#WODB and Polygraphs: Lines in the Classroom

I’ve been using these sorts of problems in my classroom intermittently for many years.  My first exposure was at an NCTM conference in Baltimore in 2004.  This type of problem was titled “Puttering with Patterns”  similar to this one here:

Screen Shot 2015-03-30 at 10.46.04 AM

I worked as the math teacher in a k-21 special education facility at the time and immediately understood the benefit of posing problems like this to students with special needs…EVERYONE can notice something meaningful to contribute.

Here are several reasons why each one is different:

Screen Shot 2015-03-30 at 10.50.22 AM

I was reminded of this type of problem by Christopher Danielson when he released “Which one doesn’t belong?  A shapes book.”

I’ve been out of the classroom for many years, but this year have returned to lesson plan for an 8th grade classroom that is being taught by a long term sub (the teacher moved out of state in October).  I’ve been in this classroom more often than not–co-teaching with the sub.  This has been my opportunity to really try out many of the activities that I have come across on Twitter–YAY!!!

When @MaryBourassa created the new site “Which One Doesn’t Belong?”, I was excited that she brought this type of problem to the forefront AND gave it a more secondary sort of spin.

A good portion of the students in these 8th grade classes that I am working with are reluctant learners.  But, #WODB pulled them all in.

We’ve been working on linear equations, including graphing lines using slope and y-intercept.  So for the last day before spring break I decided to use this:

Screen Shot 2015-03-30 at 11.06.21 AM

as a lead in for this:

Screen Shot 2015-03-30 at 11.07.06 AM

The sequence of instruction worked perfectly for these 8th graders…because, really, Polygraph is just a giant “Which One Doesn’t Belong?”

Fo the #WODB task, my students noticed that the 2nd graph was proportional, that the 3rd graph had a negative y-intercept, and that the 4th graph had a negative slope.  We needed to have a classroom discussion to determine an attribute for the first graph that didn’t fit in with the rest.  We ended up talking about x-intercept for that one (a term that they didn’t have yet).

All of these observations became questions they asked when playing Polygraphs.

I’m looking forward to making the #WODB problems a larger part of our typical daily routine.

Visual Patterns and Missing Figures

The past few years I’ve used Fawn Nguyen’s Visual Patterns site as the structure for building an 8th graders understanding of linear relationships. Students GET patterns–even the most struggling learners can identify what’s happening in a linear pattern and complete a table of data points. What I’ve done recently is used the patterns to build an understanding of finding the constant rate of change between two points. Here is an example of what the students are presented with… Instead of giving the students something like this: Missing Figures 1   I give them this: Missing Figures 2   The students work on their dry erase board to create an input-output table of data points beginning with x is 0.  We’ve spent A LOT of time creating our own tables that it has really started to become second nature.  I didn’t tell them how to figure out the missing figure numbers…they just figured it out on their own. Without prompting…the students even wrote the rule for these situations (I had only asked for the rate of change). We worked through several problems like this on dry erase boards (pulling from Visual Patterns each time) and then went to problems like this: table 1 and this… table 2 With these problems I asked them to determine the (x, y) values that would fill the purple oval.  Again, without prompting, they wrote the rule for this relationship. The follow up to this activity was via @Mathalicious …I used their Domino Effect task which was a great follow up to the missing figure number dry erase activity.  Students felt very confident in their ability working through that task completely independently. Here is a set of 5 Missing Figure Images…thanks to @fawnpnguyen for her great resource!!!

Tackk, Geogebra, and Dilations…

Ever since I discovered Tackk I’ve been eager to use it as a way to deliver content to students.

Our 8th graders have been learning about transformations without the benefit of any geometry software.  There have been issues with our license for Geometer’s Sketchpad, which is the software that we have used in the past.

I’ve fiddled with Geogebra here and there…but, have not found the time to truly sit down and figure it out.  However, I pay close attention to what these folks are doing: @a_mcsquared, @MathButler, and @mathhombre.

I spent a good chunk of my time this past Friday figuring out how to create this lesson on Geogebra so that I could upload it to GeogebraTube.  I kind of geeked out when I figured it all out…because now I can really see all of the possibilities.  And…I can understand the hype!

I decided to deliver the entire content of this lesson using Tackk because…it’s just so easy!!!  I’m pretty pleased with what I came up with…although I know there is always room for improvement.

Check out my Tackk…

Image of Dilations Lesson


Here is the link to the organizer for the Dilations Explorations.

I would love feedback on what I’ve put together!!!

