A Podcast on Twitter & #MtBos


A while back I received an email from Josh Greesonbach, one of our district’s Instructional Technology Integrators, asking if I would be interested in helping with a Podcast on using Twitter.  Our district is fairly large with over 60 schools, and they have created an EdTech Hub where they are showcasing some of the things we are doing in Chesterfield County.

I was immediately on board.  I love Twitter and find it to be such a rich resource for teaching math.  To me, it’s like the PLCs we have at school, but extended way past the limits of a physical school building.  I have amazing colleagues not just in the classroom next to me, but in Oklahoma, Kentucky, Pennsylvania…..from all over.  Resources are shared freely and so is support.

I love to share my experience with Twitter and the Math-Twitter-Blog-O-Sphere (#MtBos) because I feel so strongly that others can benefit if they are willing to try it.  I’m not sure why, but I find that many teachers are just so resistant to Twitter.  I think many still think it is just a place for celebrities to post every bit of minutia about their lives….I always compare it to television programming.  If you leave your tv on E! that’s what you are going to get.  But unlike television, Twitter offers math support!  Come visit a faculty lounge where you can hang out, bounce ideas off of each other, laugh, cry, think about things from a different perspective and be challenged.  I’m hoping this Podcast will reach others in our district (and beyond!) and encourage them to try Twitter and realize some of the benefits.

Check out Chesterfield County’s Podcast on Twitter & #MtBos here:  CCPS Podcast


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A Tale of Two In-services

August is a time for professional development in our district.  Sessions are held almost daily, with topics such as technology integration, working in a collaborative teaching environment, first aid/CPR training, and content specific training (ie. TI-Nspire training for math teachers).  I attended several sessions this August, but two in particular really gave me pause.

One of the sessions had a LOT of important information.  It was an all day session with structured breaks and a break for lunch, with many speakers addressing different topics.  There was one activity that required attendees to get up and stand in a different part of the room for about 10 minutes, but other than that, we primarily sat and listened.  The speakers were good – they were knowledgeable, had presentations to go along with their content, and most infused some humor along the way.  Even though the content was very important, a casual glance around the room revealed very little engagement.  Almost everyone had their laptops open.  Some were a little more discreet flipping through email on their phones under the table.  A few at each table were attentive, but as the day progressed, fewer and fewer people were really engaged.

A few days later, I attended a second session on a completely different topic.  Again, we were at tables, and outlets were available for our laptops.  Our introductory activity immediately had us up and moving.  We were given name tags with pizza ingredients on a lanyard, but they were displayed hanging down our backs so we could not see our own ingredients.  You had to find a group with other ingredients by asking yes or no questions about your ingredient until you formed a group of five making a complete pizza.  After finding (and confirming) four other group members, the group set to work on a jigsaw activity.  We came back to our original groups to share the information we had learned.  The day continued in mostly this fashion.  There were presentations broken up by group activities.  We had think/share questions and discussed insights and opinions frequently.  We took restroom breaks as needed (the group carried on while you were out of the room) and the inservice was over before I realized so much time had passed.  I left the inservice energized, excited about the content and reflected over it long after I was home.

I know (most) of my students enjoy days that are more like the second in-service, with opportunities to get up and move, and activities involving collaborative groups.  But some small part of me always thinks if the material is REALLY IMPORTANT, I need to structure the lesson more like the first session by telling them exactly what they need to know.  Why is that?  I can honestly say I remember the content from the second session because I was engaged 95% of the time.  I’d have to refer back to the notes I took in the first session as I was not nearly as engaged.  While both sessions offered new content, perhaps the biggest takeaway wasn’t the actual content of either session, but a reminder about the importance of engagement in the learning process.  With the new school year beginning, this was the perfect catalyst to ensure more of my lessons are structured with engagement in mind 😀


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EOC Review – Grouping strategy

Most of the activities in this review unit involve group work, and obviously, there are many ways to do this.  Often in class I allow students to choose their own partners, and frequently this works really well as students tend to work with people they are comfortable with.  Sometimes though, you end up with a group of three who are all stuck, and they spend a lot of time off task because they are not sure how to proceed.  Since I had a limited amount of time to get through the review material, I opted to create groups for the students so each group had varying ability levels.

