Second Grade Math Warm-Ups: Week of May 9-13, 2016

This week was relatively normal, but somehow I only have 3 warm-ups to share.Enjoy! Please comment when you’re finished reading and let us know what you think!

Monday

Yep, we’re still working on subtraction around here.  It’s kind of an all-the-time thing because as soon as you abandon it for longer than a few days everyone forgets how to do it!  This time I gave them the answer and the strategy and had them analyze it for me.  We had a great conversation about why this problem was most efficiently solved by making an easier problem (rather than say, the traditional algorithm or splitting and using a number line to model it) because the second number was close to a hundred.  This made it SUPER easy to subtract in just two easy steps.

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Friday

Um, yeah…not really sure what happened that our warm-ups are just from Monday and Friday.  We must have been really busy this week.  Hope I remember what we did so I can tell you about it here. LOL

Friday we actually had a bonus math warm-up because our Writing Warm-Up led us to figuring out some math and making a graph.  And yes, I ran out of paper.  We improvised. 🙂

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We are also still working on multiplication, including writing an equation and drawing a model.  This one was cool, because as often happens, kiddos thought of a model that I hadn’t: showing the repeated addition on a number line.  This was a great conversation about which number meant what in the problem (the number of groups vs. the number in the group), and we also talked about how you could flip the problem around and have the same answer.

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Second Grade Math Warm-Ups: Week of May 2-6, 2016

I am a little bit late–sorry!  I forgot a few important pictures that I needed in order to properly share.  Hopefully you’ll still read (and learn with us!).  🙂

Monday

There’s not a lot to explain behind this one except that I wanted to continue to focus on the idea of a fraction being EQUAL pieces, not just the number of pieces in the denominator.  As you can see in many of the post-its, most kiddos understand this when they partition the cookie cake for 4 people.

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Tuesday

As I mentioned with a problem or two last week, kiddos are to have a basic foundation of groups and arrays to help them with further multiplication concepts in 3rd grade.  We played a game called Circles and Stars last week, which is basically where they roll a dice twice, once drawing circles and then filling each with the 2nd number’s worth of stars.  Then they figure out an equation to go with the model as well as how many stars there are altogether.  I wanted to build on this idea and see what they’d do with a new problem.  As is seen on their answers, they almost all drew circles with stars (or dots).  I wanted to help them see the same idea as an array, as well, so I connected the equation to brownies (so they pan/array would make more sense).

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Wednesday

Somewhere I had saved a picture of my original problem which looked like this (the purple writing on the chart): If I had a pan of brownies that had 7 brownies on one side and 5 brownies on the other, how many would I have?  When I looked at the answers, I was completely baffled as to why so many had answered 6X2=12.  We had a great decision about how they used 7+5=12 and then made a multiplication equation that matched.  There were also some pretty interesting models/pictures of the equation, too, so I drew an array to show what I meant.  Once they saw it, they could see what I meant, but we agreed that the problem I had written didn’t lead them to that understanding.  I asked them to help me figure out how I could have better written the problem so that they could have seen what I meant.  We worked to revise the question so it made more sense.  This was a GREAT conversation both about math and revision, which is something Rm. 202 friends know happens ALL THE TIME, not just in writing.  They did a super job of helping me redesign the warm-up so that it better matched what I wanted to know.

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Now it reads: If I had a rectangular pan of brownies that had 7 columns of brownies on the long side of the pan, and 5 rows of brownies on the other, how many would I have in the whole pan?  Draw a picture.   Great work on the writing and the math, Rm. 202 friends!

Thursday

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Friday

We’re still working on many concepts all at once, and solidifying our understanding of them.  Love my little speech bubble?  We always talk about how the numbers in the problem scream at us to tell us which strategy is most efficient for them, so it just seemed fitting. 😀

 

Second Grade Math Warm-Ups: Week of April 25-29, 2016

We have been on a roll with warm-ups lately, and maybe since we’re still talking about many different things, they’ve given us a way to keep all the balls in the air.  Love that.  Enjoy! 🙂

Monday

One of the topics we’re working on right now is the foundation of fractions, and understanding about equal parts.  This warm-up led to a GREAT conversation about how 1/5 is always a 1/5, but the actual portion that is being considered changes based on the whole.  Oh, and we were all hungry when we were finished. 🙂

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Tuesday

It seems like addition and subtraction is a never-ending concept with 2nd graders, and we’re still working on it.  Oh well, as long as it takes.  School year’s not over yet and they can get it! Here was another opportunity to practice.

