## Friday, August 23, 2019

### Math Links for Week Ending Aug. 22rd, 2019

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

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

I like this dynamic tessellation from @MathHombre. It reminds me of this one that I did in Desmos and WebSketchpad.
Curriculum Tags: Gr7
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
Here is a really interesting construction with a surprising result.
Curriculum Tags: MPM1D, MFM1P
Wow, make sure you check out all of the comments for the different dynamic versions of this.
Curriculum Tags: All
A fraction question for you
Curriculum Tags: Gr7, Gr8

Have your students test their algebraic skills with this problem connected to the quadratic formula
Curriculum Tags: MCR3U
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
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

## Friday, August 16, 2019

### Math Links for Week Ending Aug. 16th, 2019

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

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

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

Man I need a 3D printer
Curriculum Tags: All
Here's a nice visual representation for a series.
Curriculum Tags: MCR3U

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

## Friday, August 9, 2019

### Math Links for Week Ending Aug. 9th, 2019

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
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/
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

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
Man, @dynamic_math does a great job of maximizing the potential of Geogebra's 3D engine
Curriculum Tags: MPM1D, MFM1P, MPM2D, MFM2P
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/

## Friday, August 2, 2019

### Math Links for Week Ending Aug. 2nd, 2019

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
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

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

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

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

## Friday, July 26, 2019

### Math Links for Week Ending Jul. 26th, 2019

If you haven't purchased your #mathgals shirt (or even if you have) then you may be interested on who the women are on each shirt. Thanks to @SamJShah2 for pointing this out.
Curriculum Tags: All
I'm a big fan of card sorts and so here is a nice and simple Desmos Card sort for special quadrilaterals from @Giohio
Curriculum Tags: Gr7, Gr8
https://teacher.desmos.com/activitybuilder/custom/5d39d1334d9d49026d198d11
It turns out some of the math that got us to the moon is use to help the logistics of why most planes land on time.
Curriculum Tags: All
https://www.cnn.com/2019/07/24/world/apollo-moon-math-airplanes-scn-trnd/index.html

This is pretty cool. The idea is that you give students a context for a graph and then ask them to draw what they think the graph will look like before showing them. This TheyDrawIt! authoring tool lets you create the situations. Give it a go
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U, MAP4U
https://medium.com/multiple-views-visualization-research-explained/theydrawit-an-authoring-tool-for-belief-driven-visualization-b3267a001480

Some number facts up to 10googol (and beyond) in two blog posts. Thanks to @YaBoiMack for these two.
Curriculum Tags: All
https://waitbutwhy.com/2014/11/from-1-to-1000000.html
https://waitbutwhy.com/2014/11/1000000-grahams-number.html

I have always liked the work of @taylorpeter77 and so I am quite interested to see what comes of this curriculum that he is developing that focusses on creativity and wonder in mathematics. Read about it here.
Curriculum Tags: All
https://phys.org/news/2019-07-mathematics-creativity-fun.html

Who doesn't love 3D interactive mathematical art?
Curriculum Tags: All
Some nice data about Internet usage around the world
Curriculum Tags: Gr7, Gr8

## Friday, July 19, 2019

### Math Links for Week Ending Jul. 19th, 2019

Who knew there was such a thing as a golygon? I'm sure you could have students do so much with this sort of thing. Making their own, investigating things like area and perimeter. That sort of thing.
Curriculum Tags: Gr7, Gr8
Last week I had a link to a recent Trump Campaign survey about the Democrats and how it was so biased. It turns out that this is pretty normal (maybe that is not surprising). Here is one on the media that starts out almost normal but then it quickly makes a turn. Thanks to @Esping_Math for this one.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U, MAP4C
https://www.donaldjtrump.com/landing/mainstream-media-accountability-survey

When you introduce trig ratios, it's important for kids to practice. This way they get comfortable with what they mean and how to use the. This open middle activity from @And02B has been updated by  @mathequalslove and is a nice way for them to do that. The activity isn't new but what she did was make it physical with printable cards. You might want to change some of the cards if you want to keep to the primary trig ratios but it still has a lot of potential. Check out the link for all the downloads.
Curriculum Tags: MPM2D, MFM2P, MCR3U, MCF3M, MBF3C.