Using Tackk to Share with Colleagues

I heard the best quote from a colleague last week…she said

“I used to think learning math was about doing, doing, doing…and now I know it’s about meaningfully doing.”

I’m not gonna lie…I got a little tear in my eye when I heard that phrase.

As an instructional coach (technically my title is Instructional Resource Teacher), I struggle with how much to share re: all of the great resources that I come across.  There are SO MANY great things out there…but it can be very overwhelming.  I decided that if I really want people to take in some of these resources…I need to find a bite-size delivery model.

@RafranzDavis always has great Ed-Tech resources to share…and one she shared recently was Tackk.

Tackk image for wordpress

(You can read more about how Rafranz has used Tackk here.)  

I decided to check out the site myself, and couldn’t believe the ease of use.  And IT’S FREE!

I had been looking for a way to deliver content and updates to the math department at my school~so, I decided to see what it would look like in this format.

Here is what I came up with:
See on Tackk.com

Notice I shared one blog post, a quick video, a link to a print resource…and then some important dates and updates for our department.

I plan to do this weekly…I know there are a lot of other uses for this technology and maybe my colleagues will explore how it could be used in their classroom.

A Sunday Summary–Writing SLOs and more…

I want to Keep It Sweet and Simple with this post…I’ve gotten in over my head by taking on teaching the undergrad course along with a full-time job, three kids, and a husband.  But, I do have some interesting things going on.



3 things that I’ll follow up on this week:

  • I came across an interesting folder last spring regarding writing your SLO in terms of looking at the math practices.  I plan on writing my SLO in this way because I believe it’s more meaningful for instruction.  We are going to discuss it at our department meeting…I think several in my department are on board with trying to figure out how this might be done.  Hopefully I’ll be able to post a follow up.
  • Our book study bundle of Powerful Problem Solving came in (our PTSA purchased this for us).  I’ll disperse those on Monday…and we can begin digging in.
  • I’m going in to an 8th grade classroom tomorrow to introduce Pythagorean in 3D.  I thought this lesson from Yummy Math was a good intro.  I created my own worksheet to go with it because I want to see if the students can visualize the scenario and come up with the important information needed to solve the problem.fish pic

*It’s not perfect…but going to see what happens…

2 things I’m looking forward to:

  • I’m taking the online Math Forum class–Looking at Student Work.  It began this week…I can’t wait to learn from the others that are taking this course.  I also think it will fit in nicely with writing SLOs in terms of looking at the Math Practices.
  • The nice weather that we’re having…moving further into the fall, leaves changing, going to see a Redskins game, …

1 thing I want to work on:

  • @jreulbach posted a Desmos lesson she’s working on.  I was planning on writing something similar for Algebra 1.  I want to take all of the great feedback she’s getting…and make an attempt as well.  I’ll get around to it soon…  😉

A Pythagorean Stations Lesson

I’m so glad that I’ve joined the group trying to blog weekly…although I’ve not been very good at achieving the goal.  Teaching an undergrad class (Math for Elementary Teachers) came up suddenly and it’s completely absorbed my free time. 49411-mtboschallenge_3 This week’s prompt is October Goals (you can also share a weekly summary).  Check out @luvbcd blog here and @druinok blog here for posts that are a part of this challenge. I wanted to share a lesson that I wrote for 8th grade teachers to use when beginning a unit on Pythagorean Theorem.  My goal for October will be to work on writing other lessons with a similar degree of detail. When I was still in the classroom…all of the detail of my lessons lived in my head.  I’m really working on how to articulate more clearly/explicitly the details of a lesson so that someone else can implement with ease. When researching lessons to introduce Pythagorean Theorem…I considered:

I then did some Internet research and came across this idea as a way to launch into an investigation: Screen Shot 2014-09-28 at 8.56.08 AM I liked this as a way to keep students coming back to the purpose of their investigation…which offer would you choose? I decided I wanted students to experience multiple ways of looking at the relationship between the areas of the squares on the sides of the right triangle…so I developed three different stations.  The Google Drive folder with the materials for this Discover Pythagorean Stations is here.  You should make a copy of the materials so that you can edit and make your own.

