Math Links for Week Ending Aug. 30th, 2019

Featured Links

I think any time you can take an abstract concept and make it more visible, then it's a benefit for students. In this case the concept is exponential growth and Desmos has released a new activity to get kids talking about, what looks like, cell division. 

Curriculum Tags: MCR3U, MCF3M, MBF3C
https://teacher.desmos.com/activitybuilder/custom/5d56f89cd82b4905e2def1ac

👉🚨NEW ACTIVITY 🚨👈

"Circles" will help your students think about exponents!

⚪⚫🔴🔵🔴⚫⚪⚫🔴🔵https://t.co/qZLoOzwNra pic.twitter.com/XKQ69xN0ib

— Desmos.com (@Desmos) August 19, 2019

Resource Links

Some fun with infinite series.
Curriculum Tags: MCR3U
https://twitter.com/fermatslibrary/status/1166324490760065024

The infinite gift 🎁is an interesting object where the side of the nth box is 1/√n. As n→+∞, the gift has infinite surface area and length but finite volume! pic.twitter.com/Ckm2KHp1e7

— Fermat's Library (@fermatslibrary) August 27, 2019

Opinion Links

Some nice insights from @MarkChubb3 on the differences between some of the categories of the achievement chart here in Ontario.
Curriculum Tags: All
https://buildingmathematicians.wordpress.com/2019/08/21/the-types-of-questions-we-ask-which-categories-of-questions-should-we-focus-on/

Video Links

If you have some time to kill then you might try to replicate this
Curriculum Tags: All
https://twitter.com/Ayliean/status/1163208862587076608

Exactly 100 years before I was born David Hilbert first described the Hilbert Curve - so I used my birthday to draw the seventh iteration in homage 🤘📐 pic.twitter.com/keyaHMNmcp

— Ayliean (@Ayliean) August 18, 2019

A nice visualization of scaling a vector. Watch the video then play with the Geogebra file.
Curriculum Tags: MCV4U
https://twitter.com/dynamic_math/status/1163797833457291275

Scaling A #Vector: Dynamic & modifiable geometric illustrator. Created with @geogebra: https://t.co/wEmMQsOiXR. #MTBoS #ITeachMath #math #maths #physics #EdTech pic.twitter.com/mVWgBT2YfM

— Tim Brzezinski (@dynamic_math) August 20, 2019

This cube dissection is pretty cool. Especially the 3D printed version that @MikeandAllie made (see below) and it reminds me of these two constructions seen below as well.
Curriculum Tags: MPM1D, MFM1P, MFM2P
https://twitter.com/gregeganSF/status/1160801098594054145

This is my favourite dissection of the cube: 6 pieces, with the 6 ways of permuting the coordinates in ascending order:

x ≤ y ≤ z
x ≤ z ≤ y
y ≤ x ≤ z
y ≤ z ≤ x
z ≤ x ≤ y
z ≤ y ≤ x

In higher dimensions, the n-cube can be dissected in the same way into n! pieces. pic.twitter.com/RCrOOYUSC2

— Greg Egan (@gregeganSF) August 12, 2019

https://twitter.com/mikeandallie/status/1160951997731921920

We did this dissection as a fun 3D printing math project for kids a while back and @PaulaKrieg made some neat folded boxes to hold them pic.twitter.com/CtZmarmPlh

— Mike Lawler (@mikeandallie) August 12, 2019

https://www.youtube.com/watch?v=LU-WMwlWfX0

https://www.youtube.com/watch?v=d-C_-61pJcc

Image Links

What fractions do you see?
Curriculum Tags: Gr7, Gr8
https://twitter.com/crstn85/status/1163858895623905280

Fractions in the wild!

Is #FractionChat a thing? I know #UnitChat is. pic.twitter.com/kghQlP4w33

— Tina Cardone 🏳️‍🌈 (@crstn85) August 20, 2019

I wish I would have had this advice when I started as a math coach
Curriculum Tags: All
https://twitter.com/fawnpnguyen/status/1164926849190731777

Sucks for you if you didn’t get a text like this from a true friend on your first day on the job like I did. pic.twitter.com/GFcteywPTK

— Fawn Nguyen (@fawnpnguyen) August 23, 2019

Know your numbers
Curriculum Tags: All
https://twitter.com/centerofmath/status/1164882313567703040

In case you haven't been introduced to all of them yet...#FunFriday #DOMATH pic.twitter.com/LX8BiMQX5A

