85 – Guess my Equation

Guess my equation : Trig edition. Give me a cosine equation for this curve. Give me a sine equation. Give me all sine and cosine equations for this curve. Wash, rinse, repeat (careful, these three words kill thousands of computer programmers in their showers every year).

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48 – In Boston for an IB Roundtable

Drove back and forth to Boston yesterday for an IB roundtable meeting for IB Math HL. Really great experience for me, as a new IB teacher, to get advice and support from fellow IB teachers. I got a lot of great advice on how to grade and administer the math exploration. Cool school, two blocks away from Boston Public Garden. Also I made a lot of good contacts for people to ask for help in the future!

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24 – Synthetic Division Practice

I know that Mary Bourassa has some better techniques for long and synthetic division, but I didn’t have enough time this year to get comfortable with the techniques, so it’ll have to wait until next year (and these students have never seen the area model of factoring, but they have already seen long and synthetic division).

Anyway, it’s a short amount of time that we need to practice SD and LD, about one block total. Here are students helping each other out. When they get a remainder (hence function value) they let me know and I plot the points on Desmos so they could get the link between the remainder and the function value of the polynomial.
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23 – Sum and Product of Roots

Here’s a PreCalc H student’s work while trying to prove (show) the product and sum of the roots formula. Icky algebra, but we don’t wallow in it too long. This student needs to go one step further by factoring out the coefficients in front of the x^2, and it’ll be much clearer.

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17 – Loop-de-loop in Python

Anna Weltman and Dan Meyer are hosting a mathematical art contest based around loop-de-loops. We worked on paper first (CMONMATTTHINK), and then went to python. This was day one of python for the class, so it was a great intro without going too crazy in depth. The rules: you must keep the following setup, move(some distance), and left(90). Other than that they could change the number of times it looped, how many instructions were in the loop, etc. Here’s a code sample:

from turtle import *

multiplier = 30

speed(0)
for i in range(1,100):
    forward(3*multiplier)
    left(90)
    forward(1*multiplier)
    left(90)
    forward(4*multiplier)
    left(90)
    forward(2*multiplier)
    left(90)
    forward(7*multiplier)
    left(90)

Here are some of their marvelous creations:

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Day 11 – Transformations on Desmos

The students were instructed to go to this link and match up as many parabolas as they could using the sliders a,b,c, and d. After playing around with this graph, and another set of exponentials, and talking it over with their groups, we formalized what each of the letters did.

We looked at the equation: y=a*f(b(x-c))+d and wondered why d worked opposite of c. Why did the c need a negative where the d didn’t? If you rewrite it as y-d=a*f(b(x-c)) then it’s more clear what is happening. Likewise for the a and the b. Why did they act opposite of each other? Rewrite it as (1/a)*(y-d) = f(b(x-c)) and then it’s more obvious why they are acting in different directions. Who is to blame about the y= form for everything? Can I blame Texas Instruments?

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