Here is what I did at each of the three stations:

Screen Shot 2015-04-03 at 11.39.12 AM

Screen Shot 2015-04-03 at 11.39.25 AM

Screen Shot 2015-04-03 at 11.39.36 AM

Screen Shot 2015-04-03 at 11.39.45 AM

Some think abouts for using this activity:

  • For this activity, I would definitely get another set of hands in the room (I was the second set of hands in my building).  We ran 2 groups of each station…so that you can split your kids up into 6 groups.
  • For the NLVM site…make sure the computers you get are up to date with Java.  You need to do this prior to doing the activity.  (For groups of 3-4 we used only 1 or 2 computers at each of these stations–kids worked together).
  • Kids will need the most help on the computer station and the tangram station.  Here is the answer key for the tangram station (if kids struggled…I would get them started with the big red piece location).
Displaying IMG_0037.JPG
  • For the recording document…I tried to get them to consistently draw a sketch of what they saw with any quantities that were important to figuring out which students chose wisely re: the gold.
  • I kept coming back to what we were trying to figure out.  Who made the best decision…two smaller squares of gold or the one large square of gold.  Kids figured it out after the first station…and their a-has were priceless.  I still think it was useful to work through each of the three different ways to look at it.  So at the end, I asked them to reflect on what they learned and which station was most effective for their learning.

Here is student work from the recording document: Screen Shot 2014-09-28 at 9.25.51 AM

Some Pythagorean Problems to solve:

Additional Resources you might consider:

A Favorite Activity: Create-A-Quiz

This is part of a challenge to blog weekly for the school year.  See other posts at #MTBoSChallenge.


I missed yesterday’s link up to share a favorite game or activity…and @luvbcd already shared one of my favorite games SKUNK.  See her post here.

One of my favorite things to do towards the end of learning about a topic is to have the students “Create-A-Quiz.”  The most important part of this assignment is that they MUST make it a multiple choice quiz.

I talk about quizzes and tests with the students and ask them how they think the multiple choice questions are created.  We discuss how the common errors/misconceptions are used to create the WRONG answer choices.  We go over a few examples of how this might be done…focusing on all of the different ways students might respond for a particular question.  Then, I have them work with a partner to make their 4 question multiple choice quiz.  They, of course, must have the correct answer marked for me so that I know they understand the question themselves.

I often use some of the student-created questions as quiz problems and name the authors on the assessment.

I love this activity because the students are focusing on the errors that might occur while using a ton of math talk to come up with the question and the multiple responses.  I think it would be a nice extension to have students come up with multiple select items for their quiz as well.

#MTBoSChallenge A 3 + 2 + 1 Summary

I missed blogging last week because we were trying to enjoy the “last unofficial” weekend of summer.  I want to continue on this journey of blogging weekly as part of the #MTBoSChallenge…so here goes.


I’m having a hard time figuring out how to break down my 3-2-1 summary…so I just decided to share 3 + 2 + 1 things that I’m thinking about now…

  1. This was the first week of classes at St. Mary’s College of Maryland.  This is where I spent my undergrad years as a math major and now I live about 7 minutes away.  I’m co-teaching Math for Elementary Teachers with a colleague from within my middle school building.  I haven’t taught anything like this class before and it’s a wonderful challenge.  I expect to spend lots of time perusing the blogs of @TracyZager@JSchwartz10a@gfletchy, and @Trianglemancsd.
  2. I’m super excited because I decided to ask our PTSA to purchase the book study bundle for Powerful Problem Solving from @maxmathforum for our math department.  They agreed to do it and so far about 10 out of 12 people in the department that completed my google survey said they would be interested in reading the book together.  A resource teacher at one of the other middle schools liked the idea so much, she asked her principal if they could pursue the same thing.
  3. One of my responsibilities this year is supporting our In School Intervention room for one period a day (this is for the students that have been disciplined).  While the students are in there, they are supposed to complete the work they are missing from not being in class.  I am there to give them any help that they may need.  The other day, however, the students had completed their work and needed something else to do.  I decided to check out the Math Munch games tab.  I steered the students towards Light-Bot, as I was familiar with the game because of #HourofCode.  They were completely engaged and were shouting “YES!” when they would complete a challenging level.  I plan to expose them to some of the other critical thinking games on the site.
  4. I need to start working on Professional Development that I will be delivering inside the building on September 19th.  Another colleague (reading/language arts department chair) and I were asked to co-present on accommodations and modifications in the general education classroom.  We will each have suggestions specific to content, but, our over-arching theme will be how to minimize executive functioning weaknesses.
  5. As I’m sitting here trying to think of my number 5…I’m thinking my 1 through 4 are quite a lot.  So…I’m going to take a minute to pay attention to the NFL Sunday that I’m watching right now before I continue on with my #6. [GO REDSKINS!]
  6. I’m not in the classroom anymore…so I don’t have a place to implement all of the lessons/activities that I’d want to.  This week…I’ve seen these great posts:

This Week’s Sunday Summary… A New 3-2-1

Another Sunday…another summary for the #MTBoSChallenge!  




