Fourth Grade Fractions for CCSS

Last year I was very proud of my fractions unit.  This year our district cut back on the amount of time dedicated to fractions in fourth grade.  As a result, I had to make some tough decisions on which lessons to cut, and which were non-negotiable.  And I believe if my students only learn one thing, it has to be a true understanding of equivalent fractions.  So after introducing the idea of equal parts and equivalent fractions with 1/2 with paper folding just as we did last year, we continued on to finding other equivalents.

Another priority for me was to stick with the instructional strategy of starting with manipulatives, moving on to visuals, and culminating with computation.  The ultimate goal being for my students to use the models to come up with their OWN algorithms.  Using fraction bars, circle models, (affiliate links) and even pattern blocks (this was a voluntary challenge that every single student insisted on trying, yay!) here are some of the observations they made:

The next day, they brought their recorded observations with them to quiz ME.  I repeated the "how did she do it" sessions as I modeled how to sort equivalent fractions.  As some students were able to articulate the algorithm and demonstrated that they could apply it themselves, I gave them extension questions such as comparing and ordering fractions (which our curriculum cut this year).  Those kids who were able to find equivalents were, of course, able to add and subtract fractions with ease.  Those who did not have the concept yet continued to use manipulatives with me until they were able to draw their own conclusions about the algorithm.  There were several ways I helped my remedial group:

• We used fraction number lines as a tool for locating equivalents in order to add and subtract fractions.  This way they could retain the understanding that equivalents were needed, as well as reinforce the idea of adding numerators for like fractions (not denominators).
• We explored online tools here and here to help us find equivalents at home.
• We played games online to practice visualizing, and then calculating equivalents.

Then we moved on to changing from improper fractions to mixed numbers and back again.  We started with fraction number lines, since this is a common visual fourth graders are expected to be able to interpret on MCAS.  I felt like Math in Focus didn't give quite enough direct practice on using them, so I created several number lines pages of my own (link to product) to break down the process. And that's when something amazing happened.

After using the number lines to count up using mixed numbers and later improper fractions, most of my students found it simple to use fraction circles to tell 11/3 equals 3 2/3.  With a few hints, some were even able to find the algorithm of dividing and finding a remainder.  But one of my students said, "I have a different way to change a mixed number to an improper fraction.  Just draw 11 circles, box them into groups of 3, and you have 2 as a remainder.  The 3 groups is your whole number, the 2 is your numerator, and the denominator stays the same so it's 3."

She showed me a model she had drawn to prove her point (I tried to make it darker and in color so it would show up on camera).

I asked the kids, "Does this method always work?  Try it for one of the problems we've already answered on the numberline."  Of course, they came to the same conclusion:  this was a new strategy.  One their teacher had not used before!  From that point on I referred to this as "The Sally Method," and it became a favorite!

But even better was the fact that many of the other kids from that point on had become determined to find a method for the skills we were learning because they wanted a method named after them too!

Even those students who were struggling with equivalent fractions had a respite when we started fraction of a set, since we were all back to manipulatives and then visuals.  I explained to the kids how previously we divided a single circle into 4 parts.  However, we can also divide groups, not just shapes.  I said, "I can divide this class in half easily..." and many replied there would be 8 in each group, but one of my students (the sort of student you worry about, who struggles with math, normally lacks the confidence to participate, and has some difficulty expressing himself verbally) said, "Not...like a magician's box."  I laughed before the other kids caught on, and then explained for him.  "If I divide the class in half, I wouldn't need to do the magician's trick, like, 'I will now divide my lovely assistant in half!  Just step into this box...'"  They all said, "Ohhhhhh!"  That brought home the difference between dividing one thing and dividing a group for them! 

They really got into using the fraction of a set cards (link to product).  Once again they were all comfortable using the visuals to make observations, and several told me, "I think I've found a method!"  (They much preferred "method" to "algorithm," haha).  After using the level 1 set, "Junie" put it best, "You just divide the whole number by the denominator."  We now had a "Junie Method" instead of lifting a formula from the book.  Once we started the level 2 set, another student discovered, "To find 3/5 of 15, just do the Junie method and then multiply by the numerator."  They were developing their own language for concepts that they needed.  By the time we played 40 frogs during our computer time, they were telling me that fraction of a set is easy.

So despite a few disrupted weeks thanks to weather-induced days off, and outside pressures to speed things along, fractions was once again one of the highlights of our year.  We have today (Wednesday) off again for snow, but I think they are ready for their test on Friday (in record time).    

P.S., I know I missed a post last week.  The reason is I've been trying to get better about using Facebook.  I really had to immerse myself to get into it because after 2 years it wasn't clicking for me just going on once per week.  I think I've finally started to get into the spirit of it, so if you'd like to join me my Facebook is here.  On the other hand, if you enjoy reading about my lessons/units then not to worry; I do plan to keep up my Wednesday posts here at Shut the Door and Teach.

"All New" Giveaway and a Sale

One of my blogging buddies, Meg from The Teacher Studio (formerly Fourth Grade Studio)  is celebrating a milestone: her blog is 1 year old.  It's hard to believe that she's only been at this for a year because I've learned SO much from her posts over the past year.  To commemorate her one year blogiversary her blog has a fresh new look which I'm a big fan of.  And even more exciting; this week she is holding a HUGE giveaway every day this week!   

Each of the 5 winners this week will each win over $100 worth of TPT products of their choice from the selected sellers who are participating!  Head over there now for a chance to win.  Then go back tomorrow for another giveaway, and again on Friday for yet another giveaway.  There is a different group of stores participating each day! 

