How Many Fingers Did We Cross?

Last night I send these tweets to an author friend of Rm. 202’s:

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After the conversation ended, I knew I had the plan for what we’d be doing in math this morning. ūüôā #reallifeproblemsolving #wehadtofigureouthowmanyfingerswerecrossed

So…I started by sharing the Twitter thread and telling them all about the conversation I’d had with Ame Dyckman–the one that started with shrimp and chili dogs and ended with unicorns and crossed fingers. LOL ¬†I told them all about how I’d really been wondering how many fingers we would have crossed and that I knew they could help me with that solution. ¬†First we practiced crossing our fingers (and our toes–this was really hard for some kiddos! ha!), and then I reminded them of the problem I needed their help with:

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We agreed that we were figuring out the total for 23 people (22 kiddos plus me!) and that our explanations needed the have the criteria on the right side of our chart.  Kiddos worked with their learning partners, and could choose any (or all!) of the parts of the problem the wanted to work on.

Kiddos had time to work, choosing all different parts of the chart to solve. ¬†I’m pretty sure this work went on for about 35 or 40 minutes, with partnerships working pretty steadily and cooperatively together to solve our problem. ¬†As I worked through the room and conferred with each pair, we tweaked some things, I asked questions to help them dig deeper and many groups worked to make sure their posters could be understood without them standing by to explain what the numbers/pictures meant.

After their work time was up, I called everyone back to the rug to explain the next step. ¬†While kiddos are familiar with the term “gallery walk” from math in kindergarten, I hate to admit we have not done as many of them as I’d like to this year. ¬†Because of this, I needed to make sure that they had a very specific goal and job as they went around; the scaffold of a specific question to look for was helpful for many and the “roaming” was kept to a minimum. ¬†So, during our gallery walk, their job was to hunt for the answers to our chart questions with their partners. ¬†They could take notes if they wanted to (Aadish thought it was like being a spy), and the suggestion was made to take post-its with them. ¬†They could only talk about math: questions they had about the posters, answers they saw, wonderings they had. ¬†After a few minutes, we’d meet again on the rug to see what we’d found out.

Here’s a bit of what that gallery walk looked (and sounded) like:

Once we gathered on the rug, we got to dig into some solutions kiddos had found.

We started with the first one, “How many fingers would we cross if everyone crossed 2 fingers?” ¬†Several teams tossed out their answers and we had everything from 46 and 44 to 24 and 30. ¬†What??¬†Rather than have every group explain their thinking (and perhaps confuse everyone or make it harder to get to our solution), I went with the two answers closest together–44 and 46.

We started with having Allie and Ayonna share their poster and telling about their thinking:

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If you can tell from their poster, A and A decided to organize their thinking by writing everyone’s name so they remembered to include everyone. ¬†Then, as we talked about how to count all the 2s, we decided that we could make groups of 2s to make 10. ¬†10s would make it really easy for us to then count the total number of fingers. ¬†We made an equation at the bottom to show the total of 46.

After A and A shared their thinking, we talked about the 44. ¬†Ella and Chase were sure they had gotten the right answer, and said they weren’t convinced 46 was right. ¬†This was a great addition to the conversation, and while I somehow didn’t get a picture of their work, we studied their poster, where they had also counted pairs of fingers, but with drawings (they traced their fingers). ¬†Rather than list them in rows and columns like on the poster above, the fingers were randomly placed on the page, and readers had to follow arrows around the paper to follow the thinking and see the way they counted. ¬†We talked as a class about the two examples, and Lucas suggested that even without counting, he was convinced that 46 was right because A and A had made their work organized and also included an equation. ¬†After looking at the pairs of 2s on E and C’s poster, we realized they had only drawn 22, and therefore were a couple short. ¬†They worked to add in their last fingers and agreed with us that 46 fingers was the right solution.

Callahan and Jesse showed us how they figured out 1o crossed fingers here:

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They wrote lots of 10s, and then made sure to label each 10 so they knew they had enough (23).  We talked together to clarify which line of numbers was which (fingers or people), and added labels to make that more clear for readers.  They counted the total number of fingers by making 2 groups of 100 with tens, and then finding 30 leftovers.  Their equation ended up being 100 x 2= 200, then 200 + 30= 230 fingers.  At the bottom they started work to figure out how many it would be if we did the 20 fingers and toes.

Lastly, Jamie and Kaiden showed us how they knew that if we crossed ALL OUR FINGERS AND TOES it would be 460 fingers and toes!! (We were amazed by this number and figured Ame Dyckman would be impressed, too!).

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Their thinking looks a little like Callahan and Jesse, with groups of 200 (made of 20s), though, rather than 100 with 10s.

After this one, we realized some connections between our numbers–like that¬†we could have used the 10s numbers to help us with the 20s (because 20 is a double of 10)–and so figured that we could use that same thinking to figure out “how many fingers if we cross 4?”

