The Progression of Early Number and Counting

If you’re not a pre-k, kindergarten, or 1st-grade teacher, you need to find one and give them a hug after watching this video.  They do the work of an army and many times their work goes unnoticed. There’s so much happening in the early years of school, that without this progression of early number and counting, we’d all be out of a job.

Here’s the 5th installment in the Making Sense Series. If you’re looking for other progression videos you can find them here.

Stay thirsty my friends!

Posted in Against the Norm, counting, K-2, Making Math Accessible, Making Sense Series, Math Progressions, Number Sense, Strategy Development, Teacher Content | 7 Comments

3-Act Task: A 5th-grade lesson captured

A while back I shared a kindergarten lesson and I was really happy with the way it turned out.  The 5th-grade lesson below, not so much.  The students did great but there are definitely some things I need to improve.

We recently finished up a district PL where we used The Apple and we decided it was a great place to launch our upcoming unit on fractions. Last year, we started using 3-acts at the beginning of our units because they help identify what our students know and don’t know.  As a formative assessment tool, they help unveil the misconceptions we’ll need to address in the upcoming weeks.

In the spirit of vulnerability and #ObserveMe, I’m sharing this 5th-grade lesson.  The lesson was taught in January, which means the majority of the students haven’t explored fractions in almost a year. Please share any feedback or questions you might have in the comment section below.

What went well? How can I improve?

Act 1 & 2



Here’s how some students solved:Screen Shot 2017-01-23 at 1.54.48 PM.png

Some students drew models…



….and we hit some bumps in the road.


Some students used repeated addition…FullSizeRender 2.jpg

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Lots of misconceptions began to surface…

The follow-up visit with table #4…


Act 3-Reveal


Posted in 3-5, 3-Act Tasks, 6-8, Estimation, Fractions, Intellectual Need, Math Progressions, Modeling, Teacher Content | 9 Comments

This Week a Webinar. Next Month a Workshop

On Monday night I had the pleasure of presenting the webinar 3 Act Math Tasks: What They Are & Why You Need Them in Your Class.  The webinar was hosted by my good friend Christina Tondevold and focused on the implementation of 3-Act Tasks in the elementary grades.

Christina is doing some pretty amazing things within her online community, so I was more than honored when asked me to present.

Next month I’ll be presenting a 2-day workshop in Anaheim, Califonia hosted by Grassroots Workshops. The workshop will take place January 25-26 and is open to all K-5 teachers, coaches, and administrators.

Over the course of 2 days, we’ll examine the progressions of learning through the lens of 3-act tasks and other meaningful activities. For more information check out the video below or the workshop landing page at Grassroots Workshops.

There’s one more day until the holiday break and maybe this could be a learning gift from your administrator. There will be lots of takeaways which will make our time together, the gift that keeps on giving.




Posted in Against the Norm | 4 Comments

The Progression of Fractions

I’m excited to share the 4th installment of the Making Sense Series which explores meaning, equivalence, and comparison of fractions.

Fractions are the gatekeeper of algebraic thinking and probably a big reason why we suffer from arithmophobia as a society.  I’m hoping this progression helps provide some relief and courage moving forward.  Let’s make sense of fractions together.

Happy viewing and stay thirsty.

Posted in Against the Norm | 18 Comments

I’ll Rip Your Face Off: The Art of Defacing Manipulatives

It’s our fault. We have no one to blame but ourselves.

We unknowing pigeonhole student thinking with the manipulatives we use. Take fraction tiles for example. Much to my disappointment, they come with labels and it kills me.


Manipulatives that come pre-labelled ruin everything I want from a lesson. Sure you can flip them over but the label on the backside keeps rearing its ugly face and traps lots of student thinking.

Sure there’s Cuisneaire Rods but most teachers don’t have $200 to fork out for a class set. But I think it’s fair to say that most teachers would fork out $4 for some fine steel wool.

Presto! Fraction-Cuisen-Part-Whole-Tiles!

As I finish up planning for my Grassroots Workshop in Anaheim next month, I can’t help but think how faceless manipulatives help us guide students through the progression of learning because of how they can be flexibly used.

