“It’s as fat as it is tall”: Language and Concept Development with Quick Images

Some days, things just go sideways.

It’s the reality of teaching. I watched as Grade 1 teacher Rachel led her students into the classroom fifteen minutes later than usual. Rachel is typically calm and composed — she’s taught yoga on the side — but I could tell a lot about the morning in her class from the look in her eyes. “Sorry,” she said. “We have demonstrated… low stamina for listening today. So I wanted to give them some extra time outside to see if that will help.” (No apology necessary!)

The warm-up for today’s lesson used the Quick Images routine. The routine starts with an image of a stopwatch, and then an image appears for 2 or 3 seconds before disappearing. We have done this a number of times before with dot patterns. (I have written about using the Quick Images routine in professional learning with teachers, too.) However, there was a twist today: instead of determining how many dots there were, students were being asked to draw (and replicate) shapes. It’s a brilliant twist that builds geometric and spatial reasoning. I love using it, and Rachel instantly recognized how the particular sequence of shape images for this lesson builds ideas about fraction for an upcoming investigation.

But the idea of passing out individual whiteboards to students who were quickly growing restless…? I think we had about 2.5 seconds before we lost them entirely. Today was not the day.

Instead of scrapping the routine entirely, I proposed that we do it orally. Rachel nodded, and, without any foresight or planning, we jumped in just a few seconds later. Quick Teaching!

The First Image

“How will you describe this shape so that I can draw it?” I posed, before revealing the first image.

We gave the students a few seconds of think time, and then asked them to turn and talk with a classmate. I could hear students excitedly exchanging descriptions. “It’s round! It has no corners!”

When it came time for students to share what they were thinking, that was exactly what the first student said. I drew a sample shape that matched the descriptions.

“No!” Called out Dominic. “That’s not right!”

“Are you sure? Do you want to add on to that description?” I asked.

“It’s not skinny,” Dominic added.

“And it’s pink!” I added a pink outline to the squat red ellipse I had drawn.

“Does anyone want to add anything else?”

Will pursed his lips in thought, and narrowed his eyes dramatically. I had to know what he was thinking.

“It’s fat and tall. The same amount of fat and tall,” offered Will. Brilliant.

I drew a circle. “Oh! Like this?”

The class cheered. I mean, it was a decent circle, I suppose.

“Es un círculo,” Luís, a newcomer from Guatemala, whispered. I smiled and nodded.

“We’ve been talking a lot about measuring length with our fish,” I continued. “So I want to add a word to our vocabulary. When Will is talking about how fat this shape is, he’s talking about how wide it is. It’s just as wide as it is tall.”

The Second Image

I was shocked that nobody had immediately shouted out that it was a circle in the first round. We continued into the second round.

“It’s like a smiley face with no teeth,” said Jamilah. Poetic! Now it was getting good. I drew a cheshire cat smile, but Dominic protested that it has “one straight side.” So I drew something like a canoe cutting through the water. I wasn’t ready to conclude the game just yet!

“No, no, it’s similar to a circle, but half!” Francesco called out. I recorded his thinking, and drew a semi-circle facing up, like a slice of watermelon.

“But you need to flip it,” Millie said.

“Oh, you want me to flip it. I think you’re talking about turning the shape. Rotating it. Does that sound right?”

“Yeah.”

“What should it look like when I’m done turning it?”

“The curve is on the left.”

I complied, and we concluded round 2.

The Third Image

We had now seen a circle, and then a semi-circle. This Quick Images routine was priming us for an upcoming investigation on fractions — halves and fourths — so it’s was only fitting that this was the final image in our warm-up.

Once again, students were given time to think independently and then turn and talk with a classmate. This gave them important rehearsal time: time to practice what they will say before speaking in front of the whole group, and time to listen to someone else’s thinking and integrate it into their own.

Milo spoke first. “It’s a small half circle.” I drew a tiny semi-circle on the board, while students shook their head.

“No! It has three corners,” said Francesco.

I paused. “Okay, so when you say it has three corners… the half circle that I drew before, does that have two corners?” I highlighted the two vertices in pink.

“Yeah, but this one has three.”

I was not ready to give up the game just yet, so I drew three points that would not form a right angle, like the one in the quarter of a circle.

“Oh, that looks like a third! That’s not right,” chanted Bennett.

Yu Jin raised her hand to clarify. “It’s not a third,” she said crisply. “It’s a fourth of a circle.”

“Yeah, but, again, you have to flip it so the curve is on the left,” Millie said.

The class was like a rag tag band of kid detectives at the end of a whodunit: triumphant.

In fact, they continued to call out great descriptions.

“Yes, that’s it! It has two straight sides!”

“It’s a quarter of a circle!”

“It looks like a pizza with no toppings!”

“Yeah! But just a slice!”

I did my best to record.

We took a look at the three shapes we had examined: a circle, a half of a circle, and a fourth of a circle. They’re just smaller and smaller parts.

What We Learned

Students can do beautiful things — especially when given space and structure. Classroom teacher Rachel and I were thrilled that the students were excited about this shift in the routine, and even viewed it as a game. After a rough morning, this felt a big magical.

Students had incentive both to talk and to listen. In #RoughDraftMath style, they revised both their own descriptions and built on the descriptions of their classmates to get more and more specific. Collaboratively, we used both formal mathematical language (sometimes introduced by the teacher) and varied informal math language (from “fat and tall” to “it looks like a pizza with no toppings”).

We saw how important that ‘turn and talk’ rehearsal time was for students both to practice what they might say and also to listen to and incorporate others’ ideas.

We also recognize that we changed the entire goal of the activity — from physical manipulation of space with drawing to language-based description of space. It was a good in-the-moment-decision. More importantly, it means we want to make space for a Quick Draw experience as intended, where students can draw, in the future.