Tag Archives: notice and wonder

Doing Math with #ElemMathChat

Last night we kicked off the fourth year of #ElemMathChat. Yay! It’s so exciting to spend an hour each week talking with and learning from so many passionate educators.

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One thing I’ve often heard from participants is that they like that we regularly do math together during our chats. I didn’t want to disappoint in our first chat of the year, so I dropped in a few tasks. I thought I’d collect them together in a blog post in case anyone missed the chat or wants all the pictures gathered together in one place. So let’s get started!

How Many?

This task actually appeared before the chat. I’ll admit that I sometimes try to cram a bit too much into our hour together – I want to do it all! – so I opted to move one of the questions out of the chat and instead turn it into something fun for folks to play around with during the day leading up to the chat.

How-Many

I saw two common answers to this question throughout the day:

  1. I assume you mean triangles. I see 4.
  2. How many what?

I owe Christopher Danielson thanks for turning me on to this deceptively simple question as well as for engaging with some of the folks yesterday who were tackling the question as it relates to this image.

I highly recommend checking out Christopher’s blog post where he talks more about this question and shares some images you just might want to use in your classroom. He only asks that you let him now what kids do with those images and ideas. You can share with Christopher on Twitter @Trianglemancsd.

Let’s Estimate!

For our first task during #ElemMathChat, I asked everyone to estimate the number of hats in this sculpture:

When I first saw this sculpture at the Fort Worth Convention Center at this year’s CAMT Conference, I was instantly curious how many hats were used to make it. It took some digging, but I finally came up with all the information I needed.

I asked participants to share their too LOW, too HIGH, and just right estimates. What I’m really looking for is the range they’re comfortable with. How risky are they willing to be with their estimates?

  • This is a low-risk estimate: “My too low estimate is 10. My too high estimate is 5,000. My just right estimate is 500.”
  • This is a riskier estimate: “My too low estimate is 400 and my too high estimate is 500. I’m pretty sure the number is somewhere in the 400s.”

Notice the difference? One person isn’t as comfortable limiting the range of their estimates while the other person has narrowed it down to “somewhere in the 400s.” I don’t really care about the just right estimate so much because I value helping students come up with estimates that make sense and are generally close rather than valuing whether or not they guessed the exact number. Helping students get better at estimating and be willing to make riskier estimates takes time and practice, but it’s valuable work.

Here’s the final reveal with some additional information about the sculpture, in case you want to do this activity with your students:

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Numberless Graph

As much as I love numberless word problems, I’ve been fascinated with numberless graphs this past year. I knew I wanted to include one in our chat! When I shared this first image, I asked my go-to questions, “What do you notice? What do you wonder?”

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The engagement was high and it was so much fun to see what people noticed and wondered as they looked at the graph.

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We moved on to another question before coming back for the second reveal. Again, I asked, “What do you notice? What do you wonder?”

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Adding the scale and currency amounts just increased the wonderings about what this graph could be about.

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Finally, after building anticipation and making everyone wait through another chat question, I finally revealed the full graph and asked, “What questions could you ask about this graph?”

 

 

 

The noticing and wondering didn’t stop! It was great!

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In case you’re wondering, Pokémon GO is a game you can download on mobile devices. The game is free, but there are things you can buy within the game. So what this graph is showing is the average amount people spent buying things inside of the game. In Japan, for example, looking at all the people in the country who have downloaded the game, each of those people has spent $26 on average. In the US, on the other hand, the people who have downloaded the game have each spent $7.70 on average. The interesting thing about this is that the data is a bit misleading if you don’t know more details:

This leads to a great discussion to have with kids, “If US players aren’t spending nearly as much in the game as players in Japan, then how come the total amount earned from purchases in the US is over $100 million more than in Japan?”

A Lens Looking Forward

This isn’t doing math together, but I did want to share the final question of the night.

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My lens for a long time has been play, but I think I’m due for a new one. Not sure what it’s going to be yet. What about you? What word would you choose to use as a lens for the work (and fun!) ahead this school year?

 

 

 

Two Cats and Two Tortoise

Yesterday my wonderful co-workers threw us an adoption shower, and thanks to them our daughter is an even richer girl if you measure wealth in books.

One of the gifts was from Mary Beth. She said it’s a favorite thing to do with a favorite counting book, Rooster’s Off to See the World by Eric Carle.

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Included with the book was a baggie that contained a small rectangular board and a bunch of small cards with animal pictures. My daughter pulled out the baggie and asked, “What’s this?” I said it was something we could look at while we read the book. My daughter didn’t want to wait to read the book, so this morning while I made breakfast, she plopped down on the kitchen floor to explore the baggie of cards on her own.

Within a few minutes I heard her say, “There’s two cats and two tortoise!” I looked over to see that she had filled her card with animal pictures. And sure enough, the card had two pictures of cats and two pictures of tortoises (or turtles, I’m not sure which yet). I like that all of the counting we do throughout our day has led her to notice and count things on her own without any prompting from me.

After she was sure I had seen the pictures, she cleared off the card and said, “I want to do more.” She put all the cards back in the baggie and started filling the rectangular board again. One thing that was really interesting to me was how she naturally made two rows of three pictures on her card.

When she finished filling the board up a second time I asked, “What do you notice?” I was curious if she would count again or if she would tell me something different. Her response was, “One chicken, one cat, and two fish.” A few seconds later she exclaimed, “And two frogs!”

Then she cleared the board again and started filling it with new animal cards. This time she chose only cards with fish on them. Her observation at this point was, “There’s a lot of fish on here!”

She started digging through the baggie for a few seconds before saying, “I need one more fish.” We haven’t really talked about “one more” very much so it was so interesting to hear her say that. Since she kept laying out the cards in the same arrangement, I’m assuming she could tell there was room for just one more card.

Picking randomly from the baggie wasn’t working so she pulled all the cards out and spread them out on the floor. She couldn’t find a fish so she changed the activity. She asked me, “Where’s the tortoise? Touch it.”

I dutifully touched the tortoise, and that was the end of the activity. She put all the cards back in the baggie and moved on to looking at another one of the books she received yesterday.

The one thing that came to mind as I watched all this unfold was Christopher Danielson’s message: Let the children play:

We adults have a responsibility to let the children play. We can be there to listen to their ideas as they do. We can play in parallel by getting our own egg cartons out and filling these cartons with our own ideas.

But when we tell kids to “make a pattern” or “use the colors”, we are asking the children to fill that carton with our ideas, rather than allowing them to explore their own.

I could easily have overtaken the activity by asking questions such as:

  • How many tortoises are on the board?
  • Are there more cats or fish in the baggie?
  • How many animal cards are not on the board?

All of these are great math questions, but they’re MY great questions, not my daughter’s. I want her to develop her own questions and curiosities to explore. In the end, it was much more fascinating and rewarding for me to see the ways she came up with to explore the cards and to share the things she noticed about them.

Thank you, Mary Beth, for the wonderful gift!