2nd Grade Math Warm-Ups: Week of March 22-25, 2016

We are back from Spring Break!!  We quickly got back into the swing of things with our morning routine, and I was trying to focus on spiraling back around to topics we haven’t touched for a while.  We also had a Mystery Number Skype scheduled for Friday, so the problem that day was specifically designed to help that thinking.

Tuesday

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Thursday

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Friday

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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

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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.

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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!!

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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.

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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. 🙂 )

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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.

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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.

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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!

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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:

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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.

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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!!

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.

Second Grade Math Warm-Ups: Week of February 8-11, 2016

This was another of those weird weeks in the Winter where we have less than a full week of school.  Oh, yeah, and we celebrated Valentine’s Day today which made for a funny schedule.  AND then you add in ridiculous Missouri weather and an accident (oh, no, not mine–just one that added an hour to my commute!) and this week has already been the longest in ages.  What? It’s only Thursday? Well here’s to a professional development day tomorrow, then. 🙂

So…a short week and a crazy day today means I have only three warm-ups to share.  I think they’re pretty good ones, though.  Made for great conversations.  Enjoy!  Oh, yeah, they’re all about money again.

Monday

This was the first time I’d asked a money question written in equation form.  Many were confused by seeing cents written as dollars (they kept saying “Why did you put a dollar sign there?”), and so we had to clarify that during our debrief.

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Tuesday

This was a challenge to think of amounts in more than one way.  They did pretty well with it, though.

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Wednesday

When we talked about this one, we had some great conversations about efficiency when counting coins, and how making piles of dollars (starting with the biggest coins) is a quick way to figure out the total.  We also practiced making $.25 in multiple ways (not just a quarter).  We called it “Mickey Mouse” when we found 2 dimes and a nickel, so 2 Mickeys and a 2 quarters makes a dollar, as does 2 Mickeys and a half dollar.  Just so you know. 🙂

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Second Grade Math Warm-Ups: Catching Up

If you’ve been around here for a while (thanks!), then you know that one of the “regular” posts I do is to share our math warm-ups each week.  For many reasons that hasn’t happened for the last few months.  So this post is to catch up on some of the best ones from recently. 🙂

Measurement

Before the holidays we were working on measurement (mostly length) and had some questions at the beginning to get minds thinking about how and why we should know how to measure.  The last one also addresses being able to visualize the size of a unit (centimeters) and apply it to appropriate situations.  In between and after all of these, we did lots and lots of measuring with different units, tools and objects.

Measurement (Time)

I only ended up with one picture (sorry!) of this round of warm ups, but after we came back from Winter Break we were still working on measuring, only with time!  There were several days of questions related to where the hands would fall on the clock, how many minutes would have passed if the minute hand were on a certain number, as well as one where the had to tell all the ways to describe a certain time (4:30, half past 4, etc.).

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Measurement (Money)

Now we’re on to money, and so we’re working on some foundational questions that get kiddos thinking about the numbers behind it first.  Then we’ll work more specifically on counting amounts, giving change, etc.

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This first one was just to get kids thinking about groups.  What was great (and what happens often when we discuss the problem later in the day) is that while I never mentioned anything about money, someone used that model to help them figure out the answers and then once we made that connection, it made sense to other friends, too.  Then we could explicitly connect the numbers to coins and amounts we knew (or needed to learn!).

This one got kiddos thinking about combinations that make 25 (which I knew meant a quarter, but wasn’t saying that yet)…

…and then the next day I asked that same question with new parameters (which again I knew was connected to money) to connect to that previous thinking:

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As with most everything else I throw at them, kiddos are doing great things with making connections to previous knowledge and incorporating new concepts.  It’s great to watch them think like teachers and figure out the method to my math warm-up madness–often kids will say “Hey, you asked this question because….”  Good stuff!

If you’re doing math warm-ups, do you have any to share about measuring length, time or money?  We’d love to try them!

Second Grade Math Warm-Ups: Week of November 16-20, 2015

I apologize for the fact that it’s been nearly THREE WEEKS since I last wrote on this blog.  I’m not even sure what happened.  Oh wait, I do.  Life happened.  And I was tired.  It was one of those times in life when you have to do really cool things and take pictures of really cool things, but not write about it, you know?  Oh well, here’s to trying to fix that.  Starting now.  So onward we go!

Monday

We were starting a new unit in math this past week, so the warm-ups were no longer addition and subtraction.  This one is connected to some essential questions we will be chewing on throughout the unit, as well as serving as a way for me to know with what background knowledge everyone is starting.

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Tuesday

Another essential question from our unit…

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Wednesday

This pic is obviously NOT a math warm-up but is instead a view of where we were on this particular morning.  I sometimes use our warm-up routine as a way to make plans for our day, or to highlight a goal that we will all be working on together.  This was related to the work we were doing last week with remembering to focus on caring for others rather than just ourselves first.

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Back on track with measurement.  🙂

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This last one isn’t a math warm-up, nor do I remember what day it’s from, but it was a great example of how math happens all the time in our room!  Oh, and it used skills we had just learned in our last unit, so it was great practice.  We were starting a new chapter book (Thanksgiving on Thursday by Mary Pope Osborne–a Magic Treehouse book), and were interested in knowing when the first Thanksgiving took place.  We figured out we could subtract or count up to figure it out.  We decided to use the Circle, Split, Subtract with a Number line strategy that we had learned.  It worked! 🙂 And….Thanksgiving started a long time ago. 🙂

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Whew!  It feels good to be back in the blogging game again. 🙂  Thanks for coming back to read!

Second Grade Math Warm-Ups: Week of October 12-16, 2015

This week we began a new unit on adding and subtracting within 100 (which is actually a unit we had last year, as well, so should be something that we remember.  Should…time will tell if that’s true. LOL 🙂 ).

This time around we’re focusing more on making sure mathematicians are flexible and can show their thinking in more than one way.  As with last time, we’ll also make sure they can choose a strategy appropriately based on the numbers (rather than just which strategy the like best or is easiest for them), and we’ll also continue to work on being clear with our communicating our mathematical thinking.

Here we go!

The first strategy we worked on for this unit is called HTO, or hundreds/tens/ones.  Yeah, it’s kind of an obvious name for what they are doing, so I guess it works. 🙂

IMG_5508-minEach kiddo has a workbook where we’re showing our thinking, and I had to share what Emily’s looked like after I taught this strategy.  She kind of liked it. 🙂

 Here’s more about how that strategy works:

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First you mark the first number on the chart (98) and then add on tallies to show the second number (31). Then look to see if you can find any tens or ones you need to move over to the next column. Finally, add down the columns to find your answer.

Ok, so this post is a little misleading, because that was the only warm-up I have to share.  The rest is more from what we did in our conversations in math.  Hope that’s ok. 🙂

On Friday, we started another strategy that is Adding on the Numberline (and actually using another strategy called Circle/Split/Add):

We still have a strategy or two to teach, and then we’ll just practice them until they’re solid.  The thing I have to keep reminding kiddos (especially those that are focused on being RIGHT and being FAST) is that this unit is as much as communicating and being flexible as it is about finding the right answer (although, OF COURSE that’s also expected. 🙂 ).

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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