That is totally fun? How do you think a student would describe what was happening?
Curriculum Tags: All
I don't think there is any age that it's not appropriate to ask "How many....?" "How did you count them?". Being comfortable with numbers is the first step in being numerate.
Curriculum Tags: All

## Saturday, July 13, 2019

### Math Links for Week Ending Jul. 12th, 2019

Who is the world's most interesting mathematician? That's what the Great Internet Math Off is trying to find out. Go to the link below to find out who is up for matches this year (and vote as well). Two people who frequently appear on this blog are @SamJShah2 and @MathGarden. Look for their matches and vote for them too.
Curriculum Tags: All
https://aperiodical.com/2019/06/announcing-the-big-internet-math-off-2019/

I like this Open Middle problem from @MrJohnRowe on Areas
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P

This is crazy that it's real. It's the Official Trump Vs Democrats poll. It's the perfect example of how to write biased questions. And the poll is still up so you know it's on purpose. You could certainly have a great discussion with any data management students. But just in case they actually look at the validity of the poll and take it down, @Abel_Jennifer has taken screen shots of the whole thing so you will always have it.
Curriculum Tags: Gr7, Gr8, MDM4U, MAP4C
https://www.donaldjtrump.com/landing/2020-trump-vs-dem-poll

Are you looking for your next math shirt? Here's one started by @BerkleyEverett to help remind students that they are not bad at math.
Curriculum Tags: All

Here's a great "real world" problem that could be connected to estimation or even volume of rectangular prisms
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
What a great way to make fractions auditory.
Curriculum Tags: Gr7, Gr8

Great visual puzzle
Curriculum Tags: All

Here is a nice graphic organizer for quadrilaterals
Curriculum Tags: Gr7 Gr8
https://www.instagram.com/p/Bu7B2nihte2/?utm_source=ig_web_button_share_sheet

## Friday, July 5, 2019

### Math Links for Week Ending July 5th, 2019

Being able to estimate is a great skill for students to have. And so why not estimate angles and distances in a fun way. In this activity @sergeballif does an awesome job of it with Degree Golf. Students start on hole one and estimate the angle to shoot and the distance to the hole. The number of shots is kept track of and then once they do all the holes, there is a Challenge creator for students to create their own hole for the rest of the class to try.
Curriculum Tags: Gr7, Gr8

If you like Pi and Python coding then you might like this blog post about mixing those things. The code is there and the different types of Pi calculations. And it has one of my favourite infinite series methods. So have some fun. Thanks to @yaboimackp for this one.
Curriculum Tags: MCR3U

I really like this assessment idea from @a_mcsquared. The premiss is this (I am simplifying): You give an assignment and the day before it is due you make the answers with full solutions available and then ask students to grade their own assignments. Who hasn't given out an assignment (or test), posted full solutions after grading to see very few kids actually look at them. In this case, having students do the grading themselves will likely give them better insight into what went wrong because they have done the work. Check out the full explanation here.
Curriculum Tags: All
http://audrey-mcsquared.blogspot.com/2019/06/changing-follow-up-into-rise-up.html

And speaking more on assessment, @BCphysics did a little experiment where they posted a series of marks and asked people to holistically and more formally determine a grade. What were the results? That in most cases, the holistic grade was just fine. I would go even further to say that the idea that we can somehow calculate any grade and be confident of it's accuracy is a fallacy. That is, if you calculate a grade of 83.25% (because you can), I would argue that that precision is misleading. In fact, I would argue that you are probably only confident to +/- 5%. Read more here.
Curriculum Tags: All

In this post @MathGarden talks about the idea that math is not about getting the answer. In fact, he says: "That mathematics is only worth doing if you can be correct. That mathematics can only be appreciated by being proficient. That mathematical expertise is obtainable in this narrow definition of mathematics. All of this is false." Read more at the link below. Thanks to @KMarkPet for this one.
Curriculum Tags: All
https://medium.com/@sunilsingh_42118/mathematics-in-the-age-of-brene-brown-6f0bc4a179c2

