Comments on: Visual Patterns + Desmos = Amazing!

By: First Week Highlights – Mrs. Taplin's Math

First Week Highlights – Mrs. Taplin's Math — Sun, 07 Jul 2019 13:30:27 +0000

[…] know what they will be learning the next few weeks. Then, we reviewed patterns by doing this lesson. It was a great, low prep activity that helped students review patterns and […]

By: Michael Fenton

Michael Fenton — Tue, 03 Mar 2015 23:20:44 +0000

@Deb, everything you share reminds me more and more of how things played out in one of my classes at Fresno Pacific. We often added an “arithmetic column” to help generalize, and regularly used a “helping column” to “check the neighbors” (numbers above and/or below) and perform various other strategies aimed at finding the generalization numerically.

There are so many valuable things to do with Visual Patterns. I really appreciate your comments, as they’re getting my wheels to turn about what else I can bring into my classroom.

I hope this is the first of many conversations! Thanks again for sharing your thoughts. 🙂

Take care,

By: Deb Stetson

Deb Stetson — Sun, 01 Mar 2015 22:45:29 +0000

Wow-I had no idea about the price on the Learning and Teaching Linear Functions (LTLF). I better put my copy in a safe place, as apparently it is a collectors’ item! Last time I ordered the participant’s version, it was $15, and now it has gone to about $30, which is much better than the facilitator’s version you pulled up. Geez. The main difference between the two is that the facilitator’s version describes how to conduct a series of professional learning activities for teachers. On both there are videos of teachers implementing with students which are interesting, and materials for a whole unit (which are very similar to what you and Fawn already have). Here is the url (forgive me for not being as adept at making this a live link.)

http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias=stripbooks&field-keywords=Learning+and+Teaching+Linear+Functions,+Participants

Nice graphic on the quadratic example. Thanks for sharing. I have used these successfully this way too.

You probably have already done what I will share next, something I picked up from LTLF. One of the things that Branca and Mumme and Seago suggested, was to make the table have 3 columns, one in the center for the “Indicated Arithmetic”. I sometimes change that language in the heading for kids (“show you work”, or “computation”), but the idea is to have them write an arithmetic expression for how they can count the number of circles in the figure (without just counting each one by one), and then for them to use a common method of determining the number of circles in each figure resulting in similar expressions.

It is a bit hard to explain here. I’ll refer you to a document
(https://www.dropbox.com/s/2sjwxm1t3w2i3ms/Linear_Growth_Practicum%20Deb%20Revised%202.28.2015.doc?dl=0)
that was created for teachers who, after doing some face-to-face pd, were going to team teach a lesson for students. It may make it clearer. If you have done something similar I would love to hear about it. I find this extra column useful for supporting students in moving to the algebraic, or to support those recursive thinkers (seeing the adding on pattern) to moving to an explicit function (seeing that multiplication can be used as well.) As I read a bit of Fawn’s website, I believe she noticed that delaying when they write the differences on the tables helps with that too.

Thanks for the conversation!

By: Michael Fenton

Michael Fenton — Sun, 01 Mar 2015 05:07:36 +0000

@Deb, thanks for stopping by the blog. And double thanks for the comment!

I’m not familiar with the resource you mentioned. It sounds like a great resource, though I like the price tag of Fawn’s website better than this: http://amzn.com/0325006822

My introduction to these sorts of patterns (and extending them, then developing rules for them) began with a series of activities from the AIMS Education Foundation while studying the Grad Math program at Fresno Pacific University. I fell in love with figurate numbers there…

We definitely move into quadratics. I suppose you could explore additional function types, though I feel the geometric/area connections that can be made with linear and quadratic visual patterns are the most enjoyable. In fact, we just had a conversation about this on Twitter last night! Here’s a link: https://twitter.com/mjfenton/status/571458522501799937 (The comments I’m referring to arose during a chat with @reilly1041.)

We usually discuss the geometric connection/interpretation in class, but it’s something I decided not to highlight in this post.

Here’s a small set of images suggesting how such a quadratic discussion might play out in class or in a workshop: https://www.dropbox.com/sh/jdutmsd9fh4nzqt/AABWwuHLFoCFmdBNZZ54a_eja?dl=0

Thanks again for stopping by! Looking forward to more comments in the future. 🙂

By: Deb Stetson

Deb Stetson — Sun, 01 Mar 2015 04:03:10 +0000

I have just discovered your blog and posts. I am a former high school teacher turned and now I work with lots of middle and high school teachers. You provide a rich source of reflective food for thought. I am guessing you may have seen Learning and Teaching Linear Functions (older source on DVD) by Branca, Seago and Mumme (sp?) which has a similar approach to using visual sequences to develop students abilities to understand linear functions and graphs.

I wonder if you had some students make some visual connections. In your post above, I can see a way that students can visually see when the function is y = 3x + 2. One might ask, “Where is each part of that equation in the picture? Where is the 2 for example?” They can find where there are 2 circles, and notice that there is a way to see the 2 circles in each succeeding stage, that they are constantly there (pun intended), and they can also see that there is a 3 by x rectangular array of circles, and that the width of that array is increasing (hence that dimension changes and varies).

Thank you for sharing your thoughts about having students draw the sequence for themselves, and then how you have them draw the next stage, and then leap to 10, make a table and a graph. Desmos looks like a great tool–I’ll check that out.

Do you do this for quadratic functions too?

By: Michael Fenton

Michael Fenton — Wed, 25 Feb 2015 07:12:20 +0000

@mhorley Thanks for sharing your comments, and the link! I’m familiar enough with the phrase, and think it’s a great fit here. 🙂

By: mhorley

mhorley — Wed, 25 Feb 2015 07:04:27 +0000

Great post again – thanks! You’ve reminded me of the importance of getting students to actually draw out the first few patterns. I really like the simple idea of folder a piece of paper into 4 and will be using it today!

There are some videos on the nrich site here
http://nrich.maths.org/8111
which I think are nice because they show students that there is more than one way of skinning a cat (sorry – English expression, hope that translates OK!)