— Center of Math (@centerofmath) August 23, 2019

Math Links for Week Ending Aug. 22rd, 2019

Featured Links
Words matter. Here are some suggestions from @MrsForrest dealing with different ways that you can avoid labelling kids as "high" or "low". Thanks to @BerkleyEverett for pointing this out.
Curriculum Tags: All
http://showyourthinkingmath.blogspot.com/2018/05/the-low-kids-and-high-kids.html

Resource Links
Some information about women in mathematics who have have had female students who have become mathematicians and the chains of mentors and students that came of that.
Curriculum Tags: All
https://twitter.com/evelynjlamb/status/1160932947031015425

As far as I can tell, the longest chains of women mathematicians with women PhD students starts with Olga Ladyzhenskaya (there are 5 chains of length 4). If you know a longer one, tell me about it! Also I'm proud of the picture I made for this article.https://t.co/WiE2Xk2UBw pic.twitter.com/KTZ9wzYGcb

— Evelyn Lamb (@evelynjlamb) August 12, 2019

I like this dynamic tessellation from @MathHombre. It reminds me of this one that I did in Desmos and WebSketchpad.
Curriculum Tags: Gr7
https://twitter.com/mathhombre/status/1162392153001213959

Simple slide #tessellation https://t.co/Npc2cGD0Zm and bunnies, in @geogebra pic.twitter.com/YkBQ8DPET0

— John Golden 🔗 (@mathhombre) August 16, 2019

Video & Audio Links
Listen to @ProfKeithDevlin talk about how the needs of math students have changed and how we should change the way we teach and what we teach to match.
Curriculum Tags: All
https://www.wvxu.org/post/npr-math-guy-keith-devlin-new-math-skills-we-need-future


Working with ratios? Try a ratio table
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
https://twitter.com/PamHarrisConsu1/status/1161442867895840768

More fun with Proportional Reasoning!https://t.co/1eI8AaqyiLhttps://t.co/cwBki9bJ7N@pwharris pic.twitter.com/H3tUE1qV1w

— Pam Harris Consulting (@PamHarrisConsu1) August 14, 2019

Here is a really interesting construction with a surprising result.
Curriculum Tags: MPM1D, MFM1P
https://twitter.com/dynamic_math/status/1162349898160910336

#TriangleSurprise! When we build equilateral triangles off 2 sides of ANY TRIANGLE, another equilateral triangle surprisingly emerges! 😮 Why does this occur? 🤔Source: @gogeometry. Created with @geogebra: https://t.co/lTfrId4Hik. #geometry #math #MTBoS #ITeachMath #maths #EdTech pic.twitter.com/CUeFSPKsYy

— Tim Brzezinski (@dynamic_math) August 16, 2019

Wow, make sure you check out all of the comments for the different dynamic versions of this.
Curriculum Tags: All
https://twitter.com/MathCeyhun/status/1162015492644704258

An equilateral triangle, how can it be equivalent to a square ? pic.twitter.com/1kuCcEdOS8

— Ceyhun Köylüce (@MathCeyhun) August 15, 2019

Image Links
A fraction question for you
Curriculum Tags: Gr7, Gr8
https://twitter.com/jamestanton/status/1160179112360603649

What fraction of the whole square is a single blue square in the second diagram? Third diagram? 100th diagram? pic.twitter.com/INzqAx0dl8

— James Tanton (@jamestanton) August 10, 2019

Have your students test their algebraic skills with this problem connected to the quadratic formula
Curriculum Tags: MCR3U
https://twitter.com/jamestanton/status/1161350279637491716

Love this little gem from Lill, 1867. (Google "Lill's method" to see a slew of materials on a curious geometric approach to solving polynomial eqns. But can you first see on your own how each slope here satisfies am^2 - bm + c = 0?) pic.twitter.com/PtqLwHLTax

— James Tanton (@jamestanton) August 13, 2019

Some cool cross sections of a cube. And if you want the high res Illustrator version, check out the comments and below is the dynamic "water" version from @shonk
Curriculum Tags: All
https://twitter.com/Trianglemancsd/status/1161464188348313600

Equally spaced cross sections of a cube. pic.twitter.com/9uCIvmwzUN

— Christopher Danielson (@Trianglemancsd) August 14, 2019

Here is the dynamic version
Curriculum Tags: All
https://flotsam.sellingwaves.com/post/90811439361/if-you-fill-a-cube-with-water-the-shapes-the

