I am a big fan of dynamic geometry. Whether it be Geometer's Sketchpad, Geogebra or Desmos. So I always appreciate when someone helps students work with any one of those tools. I also have a series of videos that walk you through some constructions. If you don't know a construction is when you build a geometric item that always keeps its properties (like a square). That is when you drag any of the points, it may change size or orientation but not loose the properties of that geometric figure. You can see those here Curriculum Tags: Gr7, Gr8, MTH1W https://fawnnguyen.substack.com/p/first-desmos-geometry-lesson
Real coin flips are ~49-51 not 50-50 www.scientificamerican.com/article/scie...
But you can guarantee equal probability with a simple trick! Flip 2x in a row starting with the same side up.
HT->call it H
TH->call it T
HH,TT->try again
(due to von Neumann en.wikipedia.org/wiki/Randomn...)
#๐งฎ ๐งช 1/4
I never liked the idea of memorizing math facts. I have always thought it was better to internalize them and if you are looking for a good way to do that, try this out Curriculum Tags: All https://x.com/howie_hua/status/1934960810138259951
My new #math series in the New York Times, "Math, Revealed," is aimed at everyone, whether you love math or not. Have a look! You can read it here for free without a subscription. https://t.co/M6xe5i1vPq
Teaching area formulas as how the shape is related to a rectangle helps build conceptual understanding.
Here's how to derive the area formulas of a parallelogram, triangle, trapezoid, kite, regular hexagon, and even a circle from the area formula of a rectangle: pic.twitter.com/QgiawtwJMK
I love this train of thought set of posts to solve this area problem with a surprising result. Take the time to go through @DavidKButler's solution, at least to see the surprising result but also to get a great example of the art of problem solving. Curriculum Tags: All https://bsky.app/profile/davidkbutler.bsky.social/post/3lqdbrayyx22v
Ok let me #TryMathsLive with this from @mathforge.org …
I would definitely use this problem when dealing with equations and applications of equations to have kids calculate things like the speed when hitting the water, the speed or the height, which should all be attainable from the time of the fall. Curriculum Tags: MPM2D, MCR3U, MCF3M, MBF3C https://x.com/davidpetro314/status/1927069513075277858
Les Stewart typed out every number from one to one millions on his typewriter, not in number form, but spelled out. It took him 16 years. pic.twitter.com/hnwskwkZ9U
This is the first time I have seen anyone ever articulate up front that Proofs Without Words require the reader to put in effort. Seriously it needs to be much clearer on the box that they are actually Proofs That Need You To Add Words.
If you let one row of fish follow their nose in Escher’s woodcut “Circle Limit III”, all the rest are forced to swing around wildly.
The fish here are strung out along “hypercycles”: curves in the hyperbolic plane that are equidistant from a given hyperbolic line, but no two … pic.twitter.com/iFvjEd5xoI
I never get tired of this animation to show where the area of a circle formula comes from. You can also use it in Calculus when talking about thinner and thinner slices. Curriculum Tags: Gr7, Gr8, MCV4U https://x.com/mathladyhazel/status/1880470241601622391
There are some good comments in the feed and I like the way the steps are laid out for adding integers but the line that resonates with me is the last part of this: "Get students really comfortable placing positive and negative numbers on number lines. Don't take this for granted" Curriculum Tags: All https://fivetwelvethirteen.substack.com/p/conceptual-understanding-doesnt-happen
New post: conceptual understanding doesn't happen all at once.
fivetwelvethirteen.substack.com/p/conceptual...
#iteachmath #mtbos #edusky
NEW Blog Post: ‘Four ways of seeing education, and why "best practice" is a myth’
Why do educators disagree about 'best practice'? Understanding competing visions of education's purpose reveals why universal solutions fall short.
amiealbrecht.com/2024/12/11/f...
Looking for a fun, free winter activity to cap off the year? ☃️
With this new holiday activity in Desmos Classroom (using Polypad of course ๐), students can design their own winter wonderland! They’ll color snowmen, build their own snowflakes, and more. ❄️
Check it out: bit.ly/4ix92Ru
I wrote about how I use the @desmos.com data collection screen for a Fermi problem routine in my classroom www.edutopia.org/article/tips... and here is my Desmos collection of those screens: teacher.desmos.com/collection/6...
Any other Fermi problem fans in the #mtbos #iteachmath ♾️ community?
When I looked at this I thought I would just start with a brute force method but after one calculation it was clear I should look at something more logical. And yes, it was a non intuitive result but it made sense. Curriculum Tags: Gr7, Gr8, MTH1W https://x.com/howie_hua/status/1867334829991506197
In my latest Edutopia article, Stanford prof. Denise Pope points out the glaring problem with grades:
“The first thing kids would do is go to the back of the paper, look at the grade, and never read my comments."
9 reasons why teachers should grade less:
www.edutopia.org/article/why-... #EduSky
December #ProblemSolving Calendar is here! Enjoy & share your process here.
Also: BONUS articles on Mathematical Curiosity.
Sign up to get an email for new posts ๐ (help me crack 100 followers?)
#MTBoS #iTeachMath #RecreationalMath #MathSky #MathsToday
karendcampe.wordpress.com/2024/12/01/d...
We should embrace the fact that area models with Whole Numbers, Mixed Numbers and Pure Decimals are all exactly the same.
