I participated in the St. Louis Hot Chocolate 5K with my family on Dec. 14 and of course I had to use it as a context for a problem of the day! And yes, it is a true story. I’m really slow. 😦
Tuesday
We’ve been working on addition strategies, so the numbers in this one were chosen so that hopefully kids would see the 10 and use it: 6+4 =10 and then 10+7= 17.
Wednesday
One thing I want my mathematicians to be able to do is think flexibly about numbers. Sometimes I give the the answer and ask them why it reasonable (or not!).
Thursday
I’m not sure why I wrote the word tonight on this problem (as it doesn’t make any sense since I wrote it the next morning!), but you get the idea. 🙂 The focus was both on adding a string of numbers, as well as determining whether to add or subtract. We’re getting really good at knowing when to add and when to take away, by thinking about the context and picturing the situation.
Friday didn’t have a math warm-up since we didn’t have math. We had a delightful Winter Party instead! Hope you had a great holiday break, math friends, and that you’re back into a positive January groove! 🙂
Remember last year when I told you all about Feast Week? Well, it’s that time of year again, for fractions at least, but not–it seems–for Feast Week. Instead, we’ve begun using some AMAZING new resources from Cathy Fosnot, that have helped our mathematicians think of fraction parts in a whole new way.
My favorite part of math right now is the addition of Fraction Flex Time (man, it seems like we need to add a cute name to every thing fraction related…). After we finished the investigations in our Fosnot unit (which included figuring out the Best Buys, Oatmeal Problems and Gas Tank problems), our team sat down to figure out how to divvy up our kiddos between the 7 teachers we have (Yes, I said SEVEN!! Isn’t that FABULOUS!! ??), based on the information we’d gathered during our first few weeks of study. We made the groups small and intentional, and we planned for intense teaching and practice.
Although the pacing and strategies are a little different based on the groups’ need, the goal is the same (based on our district rubric):
Just like I shared in my post about our visit from Kara Imm from Mathematics in the City, number strings have become our new best friend. I mean, honestly, before this year I really didn’t spend much time on them, but now I am not sure I can go a day in math without one–they just have such HUGE bang for their buck. Just the other day we spent 45 minutes doing a number string together. It sounds like a long time, maybe, but in that 45 minutes (during which my small group of friends was TOTALLY ENGAGED!), we were able to touch on the clock model, common denominators, reducing fractions, equivalent fractions, improper fractions and mixed numbers. So cool!
I have heard such positive feedback from my class since we’ve been doing flex time. Most mention that they love the small numbers, the focused nature of the lessons and the time they get to spend with the teacher. I agree, friends, I’m loving all those things, too!
My favorite thing from our lessons lately is all of the “lightbulb moments” that I can actually see happen. It’s so great to see that look of AHA! on a kiddo’s face, and how often these moments even have a sound. All of the “ahs” I’ve heard lately have definitely made my days.
What do you think about fractions? How do you think you would react to Fraction Flex Time? Do you think you’d like it? Please leave your feedback. 🙂
Mathematics in the City is an organization I learned about this summer when the fabulous Kara Imm came to Robinson to teach us about how to better teach addition/subtraction and multiplication/division of fractions using new units from Cathy Fosnot (another amazing math mind!).
Fast-forward to now: yesterday we (several 5th and 6th grade teachers and math specialists) were lucky to have Kara back again to continue to learn from her (and each other!) as we taught one of those units in our own classrooms! We spent the morning planning our lesson, digging into the mathematics, talking about how we’d introduce the scenario, anticipating what kiddos would do and say, and brainstorming questions we’d ask our mathematicians to help “lift their thinking.” Then our group (oh, did I mention there were like 15 teachers??) watched as Mrs. Hong taught the lesson in her room with her friends. We got to “kid-watch” and take notes on what thinking they used, how they explained their work and also practice what we’d planned during our earlier session.
At lunch we debriefed on how the morning had gone, planning for how we’d change things based on the information we gathered. Then it was time to plan for what would happen in my classroom later that day.
