The Scale Problem

 I would use weights of 10g, 5g, 2g and 1g as the easiest solution.

In the diagram below, 1H means 1g of herb, 1W means 1g of weight and so on. In the diagram, we see how we can measure 1g to 10g of herbs. We only need this diagram because if we have more than 10g of herbs, we can always take away multiples of 10g away from the "pile" of herb and measure the remainder. An example to illustrate this is 24g of herbs: Take a pile of herb and measure 10g on the scale. Take that 10g of herb away from the main "pile" and we have 14g of herb left in the main "pile". Do the same thing again to take away another 10g of herb so we have 4g of herb left in the main "pile". So think of it as base 10. So technically this does not limit to 1 to 40g of herb, it can be done to any amount of whole number. And this is exactly the extension of the problem. Another extension we can do is using only 3 weights to measure 1 to 40g.

 The thought I have when I was doing this is the monetary system we have: $10, $5, $2 and $1. These bills or coins allow us to come up with a lot of different combinations of amount.

Another method is 20g, 10g, 5g and 2g:

This just keeps going until we reach 20g so I am not showing all of them. If we go over 20g, we use the same concept as the first method. Measure 20H and move it aside and measure the weight of the remaining "pile". For example, 24g: measure 20g and remove it from main "pile" then measure the remaining 4g. Note that some of the weights, we have to measure them twice in order to be sure of the weights.

Microteaching Reflection

Our group did something different compared to other groups. We did not include a powerpoint slide presentation because we want to mimic a real classroom where teachers mostly write on the whiteboards. There were some technically difficulty on zoom where it was hard to see what was going on in the chat while writing on the whiteboard. There was also a little bit of time issue since we kind of rushed through quite a number of things. At the same time, maybe we should have included at least a few powerpoint slides for the 4 rules of square roots. But overall, I enjoyed the entire experience of this microteaching project. 

Microteaching - Square Roots Zoe, Sukie and Ivan

 

Title	Square Roots	Grade	8	Date	Nov 16,2020
TC	Zoe Zhang, Sukie Liu, Ivan Li	Subject	Math	Time	15 mins

Learning Intentions	Understand (big idea or SOI)	Know (content)	Do (skills)
	Computational fluency and flexibility with numbers extend to operations with rational numbers.	Square roots	-Finding the square root of a number  -Understanding the three rules for square roots (Pg 193)
	Learner Profile and/or ATLs (if not noted above but will be explicitly taught)
	COMMUNICATION - Public speaking and presenting  THINKING - Critical thinking skills
	Essential Questions
	Factual	Conceptual
	WHAT are perfect squares  HOW to utilize perfect saucers and square roots	Introduce 4 rules for square roots  Operating the rules to solve problems

Assessment	At the start (formative)	At the end (formative or summative)
	Task/Activity:	Task/Activity:
	What I am looking for: Have a basic understanding of what is radical and radical number Understand and use the 4 rules for square roots in operations	What I am looking for: Have a great understanding of what is a radical number  Be able to operate multiplication/division or a combination of both for radical numbers

The Giant Soup Can of Hornby Island

Part 1:

First, I searched on the internet for the actual size of the Campbell's soup can: Base diameter: 2.69 inches = 6.83 cm, Height: 4.06 inches = 10.31cm

Then I searched on the internet for the average height of a bicycle:  42 inches (106.68cm)

Then something I am stuck for a little bit, is that, the big can actually lies on the ground with its longer side touching the ground so that means the bike's length is the corresponding side of the height of the can. And the bike's height is the corresponding side of the base diameter of the can. 

Next, by looking at the diagram, I estimated that the diameter of the can is about 3 times the height of the bike. So the diameter of the big can is 42 * 3 = 126 inches (320.04cm). With the diameter, we can now calculate the scale factor of the big can to the small can. Scale factor = 320.04 / 6.83 = 46.86

We can now calculate the height of the big can: 10.31 * 46.86 = 483.11cm. Radius of the big can is 320.04/2 = 160.02cm.

Next we can find the volume of the can (a cylinder) V = pi r^2 h = pi * (160.02)^2 (483.11) = 38863726 cm^3 which is about 38845L. Then I found in general you need 400 gallons of water per minute for a typical house fire. That is about 1514L/min. So with 38845L of water in the tank, the fire has to be put out within about 38845/1514 = 25.7 minutes.