Johnny helped us think this through and figured that if we counted 46 twice that would the same as doubling.  We drew this to help us figure that out:

fullsizeoutput_facThrough our discussion and brainstorming we figured we could count by 10s to figure out most of it (and Callahan even found another 10 by using that 4 inside of the bottom 6! This made it SUPER EASY!!).

So…after our work we had decided we’d crossed A LOT of fingers hoping for a new book. ūüôā

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We ended by noticing (and we’ll come back to this much later) that the 4 is a double of 2, the 20 is a double of 10, and also that the answers doubled as the numbers doubled. ¬†Kaiden added some arrows to show our connections. ūüôā

Wow….I’m tired writing about that, but I am pretty sure my kiddos were equally tired working on it! ¬†It’s the kind of math that reminds me that real life problems are the best and that when kiddos have a real reason to figure it out, the motivation is through the roof! ¬†Everyone works hard and stays engaged because they have to know the answer! ¬†Thanks for the inspiration, Ame Dyckman!!

Lions, Rectangles and Triangles–Oh My!

We have been on a bit of a geometrical journey as of late. ¬†We’ve studied sides, corners (which we know are called angles), diamonds (which of course are really called rhombuses!), square corners, trapezoids and loads of other things. ¬†We’ve taken pictures, manipulated blocks, read books and even drawn pictures. ¬†Pictures of shapes, and now pictures of lions, too. ¬†Let me explain. ūüôā

Well, actually, let me let a guest author explain. ūüôā

Hi parents, guardians and friends of Room 202 1st graders! My name is Kate, or Ms. Holzmueller, and I work as a TA at Robinson. I’m one of the TA’s assigned to the 1st grade recess (where I often referee kickball) and lunch (where I help maintain order and pass out napkins and embellish hamburgers with ketchup smiley faces!) I’ve been spending time in Mrs. Bearden’s classroom the past few months, supporting some of the fantastic kiddos and doing a few read alouds, too! ūüôā
Last week I spent time during math rotations having discussions with kids about squares and triangles and other shapes. (One of the benchmarks for first grade learners is that they, say, recognize that a square is a square because it has four equal sides and four equal angles.) While playing with the manipulative shapes I thought of one of my favorite authors, Ed Emberley and his books that help children (and adults like me who love to draw!) draw animals and monsters and people and cities, etc. all by drawing simple shapes. I showed Mrs. Bearden an Ed Emberley book and she was kind enough to let me share his work with your students.
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So during math centers, we looked at two pictures of a lion, one real, the other drawn. We had conversations about the shapes within the lion–how it’s nose looks like a triangle, how it’s head looks like a rectangle, etc. Then we practiced drawing all the shapes we had identified on white boards with dry erase markers. After that, we followed Mr. Emberley’s tutorial on how to draw his version of a lion, again on the whiteboard. (First by making a rectangle, then another rectangle, then a triangle…)¬†

Today during math time we practiced drawing shapes again on the whiteboard and then we used cardstock and markers to draw our own lions, still using rectangles and triangles and circles, etc.

Students were allowed to use whatever colors they liked and embellish their lion as they best saw fit–some have freckles! Some have angry eyebrows! We had conversations about how many triangles they used to show the teeth, how many triangles to make the mane, etc.

The results are very colorful and scary and fun and are now greeting passers-by in the halls. 

(And BOY are they BEAUTIFUL! Sorry–this is Mrs. Bearden. ¬†Had to throw in my two cents about how great they are. ¬†AND how great Ms. Holzmueller did as she taught the lesson! Learned a few things myself that I will incorporate tomorrow. ūüôā ¬†Really, I did! ¬†Ok…back to the guest post…:) ).

If your student mentioned drawing a lion today know that Mr. Emberley has lots of other fun books they might like, too!¬†(I found two of them in the Robinson library just today!)¬†¬†And remember it’s just as easy to play “I Spy” with geometrical shapes as it is colors! “I Spy with my little eye something that is a square…”¬†

Another Number Skype–Inside Robinson!

On Friday we were able to have another Mystery Number Skype, with some friends INSIDE ROBINSON! ¬†We’ve done this before, the last time I taught 1st grade when we were learning to Skype and we called Ms. Turken’s class who was in Mrs. Fry’s classroom. ¬†This time we answered a call from Mrs. Dix and Mrs. Bell and talked to their second graders. ¬†We were excited!

We are getting so good at this and at asking questions that knock out a large group of numbers at once.  Our 2nd grade friends guessed our number and we did, too!  What a great way to practice what we know about numbers and place value!

Do you want to Skype with us, too?  Leave a message here, or tweet to us at @jbeardensclass@jbeardensclass.  WE LOVE TO CONNECT!

Math Warm Ups: Week of Oct. 19-21, 2016

I used to blog our math warm-ups every week. ¬†Then this year I changed our warm-up plan again and sometimes they are questions other than math problems and so I never really got into that routine. ¬†This week, however, they were indeed all math warm-ups so I thought I’d share what we’ve been doing!

(This was a short week of school, with only 3 days and 2 warm-ups.  Small but mighty math thinking!)

