Jim Doherty

husband, dad, son, brother, math teacher, Mets fan, proud member of the #MTBoS, #iteachmath, music obsessive ( AKA DJ Calc)

[Jim Doherty @mrdardy]

@KarenCampe This was shown to me by one of my colleagues. I have to admit I have never thought of applying FTC this way, but with our notation on integrals going to the left instead of right, I think this makes some sense

[Jim Doherty @mrdardy]

An interesting take on the FTC from a student at our school. Asked for the derivative of the integral of sqrt (t) from 4 to x^2, she identified three cases for the answer. A) 2 < |x| B) 2 = |x| C) |x| < 2

Is she overthinking it, or have I been underthinking FTC?

[Jim Doherty @mrdardy]

Trig question : for f(x) = A cos (bx) + C sin (dx) I know that the period is the LCM of the two component periods. Is there a way to find the amplitude? Is amplitude a logical question?

[Jim Doherty @DJCalc]

Tonight's show on https://t.co/GJgbDYR4XO is uploaded

Here - https://t.co/Z2NpuVm3NP

and here - https://t.co/iGynSYFHsS

Spotify Link - https://t.co/ikCyDnicu4

Playlist

[Jim Doherty @mrdardy]

@dmarain David can you give me some insight into why the (8-x+1)*(8 - y +1) formula gives me the number of x by y rectangles on the chessboard?

[Jim Doherty @mrdardy]

In Calc BC yesterday I posted a picture of a chessboard and asked for how many squares there would be. We worked our way through to the answer. I then posed the question of how many x by y rectangles there would be. One student proposed (8-x+1)*(8-y+1)
1/2

[Jim Doherty @mrdardy]

@dmarain He proposed one! (Sum of 1 to m (sum on 1 to n (m-x+1) (n- y + 1)) for rectangles of dimension x by y.

[Jim Doherty @mrdardy]

A quick check seems to confirm this. Are these formulas ones any of you have seen before? He could not really explain his insight comfortably.

3/2

[Jim Doherty @mrdardy]

His formula seems to check. Someone else then asked about the number of rectangles is the original size was not 8 by 8 but, instead, an m by n rectangle. My student who proposed the original formula thinks this is a sum of sigma 1 to m of (m-x+1) and sigma 1 to n of (n-y+1)
2/2

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/pUg7qtjV6d

and here - https://t.co/daTALaAzgX

Spotify Link - https://t.co/kZF4W1Zu2H

Playlist

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/0lXNueJZ6O

and here - https://t.co/VaOJvDLGoA

Spotify Link - https://t.co/sDeT2ZNsXb

Tonight's Playlist

[Jim Doherty @DJCalc]

Tonight's show uploaded here - https://t.co/fTvolT9K0O

and here - https://t.co/MKPOEyGEPU

Spotify Link - https://t.co/PY8I2k3vw5

Tonight's Playlist

[Jim Doherty @DJCalc]

For my show tonight on https://t.co/GJgbDYRCNm (7 - 9 PM ET) I shine a spotlight on The Bats (new album!) and feature @voxtrot @nadasurf @AmyRigby and new tunes by @cuddlemagic , Melody Chambers, Bruiser and Bicycle, and 16 others. You can stream from our site, so drop on by!

[Jim Doherty @mrdardy]

@HarMath @dmarain Fred - thanks for the reply. I am trying to remember where I found this question or what I was thinking when I assigned it. What tip could I give to my students about thinking of the 75th term?

[Jim Doherty @mrdardy]

@HarMath @dmarain
I wrote a HW problem and I cannot remember what I was thinking when I wrote it! Consider the sequence: 24, 37, 40, 63, 66, ...
a) Is this arithmetic, geometric, or neither?
b) Is 189 in the sequence?
c) What is the 75th term in the sequence?
Any elegant ideas?

[Jim Doherty @DJCalc]

Tonight's show wrap

Uploaded here - https://t.co/PuylhCYp2g

and here - https://t.co/xLbJEQifHu

Spotify - https://t.co/AGljjIaRxS

Playlist

[Jim Doherty @mrdardy]

@HarMath @dmarain @howie_hua @decompwlj @RaminKhosravi4 @sonukg4india @jamestanton @mATH_e_matics @MathCurmudgeon @pickover Wild guessing here looking for a generalization. 13/999 is repeating 13 in base 10 (9 is one less than 10)
21 repeating in base 3 is 21/22 (2 is one less than 3)
How about something like 23 repeating in base 4? Is it 23/33 (3 is one less than 4) ?

[Jim Doherty @mrdardy]

@HarMath @dmarain @howie_hua @RaminKhosravi4 @mathillustrated @mATH_e_matics @decompwlj @ybgoi @sonukg4india @jamestanton @DonFraser9 @dment37 This is a lovely and clear solution to this problem. I am curious about how long it would take some of my AP Precalc students to arrive at this solution. I think the biggest hurdle is simply writing the equation that represents the description

[Jim Doherty @mrdardy]

It has been too long since I checked in on this account and it has been way too long since I blogged about my classes. Hoping to get more engaged again and here is my starting salvo
https://t.co/Wlpk7mhdSc

[Jim Doherty @mrdardy]

@martinsean As with most things, it was filled with pros and cons. It took me awhile to adjust my pace of speaking and remind myself to be careful with math vocab. I am looking forward to seeing these kids grow in our school after years of just getting to know jrs and srs

[Jim Doherty @mrdardy]

Hey #mtbos I will be teaching Algebra I this coming year for the first time in quite a while. Can you send me or share some favorites for this level course? I've been teaching Calc and Precalc for the past 6 years exclusively