Students returned to school on Wednesday, but the week began with district-wide, pre-service professional development by content area. 

3 things that happened this week:

  • Monday was the district-wide professional development for secondary math (grades 6 – 12).  As part of the professional learning experience provided for the teachers, I created this Thinglink that allowed the teachers to work through at their own pace, based on their own needs.  This was out of ordinary for professional development in our district–and I was incredibly nervous about how it would be received.  There are opportunities for feedback built in to the Thinglink…I was ecstatic to find that most of the feedback was extremely positive!  A big thank you to @Algebrasfriend for encouraging me to move forward with my idea for providing a professional learning experience in this format…as well as for providing me great feedback for refining some of the rough edges!
  • I began to work on my schedule for providing support in my building.  I will be mentoring a returning teacher that is teaching all of our 8th grade Algebra 1 courses.  So, I have made being in her first period class part of my day.  She has 2nd period planning, so we are able to reflect and revise rather easily and determine if there needs to be any adjustments for the rest of the day.  I also know for sure that I will be co-teaching a 90-minute 7th grade class as well, in order to meet the needs of the students with special needs in the class. 
  • Our district has adopted a new model for students that have to serve in-school suspension.  One 45 minute period of my day (each period of the day is covered by certified teachers) will be working with any student(s) that have been in school suspended.  My role will be to help them complete any of the work that they missed due to being removed from class.  I am also looking into creating some math file folder activities to pull, in addition to creating a Google site where students are linked directly to games for math practice.  When I went in to work with a student this week, I used the Thinking Blocks site to help model some of the fraction problems that needed to be completed.  

2 things on my to-do list:

  • One of the teachers in my building team teaches with a special educator all day.  She is interested in how to minimize teaching to the whole class–and instead deliver instruction in small groups through the use of stations.  We will be working together this week to figure out what this will look like, and determine next steps.  I’m thinking a lot of cutting, gluing, and laminating is in my future!  (PS…if you have any input on using stations regularly in your classroom–I’m all ears)
  • I REALLY need to add more problems to this site for each grade level.  

1 thing I’m hoping to be consistent with:

  • As the resource teacher for the building, I’m trying to keep track of the great tasks, lessons, activities that the teachers in my building are using to build instruction.  I want to pay close attention to the sequencing and the pacing. I’d like to build an in-house resource so that we aren’t constantly saying “What activity did we use for….?” and then have to recreate the wheel.  


A Sunday Summary for the Beginning of a New Year #MTBoSChallenge

I’ve decided to continue on this journey of blogging more because I really see the value in it.  I’ve joined a new challenge (who doesn’t need motivation, right?)…and we’ve decided to stay connected on Twitter using #MTBoSChallenge.

As an Instructional Resource Teacher (IRT), I will approach each challenge with a different lens than if I was still in my own classroom.

We started back to school this past Thursday…but, honestly, my mind never leaves work behind.  We only have two days in as teachers so far…with students returning on Wednesday.

Here is my Sunday 3-2-1 summary:

3 things that I’m looking forward to this year:

  • I’m attempting to implement the Lesson Study process with the teachers in our 7th grade.  There are 5 of us on the team…4 general education teachers, 1 special education teacher, and myself.  I believe it will be an extension of the work that we’ve been doing…we will just hopefully dig a little deeper.
  • I’d like to implement #myfavorite at our monthly department meetings.  I stole this idea from the #MTBoS …Teachers do so many things that are great and they just don’t realize it b/c they are locked in their own room.  I’m hoping this fosters sharing and collaboration…but most importantly provides an opportunity for each person to see that they do have something to contribute to our community.
  • I’m hoping to bring some of the great educational technologies into the math classroom~Desmos, Thinglink, Plickers, Aurasma, Padlet~just to name a few.

2 things that I want to get better at:

  • Providing really strong qualitative feedback to students…and supporting teachers as they do this.  It’s a lot of work…so I’m going to be on a mission to figure out how I can help to streamline this process.
  • I have a lot going on in my head ALL the time.  I can tend to overwhelm if I’m not careful…I want to work on streamlining my own process of engaging with the teachers that are doing the work in the classroom.  I’m really glad that @approx_normal retweeted this post from @jedipadmaster


1 thing that I’m nervous about:

  • Having time to get it all done.  I probably need to prioritize a bit better…still a work in progress.