Rethinking Multiplication Strategies

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

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

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

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!



Feast Week Part 6: Now We Cook!

So before we could FEAST in Feast Week, we had to have a feast, and that meant we had to make it!  So Friday afternoon, before our big party, we got busy making things.  Remember, our appetizers were party pickles, sausage snack wraps, fruit, and guacamole.  We got into our tribes to work.

Check out our culinary creations:

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If you missed any of the previous parts of this tale, check out the Feast Week tag for parts 1-5.  Next up: THE FEAST!!

Feast Week Part 3: What’s For Dinner?

If you haven’t checked them out yet, be sure to read Part 1 and Part 2 of our Feast Week journey. 🙂  If you have, welcome back!

While we thought it would never actually arrive, December 17–the first day of Feast Week–finally came and we were ready to get started!  Our kiddos had done such an amazing job with all that they had to learn about fractions, and were now ready to apply that to a real-world situation.  They were super excited and very motivated.

Our class was responsible for appetizers.  While they were a little sad because they wanted to do dessert (everyone did, really!), they came with really great suggestions for what we could make for our portion of the meal.  Everyone came with family-favorite recipes from home, and we had some decisions to make about which we were going to use.  We got into our tribes to make these decisions, and narrowed the list down to these yummy choices:

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The next step was to shop for ingredients.  Using the circulars from Schnucks and Dierbergs, tribes got busy finding ingredients and figuring out how much their recipe would cost using these directions:

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As with everything they do, kiddos took on this job with much seriousness and concentration.  They had to feed 85 people after all!

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Read about Part 4 of Feast Week here!

Feast Week Part 2: How I Learned Fractional Parts Without Thinking About Pizza

In case you missed Feast Week Part 1, check it out here.

Feast Week was born, and we had decided what (and how) we were going to teach that big, deep list of concepts about fractions.  We utilized the UbD template for planning the unit, focusing on what we wanted the outcomes to be and then how we’d get them there.

And then we told our kids about it.  And they were BEYOND excited!  We were giddy about the plan, and my students were as eager as me to start our fraction work so we could head down the road toward the beginning of the actual Feast Week.  And just as we had hoped, this was just the motivation that 81 5th graders needed to get through a really hard unit on fractions.

But first we had to learn about fractions.  The unit was broken down into eight big ideas:

1. What are fractions anyway?

2. How are fractions related and equivalent to percents and how can they be used to solve problems?

3. How do you find fractional parts of a group (i.e. what is 2/5 of 30 students)?

4. How do you add and subtract fractions?

5. How can you multiply a whole number by a fraction? What does it mean and why would I need to do it in real life? (As a side note: this one was cool, because it is the same as finding the fractional part of a group–they just didn’t know that back at the beginning of the unit)

6. How can you multiply a fraction by a fraction?  What does it mean and why would I need to do it in real life?

7. How can you divide a whole number by a fraction? What does it mean and why would I need to do it in real life?

8. How can you divide a fraction by a whole number? What does it mean and why would I need to do it in real life?

The really fabulous (yes, I know I say that word a lot, and yes, I do it on purpose 🙂 ) thing about this unit was how many times I heard the words “Wow, this is easy!”  And how surprised so many kids were that it was easy.  For some reason, fractions is a four-letter-word to most people and honestly, I think that’s why so many of us (including me!) had so much trouble figuring them out.

We use Investigations as a math resource in our district, and I have always loved the way it works through math concepts–always starting with the why before showing the how.  And it was no different with fractions.  We did not start with straight number problems where we colored in pies that were the same amount, or with “this is the algorithm for adding fractions.”  We started with the why–or the “what” really.  What is a fraction, and how does it relate to percents, which are something that everyone already knows about.

Our fraction unit introduced many graphic organizers for kiddos to use to represent their math thinking, and the first one we used was a 10 by 10 grid.  We used it to find fourths (again, going back to something they already know), and figured out what fractions and percents we knew from those: 1/4 is 25%, 2/4 is equivalent to 1/2 and 50%, 3/4 is 75%.  Then I blew their minds when I showed them how they could find eighths on the same grid.  Yep, even though 8 is not a factor of 100.  Again, we had them think about what they knew and how they could use that knowledge to figure out something they didn’t know.  (I’ll let you stop right now and see if you can figure out how to do it.  Go ahead, I’ll even give you a 10 by 1o grid to use.)