Wednesday

Ok, so I need to explain that that picture is a pizza, not a target.  It’s based on a picture we had looked at the day before in a math conversation.  It was based on an 8-slice pizza and how we could share it fairly if twice as many people showed up for our party.  This was the way one group suggested we do it, and we had to discuss whether we agreed if it was fair.  Which piece would you want? 🙂

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Thursday

We had a FABULOUS walking field trip on Thursday at the time we normally do math warm-ups, so didn’t have one that day.  We had a great day in the park and a movie instead! 🙂 (Don’t worry–it was connected to our curriculum!)

Friday

Another topic (which I found a way to weave into this conversation, too!) is the foundation of multiplication.  We told many stories of groups of things with this one.  Great thinking, Rm. 202 kiddos!

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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).

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

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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…

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

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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!

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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:

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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. 🙂 ).

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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.

 

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!

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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:

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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.

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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.

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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. 😊

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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…:)

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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.”

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

First Grade Math Warm-Ups: Week of May 4-May 8, 2015

I had thoughts all last week of how I couldn’t wait until the Warm-Ups post to brag on the awesomeness that happened, but alas, I guess I saved it anyway….so get ready, this is definitely NOT first grade math happening here, people!

We had three problems this week, and they were all in the same vein–2-digit subtraction where kiddos were asked to try ALL 4 STRATEGIES we’ve worked on in our class this year.  And they were up to the challenge, even though it had been a while since we’d worked on subtraction.  I was SUPER impressed, and I think they were, too!

The benchmark in 1st grade says that only have to be able to subtract to 20, but since we were doing addition to 100, we went ahead and followed along with subtraction as well (why stop them if they can go farther??).  They also only had to be able to do it in 2 ways, but again, I think it’s good to be flexible with strategy and begin (even as a first grader) to learn which strategy is best for the numbers.  In this case we used each strategy each time, but talked about which ones made the most sense.  Let me show you the part we were most proud of:

IMG_3072I don’t know if you can tell, but that’s not an ordinary 2-digit subtraction problem.  Nope–it’s one that will need to use what we used to called regrouping but that honestly now we don’t really call anything.  It’s just what you do to make the problem work!  Please also notice that there’s no “stacking” or traditional algorithms here and these littles can still figure out the solution.  Nice, right?  I know some wouldn’t believe it’s possible….:)

My favorite part is when we started with sticks and dots, and we realized that we couldn’t do what the numbers told us to do–we couldn’t take 7 dots away from the 5 we had drawn.  Millie noticed it right away and then we had a great conversation about what we could do about that.  Makayla suggested that actually there were 10 dots inside each of the sticks we drew (how’s that place value work for ya?). We decided if we crossed off that last stick (which represents a 10) and added those 10 dots instead to the dots already there, then we could do it.  We ended up with 15 dots (ones) that we could take 7 away from.  We used the double-minus-1 problem of 14-7 is 7 so 15-7 is 8 to get that part of our answer.

Then, when we tried to do the same problem with splitting, we ran into the same problem–we didn’t enough to do that part of our problem.  Since we had just done it, we knew we could try it again, and moved the 10 from our 90 to make 80 and then the 5 became 15.  Voila!  It all worked out. 🙂

This is some pretty amazing stuff, and I’m impressed to hear both their fearlessness and pride when they figure out what to do.  I also love how differently 1st graders seem to tackle problems like this that are hard, or challenging, or that don’t at first seem like they’ll work–they just jump in and try something and see what happens.  They haven’t yet learned that they can’t do it, they aren’t worried about whether or not they make a mistake, they know they have many tools in their toolboxes that they can use till they figure it out.  I hope to be able to encourage this kind of approach to problem solving as I work with them again next year—crossing my fingers that I can help them keep that mindset for longer than maybe they would have…there’s hope at least. 🙂