Who doesn't like a good Calculus joke. Thanks to Mark Naber for this one

Curriculum Tags: MCV4U

https://www.facebook.com/Mathhappiness/photos/a.101142433566320/972286496451905/?type=3&theater

Math Links for Week Ending Aug. 16th, 2019

Featured Links
I like these two spacial reasoning puzzles that @mathequalslove has created templates for. Check them out and how she uses them at the links below:
Curriculum Tags: All
https://mathequalslove.blogspot.com/2019/07/square-pi-puzzle.html
https://mathequalslove.blogspot.com/2019/07/1-4-5-square-challenge.html

Resource Links
Are you a Websketchpad user? Then you might want to check out some of the new features which includes function notation tools.
Curriculum Tags: All
http://www.sineofthetimes.org/catching-up-with-new-web-sketchpad-functionality/

Video Links
Ok so this video starts off with some pretty tame graphs but the last few are just crazy. Either way, have your kids try some of these complex relationships.
Curriculum Tags: MCR3U
https://www.youtube.com/watch?v=pAMgUB51XZA

Man I need a 3D printer
Curriculum Tags: All
https://twitter.com/ThamKhaiMeng/status/1157962976474873861

This arrow by mathematician and sculptor Kokichi Sugihara can't point left. Here's how it works: It's 3D-printed with a bunch of curves our brains don't register. pic.twitter.com/Xa32GrI7ii

— Khai (@ThamKhaiMeng) August 4, 2019

Here's a nice visual representation for a series.
Curriculum Tags: MCR3U
https://twitter.com/MagicPi2/status/1159849203553767425

pic.twitter.com/FVZIhc8s9l

— Idan Tal (@MagicPi2) August 9, 2019

Image Links
Interesting burger visualization
Curriculum Tags: MDM4U
https://flowingdata.com/2019/08/06/best-burger-ranks/

Math Links for Week Ending Aug. 9th, 2019

Featured Links
I really like the idea of starting the year of with students by finding out about their relationship with math. Here is a few possible questions you can ask them.
Curriculum Tags: All
https://twitter.com/howie_hua/status/1158860573469106176

Drafting a questionnaire for my students to answer during our first week. Thoughts? Questions you would add/take away? Any feedback would be great. #MTBoS pic.twitter.com/m1FQQOLk7F

— Howie Hua (@howie_hua) August 6, 2019

Resource Links
A new activity from Desmos is here to help students describe various transformations using informal language. Try it out
Curriculum Tags: Gr7, Gr8
https://teacher.desmos.com/activitybuilder/custom/5d4380d4fc08cd0a943e099d/

🚨 NEW ACTIVITY ALERT 🚨

Shifting Shapes gives students the opportunity to talk about transformations using THEIR language before learning mathematical vocabulary.https://t.co/4X7djZGZaChttps://t.co/wapNGtV6Cq pic.twitter.com/m2pxmOHErB

— Desmos.com (@Desmos) August 5, 2019

OK it's back again, that order of operations problem. But this time @StevenStrogatz has done a great job of telling us why there is an issue in the first place. It's the first really clear reference and explanation of the idea of the effects of implicit multiplication. I have been describing this for a couple of years about this problem but this is a great one stop shopping place for a clean concise explanation.
Curriculum Tags: All
https://www.nytimes.com/2019/08/05/science/math-equation-pemdas-bodmas.html?smid=nytcore-ios-share


Opinion Links
And if you are tired of those order of operations questions then you might be ready for @StevenStrogatz's more interesting essays on mathematics.
Curriculum Tags: All
https://twitter.com/stevenstrogatz/status/1158382357151399941

If you’re annoyed by all this PEMDAS stuff and would rather savor some beautiful, genuine mathematical ideas, here are links to more than two dozen essays where I tried to explain such things in @nytimes: https://t.co/VwZttC1xf0

— Steven Strogatz (@stevenstrogatz) August 5, 2019

Video Links
Man, @dynamic_math does a great job of maximizing the potential of Geogebra's 3D engine
Curriculum Tags: MPM1D, MFM1P, MPM2D, MFM2P
https://twitter.com/dynamic_math/status/1159173087969124352

What is it about hotels that contain so much #3DMathModeling fodder? 🤔 Taking a break during break time at #PCTM19. With @geogebra #3d & #AugmentedReality, the world can be your Ss’ Math modeling playground. 🙂 #MTBoS #ITeachMath #math #maths #EdTech #PCTM2019 #HSMath pic.twitter.com/epyHMDw9bh

