sets of five

Last week, Shawna wrote a beautifully detailed account of her Hummingbirds’ experiences with fifteen second timers and exploring sets of five in counting and different representations. Here are some of the highlights:

“Approaching the provocation, I wondered what the children already knew about the object, and what strategies they would use to figure out how to measure the duration of the sand’s pour. I wondered about the ideas they’d have regarding what the sand timer can measure.

I set the timers out – two per child – and deliberately did not tell them anything about the object. Instead, I let them tell me what they were noticing as I tried my hardest to catch on camera and notepad all the cool stuff they were doing. It was so fun to watch them begin to play with their timers and explore them with the genuine interest and curiosity of an inquirer. From the photos you can see that in addition to flipping them over, they were stacking them, comparing them as their sand ran out, and turning them on their sides.”

Shawna has a great gift for documenting student conversations as they go along and always includes wonderful gems of their discoveries in her blog posts. The following is part of the conversation the kids had when the timers first came out:

Shawna asked, “How can you tell by watching the object that it’s not an hourglass and it’s a something-second-glass instead?”

“They drop faster,” Largo says. “And it’s smaller.”

“Yeah, they drop so fast. And it runs out so fast,” Lucy added.

“How can we figure out the time it takes the sand to drop?” said Shawna.

Largo said, while playing with his timers, “It’s a race between three timers. The one that runs out is the winner! I’m guessing it’s a 100 seconds.”

While watching his two timers run out, Ramses said, “They won.” In a different voice, he said, “Yay!  We won!”

Sadie counted to herself as she watched her timer, “30, 31, 32, 33, 34, 35,” and announced loudly, “This one took 35 seconds!”

Ramses said, “It looks like a machine making milkshakes!”

Largo said, in a deep powerful voice, “I have the power to stop time, mua ha ha ha!” He turned the timers on their sides to stop the sand from dropping.

After allowing the kids to explore and wonder for a while, the conversation turned to wondering how they could determine how long the sand in the timers fell for. Under Shawna’s guiding hand, they used the timer on her iphone to keep track of the seconds. They did several rounds to make sure they were being accurate, and found that each timer lasts 15 seconds. They then talked about what experiences could be measured in 15 seconds: songs, walking around the bandspace, running in place.

They revisited the concept of 15 seconds a few days later. Shawna writes, “I brought the timers, cubes, number line strips, marbles, paper and pens to the table and explained to the children that the wonderful thing about numbers is how many different ways they can be represented. I encouraged the children to choose their own preferred tools – including their hands – to represent 15 in different ways. This is a big goal I have for the children in their approach to mathematics problems is that they confidently access many different tools and ways of figuring it out and they access different methods for different problems, and based on what makes sense to them. It is all about meaning-making.”

Everyone went in a direction appropriate to their age and understanding of math. Lucy focused on representing 10+5=15 in as many ways as possible.

Ramses noticed what Lucy was doing and also chose to represent 10 and 5, but started with 5 black cubes and 10 brown cubes to count carefully which cube to draw next.

Sadie and Largo used their hands to represent 5. They counted fingers on both of Shawna’s hands, and then on Sadie’s hand to make 15. They drew three hands with five fingers each to show what they discovered.