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!

 

Second Grade Math Warm-Ups: Week of April 11-15, 2016

What? This week I did MWUs every day?  Partly that happened because we actually had every day this week at school, but also because I moved the MWU to a different time of day and it made the timing easier (sometimes mornings can get a little crazy and sometimes I have other things I need them to do instead).  Now (at least for the time being), we’ve moved Writing Warm-Ups to the morning and Math Warm-Ups to right after lunch, and that conversation is then the beginning of our math time together (that part is still the same).  Confused enough now? Don’t worry–the big deal is that I have FIVE MATH WARM-UPS TO SHARE!!  They’re pretty great, too, so I’m glad you stayed through that long intro to check them out. 🙂

Monday

We have been working on subtraction lately, and my kiddos have started to do some amazing thinking with negative numbers as a means of figuring out differences.  It started with just a couple of friends a couple of weeks ago and now probably at least half the class has tried it!  The chart here is similar to the HTO model (which we called Sticks and Dots back then) we used in 1st grade, but connected to an investigation we did with the T-Shirt Factory and refers to the inventory of t-shirts.  The come in Boxes of 100, Rolls of 10 and then loose ones.  Same idea, but inside the context it makes much more sense.  Like most times, you’ll see we did it using two other strategies, as well.  The green numbers on top are from the strategy Making an Easier Problem, in this case by adding 11 to both numbers (which we know is possible because of the idea of constant difference).

FullSizeRender 50-min

We also tried it with Circle, Split, Subtract and modeled our thinking on a number line.

FullSizeRender 53-min

And check it out–we got 289 every time!

Tuesday

Another concept we’ve been playing around with is the inverse relationship between addition and subtraction.  This one also asked them to analyze someone else’s thinking.  We tried it by adding up…

FullSizeRender 59-min

…as well as with our negative number strategy.  Again, we got the same answer both times!

FullSizeRender 57-min

Wednesday

On Tuesday during math, I gave kiddos a check-in sheet to see what they could do on their own with subtraction, now that we’ve been working on it for a while together, and the last problem was a challenge problem.  Ok, it really isn’t that much harder (just another place), but I wanted to see what kiddos would do when I added 1000s to our work.  Landen and Ava decided to that the BRL chart would probably work the same way if you just added another column, and suggested that we try it together as a math warm-up the next day.  Great idea, kiddos!

IMG_1443-min

Somehow I took my picture before we had done our work on the chart, so you can’t see it, but believe me–it worked just like they thought it would.  Oh, and when I was using this chart again with someone later that day, we decided that instead of just T for thousands (which doesn’t fit the context of the t-shirt story), we’d say T was Trucks, because you could put 10 boxes on trucks.

Thursday

We’ve been working on both geometry as well as subtraction in math for the last couple weeks (and some still also on money from our last unit), but I decided that we’d use the MWU as the start for our conversation by throwing up some geometry vocabulary I needed to emphasize.  So using examples and non-examples, I had them think about parallel:

FullSizeRender 73-min

They were able to figure out the meaning (for the most part), although many kept saying it meant “straight” and we had to clarify what they really meant, because ALL of those lines are straight….and while I don’t like math tricks, I did show them that in the word PARALLEL are clues to what it means: PARA for the PAIR of lines, and that the l’s make two parallel lines themselves (ok, well they do if they’re lowercase…see, told I don’t like tricks).

Friday

Today’s MWU was geometry again, related to work we’d done this week, as well as connecting to the work I knew I’d have them do during Math Workshop today.  Win/win! (Oh, and I realize now I mislabeled the trapezoid as a parallelogram.  Oops.  I’ll fix that on Monday. 🙂 ).

FullSizeRender 72-min

After this conversation we went on a great shape hunt challenge outside, but you’ll have to wait about it.  We’re not quite done yet.  🙂

Note: See that “next” on the bottom?  I’d tried many versions of that extra question this week on math and writing warm-ups.  It seems that when I put “bonus” there, kiddos thought that meant they didn’t have to do it. LOL  So I tried “next” and also “big ?” to help them see that they could do both of them. Or at least start thinking about the answer, since it would be what we’d be talking about anyway.

