unit plan draft 1

 UNIT PLAN

Maxine Beckie

Cambie Secondary, Math 8

Unit: Fractions 

Textbook: Math makes sense 8

Units SA will teach before I teach this unit: 

Integers 

(1) Why do we teach this unit to secondary school students? 

Fractions is in the curriculum taught to younger highschool students because they are a fundamental part of arithmetic, and are widely used in the real-world, for example in baking measurements, mechanical things using imperial nuts and bolts, and so on. 

The math 8 fractions unit assumes that students already know how to add and subtract fractions, but I will likely have to review this as many students struggle. I am hoping they leave with a basic understanding of how to add, subtract, multiply, and divide fractions, and also to convert between mixed and improper fractions. 

I'm not sure if students will necessarily find fractions beautiful or interesting, but they are certainly useful, and it would be fun to show them the geometric proof that sum 1/2^n = 2. 

(2) A mathematics project connected to this unit: 

Fractions 

-Describe the topic, aims, process and timing

-What the students will be asked to produce

-How you will assess the project. (250 words)

(3) Assessment and evaluation: 

-How will you build a fair and well-rounded assessment and evaluation plan for this unit? 

-Formative and summative, 

-Informal/ observational and more formal assessment modes. (100 words)

Textbook chapters:

3.1 Using models to multiply fractions and whole numbers 

3.2 Using models to multiply fractions 

3.3 Multiplying fractions 

3.4 Multiplying mixed numbers 

(Mid-unit review)

3.5 Dividing whole numbers and fractions 

3.6 Dividing fractions 

3.7 Dividing mixed numbers 

3.8 Solving problems with fractions 

3.9 Order of operations with fractions 

(Unit review)

BC Curriculum content guide: 

Operations with fractions (addition, subtraction, multiplication, division, order of operations)

More detail: 

-includes brackets, excludes exponents 

-using pattern blocks or cuisenaire rods 

-simplifying 1/2 divided by 9/6 x (7 - 4/5)

-drumming and song: 1/2, 1/4, 1/8, whole notes, dot bars, rests = 1 beat

-changing tempos of traditional songs depending on context of use

-proportional sharing of harvests based on family size

Lesson Topic

1 Adding and subtracting fractions with a common denominator, simplifying

2 Adding and subtracting fractions with a different denominator

3 Multiplying fractions (3.1, 3.2, 3.3) 

4 Dividing fractions, reciprocals (3.5, 3.6)

5 Quiz 1 and history of fractions

6 Arithmetic with mixed fractions (3.4, 3.7)

7 Order of operations involving fractions (3.9) - Whiteboard vertical surfaces

8 Applications involving fractions (3.8)

9 Quiz 2 and art activity

10 Review

(11) Review

(12) Test

Blog post reflection on Mihalyi Czikszentmihalyi's ted talk

A common time I experience a flow state is when I'm riding my motorcycle. I connect with Mihalyi's idea that a flow state is possible when an activity is not too hard, but not too easy either - when I first started riding motorcycles, I was mostly terrified, not exactly in a flow state. And if I'm stuck in traffic the experience is boring (unless I'm blasting music from my speaker). But the middle zone, when I'm riding, comfortable but not too comfortable, is when I achieve a higher level of focus. 

There are many other experiences that can allow me to cultivate a state of flow. Reading, writing, listening to music. I can experience flow doing chores. Painting my nails. Being around people who I love, and making silly jokes. 

What exactly prompts a state of flow is not entirely clear to me. Because not every experience that is within the right difficulty zone will induce a state of flow. Renewing my passport is not particularly easy, and it's far from the most difficult thing I've done - but in no stage of the process have I been in a flow state. 

Many kinds of magical and spiritual practices emphasize states of mind that allow people to be fully or partially engaged with their subconsious - trance states, gnosis, meditation, and many more names. I propose that the key element of a flow state is not the difficulty being in the right level (although that is a prerequisite), but rather the relative engagement of the subconscious and the relative disengagement of the overseeing conscious. Is your conscious mind following your gut, or is it mystifying and clouding your understanding?

