph given the points

Development of idea/skill:

• Start off with Kahoot Quiz
• state that students are able to get into groups (MAX: 2) so this allows students to collaborate
• Group Activity: groups receive envelope and either have to create a situation for a given graph, or create a graph for a given situation
• if time permits, each group gives their answer
• Conclusion/come together and talk about underlying message of lesson

Conclusion: Go over key points of the lesson (i.e. rate of change)

Further extensions/Applications:  Extra envelopes for students who finish earlier, talk about speed in physics (driving and the speed you drive)

• exponential growth can be related to decay and half-life, and also finances (analyzing stock market history…?)

2-column problem solving

Hewitt article: Arbitrary and Necessary

      Hewitt defines arbitrary as something someone could only come to know it to be true by being informed of it by some external means - whether by a teacher, a book, the internet, etc...  If something is arbitrary, then it is arbitrary for all learners, and needs to be memorized to be known.  Necessary in this context refers to aspects of the math curriculum where students do not need to be informed - things which learners can work out for themselves, depending on their respective realm of awareness.
      For any given lesson, if I believe that it will save the students time in the long run, I will teach a topic as arbitrary as opposed to necessary (even though less 'math' appears to be involved at the outset).  As interesting as it would be to have students devise their own nomenclature when learning something new, imagine the challenges they would encounter attempting to communicate with the rest of mathematical culture subsequently.  My justification for this teaching style comes from an experience I had as an undergraduate.  My Number Theory professor had an assigned text for the course (A Classical Introduction to Modern Number Theory) and a recommended text (An Introduction to the Theory of Numbers).  During the course, I learned from the required text only due to time constraints.  Later on, I was keen on learning more so I looked up G.H. Hardy's book.  The issue was that Hardy's text was written over a half-century prior to the one I was familiar with, even though similar topics were contained within.  I found myself doing much less math while reading the Hardy book no due to lack of material contained within, but simply due to notational differences.  I had to create a rudimentary translator so that I could follow along while reading the theorems.  Once naming and symbolic conventions have been established, it's prudent to adhere to them so that you are free to focus more on building mathematical knowledge using those conventions.  If time permits and I am confident that, if my students' realms of awareness are sufficient, I'd devise an activity (perhaps involving appropriate givens) to have them derive a concept (necessary); I would provide guidance afterwards to ensure uniformity.  Either way, students maximize their mathematics in the classroom, either by using conventional terminology to solve problems or by deriving new concepts using their current cognitive abilities.  
           

Math Fair @ the MOA

      This week our class attended a math fair at the Museum of Anthropology (MOA) on the UBC campus.  The students who designed the exhibits were sixth graders working in pairs from West Point Grey Academy, a K-12 private school in Vancouver.  Their class had visited the MOA a few weeks earlier to gain inspiration (many entries were based loosely on real exhibits).
      Since I was only able to stay for 45 minutes or so, (I had a class at Scarfe immediately after this one) I was only able to visit a few student exhibits.  The first one was based on Aboriginal canoe carving: you and a partner take turns carving either one or two canoes per turn, given a set number to start with - the person who ends up carving the special (last) canoe is declared the winner.  The students read us an interesting back story on prepared cue cards and even provided us with variants of the game (e.g. the special canoe has termites so the winner must avoid carving it) and hints/tips to winning.  The second exhibit was based on the mythological hydra where you played a hunter who had to destroy a creature with three heads and three bodies with your sword (the heads can live independently of the bodies and vice-versa).  The trouble was that if you destroyed a body then two heads would grow in its place, if you destroyed a head then a body would grow in its place, etc...  Again, the students were very well-prepared and had a few of their worked solutions available (hidden) and some hints (also hidden) for those who were stuck.  They even had prizes for guests who were able to solve the puzzle without resorting to hints!   The final entry had visitors develop a strategy for determining which (indistinguishable) paper maché cabbage weighed more than the other eight - there were nine in total.  The challenge here was that you weren't allowed to touch the cabbages and you were only allowed to use the balance beam scale twice.        
      Overall, I was very impressed with the amount of research the elementary school students performed, how well they each knew their topic, and how well they all conducted themselves in front of people twice their age.        
         

Math Art Project - Borromean Cube

      Our group of three (Pacus, Simran) attempted to create a Borromean Cube using three different colours of paperclips.  The model cube consisted of 81 paperclips (81 / 3 = 27 of each of colour) where the green, red, and blue clips were oriented to be parallel to the x, y, and z-axes, respectfully (i.e. two clips are orthogonal if and only if they were a different colour).

      It was fascinating looking up the history of the Borromean ring (the base unit of the cube) and how different cultures (independently) discovered the ring without having any knowledge of Knot Theory (branch of Topology) as it wasn't formalized until the late 18th century.

      We had a significant amount of difficulty constructing the full cube due to our inability to bend/unbend the small paperclips and fit the ends into confined spaces (picture trying to fit a rope through a small loop without having any slack or being able to easily bend/unbend the rope).  Instead we settled on a 'frame cube' which was comprised of (4/9)*81 = 36 paperclips (12 red, 12 green, and 12 blue).  Our cube looked similar to the model cube except ours had the interior missing; it took on the appearance of a 3-dimensional cube drawn on a 2-dimensional piece of paper.

      Our class presentation was an enjoyable experience - we outlined some Borromean Cube history, showed/discussed our creation, created our own link using our arms, (as there were three of us!) and even had the class attempt to create the base unit/link using the clips.  Most of our colleagues were able to figure it out with little or no assistance from us.  Overall, our group had fun with this math art project (personally, I haven't combined math with art in many years).  If we were to build another cube (or similar) we'll have to remember to choose more pliable materials.    

SNAP Math Fair?

      I would certainly run a SNAP-style Math Fair at my practicum school, New Westminster Secondary School, because of the diverse academic ability of the student body.  NWSS offers an array of streams catering to all types of learners: Honours, Non-Honours, Apprenticeship & Workplace, and International Baccalaureate Standard Level & Higher Level.  The non-competitive nature of the SNAP fairs I consider to be highly appropriate for adolescent learners for two main reasons: it removes the incentive to seek out parental/other adult assistance, and (more importantly) it focuses the event on the math, not the trophies.  The problem-solving nature of SNAP encourages those students at NWSS who may not possess a heavy theoretical knowledge base to solve a variant of a problem that is relevant to their own lives and is appropriate for their age/skill set.  Having the students involved in the presentation helps their confidence not just with explaining mathematics but with speaking in front of others in general (recall, the students initially only pose the problem, not the solution).  I would partition the NWSS fair into academic streams so that visitors could see how similar problems (generalization/special case) are approached by different learners (e.g A&W and IB).  Since the SNAP fairs encourage group work, it's very possible that the visitors (who come from diverse backgrounds themselves) can better learn from certain members of a group (e.g. someone who is proficient at geometric explanations) or from a specific stream (A&W vs. IB) than others.  A key benefit to drawing the problems from archives of professionally-constructed books is that (quite often) there are many different ways of extending, simplifying, and explaining the solution.