— Tim Brzezinski (@dynamic_math) August 7, 2019

Image Links
Some great comparisons from @MonaChalabi based on this week's mass shootings. Make sure you scroll through all the images.
Curriculum Tags: MDM4U, MAP4C
https://www.instagram.com/p/B01POJ7Fwai/

View this post on Instagram

SWIPE TO SEE HOW THE MEDIA DISTORTS REALITY >>> The study where I got these numbers had this conclusion: “𝕋𝕙𝕚𝕤 𝕨𝕠𝕣𝕜 𝕗𝕚𝕟𝕕𝕤 𝕥𝕙𝕖 𝕞𝕖𝕕𝕚𝕒 𝕚𝕤 𝕕𝕚𝕤𝕥𝕠𝕣𝕥𝕚𝕟𝕘 𝕥𝕙𝕖 𝕣𝕖𝕒𝕝𝕚𝕥𝕪 𝕠𝕗 𝕞𝕒𝕤𝕤 𝕡𝕦𝕓𝕝𝕚𝕔 𝕤𝕙𝕠𝕠𝕥𝕚𝕟𝕘𝕤… 𝕋𝕙𝕖 𝕚𝕞𝕡𝕝𝕚𝕔𝕒𝕥𝕚𝕠𝕟𝕤 𝕠𝕗 𝕥𝕙𝕚𝕤 𝕡𝕠𝕥𝕖𝕟𝕥𝕚𝕒𝕝 𝕞𝕠𝕣𝕒𝕝 𝕡𝕒𝕟𝕚𝕔 𝕞𝕒𝕪 𝕓𝕖 𝕚𝕞𝕡𝕒𝕔𝕥𝕚𝕟𝕘 𝕡𝕠𝕝𝕚𝕔𝕪 𝕣𝕖𝕤𝕡𝕠𝕟𝕤𝕖𝕤 𝕥𝕠 𝕥𝕙𝕖 𝕡𝕙𝕖𝕟𝕠𝕞𝕖𝕟𝕠𝕟... 𝕋𝕙𝕖 𝕣𝕖𝕤𝕦𝕝𝕥𝕚𝕟𝕘 “𝕤𝕪𝕞𝕓𝕠𝕝𝕚𝕔 𝕝𝕖𝕘𝕚𝕤𝕝𝕒𝕥𝕚𝕠𝕟” 𝕥𝕙𝕒𝕥 𝕥𝕒𝕣𝕘𝕖𝕥𝕤 𝕥𝕙𝕖𝕤𝕖 𝕙𝕚𝕘𝕙𝕝𝕪 𝕡𝕦𝕓𝕝𝕚𝕔𝕚𝕤𝕖𝕕 𝕣𝕒𝕣𝕖 𝕚𝕟𝕔𝕚𝕕𝕖𝕟𝕥𝕤 𝕚𝕤 𝕤𝕦𝕓𝕤𝕖𝕢𝕦𝕖𝕟𝕥𝕝𝕪 𝕗𝕒𝕚𝕝𝕚𝕟𝕘 𝕥𝕠 𝕒𝕕𝕕𝕣𝕖𝕤𝕤 𝕥𝕙𝕖 𝕝𝕒𝕣𝕘𝕖𝕣 𝕞𝕒𝕤𝕤 𝕡𝕦𝕓𝕝𝕚𝕔 𝕤𝕙𝕠𝕠𝕥𝕚𝕟𝕘 𝕡𝕣𝕠𝕓𝕝𝕖𝕞: 𝕡𝕖𝕣𝕡𝕖𝕥𝕣𝕒𝕥𝕖𝕕 𝕓𝕪 𝕡𝕣𝕖𝕕𝕠𝕞𝕚𝕟𝕒𝕟𝕥𝕝𝕪 𝕨𝕙𝕚𝕥𝕖, 𝕞𝕚𝕕𝕕𝕝𝕖-𝕒𝕘𝕖𝕕 𝕠𝕗𝕗𝕖𝕟𝕕𝕖𝕣𝕤, 𝕦𝕤𝕚𝕟𝕘 𝕙𝕒𝕟𝕕𝕘𝕦𝕟𝕤 𝕚𝕟 𝕒 𝕨𝕠𝕣𝕜𝕡𝕝𝕒𝕔𝕖 𝕤𝕖𝕥𝕥𝕚𝕟𝕘𝕤." Sources: Mother Jones database 1982-2019 and the International Journal of Comparative and Applied Criminal Justice, 2019