I sorted the students by their year long grade and made five groups (class of 25).  I placed one of the top 5 students in each group to be the “leader.”  Then I looked at the next five students and placed one in each group, and so forth.  Then I looked at the bottom 5 students and placed them in the group where I thought they would be able to work best collaboratively.  I had to tweak it a bit to ensure weak students had someone who was stronger AND would be someone they would feel comfortable enough with to ask and receive help.  I also looked for possible conflicts, but for the most part, each group had a strong leader who could support others, and who would not be afraid to ask me for help if they needed it.

Before students got into their groups I role modeled how it feels to have someone say, “oh GREAT.  Mary Williams is in my group – she is such a PAIN to work with,” and how that would hurt my feelings.  Then the old, “your group is going to be GREAT because YOU are in it!”  Yeah they’ve heard that before, but it warrants repeating.

I called out group member names one group at a time, and for the most part students found their group members without complaining.  We rearranged the desks and this became the permanent arrangement for the next two weeks.  I did tell students the groups were thoughtfully crafted based on their strength in math.  I asked those who are super talented in math to realize some group members will need support.  I reminded those who are not super talented in math YET that it is up to them to ASK for help, and then be willing to listen to that support.

This grouping strategy worked really well!  I especially like the “Fish in the Reef” activity where all students have to be prepared to explain their group’s answer.  The conversations that happen, and listening to students verbalize their thinking…it makes me realize I need to incorporate this element much more frequently.


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EOC Review: Day 1 – flight to Europe

We started our Algebra 2 review today by boarding a “flight” to Europe.  My plan is to visit a country a day, with an activity and a snack as a tie in with the topic we are reviewing.

signupLast week I created as Sign Up Genius for each of my classes, asking parents if they would be willing to donate snacks for the review unit.  The response was overwhelming!  The freezer at school is full of Italian Ice for our Venice Gondola races next week, and I’ve been busy stuffing goldfish and Swedish fish into baggies for this week.  One of my 3 sections completely filled up the Sign Up Genius, and the other two are pretty full.

Some of my students have flown and some have not.  I thought it would be fun to show a video of a flight attendant reviewing the safety instructions that you typically see at the beginning of every flight.  Delta and Air New Zealand have about a dozen different videos (there’s a Hobbit themed one and a Holiday one with Santa & some elves 🙂  I decided on this one by Delta (I especially like the girls with the Jenga game and the “No Cartwheels” sign).  The kday 1 flightids definitely got a kick out of it.

We had Goldfish crackers as our “in-flight” food today.  One of my parents sent in the individually packaged ones so that was a breeze.  Tomorrow my other two sections will have them from baggies that I will finish filling up tonight.  Kids enjoyed the Goldfish as I reviewed the most frequently missed problems on the district assessment that they finished up during our last class.

Next stop:  Snorkeling!


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Reviewing for EOC Test

Our end of course test for Algebra 2 is in two weeks. Since this is my first year at a new school, teaching new content, I feel an immense amount of (self-inflicted) pressure for all of my kiddos to do well.  Typically my results are strong, but no one at my new school knows that.  I am confident my results will be compared to those of my colleagues who have been teaching this content for many years…..

I’ve spent the past week trying to wrap my  brain around a plan to best review a massive amount of material in the 5 class periods we have left.  I had thought I would have 2 more class periods, but the mandated district assessment took two.  It is an incredibly challenging assessment, written by our district as a simulation test.  It is always much harder than the actual EOC test.  Do I spend time going through that test with students, even though many of the questions are written differently than the EOC test?  I have lots of data, but because the questions are higher rigor, I cannot tell if students missed the question because they don’t understand the content, or if they couldn’t figure out what the question was actually asking??