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Yeah, so I’m sure you’ve figured it out, but I’ll show you anyhow:  If you find fourths, then think about what an 1/8 is.  It’s half of a 1/4, right?  Yep, 1/4=2/8.  Since you know that 1/4 is 25%, then you can easily figure out that 1/8 is the same as 12 1/2%.  Now you can use that to figure out the percent that is equivalent to any fourth or eighth, just by adding more of them.  3/8 is 37 1/2% because you know 2/8 (1/4) is 25% and then 1/8 is 12 1/2%.  Crazy, right?  I LOVE THIS PART!!  It’s so freeing to kids who have thought all along that fractions are impossible, too hard for them, some secret that they haven’t been told.  But now it’s just another puzzle–and they have the pieces to help them solve it!  This fraction/percent equivalence plays a HUGE part in the whole rest of the unit, so we spend lots of time at the beginning working with those numbers in different ways to help get it sold in their minds.  They had a chart they used as a resource, as well, throughout the unit.  Math doesn’t have to be a mystery.  It isn’t something you have to memorize.  You have tools and you just have to know when and how to use them!

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Another organizer we used were 4 x 6 and 5 x 12 rectangles.  They’re arrays, just like the 10 x 10 grids, but work better for other numbers that have factors like 3, 4, 5 and 6 (thirds, fourths, fifths, sixths, etc.). We could use them to find the fractional parts of almost any number that way.


These were used when we moved on to finding thirds and sixths (which you can do with percents, as well, too).  These were cool, too, when they figured out that 1/3 was 33 1/3% and that 1/6 is half of that.  That’s a crazy question: what is 1/2 of 33 1/3?  Wish I would have recorded them figuring out that it’s 16 2/3%. Really.  It is.  Try it.  Here, let me show you:

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The first time I did that it heard my head.  The second and third times it did, too.  Yeah, I’ll admit it.  Some of the things I ask my kids to do seemed crazy in the beginning.  Mainly because it’s not how I learned it, but this time around it totally makes sense.   I wonder what it would have been like to do math like this when I was a kid…

(Ready for Part 3?  Find it here.)

Feast Week Part 1: The Birth of Feast Week

First of all, Happy New Year!  I don’t know when you’re reading this, but I’m writing it during Winter Break, on New Year’s Eve Eve.  This is a time of year I both love and hate: the fresh start that comes both personally and professionally in January is one of my favorite things–there is an air of anticipation of new and wonderful things to come; the fact that Spring Break isn’t for another two months is a little disheartening.  Winter can be long in Missouri.

That being said, I am excited to tell you a story about what was happening in my classroom–well all the 5th grade classrooms at my school really–during the months of November and December.  It was a fun and exciting time in our school, full of learning and anticipation; an eagerness that had nothing to do with holidays or vacations.  We were doing hard work, focused on something that at that time seemed like it was forever in the future: Feast Week 2012.

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This year I have a whole team full of new friends, and with that comes new ways of doing things–mainly just because we have all done it differently in our previous teaching “lives,” and because we want to plan new things together.  So…when it came time to talk about fractions and how we were going to teach that dreaded fabulous unit, we knew it was something we wanted to do together.

First we looked at what we had.  I have taught a fraction unit of some sort for the last 7 or 8 years, in 4th and 5th grade.  Previously, we really just had to get our friends to a solid understanding of what “fraction” means (part of a whole), and be able to use fraction/percent equivalents to solve problems related to parts of a group.  There was also a small part that included adding and subtracting fractions, using the equivalents as the basis (rather than finding common denominators, which is a common practice).

This year, however, our school district is really trying to dig into the new Common Core Standards–hoping to get a feel for what they ask of our kids and how they’ll change things for us as teachers.  This is happening most deeply in math; all of our curriculum and rubrics were rewoven to match the CCSS this past summer.

Now, instead of just the basic foundation like I mentioned previously, our kids have to be able to do this:

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Can I be honest here for a minute and tell you that we were a little FREAKED OUT by all of that!  Unfortunately, until you get to know the CCSS really well, and dig into what they mean and are actually asking your kids to do, I find that they are written in a really complicated way.  Needless to say, the first time we even read those expectations we were scared: how were we supposed to get 10- and 11-year-olds to be able to do those things (and do them well, with a deep understanding) if we couldn’t even understand what the standards said?

So after we picked our jaws up off the floor, dried our tears, and got our heart rates back to a somewhat normal rate, we sat down to figure out just how we were going to tackle these things with our students. We began with the belief that they could do it, we could do it and we were going to do it well.  We wanted to do it in a meaningful, authentic and real-life way that would help build a “forever and always” understanding, rather than just an “I-get-this-now-but-will-forget-it-after-I-take-the-test-next-week” understanding.   That meant rewriting assessments, possibly reworking assignment and activities and rethinking our own working knowledge of fractions.

And so Feast Week was born.  It began as an assessment idea, really, but quickly melded into more of a celebration–a culminating activity that would incorporate all that we expected our kids to know and be able to do.  It was to take place the last full week before Winter Break, and would include all that goes into creating a Winter Feast–planning, shopping, cooking, and then of course, eating!  We based it on an activity I had done in previous years around Thanksgiving where I had students use the circulars from the grocery stores to plan dinner for their family.  In that scenario, however, the whole situation was hypothetical.  In this reincarnation, it was for real.  We set the 5th Grade Fraction Feast to take place as our Winter Party, and the kiddos were entirely responsible for making it happen.  Talk about real-life.  Authentic.  Engaging.  Motivating.