 

Mindfulness in the Classroom

Over the past weeks, one of our counselors, Ms. Howe, has been walking Rm. 202 kiddos through several lessons in being mindful learners.

The first step in the process was to help my students understand what in the world “mindfulness” was. She showed them this video, about a book called Mindful Monkey, Happy Panda.

In the weeks that followed, she led the class through how the brain works (and she tied this to Star Wars!), then how each sense can help you be more mindful, present and in the moment to help your brain do its best work.  We talked about how stress affects learning, and she showed us two apps that we can use to help us when we need to be calmed down.

Another thing she introduced was using coloring activities to help us calm down and we’ve begun to use them both in transition and in listening situations.  The images she gave us are very detailed and required us to really focus in.   A couple of times a day (like when we’re coming back from lunch or specials) we color for a few minutes to get us ready for quieter learning in our room.  Many kiddos also get them out during Read Aloud now, too, and color while we enjoy a story together.  The challenge is to get as many colors as we can in as many tiny spaces as possible.  And when someone finishes it’s a big deal.  So celebrate with us. 🙂

I am not entirely sure yet how these lessons will work for us.  There are definitely parts that help us transition and I have already been able to remind them to be present, to think about what we’re doing at that moment–not about something that happened (that maybe made them upset), or something that will happen (that may be distracting them).  There are many upper grade levels doing this same work, as well, and it will be interesting to see how this knowledge helps as they grow as people and as learners.

How do you use mindfulness in your life? How does it help you to be calm, present and focused? What can you teach us? Please leave a comment and tell us your story or advice!

 

Second Grade Math Warm-Ups: Week of April 4-8, 2016

We started a new unit this week on geometry, but aren’t all quite solid with adding and subtracting within 1000 yet, so we came back to that as well.

Monday

Somehow I got home today (it’s Friday, when I usually post these while I am eating pizza and watching our family movie) without a picture of Monday’s MWU.  Oh well, I’ll just tell you.  The chart simply asked the question “What is a polygon?”  Well, I thought it asked it simply, but I was surprised that many kiddos answered it very differently than I expected.  What I thought I was asking them to tell me was the definition of a polygon.  What most of them game me was a picture of a hexagon.  Those that didn’t draw a hexagon pretty much described one in a few words.  I was puzzled by their responses, but as has happened more than once with these problems, it was a great lesson in asking better questions.  Had I asked “What is the definition of a polygon?” or even “Use words to tell what you know about polygons,” it would have made more sense to them.  I guess I did get information that they knew that a hexagon was a polygon, and that they didn’t understand the word itself, too, so it wasn’t a total wash. LOL

Tuesday

This one was another attempt at a vocabulary question, and was based on responses to the pretest from our geometry unit.  We had a great conversation about the difference between these two things, and how one is for 2D shapes and the other is for 3D.  We got out the rectangular prism and a Power Polygon that was a square and looked at the differences.  Oh, and notice how they connected the word “difference” with comparison, and so many of them drew a Venn Diagram.  Nice work, Rm. 202 kiddos!

FullSizeRender 35-min

Thursday

This was a great day, because Ja’Mia and Ava volunteered to create our Math Warm-Up (like has happened with lots of things in our room lately!), so I told them to have a go.  They had to solve their problem, too, so that they would know if we got it right.  Unfortunately I changed the numbers just a teeny bit when I wrote it, but I do know I got the -18 part correct from their original problem.  Check it out:

FullSizeRender 25-min

Want to explain a couple of things on the chart, based on our conversation.  The 900 at the top is because we talked about how estimating the answer before we solve the problem is a way of helping us know if we’re right.  We knew that the 300 and 500 would be at least 800, but then since both of the numbers were so big, it would be closer to 900 than 800.  We decided that the 69 in 369 was screaming at us (do you hear it??) that we should compensate and make the problem easier so we moved 1 from the 532 and made 370+531.  Then we moved 30 over to the 370 to make 400 and added together the resulting numbers.  Once we got to 901 – 18, we remembered what we had learned about constant difference and knew that if we added the same thing to both numbers we could get the same answer with an easier problem–thus we did 903-20, which is super easier than subtracting 18.  I was impressed with their hard work and glad to see that so many of them could apply the strategies we’ve been practicing.