To honor her "All New" blog theme, not only can you win $10 worth of products from my store (in addition to a handful of other bloggers' stores for a combined value of around $100) if you enter today's contest, I'm also putting my "All New" product on sale for 50% this week only. 

 I recently finished Math in Focus Chapter 2 with my fourth graders, and I always like to have some math review games at my disposal to help the kids retain their skills all year.  My

Prime or Composite Board Game and Least Common Multiple Dice Game have really helped since I created them last year, and this year I rounded out the set with my "All New" Greatest Common Factor Game. 

So if you're looking for some fun review, check it out while it's still on sale! 

Estimating to a Given Place Value with Money

In another post, I wrote about how my students who were great at estimating problems such as 39,253 or 32,025 to the nearest ten thousand did fine, but really struggled when it came to rounding those same numbers to the nearest hundred or ten.  Estimating on a number line was new to them, so I gave them an activity that got them moving around the room and sticking numbers onto number lines until they got more comfortable with this tool that has a lot of potential to help us estimate. 

I wanted more of a hook, however.  Number lines are a great tool to help us visualize, but when it comes to real world estimating I think most of us think first and foremost about money.  Kids think about it too.  Just this week we have the book fair and kids ask, "Do I have enough to buy this book?"  And I answer, like any teacher would, with a question.  "Do you need to add $9.99 plus $5.99, or can we make those numbers easier to add in our head?"  Soon the kids are estimating to answer their own questions.

But back to the issue at hand:  how to understand estimating to a specific place value.  What I did was I paired up half the class who were really struggling with this concept.  I told them each I was going to give them about $35,421.  That got their attention.  I told them also that I'm really sorry, but I might just run out of money, so although they'll all get about that much, they won't all get exactly that much, and is that okay?  They agreed they could live with that.

So for the first pair, I told them I had run out of ones.  I could give them 3 ten thousand dollar bills, and 5 thousand dollar bills, and 4 hundreds.  I could even give them some tens, but no ones.  So for one student, I gave them all that and 2 tens, and the other student got all of the above but only 1 ten.  We talked about who had closer to the original amount and how we found the difference was to subtract.

For the next pair, I told them that not only did I run out of ones, I also ran out of tens.  I could give them 3 ten thousand dollar bills, and 5 thousand dollar bills, and even some hundreds. But I could not give them any ones or tens.  So I gave one student 4 hundreds and the other student 5 hundreds.

I did the same thing again, running out of hundreds and finally running out of thousands, the whole time talking about the difference, how much more of a difference it was between those kids who had only ten thousand dollar bills vs those who were only missing the ones (it can work out in your favor either way, they learned!)

All the while they were comparing numbers before and after and visualizing exactly what an estimated amount looks like.  

How do you help your fourth graders round to a given place value?

Math in Focus Chapter 2: Making Long Division Easy

Today I made long division easy.

Last year, when we adopted Math in Focus, we were all shaken up about bar modeling during our 2 in service days at the start of the year.  Once we started teaching the first unit on place value, things did not seem quite so bad.

And then we started Chapter 2.

With NO background in division and little experience multiplying beyond their facts (which most of them forgot) this was a nightmare for children and teachers alike.  I was frustrated that it was so new to me that it was all I could do to keep up with the materials gathering and pre-teaching, and it was killing me to see kids who used to think they were smart, now feel like failures.

I was NOT going through all that again. 

The second year is always better.  Their third grade teachers had the same frustrations with the new program last year, but at least this group of kids got a taste of the methodology.  I had a better sense of what they need to do BEFORE hitting Chapter 2 (5 weeks of extra facts and regrouping practice for identified students for a start) and also what they needed to know by the end (they don't actually need to be expert long dividers or 3 by 1 digit multipliers because that comes later, in Chapter 3)  Instead, I could focus on the bigger picture:  developing stronger number sense.

So as I went through the chapter again this year, and they hit their first significant stumbling block, instead of feeling overwhelmed, I was ready.  I realized that all the place value work that seemed silly in Chapter 1 (why do they need to know 140 is 14 tens?) suddenly made perfect sense.  Suddenly, I realized that this is the key to why the long division algorithm actually works!  And then, the day after a lesson that semi-failed (5 kids mastered it, 8 got it but only with support, and 6 felt like they would never be able to do it) I had an epiphany.  I saw just how to set up a long division problem so that they wouldn't forget where to write that multiple and where to write the answer (any 4th grade teacher knows it is SO hard for some kids to get used to writing their answer at the top instead of bottom!)

Now, when the first lesson (the purple visual on the left) didn't work out, I took a step back and whipped up a quick worksheet for homework that got them practicing one isolated step:  namely, step 3.  I gave them a problem like the 4 divided by 14, and modeled on the worksheet how to count by 4s and write 12 under the problem.  And NOTHING else.  No zero, no place values, no estimated quotient.  Just listing multiples to find what to write underneath.  That was something they were ALL successful with, because we'd been practicing multiplication and division facts since the first week of school.  But that wasn't my stroke of genius.

Look again at the diagonal red line.  It crosses out the 14, leaving the 4, 12, and 3 fact family plain as day!  As I told the kids before I started, "You're going to love this, it's going to be like a magic trick."  And they ate it up.  I knew I created a system that worked when more than one student thanked me for teaching this to them.  "Mrs. Thomas, I finally GET it now!"