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My kindergartener, Allie, created this one for Rm. 2o2 kiddos and was very excited to share it with them.  I was impressed with how they are getting better at telling stories and creating word problems to solve.

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Some highlights of the answers to this one:

We also tried one during math on Friday as an extension after we’d talked about the warm-up together. ¬†We’re learning how to use Padlet, so it’s been the place we’ve been sharing our thinking lately (and since we’re still working on the logistics, some friends didn’t quite get their answer on the board).

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Great thinking lately, Rm. 202 friends!  More to come soon!

Digital Recording: Counting Strategies

I shared the story of how we have been counting EVERYTHING in our room this week, but there’s a quick story that actually come just before that, as we started our initial journey into practicing counting and recording our strategies.

Kiddos were given a partner and a “mystery bag,” which was full of between 10-35 of something (bags were differentiated for different counters), and asked to figure out¬†how many things were in it. ¬†They were to use an efficient strategy and somehow capture an image to demonstrate how they counted their item(s). ¬†Partners worked together to determine the¬†most efficient way to count their items, took pictures together, talked about their work and added explanations to their pictures via the Notability app on their iPads.

Through the information I received from seeing their images, as well as through observations and conversations conducted during their work time, I was able to more effectively create pairings for later in the investigation.  Partnerships were formed to best challenge and support mathematicians in their continued learning.

Mathematical strategies and digital tools for the win!

 

Gotta Count ‘Em All!

We’ve been working on a beginning counting and place value unit in math lately, and the premise behind the investigation is that we need to organize and do inventory on things in our classroom (this came after we read a story about a messy family called the Masloppys and how their son Nicholas does just that in their house so they can find things!). ¬†We’ve been counting everything in our room. And I do mean everything. ¬†If it’s not attached to the floor (or too heavy to pick up), someone has put their mathematician fingers on it!

Kiddos worked in pairs to catalog a¬†collection of classroom¬†items (and then many more as they finished), focusing on using efficient and accurate ways to count the group. ¬†Students were charged to find a way to easily share their thinking with others; counting by groups or keeping track made it easier to tell someone else what they had done. ¬† Callahan and Jesse were especially proud to share the learning¬†they had brought with them from kindergarten (“Mr. Peacock taught us to make groups of 10!”), and they made bunches of 10 crayons into a bundle of 100!

We have had many conversations sharing kid strategies, tips and suggestions for how to count large groups of things, and then we started to look at the numbers of totals.  We wanted to know how many bundles of 10 we would have in each amount (if we counted like Callahan and Jesse!).  Our chart began together with some class numbers, and then kiddos got in on the fun (work!) as they continued to count EVERYTHING in our room:

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(As a side note, I am always excited with how many possibilities there are for ELA in math–here for example as I could conference with kiddos as they wrote on the chart and helped them work through sounds in words!)

It was funny as kiddos kept running up to me asking “Can I count this?” ¬†The more they counted, too, the smarter they got at using efficient groups–notice all the rubber bands, cups and baggies in our pictures?

We counted so many things we needed to record that Rachel asked for a new sheet.  Love it!

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The next phase is moving into further connections with 10s, as we think about how many we’d have to had to have whole groups of 10 for each item. ¬†We’re playing math games to make combinations of 10 in a variety of ways , and will continue this thinking as we move into addition and subtraction. ¬†Place value discussions throughout the year will go back to these beginning inventory experiences. ūüôā

 

#FDOFG: Guided Discoveries–Math Manipulatives

I realize this post is a little bit after the true “first days of first grade,” but I’d say it still applies, and the actual learning actually took place then anyway, so that counts, right?

One of the things we do a lot of in the beginning of our time together in first grade is explore.  These guided discoveries take on many forms, and have been done with colored pencils, pattern blocks and play-doh before (among other things that are done less formally).  In the beginning days of math workshop, guided discoveries of math tools are an important learning activity.

Rotating through 6 stations–dominoes, power polygons, multilink cubes, Geoblocks, square inch tiles and Cuisenaire Rods–students were posed two¬†simple questions to consider while they worked: “What could a mathematician use this tool to learn more about? ¬†What are the possibilities?” ¬†Then, in small groups, they explored the tools, for only about 7 or 8 minutes each:

Dominoes

Most kids built things to knock over. LOL

Power Polygons

Many¬†kids put these together in piles and looked through them–they’re made of pretty colors. ūüôā (And yes, we’ll talk about more mathematical ways to use them later–right now it’s just work to figure them out and try things!)

 

Multi-Link Cubes

These tool may be the interesting just because it’s one of the most versatile. ¬†Lots of different kinds of exploration happened in this station.

 Geoblocks

Inch Tiles

Also a versatile tool, kiddos stacked and counted, sorted and created with these little squares!

Cuisenaire Rods

While these blocks have many place value uses, many kids use them as building blocks, and many sorted them by size or color.

The last step was to chart some thoughts on our answers to those questions I posed at the beginning.

It was just the beginning, but definitely got us off on a good foot to some smart mathematical thinking this year!