A post shared by Mona Chalabi (@monachalabi) on Aug 6, 2019 at 11:01am PDT

Math Links for Week Ending Aug. 2nd, 2019

Featured Links
I came across this Tweet from @ddmeyer and kind of dismissed it but later on I saw a reply in the thread that said this:"You're gonna say something this year – it might feel innocuous and forgettable – that one of your students will be recounting with his voice cracking TWENTY YEARS LATER." That got me curious and looked at the thread. It was in response to something a principal (who was part of the audience) said: "One principal told me afterwards about the time in 7th grade that he felt belittled by his math teacher and gave up on math.". No doubt, that we have all done this at one time or another. Makes you really think about the power and influence we have and how we can affect the most vulnerable students so easily. Read the whole thread below:
Curriculum Tags: All
https://twitter.com/ddmeyer/status/1157353070814216192

Gave a new talk in #omahapublicschools today. Really meaningful conversations w/ principals and administrators afterwards. Thanks, @OPS_LoganSupt & @OmahaPubSchool for your hospitality! https://t.co/uBnKjRn5Ce pic.twitter.com/1OrCtrkrzy

— Dan Meyer (@ddmeyer) August 2, 2019

And along a slightly different line, @CarlOliwitter has started a new hashtag (and slow chat) #MakeMathJust to talk about social justice and equity issues in mathematics. Check out the conversation at the link below
Curriculum Tags: All
https://twitter.com/hashtag/makemathjust?src=hashtag_click&f=live

Want to make math social justice activities and help students use math critically?

Then add #makemathjust to your tweetdeck and join this week's slow chat around transportation!

8/1: What is this situation?
8/2: How can we explore it with math?#mtbos #ClearTheAir #iteachmath pic.twitter.com/81MRVxjeX7

— Carl Oliver (@carloliwitter) July 31, 2019

Resource Links
I probably should have posted this last week but you might still have some time to see some of these webinars from so many good speakers in this year's Building Math Minds Summit. you can see them from the link below and if you are too late, at least you can get something out of the back channel hashtag #BuildMathMinds19
Curriculum Tags: All
https://mathematicallyminded.lpages.co/vms-speaker-page-day-1/



Well, I guess it's that time. And by that, I mean time for another one of those "viral" math problems. This time it's another one of those "BEDMAS/PEMDAS" debates dealing with implied multiplication: 8/2(2+2). Now, full disclosure, I would have been one arguing for the answer 16 but now I am firmly in the 1 camp. Of course, by standard order of operation rules, the answer would be 16 but like most things in school, we don't give the whole picture and it turns out that there is a rule about implied multiplication that gives it precedence. You can read a thread I posted about this issue a couple of years ago here where, among other things, you can see an explicit mention of this rule in a calculator manual. That being said, I do like @StevenStrogatz's take on it which is more to talk about the importance of notation than to give the correct answer. Thanks to @JPJacula for pointing this one out.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
https://www.huffingtonpost.ca/entry/math-problem-twitter-bedmas-pemdas_ca_5d420367e4b0acb57fc6b0fd

Some cool ideas answering the question "What math teaching strategies works best?" from @mashupmath. With answers from a bunch of educators (including some Ontario teachers @mathletepearce, @mathgarden, @BrianAspinal and @MarkChubb3). Thanks to @BartVanslack for pointing this out
Curriculum Tags: All
https://mashupmath.com/blog/math-teaching-strategies-featuring-jo-boaler

What Math Teaching Strategies Work Best? 16 Math Education Experts Share Their Suggestions. — Mashup Math https://t.co/T6RnlGbLOi

— Peter Liljedahl (@pgliljedahl) July 30, 2019

Image Links
I thought this graph was pretty telling and probably something every teacher should be aware of. It was in response to @ddmeyer's Tweets from above.
Curriculum Tags: All
https://twitter.com/MathPhan/status/1157382411375861761

Hard to supervise and support with differing experiences for sure! How many math Ts out there know what it's like to struggle and not like math in school. Based on my survey from #OAME2019, very little share the same math experience...but I tend to go rogue 😉 pic.twitter.com/5RIRkRRxp8

— TT Phan (@MathPhan) August 2, 2019