And yes, it was.  None of it was easy.   And yes, I can admit there may have been some tears shed along the way.  But we made it, and yes, it was FABULOUS!

Hopefully you’ll hang on for the rest of the story of Feast Week! I promise it’ll be worth your time.  🙂

(**Be sure to read Part 2 here!**)

Close Reading

We’ve been working on close reading lately in Rm. 202.

I know–before this past summer I wouldn’t have known what that was, either.  If you haven’t heard about Common Core yet either, it’s another thing that is on the forefront of every educator’s mind right now, too.  And while reading closely isn’t a new thing, necessarily, the importance of it is perhaps emphasized now, more than ever.

I found a great post about close reading when I was doing some research on it the other day.   I was looking for directions for exactly how to present to my 5th graders.  What I love about this one, is that the way it was described had pieces that I knew my readers would already be familiar with because of the S.H.A.D.O. strategies we had learned earlier this year in Reader’s Workshop.

I love how Dr. Douglas Fisher describes it in a recent video:

A close reading is a careful and purposeful reading. Well actually, it’s rereading. It’s a careful and purposeful rereading of a text. It’s an encounter with the text where students really focus on what the author had to say, what the author’s purpose was, what the words mean, and what the structure of the text tells us.

So I made this chart to help my friends remember what to do:

IMG621So like I said, it’s not really anything new (at least not to me and probably not to you, because we’ve been reading for a while now), but to my 5th graders, it does equal something new in how deeply they are expected to look at text.

While I’d love to say that I’ve always taught students to read and reread and reread again, I’d be lying if I did.  Yes, we talk about rereading as a fix-up strategy for monitoring comprehension, I’ve never emphasized it as something that good readers do on a regular basis.  And I know I’ve never talked about it this in-depth.  It’s never before been an expectation for how my readers will dig into a text to really get at the what and why, the “meat” of a text.  And it’s never had a name.

I think the big thing I’m trying to get at, really, is that I haven’t ever emphasized it this specifically with my students.  I haven’t asked them to pay such close attention to when they’re rereading and how they’re rereading.  Reading and rereading have now become one.  Now the expectation is that they will always reread, more than twice, as a means of better understanding the text at hand. The big idea of reading now, forever and always, will be to dig deep into a text, to really get to know it well, like a good friend.  Regardless of what that text is, I want them to make it their friend–knowing it so well and closely that I could ask them anything and they’d be able to tell me more.  And yes, ideally, I’d like them to want to do it because they desire to be a better reader, not because their teacher said so.

And so that brings up an interesting conversation we had today during Reader’s Workshop.  We were reviewing some questions we’d answered on a monthly benchmark assessment from the other day; we’d practice closely reading on the text and so were expected to have really understood what it was trying to say.  As we discussed our answers and gave evidence from the text to support our thinking, I could tell that most had done a reasonably good job of getting the main idea of the text; most of our answers were correct also.  As we were moving on, and most of us had agreed that reading more closely had helped, a question was raised:  But do we always have to do a close reading?  I don’t really want to.  It takes too long.

AHHHHH!! Just when I thought I had them, there it was.  A friend who needed convincing.   And what I loved was that many other students jumped in to answer the question for me.  That’s key, I think, actually–often times things mean so much more when they come from peers rather than adults.

What came next, though, instead of a real answer was another question, and this came from me.  It was related to purpose: So yes, you should do a close reading every time you encounter a new text, but why?  Why should you want to?

Their answers were interesting and got me thinking about how we define reading.  Many of their answers were related to “getting good grades” or getting the “right answer.”  So I kept digging: Ok, well let’s back up.  What is reading?  How do you read?

Again, answers were all over the place, none of which really getting at the main purpose: Reading is making meaning.  It’s understanding what the words on the page mean, and how they work together to help you understand the message of the author.  And as a reader, you should want to understand.  You should not be happy with not “getting it.”

At the very least, this conversation today got me thinking about how I proceed.  And how I start next time.  Perhaps we should have talked about close reading way earlier than now; had I named this strategy in August and set it as the expectation from Day 1, it wouldn’t be so scary now.  But I’m also intrigued by what we’re teaching our readers (and writers and scientists, etc.) about why we do what we do.  Somewhere they’ve still gotten the idea that they’re supposed to do something for the grade, the right answer, or because their teacher told them they were supposed to do it.  That their motivation should be something extrinsic, not just the mere enjoyment and satisfaction of learning something, understanding what an author is trying to say to them.  I hope to begin to grow a group of readers (learners, really) who know that they have a toolbox of strategies that they can use–that they should know how to use and when–and that use them at their discretion to solve problems, to understand and to learn.