I thought this video on the Fourier Series from @3blue1brown was awesome. It does get into the weeds a bit but the visuals are great for talking about adding vectors, adding functions, limits, calculus, transformations and more high end stuff. It's a bit long but I think it would be cool to have students watch it and talk about all the parts that relate to the math they are doing. And honestly, I love that a 25 min long video on Fourier series can get over 600k views in a few days.
Curriculum Tags: MHF4U, MCV4U

And for a slightly simpler version, you might like this one from @smartereveryday
Curriculum Tags: MHF4U, MCV4U

who doesn't like fun with an Apollonian gasket where the numbers show 1/r, where r is a given circle’s radius.
Curriculum Tags: Gr 8

## Friday, June 28, 2019

### Math Links for Week Ending Jun. 28th, 2019

New updates on the Mathies Pattern Blocks app. That is, they have added some new shapes. The dart, the kite and the right angle are all part of the 21st Century Pattern blocks found on the Talking Math with your Kids site. Now there are a pile of options when you have your kids build with the pattern blocks. This is just the development version so I'm not sure when you will see it in the public version but you can play right now with the link below.
Curriculum Tags: Gr7, Gr8
https://mathclips.ca/swfPlayer.html?swfURL=tools/PatternBlocks21.swf&title=Pattern%20Blocks%2B%20Dev
When we were at #NCTM2019 in San Diego this year the funnest way to get around the city was on these electric scooters. Well @MrOrr_Geek with the help of @mathletepearce has created a 3Act Math task. Watch a video to pique students interests. The video shows a split or POV riding with the app screen. Then you can use linear relations tools to figure out the total cost of the trip.
Curriculum Tags: MPM1D, MFM1P
https://mrorr-isageek.com/no-bikes-allowed/

Have your kids give this a try. Take the parabola y=x2 and pick two points on the parabola. Multiply the x values of the points and the product turns out to be the y intersection of the line connecting the two points. Why not try to investigate why this works?
Curriculum Tags: MPM2D, MCR3U

Have you heard of the Tribonacci sequence? How about the Rauzy fractal? Well I can say that I have played with the tiles that @Gelada shows here but I didn't know all the other stuff. So fun
Curriculum Tags: All

Here is a great way to gain some empathy with your ESL students
Curriculum Tags: All

## Friday, June 21, 2019

### Math Links for Week Ending Jun. 21st, 2019

I always love when @AlexOverwijk shows these time lapse videos of his classroom. In this case, it's the final exam for Calculus. Part of the exam was done in groups (on VNPS) and the rest was individual. I know that people like the idea of these collaborative classes, but often abandon those ideas for more traditional experiences once students get to the higher grades. So it is great to see that students can thrive and succeed in these senior math classes with these more progressive types of assessments.
Curriculum Tags: MCV4U, All
Do you want a wealth of fraction resources that conceptualize the ideas of what fractions are all the way from their meaning and representations to operations. All research based and well documented.
Curriculum Tags: Gr7, Gr8
Do you want to have some fun with square numbers? Then @mathgarden has your back. Last week I included this image as a single Tweet but now he's turned it into a full post on Medium. Whether you look at it from the patterning view as created by sums of odd numbers or geometric view as the area of a square with whole numbered sides, there is something here for you.
Curriculum Tags: Gr7, Gr8

I have said it before, I like self checking activities for practice. Though this isn't exactly a self checking activity, the design of it makes it easy to check. Basically it's four questions and their answers are to be summed and put in the centre. As the teacher, you need only check the sum to see if it's correct. Download all five sets from @marybourassa's blog
Curriculum Tags: MPM1D

Registration has opened up for this year's @OAMEcounts Leadership conference. This year it's incoming president @Paul_math's turn to organize the event and it looks like he's got a great line up. With @NatBanting, @MrAspinal, @EmDelSordo, @NHenryFundi, @marian_small, @hirenbmistry1 ‏and @dduff77, More details at the link
Curriculum Tags: All