We decided that Kara would lead a number string with my students, focusing on fractions, but using the context of money. Her string looked like this:
See the red parts? Those are the problems she gave students to solve (remember when we did number strings together at our Curriculum Night? Same idea, only with a different concept). The black is documenting kiddos’ thinking, and the blue is how she was modelling their thinking. The story she told here (that gave kiddos an entry point and helped them make connections to what they know) was about how she’d found some money as she walked along this morning. What a great way to talk about fractions huh? TOTALLY made it less scary, and who doesn’t know at least SOMETHING about money? The thinking they were able to share was fabulous, and the kiddos who felt confident to share their thinking was great, too; some kids who don’t normally share during number strings were more than willing to do so with this one!
I know that pictures of this totally don’t do the fabulous thinking justice, but here are some shots I captured during our work yesterday. Check them out!
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What a fabulous (man, I say that alot, but it’s true!) opportunity to learn with such great minds! Can’t wait to see how this helps our math thinking progress as we begin a new investigation and more number strings!
If you’re a parent, be sure to share what your kiddos said about this experience. If you’re a teacher, have you used number strings in your room? Do you know Kara or Mathematics in the City? Do you use Cathy Fosnot units with your learners? What do you think of them?? I’D LOVE TO HEAR ABOUT IT!!
First of all, I know. It’s been forever. Man, I’ve been saying that a lot lately. All I can do is apologize, though, and ask that you’ll kindly keep reading. Life is nuts these days. 🙂
So…we are just about at the end of a study of multiplication and this year I’m asking my friends to think in a different way about the word efficient when it comes to multiplying.
Based on our district rubrics, which have recently been rewritten based on work related to Common Core and an updated curriculum, the standard for 5th grade has changed. Instead of just being able to use the traditional algorithm, students are expected to be able to fluently use a variety of strategies. But get this: the strategy they choose to use should be based on the numbers in the problem, rather than personal preference or the strategy they know best. WHAT??!! I seriously have some friends whose heads might explode.
But it’s not really their fault, I guess, because for years the algorithm was the goal. And once they learned how to use it, that’s what they stuck with and used every time. For years, we (or they) saw the other strategies as lower-level–ones used by friends who didn’t yet “get” how the algorithm worked.
District Math Rubric for Multiplication
Now we’re thinking more about how mathematicians should be able to be flexible with their thinking, to use place value correctly and to explain their reasoning based on what they know about numbers. This doesn’t mean that the algorithm isn’t something kids should know how to do, but that it’s not the only thing they should know how to do. I mean think about it in the real world: there are times when you have to be able to do math in your head, in an efficient way–without paper. The algorithm doesn’t really fit into that model.
So what does this look like in our room?
First of all, here’s an anchor chart that now hangs in our room (made based on our knowledge of how to solve multiplication problems):
Classroom anchor chart for multiplication strategies
While I don’t have any pictures of the math warm-ups we’re doing right now, this is where many of our opportunities come to try out this thinking. The problem today, for example looked like this:
Math Warm-Up for October 14
There are obviously (based on the chart) multiple ways to do this problem. But based on the numbers (which were chosen on purpose), the strategy that makes the most sense is to either use splitting or a close 10 to solve the problem. That way, you can solve 75 X 20 and 75 X 3 and then add them together, which can easily be done in your head–without paper. If you chose to use the algorithm (which most would do–even most adults!) you’d have to do 5 X 3, then 70 X 3, 5 X 2 and then 70 X 2 and add it all together–many more steps than the other strategy.
So while this is still a little tricky for some friends, it will get easier with time. We just need some more practice. 🙂
What strategy would you have used to solve 75 X 23? Do you know more than one strategy to multiply? Is the traditional algorithm your “go to” strategy? I know my 5th grade mathematicians would love to hear your answers!
First of all, to my friends in 5SK, I’m SO sorry you’ve been waiting so long for this post! We ended up needing another day to get our presentations “just so” before we shared them.