But alas, this is not something I’m going to change today.  Or tomorrow, even.  But I can start.  I’m hoping that I have started this already with my “forever and always” thinking we talk about so often.  This fits into that beautifully: I want them to learn to closely read a text so that they will “forever and always” be able to understand any text they encounter, not just to get the answers right on their monthly Edison benchmark assessments in 5th grade.   I just have to keep pushing to convince them that this matters.

So I have a question or two (or four) for you:

1.  How have you presented close reading with your students? I’d love to hear what you’d add, or suggestions you have.

2. How would you define reading?

3. What reasons do you give for why we should want to understand text we read?

4. What other thoughts do you have?



Don’t Steal the Struggle

I’m not even sure who said it,  but I know I first heard talk of it this summer when I was working with other teachers in my district.

First a little background: In light of the new Common Core State Standards, which are changing the expectations for teachers and students, our school district is reweaving our curriculum to match up with CCSS.  The best part of this whole deal is that teachers are at the heart of the work.  We spent four really intense days this summer learning and writing together, and then all this year a smaller group of us will continue that really great thinking to complete the documents for English/Language Arts (ELA) and Math.

Ok, so during our work this summer, a phrase was floating around that said: “Don’t steal the struggle.”  From the second I heard it, I knew it was something I’d be on board with. It’s actually something I’ve always felt really strongly about as an educator, but now I had better words for how to describe it–both for myself and to my families.

Then I had a situation within my own life happen last week that really highlighted the importance of this phrase for me.  And I’ll warn you ahead of time, that it’s an example I share as the “what not to do in this situation.”  I’m taking a class right now, and had an assignment due on Wednesday for the discussion forum for class.  I, unfortunately, had waited until late to do it, and so was in a little bit of a time crunch.  Last week was nuts at school with lots of meetings and conferences on Thursday night, so I had a lot on my mind (i.e. I was a little stressed out already!).

I sat for close to an hour drafting my answer to the discussion question (which was related to whether or not there is a paradigm shift in education from information acquisition to knowledge creation in American education), and was ready to post it.  And then–yes, you guessed it–when I hit POST, I got a weird ACCESS DENIED error message and everything I had worked on was gone.  Gone.  And no, I had not saved along the way.

So obviously there are probably other lessons to learn here besides the one I’m going to tell you, but this next part was the one I shared with my class related to struggles.   Unfortunately, my first reaction after that little bump in the road was to cry.  It’s kind of how I roll.  When I am dealing with something stressful, first I cry, then I write (usually in my own Writer’s Notebook, so I can figure out my feelings) and then I can figure out a way to deal with said frustration.  So here I cried.  Then I wrote–which was some rambling email to my teacher about what had happened and how I hoped she’d show a little grace when she graded my discussion post this week–and then I was able to think about what I should do next.  Pretty much I had two choices:  1) I could just quit, and not turn in a discussion answer this week (which would have several negative consequences) or 2) I could start over.  Well, needless to say, I chose option #2, and reluctantly started over with my answer.  Luckily, I remembered more of it than I first thought I would, and honestly I think the second version was actually a little better.

Ok, so what’s the connection to my classroom?  Well, go back to the “don’t steal the struggle” phrase from earlier.  The big idea there is that as an educator, I want to focus on not “rescuing” my students when things are hard.  Whether it’s in learning or something social or any other kind of problem they might have, it’s not in my students’ best interest if I swoop in and save the day every time they struggle.  I only teach them that things should always be easy, and that only an adult can solve problems for them.  That struggle is bad and that I’ll make it all better and fix it for them.

But of course that’s not true.  Some struggle is a good thing.  It’s during those feelings of disequilibrium, “pain” so to speak, when students are forced to figure things out for themselves.  To solve problems and use what they know to figure out what to do next.  And my students would tell you that they know that’s a really important thing to know how to do.  We had a discussion about this the other day and they had smart words about the topic.  They agreed that they wanted a chance to figure things out on their own first, knowing that I would support them as needed, but that I wanted them to try something first.  They knew that this was important because I’m not always going to be there.  Some day they’ll grow up will have to be able to know how to do that alone.  And several even mentioned the pride that comes with figuring out an answer for themselves.

My story was a picture of both what I hoped they didn’t do (just cry), but also what I hoped they would learn to do in a hard situation–figure out what to do to solve the problem.  Not quit.  Persevere.

So my new motto is Don’t Steal the Struggle.  It’s going to hang in my room for all to see, and to hold me accountable.  My kids understand it, and I think it’s vastly important as I help grow these learners into confident, capable citizens of tomorrow.  And like I tell them everyday, hard is good.  Hard is when we learn.