Although I've sometimes experienced flow states in the past with mathematics, when I'm deep in focus working on a challenging problem, I don't typically experience flow states with math these days. I suppose it is possible to get some or most students in a classroom to enter a flow state with math, but it seems extremely difficult, since most students are either bored or overly confused in a math class, and most students don't want to be in the classroom. I typically don't experience flow states in classrooms because they are places with very chaotic and disgusting energies. That's not really something I can change, but I could make math class a little ritualistic, being intentional about lighting, sound, and timing. Anyways, what's a math test if not a ritual? 

Campbell soup problem

 So first off, I estimate the diameter of your wheel to be 30 inches across, because I know from bike industry work that your rims are 28 inches, and the tire is probably 1 inch on each side. 

From perspective it looks like the "O" in "SOUP" is about the same size as your wheel. From putting a ruler over my screen, it looks like the "O" is about 1/7th the half-circumference. So I'll estimate the circumference as 14 * 30 = 420 inches. Additionally, from the same method, the "O" is about 1/12th the height of the cylinder, so I'll estimate the height as 12 * 30 = 360 inches. 

So, to find the volume, the radius is approximately 420 / 2pi = 67 inches. Then the volume is pi * r^2 * h = pi * 67^2 * 360 = 5 * 10^6 cubic inches. This is about 21,645 gallons or 81,935 liters. 

The google AI says that the average house fire takes 3,000 gallons to put out. So yes the water tank should be sufficient for all but the craziest house fires. 

I'm not really sure where there is a distinction between "teacher bird" or "student bird." I'm not a bird unless you mean in the sense of the Nelly Furtado song (she's from Victoria btw), and besides I work through problems in the same way regardless of whether I'm a teacher or student. I've noticed that people tend to infantilize students and act like teachers don't have their own emotions. So I'd rather think of myself as neither a student nor a teacher, but both and none of them at the same time. I'm just a person. 

ANYWAYS this puzzle could be modified to estimating the dimensions of basically any object. There was this guy who was going viral on the internet awhile back for estimating people's height based on intricate geometric estimations and knowing the size of objects in the photo. He was pretty scary accurate at it and it could definitely be a fun challenge for students to estimate the dimensions of objects based on photos or videos. 

Hewitt response

Arbitrary.

"I describe something as arbitrary if 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."

Necessary.

"They are parts of the mathematics curriculum which

are not social conventions but rather are properties which

can be worked out from what someone already knows."

I agree with Hewitt when he says "[i]nviting students to 'think about it' is appropriate for

what is necessary, but not for what is arbitrary." There is indeed, no point in asking a student to ponder on what the word is for a three-sided regular polygon. 

Hewitt says "[s]uch division of the mathematics curriculum into arbitrary and necessary is based upon the philosophical roots of the notions of 'contingent' and 'necessary'." He also makes a distinction between "awareness" and "memory," the former associated with "necessary" and the latter with "arbitrary." Later on, he says that "what is necessary comes as a consequence of certain accepted givens," which contrasts somewhat with his earlier hinting that "the necessary" is the objective heart of mathematics. Or maybe he shares my view that the objective is a consequence of accepted truths, mostly subconscious, and the distinction between awareness and memory is not clear-cut - but I somewhat doubt this. I don't see the distinction between contingent and necessary as clear-cut either - sure, we can say that it is necessary that the definition of a Lie algebra forces their classification into the simple and exceptional Lie algebras - but without the contingency of high-energy physics, powered by uranium and with applications in war and industry - would anyone care about Lie algebras enough to classify them?

Despite my philosophical rambling I think Hewitt's article brings some interesting points to mind that may affect my teaching. There is no point for me to ask students to ponder the arbitrary, and as much as possible I want to let them discover the necessary for themselves. When it comes to Hewitt's division of math into the arbitrary and necessary - I was already thinking about this implicitly, after guidance from my SA to let the class figure out more things on their own, without giving away the answer so soon - and this is part of my frustration with academia: its tendency to give names and symbols to concepts that many people already understand, and then one person can claim this knowledge as their own when really they were just the first to put it to paper, not the first to have the idea. As someone who tends to learn things first implicitly, and then later (if ever) explicitly, I find the act of watching an experienced teacher much more helpful to my teaching practice than any article.