Friday

Today is a busy morning usually, because we do a Week-in-Review sheet that takes the place of the math warm-up.  Often we don’t even get to it, but I decided to try it as our right-back-from-recess activity and it worked pretty well.  We tried another one like yesterday’s but I changed the numbers a bit.

FullSizeRender 48-min

This one has many annotations, too.  Let me explain:

We had to have a quick explanation of the directions, as many of them thought I meant that they should use their calculator.   I just meant I wanted them to figure it out. 🙂  The 800 is our estimate, which we figured out by thinking about 500 + 400, but then realizing that 73 is about 100 so we subtracted that next.  The red words were a request for a reminder of the strategies we have learned (as well as a reminder that I still owe them an anchor chart!): Circle, Split, Add; Circle, Split, Add with a number line; splitting; a chart that we’d used during our investigation into the T-Shirt Factory (that is really a visual form of regrouping 10s/1s); and compensation (making an easier problem).  As we were deciding upon a strategy to try together, I reminded them that good mathematicians choose one based on what the numbers tell them, not based on their favorite or the one they know the best.  Kiddos decided that the numbers were telling them to subtract first, because they noticed that the 75 in 475 could help us subtract the 73.  Once we rearranged the numbers, we realized our problem was a SUPER easy addition problem.

On a side note, at our class meeting today, the topic of math came up and many kiddos marked it as their “trouble spot” with a red dot.

Screenshot 2016-04-08 19.21.49

Again I was puzzled by this (probably because I define trouble spots as places where our class has something to figure out together or areas/activity where our choices could use some reworking and they instead mark them as things that were hard for them to figure out), so I had them explain.  Many said that the warm-ups were hard this week because they had to both add and subtract in the same problem.  We came to the conclusion that it was probably “hard” because we still needed practice.  We also discussed that labeling something as “hard” can sometimes lead us to believe we can’t do it.  If our self-talk is always negative instead of saying “I just don’t get it YET”, that ends up being our reality because we’ve quit trying.  We agreed that I could give them just one operation in a problem and that they would work on positive self-talk as they tackled these tricky problems next week. Win/win. 🙂

 

Second Grade Math Warm-Ups: Week of March 28- April 1, 2016

We were continuing with our study of subtraction this week, and so all our MWUs are related.  Happy calculating!

Monday

This one is just to keep our brains fresh about money and time, since we’ve “officially” moved on, but that we obviously should not forget. 😊

IMG_1092-min

Tuesday

This problem pushed my kiddos to think about the reciprocal relationship of addition and subtraction.  I had to remind many of them how this could be solved with subtraction, but we had a great conversation once I convinced them it was possible.  The strategies are ones we had been working on in Math Workshop lately.

Wednesday

Just because, you know, I don’t want them to forget how to add…:)

IMG_1088-min

Thursday

Tried this format again because I wanted to see what they remembered.  The great question after we modeled our thinking with the number line was “Where is our answer?”  This one took a few minutes for those that still didn’t see the connection between the parts and whole, between how we could either add or subtract.  It was also surprising (still) to some that the answer to the second equation is the same.  Ja’Mia had to convince us of you she knew.  And yes, she was able to do that by telling us about how addition and subtraction are “opposites.”

IMG_1087-min

What would you add to this week of warm-ups? 🙂

Second Grade Math Warm-Ups: Week of March 7-11, 2016

This week was a FULL one!!  It was also another great example of how these warm-ups were meant to be used.  I know…wish it was always like that.  But anyhow, they were all directly connected to what we were doing in Math Workshop, and gave kiddos a great opportunity to think about the work we’d be doing later on in the day.   It was really cool to watch how their understanding would be deeper when we debriefed later on, or when they had a chance to discuss the problem with their partner or a small group.  Also, since they are connected to our regular math work, I have lots more to say about many of them than I will do here.  But that’ll be in a later post, so be sure to stay tuned!!  Here you go!

