This Week at the Global Math Department

Edited By Casey McCormick  @cmmteach
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Online Professional Development Sessions


A Computational Approach to Functions
Presented by Patrick Honner

Looking for a new approach to teaching domain and range? Or an opportunity for students to use their crossover computer science skills? Taking a computational approach to functions allows for the rigorous development of all the fundamental concepts in an active and creative way, while at the same time offering endless opportunities to extend deeper into both mathematics and computer science. If you teach about functions—and what math teacher doesn’t?—you will leave with something new to think about for your math classroom.

To join us at 9:00 PM EST for this webinar click here!

Next Week

Strengths-Based Mathematics Teaching and Learning:
5 Teaching Turnarounds to Build Student Success

Presented by  Beth Kobett

Explore teaching turnaround strategies that can reframe and open up students’ mathematical learning opportunities. Learn to identify and leverage students’ strengths to develop powerful and strategic learning moments that recognize and bolster students’ strengths to build mathematical success.

Register ahead of time by clicking here!

You can always check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

From the World of Math Ed

Fractions: Inside & Out of the #MTBoS

First things first, S/O to Liz Caffrey (@AsymptoticLiz) and her awesome shoes, who’re redefining fashion in sequence.

Lately, I’ve been fascinated by fractions and the conversations that we, (the #MTBoS community-at-large) have about them. When I did a Twitter search for the latest/top tweets (#MTBoS and Fractions), I saw the following words used to describe fractions or the relationship that students have with them: demystifying, challenging, struggle, gatekeeper, break down, and misconceptions. As math educators, we are aware that students’ learning of fractions feels like a make or break point for whether or not students will develop a productive disposition & positive identity in mathematics.So I thought it’d be interesting to look for cases in the #MTBoS and outside the #MTBoS where fractional understanding was of imminent importance.

This week, we got to listen in on a conversation in Marian Dingle’s (@DingleTeach) classroom as her students used the transitive property to make sense of fractions being division. Fractions are Sharing; Sharing is Division; SO FRACTIONS ARE DIVISION!

Berkely Everett (@BerkelyEverett) shared a #samedifferent post to help us think about the way we count denominators.

One of my favorite resources for understanding the conceptual fluency, strategic competence, and adaptive reasoning in fractions is Graham Fletcher’s (@gfletchy) video series on the Progression of Fractions. This was a really helpful video for me, as a high school teacher who sometimes forgets how students develop their thinking in fractions.

Here are a couple of examples I found outside the #MTBoS, where the understanding of fractions played a critical role:

This week, Amber Guyger, a former Dallas police officer who shot and killed her unarmed neighbor was sentenced to ten years in prison after a criminal trial. Several weeks ago, the defense attorney in this high-profile case requested that the case be moved to a different district, to “assure a fair trial”.

In this tweet, S. Lee Merritt, Esq. (@MeritLaw) discusses the importance of having the Botham Jean murder trial heard in Dallas County, where the crime took place, instead of relocating to a different site.

How are fractions being used in this case?  How closely does the jury’s racial makeup “reflect the diversity of Dallas County?” To what level of precision (SMP.6) is the prosecutor attending to when defining the diversity of Dallas County? Does the fractional relationship in diversity change depending on this definition?

In another critical example, an impeachment inquiry against the President of the United States of America was filed this week. The President (@realdonaldtrump) tweeted the following in response:

In the thread under this original tweet, the following maps were given as counterexamples to the map provided by the President. Several Twitter users cited the number of popular votes or electoral votes for the different candidates in the 2016 election (“That’s 65,844,954 blue dots for Hillary Clinton and 62,979,636 red dots for Donald Trump.”). Find the Official Election Results here.

Source: (Mark Newman/University of Michigan, 2016 election.)

What is the fractional relationship between blue and red in each map? Why are these fractional relationships so different, even though they span the same area (the United States)? What viable argument might each of the Twitter users be trying to construct (SMP. 3) with the map they chose to post? (Tangent Time: Why aren’t Hawaii & Alaska on all 5 maps?! Talk about erasure!)

It seems that fractions are not only of critical importance for developing a positive mathematical identity for our students, but also in making sense of the world in which our students live.

Written by Lauren Baucom, @LBmathemagician

Something Old, Something New, Something Borrowed, Something Blue.

It goes without saying that there is a lot that passes through the daily stream of tweets. What I’ve picked out below come from some significant MTBoS contributors and the four highlights are merely a taste of the gold they consistently sprinkle my Twitter feed with on a daily basis. I hope you enjoy it as much as I did.

Four Stages of Using Models

Brian Bushart (@bstockus) got us all thinking about what type of thinking we might be biased towards when facilitating a number talk by sharing his thinking on the Four Stages of Using Models. As Kathy Richardson (@letkidslearn) describes, these four levels unpack how students use models to solve problems, highlighting that although we’d love all students to be demonstrating thinking at Stage 4 (solving the problem mentally), there are some important distinctions between what students are doing prior to that, and that just because students are at Stage 4, operating in Stages 1, 2 and 3 can still support their learning. If your thinking resonated with what you read on that post, perhaps you want to also check out the one Brian pushed out four days later on Multiplication Number Talks Using Models.


He’s at it again, folks. Steve Wyborney (@SteveWyborney) has started releasing the first of his 51 brand new Esti-Mysteries challenges. If you haven’t seen these before, Steve’s original post is a great starting point. One particular thing that I love about them is the range that appears and adapts based on the clue. Here’s an example, which would be great for introducing inequalities:

Can you visualise this? 

There aren’t many things I love more than seeing something and immediately thinking “hmmm is that right?” then going to check it out and end up thinking, “well, would you look at that? It is right!” I went through that exact process when I saw Mark Chubb’s (@MarkChubb3latest post:

The best thing, I thought, was that I was left with the “I wonder if…” types of questions. This is part of a nice little post he put out through the week, which is definitely worth checking out. Better still, let Mark know some of your answers!

The Domino Effect

Sarah Carter (@mathequalslove) showed her generosity by contributing her files she used to create a whiteboard display of the Domino Effect puzzle. Originally from Brainteasers : 195 Puzzles to Keep You Sharp, Sarah posted this on Twitter through the week and, if you were like me and read it as any eight dominos, you would have had the extra fun of finding eight dominos that could be possible.

Written by John Rowe, @MrJohnRowe

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