When we label items we avoid lots of opportunities to listen and build on student intuition. This was something I took away from Tracy’s most recent post. Tracy helped me see that I need to provide students with more opportunities to play and explore…WITHOUT INTERFERING.

I think this gives them a much better chance.

Screen Shot 2016-12-07 at 9.38.41 AM.png

What the value of the orange? It sure isn’t a third.

With that being said, even when we do get our hands on unlabelled manipulatives we usually assign the same value to each piece…every time.

Pattern blocks are a perfect example. Most of the time we assign the hexagon a value of a whole. This creates a false sense of understanding which is really hard to unmask.


Where’s my head at right now?

I’m continually seeking ways to undo student learning and identify what understanding they truly own. In order to do that, I need to be sure I’m not “pigeon-wholing” student thinking.

Question: Where else in mathematics do we pigeonhole student thinking? This can be within our instruction OR through the use of manipulatives.  

Please share your thoughts below.

Posted in 3-5, 6-8, Against the Norm, Fractions, Making Math Accessible, Making Sense Series, Math Progressions, Math Tools, Strategy Development, Teacher Content | 22 Comments

Where’s Poly? An Exploration in Geo-Dotting

What’s geo-dotting?  I have no clue but that’s what I’m calling this lesson.

We started by asking, “What do you notice?”

Where's Poly (Geo-Dotting) copy.003.jpeg

Our favorites:

  • Looks like Pac-man
  • I see dots and they make a “Y”
  • Looks like someone went crazy with a hole punch

We needed to wrangle in student thinking a bit so we gave them some information…

Where's Poly (Geo-Dotting) copy.004.jpeg

Where's Poly (Geo-Dotting) copy.005.jpeg

Unanimous vote. “I see a square and a triangle.”

We asked students to explain their reasoning and one said:

I know there are 7 corners, I mean “vertexeses”, and 4 of them make up a square which leaves 3. I can’t make a shape with less than 3 dots because then it’s not a shape. So the only shape I can make with 3 dots is a triangle.

We have a winner…

Where's Poly (Geo-Dotting) copy.006.jpeg

Now that students had the hang of it, we went here next…

Where's Poly (Geo-Dotting) copy.008.jpeg

What do you notice?

We let them play, talk, and share for a couple minutes and triangles seemed to be the shape of choice.  Then we revealed the mystery polygons.


By now we felt students were ready to tackle the opening slide again.

Where's Poly (Geo-Dotting) copy.003.jpeg

On our second time around there was no Pac-man or letters, only shapes.  But this time instead of just talking about the dots, students were encouraged to put their thinking on paper.

Screen Shot 2016-12-05 at 2.11.56 PM.png

Students used only the top three boxes for about 5 minutes. This allowed them to flush out each other’s misconceptions.

This helped students construct their own understanding.

After about 5 minutes we slow-released the following criteria, giving them one new nugget every 3 minutes:

  • Total of 5 shapes
  • No dots left over and each dot can only serve as 1 vertex for 1 shape
  • Shapes can overlap
  • Only 2 triangles
  • One square and one rectangle

Students compared work to ensure the criteria was met.  “Looks like you have 2 rectangles in the bottom corner. Try again.”

As we wrapped things up, students came to the board and shared their solutions.

Screen Shot 2016-12-05 at 1.16.34 PM.png

Screen Shot 2016-12-05 at 2.20.44 PM.png

My takeaways:

  • Talking about the shapes and their properties before moving to paper really allowed for students to engage in SMP#3 once we made the leap.
  • The slow release of information allowed students the opportunity to build problem-solving stamina.

If you want to give the lesson a try here’s the slides in a pdf file and student work mat. Please report back and let us know how it goes.  I’m wondering what takeaways you can share.

Posted in Geometry, Making Math Accessible, Who Knows? | 11 Comments

GCTM 2016 – Ignite Talks

For the second year running, we tackled Ignite Talks at Georgia’s Math Conference.

Screen Shot 2016-10-19 at 9.12.31 PM.png


Mike Wiernicki

Katie Breedlove

Jenise Sexton

Karla Cwetna

Carla Bidwell

Brian Lack





Posted in Against the Norm | 2 Comments

Colorblind Teachers, Invisible Students (Ignite – GCTM 2016)

We recently finished up our state math conference here in Georgia. Last year I shared our Ignite Talks in this space and plan to do the same with our 2016 session.  As I edit the videos and prepare to release them, there’s one talk I’ve watched multiple times.