Should I instead try to hit a strand or two each day?  I found a great Algebra 2 review from York County.  I don’t have time to do all of these, but we could practice in class and then they could work some of these practice problems for homework.

What about calculator tricks?  All year the focus has been on the math, sans the tricks.  For example, simplifying complex numbers.  Do we keep working on reducing i^49th power, or do we practicing changing the mode on the calculator to a+bi so they can check their answers on the calculator?

For the past few years I have reviewed (at my prior school) for the EOC test using a theme with activities and food.  This was sooo successful!  It really brought the stress level down for my students.  I mean, how stressed can you be when you are eating Italian Ice, working in collaborative groups in a Gondola Race, moving your gondolier along with every question your group gets right?  I want to do this same type of unit with my Algebra 2 kids, but feel a little shy when my colleagues are doing more practice test type of review in class.  I did create a “Sign Up Genius” for each of my classes, and I’ve asked parents for donations of goldfish crackers, Italian ice and Swedish fish.  I’m not sure I’ll be able to run the review as elaborately as I have previously, but I do think it is worth the effort!  I’m hoping to post about the activities during #MtBOS30 🙂

I’d love to hear how you all review for the EOC test!!!

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Treading water…barely

During my first year of teaching, a colleague told me the first year was all about keeping your head above water.  Year two, you make notes about what went well, and make modifications to things that didn’t.  Hang in there because year 3 was when you finally felt like you could breathe.

I knew changing schools and content would be challenging, and frankly, I really wanted that.  I’d been teaching Algebra I for 10 years and felt like I needed the challenge as I was in danger of getting burned out.  Well, I asked for it and I GOT it!  I am absolutely loving being at the high school and teaching older students.  It’s great to be thinking of different strategies for rationalizing denominators instead of integer rules for the millionth time, but I do feel like I’m back to year 1 and barely treading water.

The math department at the high school is awesome – we all eat lunch together every day, and since we do not have common planning time this is great.  It’s a supportive group of people and everyone is nice.  Seriously.  EVERYONE.  This is the first year the high school has implemented 1:1 Chromebooks, so I have enjoyed being able to share some resources with them (most had not heard of Desmos and only one was using Google Docs).

It has definitely been overwhelming learning new content and developing materials – I’m creating a lot of foldables (and a HUGE shout out to @mathequalslove‘s Sarah Hagan because her blog has been so helpful for Algebra 2!!).  I anticipated the content development would be time intensive, and knew I’d be putting in more hours at school.  My family has been so supportive.  God bless them for not complaining about me picking up dinner at times (I do fear they are weary of rotisserie chicken).

One aspect though that I really did not anticipate is how these new demands have impacted my time with my online PLC.  I barely have time to read my Twitter feed, much less contribute anything substantial.  I kept up with the #Teach180 Instagram posts pretty well for about five whole minutes (I do plan to do a better job with this – I enjoy the sharing, and really, surely I can find a few minutes a day to do this).  I miss Global Math and I miss math chats.  I miss the camaraderie, and collaborating over strategies and lesson ideas.  In trying not to post “I’m overwhelmed” every day, I haven’t posted a lot – I actually felt guilty today when I saw I had a new blog subscriber and thought how long it had been since I had blogged!!

Soooo, know that this is only temporary.  I’m hoping 2nd nine weeks will be more like year two, and by the third nine weeks I will be breathing more easily and a little more present in the online world.  I miss you all and can’t wait …but first, I need to grade 120 quizzes and figure out what I’m teaching tomorrow…

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Factoring Foldable

My 8th graders really got factoring this year!  Because of all of the time lost due to snow days, I was attempting to compact the curriculum, and decided to teach factoring and solving quadratics at the same time (instead of factoring first, and then solving afterwards).  We also used Desmos to graph the equations as we went.  As a result, students appreciated the point of factoring as a tool to find solutions and graph quadratics.

