Wednesday, May 25, 2016

Introducing EMBARC.Online

I’d like to introduce you to EMBARC.Online.

EMBARC stands for Eureka Math Bay Area Regional Consortium.

Our vision is:
  • To build a collaborative community of Eureka Math users
  • To provide a common website to support all users of the Eureka Math curriculum
Two years ago (2013-2014 school year), teachers in my district began using using bits and pieces of the EngageNY math modules. The following year nearly two-thirds of our teachers used EngageNY as their sole math curriculum while the Math Curriculum Adoption Committee spent the year deciding on a curriculum to adopt. As it turns out we adopted EngageNY, although we officially use the Eureka Math branding. (I could not be more proud of the teachers who specifically made the decision to adopt an ambitious curriculum that, while great for students, is challenging for adults.)

During our time dabbling in using this wonderful curriculum, it became very clear to me - as the TK-5 Mathematics Instructional Coach - that our teachers were going to need a lot of support in order to fully understand and implement it. Thus began a steady stream of emails from me to my teacher community, sharing the “latest and greatest” web URLs, links, and resources.

I had every intention to be helpful. Indeed, I thought each new resource I shared was worthy of being used by the classroom teacher. Unfortunately, the teachers were drowning in the sea of “helpfulness” that was spewing from my email. The problem was that teachers had no time to read through the latest resource I shared, understand how it relates to the Eureka Math content being taught, and then assimilate it into the already lengthy lesson. After all, teachers were already complaining that the 60 minute Eureka Math lesson takes 90 minutes or more to complete...and now I was asking teachers to consider including this latest and greatest supplemental resource?

This is where EMBARC comes in.
Rather than sending teachers out to a variety of third-party locations (Illustrative Mathematics, Inside Mathematics, Zearn, Three-Act lessons, to name a few), we will curate the best of the web and organize it on Great supplemental resources will be placed right at the topic or lesson where they will be most useful. 

Are you a 5th grade teacher doing Module 5 Lesson 18 tomorrow? Navigate there and you will find great resources to choose from to supplement, augment, or totally re-write the lesson. The teacher can access the exact support she needs at the exact moment she needs it.

Curating outside content into the curriculum is the first way that EMBARC distinguishes itself from other EngageNY/Eureka Math website. Nearly all EngageNY/Eureka Math websites have the core materials as PDFs ready for download and that’s about it. For additional resources, teachers are usually sent to external links to fend for themselves. EMBARC curates to make things easier on the teacher. We bring the resources in for the teacher, rather than sending the teacher outside to other sites.

A collaborative community
A second, more profound distinction is the collaborative community on EMBARC. Every module has a “Faculty Lounge”, in which our users can share ideas: new resources, shared Pinterest link, ideas for pacing.

Our EMBARC editors will find the best ideas shared in the Faculty Lounge and integrate them through the rest of the module. Teachers learn so much around the lunch table! We re-create that experience in the Faculty Lounges on EMBARC.

Now what?Join the community! Take part in a community of Eureka Math users who support each other, share ideas, and collaborate.

EMBARC is entirely free to use. No account is necessary. However, you will need to create a free account in order to contribute to the discussion in the faculty lounges.

The more people who join in on the conversation, the more we support each other, the better we will be for our students.


Tuesday, May 10, 2016

Is a parallelogram also a trapezoid?

A famous bard once said, “A trapezoid by any other name would still be a trapezium”.

Okay...totally not true. But it brings to mind the question I am often asked, “What is the definition of a trapezoid?” In fact, I was asked this question today. So here is my answer…

For mathematics, being a subject that is supposedly the “universal language”, this question opens a huge can of worms and has a surprisingly involved answer.

There are three – yes three – different ways one can define a trapezoid. Let’s get started.

If a person walks up to you and says, “Let’s discuss trapezoids”, the first things you should do is listen his accent. Is it American? Is it Canadian? Or some other English-speaking accent? This matters.

For the words trapezoid and trapezium, America and Canada defines them one way, but in other English speaking countries these same two words have their meanings switched.

In America and Canada...
trapezium trapezoid

In other English speaking countries...

trapezium trapezoid

In America a trapezium is a quadrilateral that has no parallel sides. Sometimes this is called an irregular quadrilateral.

So now that we have define a trapezoid to be the figure that is not a trapezium. There is still the matter of the two definitions of trapezoid in America.

Let’s start with this figure…

Most people would immediately recognize it as a trapezoid. There are two ways we can classify as trapezoid: the inclusive definition and the exclusive definition.

T(I): a figure with at least one pair of parallel sides
T(E): a figure with exactly one pair of parallel sides

Both definitions are legitimate, but they each lead to other differences in classifications.

For example, a parallelogram is just a parallelogram in T(E), but a parallelogram is also a trapezoid in T(I).

In T(I), even a square is considered a trapezoid!

Why can’t we all just get along?
We don’t need to argue over which definition is correct. They both are. So, this means when we speak about trapezoids, we must preface it with an agreement of which definition we are least for that instance.

T(E) seems to have its origins in the 1500’s prior to the advent of calculus. When calculus came along, we began using trapezoids to estimate the area under curves.

Public Domain,

CC BY-SA 3.0,

As the animation shows, some of the trapezoid slices begin to look suspiciously like rectangles. Aha!!! This is when T(I) got invented.

Common Core Standards
In 5th grade the standards are non-committal on the trapezoid issue.

The 3rd grade standards also sidestep the issue.

But the Progressions Documents for the Common Core Math Standards make it clear that mathematicians prefer we use T(I).

Since a key component of the Common Core Standards is that students will be college and career ready, it seems the best trapezoid definition to use is the one that leads to calculus...T(I).

These are all trapezoids…


A trapezoid is a quadrilateral with at least one pair of parallel sides.


Monday, May 2, 2016

Eureka Math Grade 5 Module 6 #engageny #eurekamath

For the rest of our Eureka Math resources, visit




What research says about the value of homework: Research review

Used with permission from Wikimedia Commons

Given that homework is such an engrained aspect of the K-12 culture, you'd think there must be clear evidence that the homework being assigned is beneficial. You'd be wrong.  Researchers are nowhere near consensus on the benefits of homework. In general, there appear to be something research agrees on...
Homework in elementary school has zero effect.

To read more about the confusing state of what research says about homework, go HERE.