Carla Bidwell’s talk was a gut check and really spoke to me as a white educator. I hope it does the same for you.

All of us are smarter than one of us.

Posted in Against the Norm | 1 Comment

The One-Handed Clock in a Digital Era

It’s tough to make a case for the analog clock in our digital world. I’ll leave the debate of its relevance up to the professionals. Nonetheless, the analog clock remains a staple in the majority of math curriculums.

Let’s take the following standard for example:

MCC2.MD.7 – Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Screen Shot 2016-10-31 at 8.04.13 AM.png

One could say that this standard applied to a digital clock inadvertently supports the work of rounding in 3rd grade.  8:04 is nearest to 8:05.

But in the same breath, I can hear the conversations taking place when students try to apply the same understanding to the analogue clock.

Screen Shot 2016-10-31 at 8.08.04 AM.png

“Which one is the minute hand? The long one is the hour right? No wait. Which one is the hour hand?”

What if we asked students to estimate the time with the hour hand and completely ignore the minute hand? Then, once they own the estimation of time using the hour hand we introduce the precision of time using the minute hand?

This is not a new idea and I’m definitely not the genius that thought of it. Patricia Smith and John Van de Walle have both tackled the issue of time well before this post.  I just figure the more that know the better.

So let’s give it a try…About what time is it?

Screen Shot 2016-10-31 at 8.13.04 AM.png

Time we go to specials.

Screen Shot 2016-10-31 at 8.13.27 AM.png

Recess time.

Screen Shot 2016-10-31 at 8.13.46 AM.png

Time to go home.

Screen Shot 2016-10-31 at 8.14.09 AM.png

Bed time.

A friend in my district reminded me of a conversation we had last year about using a one handed clock and it’s almost that time of year for 2nd and 3rd grade.

Share these pictures with your class and ask “What do you notice?”  Turn them into some kind of Time Talk and report back. I’d love to hear how it goes.

Does EVERY student need this clock? Not at all. It’s just another way to make learning accessible.  Remember what Dan said “You can always add to a lesson, you can’t subtract.

The same applies for clocks as well.

Posted in Against the Norm | 5 Comments

3-Act Task: A kindergarten lesson captured

Over the past few months I’ve been asked for videos that capture a 3-Act Task being taught in the elementary grades. I didn’t have any, or know of anyone that has captured an elementary 3-Act except for this Teaching Channel piece.

Before moving forward, this post wouldn’t be possible without Dan’s trailblazing skills and introducing us all to 3-Act Tasks.

Last week while visiting a kindergarten class we tackled the Candyman. So in the spirit of vulnerability, here it is and I’ll take whatever feedback you can offer.

Act 1: Notice and Wonder

***The blur will disappear after 30 seconds. Little man had to blow his nose***

Act 2: Identify Variables and Solve Conflict

Here’s the kindergarten recording sheet our friends used to make estimates and show their thinking.

After students estimated, we shared and identified the variables needed to answer the question, “How many candies were in Mr. Fletcher’s hand?”

At this point students were good to go and got their model on.  We didn’t scaffold learning in any way because we were using this as a formative assessment.

Here’s what we got…

The context and colors of the candies really helped students explain and model their thinking.

Not all was gravy. There’s still lots of work to go but that’s to be expected. It’s kindergarten and we’re in October.


This student has mastered the art of drawing zeros. Lots of them.


Others looked rough too…


But when we looked closer and talked with the student, they counted the square pencil boxes for us. Awesome to uncover this hidden gem.

Really surprised to see this…


But my mind was blown with this little guy…


10 was his answer but 8 is what he modeled.

So we wanted to know more…

Mic drop.

Act 3: The Reveal

It’s always great to engage the youngins’ in 3-Act Tasks. I’ve heard colleagues say, “I don’t have time to do these types of lessons.”

I hope this helps in showing that we don’t have time, to not have the time.

Thoughts and feedback welcome.

Posted in Against the Norm | 22 Comments