If you’ve read any of my previous blog posts, you will know I am a huge fan of foldables.  I really believe these teach students how to organize and summarize notes, and most importantly, then refer BACK to their notes as a resource.  So many 8th graders will dutifully take notes and then never look at them again, but I find they will refer to their foldables because they are organized and contain the most important topics.

cover1For factoring we created a “waterfall” foldable using three sheets of paper.  Stack the three sheets of paper and stagger them so there is about a half-inch band of color before the next paper starts.  Fold the top three sheets down and crease (the middle section will have the same color twice).  Staple across the top (make sure you get all three pieces of paper in the stapling).  We wrote Factoring on the front, then labeled the tabs at the bottom, “GCF, 2 terms, 3 terms x^2+bx+c, 3 terms ax^2+bx+c and 4 terms.


We reviewed GCF’s last week and put these notes in the foldable on the GCF tab.  I chose to skip over the 2 terms tab at this point and came back to that after factoring trinomials. We did finish the foldable (pictures at the bottom), but what made this lesson so effective this year was integrating the solving and graphing as I taught factoring.

We started with the x-puzzles that @jreulbach talks about in this post.    Students love these – it usually doesn’t take long for them to get the hang of them, and soon someone says, “well these are fun, but what does it have to do with Algebra?”  Yaaas.

I told students we were going to use their awesome puzzle solving skills to learn how to “undo” multiplying binomials.  They multiplied (x+3)(x+4), and then we talked about how we could possibly go backwards from x^2 +7x + 12 to find (x+3)(x+4).  They brainstormed a bit and then I drew the x for an x-factor and put the 7 and 12 into it.  Immediately there were shouts of “positive 3 and positive 4!!”  We did a few more examples, working some with negative numbers.  Then we talked about what y=(x+3)(x+4) and y=x^2+7x+12 would look like if graphed.  The majority of students believed they would be the same, so we graphed them in Desmos and talked about how graphing this way is a good way to check their factoring.

parabolaNext, I projected two graphs and we did a little, “what do you notice, what do you wonder?”  This was followed by a great discussion about factors versus solutions, and the relationship between the two.  From there we talked about the zero product property, and in one block period students had factored and solved a quadratic, and seen the relationship between factors and intercepts.

For homework they practiced their factoring skills, and the next day we expanded factoring to include quadratics with a leading coefficient greater than 1.  Anyone who has taught Algebra knows this is fairly challenging for some students.  Our district strongly encourages factoring by grouping as the primary method, so students took notes on how to split the middle term, and then factor out the GCF of both groups.  Again, we graphed the expanded quadratic and the factored quadratic in Desmos to ensure we had factored correctly.  Some students in each class noticed that the intercepts were not necessarily integers, which was a lovely tie-in to taking each of the factors, setting them equal to zero and solving for x.  Here are pics of the two pages on trinomials we added to the foldable:


By the next day, I had a few students coming in just grinning that their older siblings had shown them “a much easier” way to factor.  This is always so cute – I just love that A) there is a discussion about MATH going on at home (win! win!), and B) that students are excited to think they’ve outsmarted me (again, win! win!).  At this point we talk about the Divide and Slide method.  I personally do not care which method they use, but am just happy they have found a method they can rally behind and not get to high school pretending they’ve never even heard of factoring.

Here are the final two pages for the foldable.  We went back and revisited factoring 4 terms (they already knew how to do this because of factoring by grouping), but we also talked about how a cubic function can have 3 intercepts, and how they need to look for an x^2 term to potentially factor as a difference of two perfect squares (I include an example of this on the top of that tab).  Finally, we finished with the 2 term tab:


The proof will come when we come back from Spring Break on Monday when I see if they remember how to factor after a week of not doing ANY math!

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