And so for those of you who are not from 5Sk (a Year 5 class in Queensland, Australia), let me fill you in on what’s going on.
I have been talking to Ms. Scharf for a little while, and received an email from her the other day with a request. She also posted it on her blog:
The challenge from Ms. Scharf for her 5SK friends.
I was beyond excited about this question because 1) I knew my friends could answer it and help their Aussie friends, and 2) this was a REAL, AUTHENTIC audience with a REAL problem that we needed to solve–talk about motivating!
So after talking through what we needed to do first (which was research the Australian money system so we knew what connections to make and so we’d have some background knowledge), as well as all the things we needed to include in our responses.
And so, after two days of working, here’s what we came up with for our friends:
And last, but not least, one group made a poster to explain their answer:
Fiona, Anna K., Sammy and Rebekah chose to explain their thinking in a poster.
So what do you think? 5SK friends–did we help you? Please write and tell us what you think. We’d also love to hear how your Pocket Money Challenge went today! 🙂
Hopefully you’ve caught the first two parts of this story already. If not, they are here and here. 🙂
After we had our cooking lesson, we got back into our groups to do a re-try of our posters. Another thing that my friend Pam mentioned to me when we were talking about what could have gone wrong was that maybe the paper they were using was too big. What?! Something that simple? It’s funny, because I hadn’t really considered that before she said it, but as soon as she did, it made perfect sense. They only had a certain amount of information to share with other mathematicians, and many groups ended up with lots of white space they didn’t know what to do with. Maybe it wasn’t a factor in our troubles, but it was worth taking a look at. So as we started again, we used smaller posters. 🙂
We tried something else with this investigation, too–we invited another class (who didn’t know anything about our problem) to do our gallery walk with us. This, we thought (ok, well I thought) would give us an even better idea of how we could revise our first drafts, since it was a “cold read” for them–they could only use the information we gave them to make sense of our mathematical ideas, rather than the context of the problem or background knowledge of the process. So we invited Mrs. Hong’s class to work with us. This was a PERFECT situation, because they had just finished a big problem, too, and needed someone to help them revise, too. Match made in heaven, right?
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I mentioned in my last post that I’ve been thinking about incorporating more with cooking into math next year, and this whole trade-classrooms-and-do-a-gallery-walk thing is another idea my team is considering doing more of. We want to be more purposeful in how we create real-life, meaningful scenarios for our kiddos to solve, then use the knowledge and ideas of each other to help make the work even better. Seeing another version of a problem you’ve also solved is very different than looking at a poster that is completely new. The mathematician has a much bigger job to do for these new viewers; every word, number and symbol they write is a clue to help them figure out the puzzle.
So what have you done with posters, gallery walks or real-life problem solving in your class? What advice do you have for us as we work to continue these ideas with our mathematicians for next year? We’d love to hear your thoughts. 🙂
Wow–I’ve been doing a horrible job with updates lately! I’ve left this one hanging for over a week, and I’m sure you were waiting on the edge of your seat to hear the rest of the story, right? Well, thanks for being patient. 🙂 The “rest of the story” will actually end up being told in two more parts.
Remember how we were working with a problem about ranch dip and I was baffled by what was going so wrong?
Ranch dip problem, part 1
Part 2
Well, what I don’t think I told you last time was that I had a conversation with a colleague of mine, who happens to be a fabulous math teacher, too, and we agreed there could have been many reasons why this was trickier than I had intended. I decided to tackle these issues one at a time. The first one we thought of was related to the context.
I think I may have taken for granted the fact that my kids would know about teaspoons, tablespoons and just the whole act of mixing it all together. There were actually several kiddos who could not relate to what I was talking about with making the dip, so I decided to fix that problem. I hoped that using the recipe would help them better understand what I was asking them to figure out. So we got cooking!