Monday

IMG_5782-min This one is related to the work we’ve been doing with The T-Shirt Factory, and would help them with the work they’d do later on with breaking up larger numbers into smaller groups.

Tuesday

IMG_5786-min

Wednesday

So we didn’t get a chance to discuss the problem all together on Tuesday, so I analyzed their answers on my own, and instead used their post-its to help me build the problem for Wednesday morning.  It was based on our work the day before in Math, as well as their answers here.

Thursday

This one was asked with the idea of stretching their thinking for later in the day about how a number can be broken apart.  Up til now, kiddos have typically just been thinking about a number in terms of hundreds/tens/ones.  I wanted to nudge them into thinking about a number in a variety of ways, using the parts to compensate and make problems easier.

IMG_5787-min

These were two close-ups I needed to share.  The first was just so you could see more of their answers to this one–they almost all connected this question to the work we did on Monday, even though I wasn’t sure they would.  Nice!  The second is just a great example of grit in our classroom.  Kiddos know that they are not to write “I don’t know” on a post-it; they always have to try something.  Often we use the stem “I don’t know yet, but here’s what I”m thinking right now…”  Do you see what Ella Marie wrote there?  Love it: “I have no idea what you mean by this, but I will do what I think you mean….76 is 70 and 6.”  This is a great example of trying something she isn’t sure is right, but that she feels safe enough to take a risk.  🙂

Friday

Again, this was connected to our work all week, and I wanted a way to take a little assessment, so they turned their work into me rather than putting it on the post-its like normal.  This will help me as I group and plan for our next days….after Spring Break!!

IMG_5793-min

Second Grade Math Warm-Ups: Week of February 29-March 4, 2016

Remember last week when my kiddos were my teachers?  This week it kind of happened that way again–again without my real planning it that way.  And you know, sometimes those are the best kinds of warm-ups–when they happen at just the right time as just the right response to something that happened in our classroom.  Here we go. 🙂  (Oh, and I think somehow we ended up with a warm-up for every morning this week!  Hot dog!)

Monday

We ended last week with the beginning of our new addition/subtraction unit, so I started with a 3-digit problem.  And no, it wasn’t until we sat down to talk about the solution that I realized that the answer went up and over 1,000.  Oops.  But hey, if you can do those hard ones, then everything else is just cake, right?  No one seemed to notice.  And many of them got it right, which was nice and exciting.  We talked about both compensation (making the problem easier by making 620 + 541) and splitting it by place value to add.

IMG_0779-min

Tuesday

Ok…so Tuesday’s warm-up didn’t end up the way I thought it would.  (Man is there a theme here lately?)  I wrote this problem BEFORE school, knowing that it would tie into our place value work, as well as remind them of work we had done previously with this topic.  And then I had some AMAZING professional development work in math with Kara Imm (an amazing teacher from Mathematics in the City out of NYC) and the rest of my 2nd grade team that afternoon.

(Sorry, she’s so amazing I have to stop and introduce you to her for a second. 🙂 )

Screenshot 2016-03-04 20.56.11

During our planning we decided that we were working to launch a new investigation called The T-Shirt Factory, which is based in the context of a family who starts a t-shirt factory.  Nicholas, the son in the story, works with rolls and loose shirts to organize and keep inventory, and the kiddos work alongside and within this context to solve similar problems to the ones he encounters.

Anyhow, after I had written this problem, we planned our lesson and I soon realized that my warm-up didn’t really fit in the pacing and sequence we’d decided upon.  It wouldn’t make sense further on down the line if we discussed it on that day.  So instead of fulling working it out and digging into how and why and what their strategies were, we just shared our initial thoughts.  And then, like  a happy accident, I figured another way I could use this debrief and the results I got to help plan my next lesson–just not in the way I thought I would originally.

