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. 🙂

 

Second Grade Math Warm-Ups: Week of February 22-26, 2016

I have three warm-ups to share this week.  We had a surprise snow day (which was a little funny because where I live there was no snow!) on Wednesday, so no warm-up that day!  We are in the middle between our money unit and addition/subtraction up to 1000, so the problems reflect that.

Monday

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As we discussed this problem, we tried a similar one:

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Tuesday

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Friday

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IMG_0737-minWe modeled the solution to this one in three different ways (which we related to the ways we had done 2-digit addition earlier this year).

Ok, now for a confession…I was surprised when my kids made some of the connections they did this week between money and 3-digit addition.  I know, right?  Probably shouldn’t happen that way, but it was honestly something I hadn’t really noticed, or at least thought about it as specifically as they did.  I think it was nicely pictured in the problem from Tuesday, where we solved each problem in red–they made connections between how you can add whole dollars just like the hundreds in the 2nd problem (and that’s just like 100 cents, making the amount with pennies); the tens were dimes and then the ones were pennies.  Ok, so that part is not surprising to me–obviously I have this knowledge as an adult–but I honestly didn’t expect kiddos to use this to help them solve the 3-digit addition.

It went even farther yesterday when I had a kiddo working on a pre-assessment for this next unit and was doing the problem 451-238.  He told me he needed the money bag so he could use coins to help him.  Since I always allow kiddos to use whatever manipulatives or strategies they need to figure things out I said “ok,” but I honestly was thinking this would hinder him more than help him, or that he’d end up more confused.  When we first looked it he seemed confused with how he’d subtract 8 from 1 (which told me he wasn’t really solid with regrouping yet).  He started by making $4.51 with half dollars, dollar coin, dimes and a penny, and seemed a little unsure about it as this point, too, asking me about names and values as he made his amount.  But once he got his $4.51, he could easily take about the $2 from $2.38, as well as the $.30, which he did with 3 dimes (and I wonder if he made that $.50 that way on purpose since he could think ahead to having to break it apart later on).  Then he sat with only 1 penny, and the need to subtract 8 cents.  And so yes, here’s where the money came in handy–the concrete nature of being able to think about trading a dime for 10 pennies (which is what he is doing abstractly when regrouping) helped him see the constant value and how he could then actually take about the 8 pennies (8 ones) from what was there.  He then counted the money he had left and told me it was $2.19.  We then talked about what that would be if we were just talking about hundreds/tens/ones instead of money and by drawing it in a chart he eventually saw it as 219.

I’m excited to see how this connection to money plays out for some of my friends who need to actually hold/touch/feel the addition and subtraction.  Yes, it’s something we’ve done with other kinds of math tools and strategies, but I wonder if this might even be the best connection, yet, since it’s all based on place value anyway.  Oh yeah, and maybe that’s why this unit was placed after this one in the sequence….

The conversation around this problem the other day was the kind of thing that reminds me that I don’t know everything.  Obviously I know this, but it’s refreshing when kiddos remind me that they are figuring out things I hadn’t thought of.  I love sharing with them those moments, too.  It reiterates the fact that I am not the only teacher in the room, and that I have things to learn as well as they do.  And I hope it’s a lesson that all of us will remember–and use–for days to come.

The Writing Process–in Math??

Yep, you read correctly.  We’ve been learning the writing process–mainly in regards to our work in Writers’ Workshop–but also in math!

A few years ago, when our school started working with Cathy Fosnot and Mathematics in the City, I learned about how many parallels there are between communicating in mathematics and communicating in most any other setting.  At the time it was kind of mind-blowing to think about how mathematicians revise and edit their work just like authors.  After hearing more, and thinking it through, and then trying it with kids, it made sense.

So…as with many other things I learned about with older kids, and protocols that I know work well with any age, we’re talking about the writing process in mathematics again.  In 2nd grade. 🙂

The first unit we worked through this year was about place value, and was related in many ways to money; this made sense to kiddos and helped them think through how to “trade” 1s for 10s, 10s for 100s and just how to make groups in different ways to “make” a number.

One day they were challenged to consider this story:

Screenshot 2015-10-08 20.37.03-minWith their elbow partner they were supposed to figure our the answer to that question: If Jerry has $1000 to share, with how many people could he share a $10 bill?

Kiddos worked for almost 2 math periods to figure out their answer (which was really the answer to the question of how many 10s are in 1000) and clearly share their thinking on a poster.  For many, the answer of how many people was easy, the way to share their ideas not so much.