First, we reviewed the recipe and talked ingredients so we made sure we knew what to do. See how handy our iPads are for jobs like this? 🙂
Sorry, this ones a little blurry, but we’re smelling the spices the recipe called for: onion powder, garlic powder, parsley and dill. Many hadn’t ever seen these before!
Oh, and there’s basil in it, too! Smells yummy already!
The recipe calls for sour cream, but I decided to use plain yogurt instead. Man, I must have been stirring fast!
We discovered another part that was important (and in many cases missing) knowledge–knowing the difference between the sizes of teaspoons and tablespoons. Knowing that there are 3 teaspoons in a tablespoon was necessary for use in the final answer, but this was hard for some kids to image without seeing it.
Spice mix ready to be stirred!
We needed a 1/2 cup of yogurt for every tablespoon of spices.
Looking good!
I forgot a knife. 😦 Cutting a cucumber with the back of a fork is harder than it looks! Eventually I made it happen, though. 🙂
Yum! Ranch dip with cucumbers and Triscuits for our morning Math snack!
So while my cooking class didn’t solve every problem we were having (which I’ll tell you about in Part 3), I do think it gave many of them the ability to make connections they were unable to make before. And there is so much math (and science) in cooking and baking, I don’t know why we don’t do more of it. TOTALLY wish my classroom had a kitchen! It has also made me and my team think about how we want to purposefully involve more of these types of activities into our classes for next year. We’re thinking it would be a great addition and preparation for next year’s Feast Week, too.
How do you use cooking in your classroom? What connections do you make for your kiddos to math and science? Or maybe even reading and writing? We’d love to hear your thoughts and suggestions as we make plans for next year. 🙂
Or maybe it’s Spanish or Chinese or Pig-Latin, but today I felt like I was definitely not speaking English to my kiddos during math. Meaning no one understood what I was trying to explain, and many kids ended up more confused than when we first started. WHAT? It’s not like I’m new at this, nor to the topic. We were even working on a problem that I made up! Needless to say, we all wanted to throw in the towel, or rip up our papers and start over. Or something else that you shouldn’t do when you’re frustrated. And no, in case you’re wondering–we didn’t. But we did put the problem away until tomorrow when we’re fresh and can tackle it again. And I am already armed with a different plan for how to address it, but am hoping you can help me, too! (And by the way, after how fabulous the first round of problems-with-posters went the other day, this was all the more mind boggling!)
Ok, so I’m hoping that you can help me figure out what might be making my friends so confused. Here is the problem that we were working on yesterday and today:
This problem is 1) based on a real-life problem, 2) uses math skills we already have (or at least that are not new!), and 3) really just focuses on making sure they use clear and concise notation to record their solution and thoughts.
Part 2
PLEASE give me feedback on parts you see that may have tripped them up. After working on it for two days, I see a couple of things, but I really expected this to be a rather simple fraction problem; the difficulties they were having were not ones I had anticipated. My hope was they could focus on the poster part, as a prep for how they’d answer questions as we start testing next week. Instead, now they’re all convinced that math is hard and confusing. Pretty much a teacher fail, huh? 😦
Thoughts? Oh, and I guess it’s a given that I want you to be nice. Truthful, but nice, please. 🙂 And maybe you could even tell me what you think the answer is. That might help me see if the problem reads the way I intended it to. THANK YOU, FRIENDS!
Wow–how has it been a whole month since I last posted math warm-ups? Oh, yeah, because MARCH was crazy–including a SNOW DAY and SPRING BREAK right next to each other. And not that April is any less busy, but at least this week could be considered somewhat normal. Oh, not it wasn’t–I had a sub on Tuesday. But hey, what’s normal anyway, right? Regardless, here are some recent math warm-ups I haven’t shared yet.
First of all, a couple from last week:
This one was to help discuss fraction place value, and also to help us talk about writing clear and concise answers to questions like these (in preparation for MAP testing in just over a week).