IMG_0778-min

When we met on the rug to talk about this problem, I started with questions.  They were to listen for the number of 10s they had marked on their post-it and then stand in a certain place in the room.  I called all combinations that kiddos could have said (9, 2, 5, 52, 29, 20, 500), and we ended up with two groups: 52 and 2.  This was not surprising, based on two common understandings of what I mean when I say “tens” and how numbers are “inside” other numbers.  Next, instead of sharing out how and why 52 was the correct answer or why one group only said 2, each group talked to a partner in their SAME group to share why they had decided upon 52.  The focus was on communicating how they knew; this is something that is tricky for many of my friends to whom mathematics comes easily.  The “2” group did the same thing within their ranks.  Then, I paired them up with someone from the opposite group and they had to then work to convince their new partner why their number made more sense.  And then we stopped, knowing we’d pick up that same conversation again on a later day during our t-shirt factory work.

Wednesday

Remember the theme of unexpected results?  Here’s another example of that.  Usually when it’s time to talk about the math warm-up, we meet together on the rug and talk about the problem.  We don’t necessarily refer to specific post-its, these just serve as the kiddos’ opportunity to think about it prior to our conversation.  On Wednesday I was out of the classroom during our normal debriefing time (because of more math conversations with Kara and the team), so I only had their morning work to look at.  I gathered info about who knew what to do with these 3-digit numbers and who still showed that they needed to continue to practice (it was about 50/50 I’d say).  It gave me an idea, then, for the next day’s problem, building on the solutions I saw given here with this one.

Thursday

First of all, I have to giggle as I remember when Ja’Mia asked me today if this story was true.  Of course, my friend’s son volunteered to help us with our math lesson! (wink, wink!).  But really, I did see my friend’s son that day, so there’s something. 🙂

Ok, this one taught me something I had forgotten about 2nd graders: 1) they haven’t yet done a problem like this one where I’d asked them to analyze someone else’s thinking, and 2) they answered ONLY the question I ask.

IMG_0773-min

See?  The question (which I crossed off today during our conversation as we talked about what the problem really wanted us to think about) could simply be answered with a quick and simple “yes” and so most of them did that.  They probably thought I had lost my mind by giving them a question like that!

IMG_0775-min

I did have a couple who did get to the thinking I was looking for (but who knows how since I asked the question in the TOTAL wrong way!).  For example, I wanted kiddos to notice that rather than just taking jumps by place value (200 + 70 + 5), the tiny jump of 3 made sense next because it got us to a 10, which is easier to work with.  That resulting 570 also creates an easy double to add mentally (570 + 70, like 7 + 7), leaving a quick +2 to finish up.  Here’s Khalani’s answer example:

IMG_0774-min

Friday

The whole “my friend’s son” thing got me to ask my real son for some help and he was more than willing to do so (plus it meant that if he was helping me with my homework that he didn’t have to work on his own!).  I gave him the problem 519 + 365 and asked him to solve it using a number line to model his thinking since that’s what we’ve been working on.  He did not do it on purpose, but we realized after he finished that he had left out a part, and we actually decided that was a great thing to have happen; my kiddos might have more to talk about if they weren’t just reviewing their own work and saying “yep, it matches.”  Having a different answer and having to figure out why it is different was a new kind of thinking for them.

IMG_0769-min

We didn’t have time to completely finish the debrief, but we were able to talk about how he started, like why he put 519 first as well as why his first jump was just 1 rather than 300, which would have been a typical “place value” jump.  They talked through what he had done and noticed that he misrecorded his +30 jump as only a +3, and that his answer seemed too small; most figured he had forgotten to add on the last 300.

This week’s warm-ups took on a new role.  Our thinking was really deepened, and we dug into how and why in a way we haven’t done in a while. Plus it was great to be able to have 5 in a row!!

What do you think about our thinking?  What had you tried with analyzing others’ mathematical thinking?  Do you have any problems you can share with us?  We’d love to hear from you!!