As a means of helping them know when they were “finished,” we discussed these parameters for their work:

Screenshot 2015-10-08 18.51.45-minAfter we had our posters finished, we were ready for our gallery walk.  During a Gallery Walk, students put their posters out for other mathematicians to read and comment upon–with the goal of helping deepen mathematical thinking and help create more meaningful representations.  It works much like a writing celebration, which is a great connection because all of our kiddos know how to do that. 🙂

Before we were ready to start commenting on others’ work, we needed a review of how to make effective, meaningful notes on our friends’ work.  We sat for a quick refresher using this flipchart:

Screenshot 2015-10-08 18.51.56-minThen we practiced recognizing helpful comments that followed the guidelines.  I gave examples and non-examples, and then we modified the ones we have given a thumbs-down (which mean they were not specific, kind or math-related).

After that, we were off to work in our gallery walk.

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We did pretty great with our first walk of the year, and I’m sure kiddos brought their kindergarten and first grade knowledge with them to help as they shared their thoughts with other groups.  I was impressed with how questions were used and kids were specific with what parts didn’t make sense or that they thought others could improve upon.

After adding comments, partners were given a few minutes to review what others had shared.  In order to debrief and think about how to use this to help us next time, partners had to share out with the larger group one thing they would do to revise their poster to make it better (and ideally we’d have taken time to actually revise them, but we ran out of time!).  Next time we are ready for a math congress and gallery walk, we’ll definitely come back to this moment and remember what we learned. 🙂

Second Grade Math Warm-Ups: Week of 9-14 to 9-18, 2015

We are in the middle of a unit on place value in second grade.  The warm-ups this week took on a little bit of a different spin, as a couple of times kiddos were expected to finish up work from the previous day’s Math Workshop.  That then became how we started math groups later in the day (I hope that last sentence wasn’t confusing…).

Monday

On this day, we were working on modeling numbers in bundles of 100s, 10s and 1s, like we had done during our place value challenge the week before.

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Lesson 2 Problem Set:

Tuesday

Pretty exciting question, huh?  See the example of what this page looked like below the picture.

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Thursday

On Tuesday during math we had been focusing on representing a number in many ways, so I gave them a quick one to remind them of word form and expanded form.

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Friday

Another one….we also practiced the word numeral for number form, as well as focusing on making sure our numbers go the right way (as we still have some friends who forget. 🙂 ).

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Math Place Value Challenge

I mentioned on the math warm-ups post that we had been working on place value, and that mathematicians had a challenge to figure out how many sticks were in a big ‘ole pile.  They were given a small group (their partner plus another partnership) and two questions: How many sticks do you have? How can you count them in a way that will be easy to show someone else what you’re doing?

Each group was given a pile of popsicle sticks and they got busy!

As I went around to each group, I asked how they had decided what to do, and how they were determining how many sticks they had.  Most were bundling in 10s (yay!) and I nudged them to make an even easier way to see how much is in a big pile.  Could they continue to bundle and make a bigger group?

In the end, most groups ended up with bundles of 100, some 10s and–if their pile had any–some leftover 1s.  They put their collections back in the tubs, and marked how many they had with a post-it note.

Then we worked for a bit on how to model the numbers we had made.

IMG_5304The next step was to figure out how many we had altogether.  Many suggested that we could put our bundles together, but weren’t (at first) sure how to do that.  We talked about how they had made their 100s bundles–with 10 10s–and then guessed that we might be able to make some more 100s from the loose 10s in everyone’s tubs.

Left with a massive pile of 100s, that eventually led us to thinking there must be a better way to show how much that pile had in it.  I asked if they thought we could bundle any bigger numbers and honestly most of them thought I was crazy!  I just began collecting 100s in my arms and counting: 100, 200, 300, 400….and they got the idea.  They going until they got to…10 100s!  That was a great conversation next about what number we had just made.  10 100?  We figured out that it was a 1000, and that when we said “10 100” that helped us know about how many bundles were inside, but that it wasn’t the right way to say the number.  We stretched a big ‘ole rubber band and made a 1000 bundle!!  We counted the whole thing and agreed that we had one-thousand, four-hundred twenty-six sticks!