Part 2:

Below are 4 pictures of different views (top, front, back, side) of the school where I did my 2 week practicum. As one of the class activities for my Math 8 class on surface area, I asked my students to draw me a 3D diagram of the school based on these google map images. The purpose of doing this is to allow students to explore 3D objects and transition from 2D geometry (perimeter and area) to 3D geometry (surface area and volume). To extend this even further, we can give students the scale factor of google map image to real life object (can be found on google map) and ask them to find the surface area and volume of the school. 

“Flow”, engagement and the Thinking Classroom

 In the video, Mihalyi Csikszenmihalyi describes "flow" as a person in an ecstatic state while doing something. The person knows that he or she is doing something extraordinary, not our mundane chores like brushing teeth, making dinner or commuting to work (unless the person truly enjoys doing these things). In my opinion, I think to promote "flow" in class, we as teachers have to show our students that we are really passionate about what we are doing. We have to get into the state of ecstasy before we can influence our students to do the same thing. I believe that our enthusiasm is contagious and students would feel it if we show it in our classes. A question we have to ask ourselves is do we truly enjoy teaching our math class? Another thing we can do is to do something that students enjoy. In our recent practicum, I was giving a lesson on 3D diagrams, nets and surface area for my Math 8 students. So I gave the top, side and front views of the school to my students and asked then to draw a 3D diagram for me. There were whiteboards on all the walls of our classroom so students just picked up their whiteboard markers and started drawing. During the process, the classroom was in complete silence because everyone was just so focus on their drawing. At that moment, we teachers just needed to step back and let the students enjoy the activity. I did not realize this during the class but after watching the video, I asked myself: "Isn't this what "flow" is all about?" This is exactly the kind of atmosphere and learning environment we want to create in our classrooms. During the course of the activity, the students had no concern about time. Some students was even complaining that they needed more time at the end of the activity (I had to cut them off due to time constraint, but my SA actually told me I should have let them continue with it since the students were enjoying is so much). 

Homework reading and response: The new BC curriculum & secondary math course pathways structure

One thing that surprised me is the inclusion of history of Asians and south Asians communities and their contributions to the development of our province. This is not something I have seen either when I was in school here or when I am a teacher candidate. But I do understand that the government is being transparent about what they have done wrong to these communities, just like what they have done to indigenous people here.

Another thing is a surprise but at the same time is not really a surprise is the choices of words found in the glossary. It is a surprise in the sense that they all look very familiar to what we are learning in this program. Familiar words like 'constructivism', 'competency' and 'indigenous' are very common in our program. This means current teachers in BC are using them a lot and students would be familiar with them as well. It is not a surprise since this program is based on the education system in BC. But it has changed so much since I was in high school here. This shows the BC curriculum has progressed so much over the years.

Schematic Chart for Math 8 to 12:

Geometric/ numerical puzzle

 Just like our locker problems we did earlier, I tried using fewer numbers and see what observation I can obtain. For a number to be diametrically opposite to another number, they have to be 180 degrees apart. So with 4 numbers (1 to 4), the angle between each number is 360/4 = 90 degrees. So if we want to find the number that is diametrically opposite to the number 1 is 3 because 180/90 = 2 (we add 2 to the current number in order to get a number that is diametrically opposite to our current number).

 

Next I tried 12 numbers using the same idea. 360/12 = 30 degrees. If we want to find a number diametrically opposite to our current number, we add or subtract 180/30 = 6 to our current number. From these 2 observations, to get a number that is diametrically opposite to our current number you just need to add or subtract n/2 where n is the total amount of numbers.

With this conjecture, if we have 1 to 30, the number diametrically opposite to number 7 is 7 + 30/2 = 22

 

My work process is shown in the picture below.

 

We can extend this to problems where n is larger, like n = 90. Another way to extend it is: If n = 90, what is the number diametrically opposite to 85? So in this case students have to subtract, instead of adding 45 to 85 since it goes over 90.

 

To make this puzzle impossible, we can make n odd. For example, if n = 15, what is the number diametrically opposite to 2? In this case there is no number that is diametrically opposite to any number because 180 is not divisible by 24 degrees (360 / 15 = 24).

 

Our problem seems easy if n is a nice even number since we just have to divide n by 2 to get our answer. There is really not much geometry going on because we can solve it without geometry (even though I used geometry to help solve it in the first place) . Only if n is an odd number then we realize it does not work, and it brings us back to the concept of geometry. So the puzzle is truly geometric if we have to solve it using the concepts of angles and geometry, rather with just logic.