Digging in the Closet: The Return of the Museum of Rarely Used Math Manipulatives (MoRUMM)

My officemate and I have an embarrassment of riches — in the form of math materials. In the first district where I taught, manipulatives were hard to come by. My classroom was outfitted with a bin of base-10 blocks and some pattern blocks. I remember finding some spare fraction tiles tucked away behind the school’s stage, and I conducted a full reconnaissance mission to sneak those babies out.

But now? We have a full “archive closet” that I dubbed the Museum of Rarely Used Math Manipulatives, or, as Christopher Danielson (@trianglemancsd) ordained it, MoRUMM.

(Guilty: I embedded that tweet, at least in part, to document that Christopher said such flattering things about me. 🙈)

I had no memory of writing this phrase. It felt so dismissive of students. Lo and behold, I re-read my original post, and found the line at the end:

As a math teacher and compulsive collector, I delight in my pattern blocks that model 1/4 of a hexagon. They’re fun. They reveal new relationships. There’s so much potential for play — for me — but most of my productive play comes out of years of experience modeling mathematics with the classic pattern blocks. Most students aren’t ready for that, so… back to the Museum they go.

“The Museum of Rarely Used Math Manipulatives: What Do We Need?”
December 20, 2018

Hmm. This gave me pause. How do we decide whether students are ready for something? I stand by the idea that familiarity and experience with a particular material generates more creative thinking than the constant introduction of new material. Plus Steve and I only have so much space in our small office, so we have to make decisions about what we will keep easily accessible. But maybe I’m closing students off from potential avenues of thinking if I hide some of these things in the closet…

Pattern Blocks in First Grade

from Investigations Grade 1, Unit 2, Lesson 1.6

Our first graders are currently deep into a 2D geometry unit that leverages pattern blocks to explore geometric ideas of composition and decomposition. Yesterday, during math workshop, students were working to fill the outline of different shapes with pattern blocks. They were tasked with figuring out a way to cover the shape with “more” blocks, and a way with “less.”

Students had, at their disposal, the “classic” pattern block shapes: the yellow hexagon, the red trapezoid, the blue rhombus, the green triangle, and also the tan rhombus and orange square.

As students worked, the classroom teacher and I observed. We decided to close the lesson with a discussion of strategies for generating designs with more blocks. The smaller the block, the more blocks required to fill the shape.

Lyra’s Work

“Lyra” volunteered to let us use her work to anchor the conversation. This took a little bit of courage: I told her that we might be changing her work together, as a class. She was still proud to use her work.

Here’s how Lyra covered the shape.

She used 8 total blocks to cover it. I asked students to share how many blocks they used to cover it. Students volunteered their totals:

11
9
23
10
12

Hmmm… I asked the class to think about how we could trade one of Lyra’s blocks so that she would be using more blocks in all. Lyra’s hand immediately shot up: “oh! The hexagon can be a triangle!”

“The hexagon can be a lot of triangles!” Owen added.

“How many blocks is that now?”

Most students wanted to add on 6, to get 14. However, in adding 6 triangles, we lost one hexagon, so there are only 13.

We continued trading and counting up our total number of blocks. Could we use trades to have even more blocks?

“Cut the rhombus in half!” Kai shouted.

“Which rhombus?” I queried.

“The blue one! Cut it in half and you get triangles.”

I elicited counting strategies to keep track of our total amount. (Fumi suggested we use draw a dot on each pattern block to mark that we have already counted it.)

And I thought we were done. 19.

No idea how that kid got 23.

But… moving on.

“Let’s cut the other rhombuses!”

Lyra wasn’t ready to move on, though. “But! Let’s cut the other rhombuses!”

It was one of those record scratch moments.

“Which rhombuses?” I clarified. “The tan ones? Let’s see if the green triangles will fit…”

Spoiler: I knew they didn’t, and it was time for library.

But I drew the lines slicing through the thinnest part of the tan rhombus, forming two triangles.

“Those look funny.”

“They look pointy.”

“They’re too skinny.”

This was actually emerging as an opportunity to talk about the triangle-ness of it all. What makes a triangle a triangle? Students were so accustomed to using equilateral triangles in class. Now, they were faced with another triangle.

“They have 3 sides.”

“Triangles can look different. It can be stretchy.”

Then, I thought about the properties of these pattern block triangles. The green triangles are regular, with perfect 60° angles and one-inch sizes. The tan rhombus doesn’t have 60° angles. But, wait…

I was reminded of some pattern blocks I keep in the MoRUMM closet. I bought them mostly as a novelty, to indulge my nerdy self. Each of the purple triangles represents 1/12 of the hexagon, and each of the brown trapezoids represents 1/4 of the hexagon.

Two of the purple triangles fit neatly into the green triangle.

And, wait… two of those purple triangles also fit neatly into the long, pointy tan rhombus.

Well. Lyra had inadvertently discovered a use for those purple triangles!

We counted our total number of blocks again: 22. That had to be a record.

This afternoon, I should dig those blocks out of the closet.

Here is what the visuals looked like, improvised using the documentary camera in our last few minutes of math class.

________________

If you want to play around with a digital version of pattern blocks — sadly missing the unusual purple triangles and brown trapezoids — you can play around with this outline on the Math Learning Center’s web based Pattern Shapes app.

An Important Addendum

Well! Here I thought this was a charming tale about students discovering a new pattern block…that already exists!

It turns out I was ever-so-wrong. Half of the tan rhombus is decidedly not congruent to the purple triangle (half of a green triangle). I’m ever so grateful to Simon Gregg (@simon_gregg) for reaching out and talking through some geometric ideas. Read about it here: “Exploring Geometry with Simon Gregg (Addendum to ‘Digging in the Closet’).”

5 Comments

  1. I love this, Jenna! Is there any way I can get a hold of that worksheet? I’m working with a first grader currrently, and I think this would be a great spatial activity to do with her that would also give her practice counting.

    On Thu, Nov 18, 2021 at 3:08 PM Embrace the Challenge wrote:

    > Jenna posted: ” My officemate and I have an embarrassment of riches — in > the form of math materials. In the first district where I taught, > manipulatives were hard to come by. My classroom was outfitted with a bin > of base-10 blocks and some pattern blocks. I remember fi” >

    Like

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