IMG_5288But how in the world do you WRITE the number one-thousand, four-hundred, twenty-six?  We gave it a go.  Many of us remembered that when we went from 2-digits to 3-digits it was a 100s number, and since we had 4 groups of sticks, maybe that meant our number had 4-digits…

IMG_5287 Our model of this number–1,426–looked like this:

IMG_5306Many minds were blown as we figured out how many 100s and 10s were inside that big number.  We figured out that it was actually than just what the digit said, because of all of the groups inside of groups.  I loved how many kiddos kept saying, “Wow, this is fun!” and “Man, we’re learning so much today!”  Definitely lots of great mathematical thinking happening here!

UPDATE:  I got this email after the first posting of this story.  Love this stuff!  Thanks for sharing, Shannon. 🙂

Hi Jennifer!  
You had so many math posts on the blog this weekend, that I wanted to share a story with you.  We have a Curious George story CD in the car that we listen to a LOT and in one of the stories George gets 10 dozen doughnuts.  The other day when this story was on, Millie asked me if 10 dozen was 120!  I was so surprised!  I said that it was and asked her how she knew that.  She told me “5 2’s are 10, and then another 5 2’s makes 20 and 10 10’s is 100 so, 120”.  It took me more than a minute to follow the math just because it wasn’t how I was used to thinking of problems, but she was totally right and I saw this “new” math stuff in action :).  It was kinda cool!  She was doing multiplication and didn’t even know it.  Thanks for teaching her such great foundational skills that allow her to do these kinds of problems in her head!

Second Grade Math Warm-Ups: 8-24 to 9-4 (2 weeks worth!)

We’re in the swing of some things in 2nd grade.  Math warm-ups are one of those things–just I’m not yet in the swing of writing about them!  Here are last few warm-ups we’ve been working on:

Monday

Even though we worked on this last year, many kiddos had a hard time with the answer to this question.  We’ve since been doing many things (games, two-pen tests, conversations) to help us remember (or learn!) our doubles, near doubles and combos of 10.  They all form the basis for the bigger things we’ll do with numbers later on.

IMG_5294Tuesday

While I’m not entirely sure about the order of these next few warm-ups, the concept that is highlighted in them all is certain–the importance of place value.  Here was another that many had a hard time with.  Most of their answers were “I don’t know yet...”

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Wednesday

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Thursday

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This one was an easy connection to the essential question (EQ) I had asked earlier.  They had to think about place value to answer this one, knowing which numbers to add to each other.

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Although not related to place value, this warm-up was related to a conversation we had had in math workshop the day before, and is definitely something all 2nd graders need to know how to do–tell time!  Often I will spiral older concepts into math warm-ups to keep them on the front of our minds!

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Thursday

This warm-up, although badly worded, gave kiddos a little peek into a task I would have them do later that day in math workshop.  The question was really about the most efficient way to count a big ‘ole stack of something, which they’d have to do with a pile of popsicle sticks in a group that afternoon. I was happy to see how many of them were already thinking about bundling into 10s and 20s (rather than counting them all by 1s).

IMG_5303Friday

The warm-up on Friday was actually the end of the lesson from Thursday, and mathematicians completed their thinking with their learning partner in their math journal, which is different from how they MWU normally works.  I love how we can adapt this structure to work for our needs!  Since many of us have been doing this for a whole year now, it was easy to make that little tweak and still have them know what to do.  In this warm-up, kiddos were asked to model the counting we had done together the day before.

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Sticks and Dots, Compensation and more!

Yesterday I posted last week’s (or at least the LAST week that we were in school’s) math warm-ups.  I mentioned that there’d be more about the strategies on which we’ve been focusing.  Well, that time is now.  Hope this makes sense and gives some insight into the work we’ve been doing for the last few months.  Well all quarter, really…but I digress.  Here we go. 🙂

Screen Shot 2015-03-25 at 8.46.12 PMOne thing I wanted to do was to be able to SHOW how these strategies work, and even better, have KIDDOS involved in that work.  So, just before we left for our break, many of them volunteered to help me with a project.   I have a Tweep (that’s a friend you know from Twitter, for those who might not know) named Shannon in Alabama who was interested, too, so this is for you and your friends, lady! 🙂

Ok…so here are some videos of our Rm. 202 kiddos explaining more about how to add 2-digit numbers using place value strategies!  (I will mention, though, that they are a little rough, so ignore the bumpy parts and see the big ideas, ok? THANK YOU!! 🙂 )

Sticks and Dots

Splitting 10s/1s

Keeping 1 Number Whole

(This one’s a little long, and shows more than 1 strategy, so be prepared for that!)

Compensation

Hope this helps–and WAY TO GO, RM. 202 KIDDOS!!  You are ROCKING mathematicians!! 🙂