Can you tell I ran out of paper and didn’t have a chance to get more for a couple of days? Sorry. 🙂 This one is another place value one, hoping that students would see the relationship between money and fractions, and how they can just “move” the decimal (by multiplying by 10), rather than having to use the algorithm to solve the problem.
This week’s warm-ups:
Wednesday
We needed to reminded (again) about equivalent fractions, as well as their tie to decimals.
This one came right off of our Edison benchmark practice from this month. We’re using the problems on that assessment to help us analyze the “why” of the ones we get wrong. This can help us not make those same mistakes again the next time we encounter them.
This is another Edison problem, but I changed the numbers. Many students are still not remembering to make the denominators the same before they add. This one also elicited great conversations around simplifying answers–both how and why here as well.
I’m hoping I’m back in the routine of posting warm-ups. Sorry if you’ve missed them! 🙂
So I realize it’s really only been a couple of days since I posted my Week 1 Reflections, but since today was technically the end of Week 2 and we had such a fabulous tech day, I thought I’d tell the story today.
Since our horrible experience last Friday trying to get our Dropboxes all figured out, we’ve had some pretty successful days with our iPads. Today was a particularly great day, with many great ideas flowing about how we could enhance our learning by using our iPads to record our thinking.
On Monday, we started an investigation in math that was focused around my son, Riley’s, allowance.
Riley’s Allowance Problem
Now, the math involved in this problem was not difficult; the focus here was on using clear and concise notation to record thinking, as well as revising your work before “publishing” it for others to see. We focused on making sure we followed all of the directions and did the whole problem (which is a great skill to review since we’re doing state testing starting in about a week and a half. 🙂 )
Kiddos spent two days working on the problem and then creating their posters. After everyone had a poster, we did a gallery walk where groups were responsible for leaving feedback for others related to how well they accomplished each of those goals. They left plusses and deltas for the group to consider as they revised their poster later.
Revising based on what classmates said about their poster.
One of their “deltas” was that they had too much white space and not enough numbers. They added in equations to show how they got their answers.
Creative use of paper scraps as “white out” to cover parts they needed to change.
Don’t you just love the combination of “old school” and “new school” here? IPads right alongside big ‘ole paper and markers. 🙂 They’re using one as a calculator and the other has a screenshot of the original directions where they did their draft work before the poster.
Adding headings to each section (which classmates thought included too much writing) helped their thinking make more sense.
Then, I gave them one more direction: make a video to summarize your post-its, share your revisions and explain why they would help learners better understand your poster. Pretty cool, huh? Here’s what they did next:
I’m trying to decide when to mention that it took SIX STEPS to get those videos from where they were recording to being able to embed them on this blog post!! WHAT? I’m sure some of it was me not knowing some details about Dropbox (where I was hoping to be able to upload the videos so I could have access to them on my computer after school), but honestly, some of our biggest problems come from the filter that our Minis have embedded on them. Obviously an internet filter is a necessary thing to have, but so often it also keeps us from efficiently doing what we need to do as learners. So…the videos went from kiddo iPads where they were recorded——–>they were sent to me through iMessage (which ended up being the only way we could figure out to export them, and by the way, we had to set up before we could use today)——-> then I learned how to upload them to the Dropbox app on my Mini so I could access them———>then I had to download them to my computer, since the Dropbox they were in is not the same as my personal Dropbox linked to my computer—–> then they were uploaded to YouTube——-> and THEN they could be added to my blog. Are you tired yet?
That definitely wore me out a little. Surprised I had any energy left to even write all these words! Is that crazy to anyone but me? PLEASE, PLEASE, PLEASE tell me if you know an easier way to get video from kid iPads to a usable form for me. I want to use them more often for things like this, but I’d love to be able to do it without so much work. 🙂
(And so here I was going to add a really SUPER idea that my friend ZB had today about how to show our thinking about poetry, but surprisingly the examples I wanted to share are still on the iPads where we recorded them today. Just didn’t have enough hours in the day to figure that one out. Hopefully tomorrow. 🙂 )
20somethingkids and 1kookyteacher 