#MathSky #EduSky #ElemMathChat
Area changing illusion ๐ Why does the area seem to change? ๐ค For an explanation as to why this happens, see youtu.be/6leIwa3PA2E?.... #MTBoS #ITeachMath #math #maths #illusion #paradox #edusky
I think @Howie_Hua sums up what I think about these types of questions. Don't get me wrong, I think they are great. But they also show students that algebra doesn't have to be as hard as it seams. Curriculum Tags: All https://bsky.app/profile/afreeparticle.com/post/3lcjn5cqawc2r
Trying to have people solve a system of linear equations on social media:
#math #ITeachMath #EduSky
We tried a mashup last week: #OpenMiddle – Mild, medium, and spicy results lead to more engagement and strength-finding.
jplgough.blog/2024/11/24/o... @robertkaplinsky.bsky.social
I absolutely love these Congruence puzzles by @unsolvedmre.bsky.social so I've turned them into an online worksheet. Thanks for letting me share Matt. Perfect for LogiqBoard ๐ #EduSky #maths
logiqboard.com/worksheets/W...
This is an incorrect calculation of the area of a triangle by a young Babylonian student at school around 1900-1600 BCE, excavated from the ancient city of Kish.
It’s a moment in the history of math, of education, of children, of mistakes, of people being people. I love it.
Humans have been using spreadsheets for millenia!
But we still don't teach spreadsheets* in K-12 (the little hill I plan to die on)
#iteachmath #mtbos
*with exception! don't @ me
Even if you are talking about division of polynomials, I think it's important for you and your students to have a good understanding of the basics. For that, start with one of @GFletchy's progression videos. You can check them all out here: Curriculum Tags: All https://gfletchy.com/progression-videos/
NEW VIDEO: Progression of a Strip Model Diagram. I love this model because it lays a foundation for understanding unit rate and proportional thinking. https://t.co/nbDPv6yUXe
I always used to start my lesson on squaring binomials with this but extended it to the form (n + a)2 = n2 + 2na + a2 and would start by asking kids for whole numbers close to 50 and I would square them in my head before looking at the algebra that showed why it worked. Curriculum Tags: MPM2D, MFM2P, MCR3U, MCF3M, MBF3C https://x.com/howie_hua/status/1845116066386804979
If you know one perfect square, here's how you can mentally calculate the next perfect square: pic.twitter.com/ugD9qCOfb2
I appreciate that @JennaLaib continues to add to her collection of slow reveal graphs and I also like the reminder that we shouldn't steer away from controversial topics. Check out some of the new graphs including the one on the correlation between gun deaths and gun laws. Curriculum Tags: MDM4U, MAP4C https://slowrevealgraphs.com/
I have always liked the idea of having a bunch of small little applets to use to have students work on and discover properties. curriculum Tags: MTH1W https://www.geogebra.org/m/myqhscbz
I think this video would give you some things to do with students when talking about number systems and types of numbers or even something to do that is connected to factoring Curriculum Tags: Gr7, Gr8, MTH1W https://www.youtube.com/watch?v=Zrv1EDIqHkY
Image Links
Like many, I have some serious #NCTMChi24 FOMO but these sketchnotes from @JGough may help alleviate that, starting with those from #NCSM Curriculum Tags: All https://x.com/jgough
#NCSM24 Opening @MathEdLeaders Keynote from @edtrust Denise Forte: Not Counting Our Kids Out: Equipping Communities with the Picks, Shovels, Scaffolds, and Other Tools Needed to Develop Math Mindsets in ALL Students pic.twitter.com/LLNiPITK8t
OUT with the Old (Rules that Expire) IN with the NEW (Meaningful Representations and Generalizations) with Sarah Bush and Karen Karp #NCSM24pic.twitter.com/3Gogmg08KA
Helping Teachers Keep Their Students Whole While Identifying Holes in Their Mathematical Understanding Before They Become Barriers to Student Success with @cfryschrock#NCSM24pic.twitter.com/v3cCxiozqd
Learning Together: Organizing Schools for Teacher and Student Learning with Elham Kazemi, Jessica Calabrese, Alison Fox Resnick, Lynsey Gibbons, Becca Lewis #NCTM24pic.twitter.com/qVHYHfRzmh
Join the Data Revolution: Why Statistics Rocks K-12! With Kaycie Maddox and Christine Franklin #CPAM HMW foster and develop statistical reasoning and problem-solving for all students? pic.twitter.com/LePDyF7fDY
Helping Students Become Powerful Math Learners with @fawnpnguyen#NCTMChi24 What actions will you take to empower your learners to move to powerful from feeling powerless? pic.twitter.com/lmxUBP1Nhf
Centering Student Voice and Discourse in Primary Classrooms with @ZakChamp#NCTMChi24 What pedagogical moves do you choose to make? How do you check yourself so that we listen more to give airtime to students? #identityworkpic.twitter.com/lwf7Nd3zLI
Accommodations, Not Modifications for Equitable Learning Opportunities with Dan Ilaria #NCTMChi24 plan to leverage students’ strength to open up access to grade-level mathematics for all. pic.twitter.com/yRAyYL8FSe
I don't think it's important for students to memorize formulas like this, however, I do think it's good for them to know that they exist Curriculum Tags: Gr7, Gr8, MTH1W https://x.com/ZahlenRMD/status/1812647795226284116
