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

 

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

Some students drew models…

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….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.

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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.

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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.

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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?”

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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…

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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…

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

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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.

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

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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.

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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
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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.

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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.

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Mike Wiernicki


Katie Breedlove


Jenise Sexton


Karla Cwetna


Carla Bidwell


Brian Lack

 

 

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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 | Leave a comment