Easy Fraction of a Set Game

Fraction of a set can be a challenging concept for fourth grade.  Often they are still trying to understand the idea of fractions dividing a whole into equal sized parts.  So looking at a given number of equal sized groups that relate to one as "one whole set" is very confusing.

To begin, we go back to the division dots task cards that we used earlier in the year.  This gets them comfortable.  I much prefer the "we did this already" as opposed to the, "I don't get it."  Because the moment they are bored I tell them, "Good, you remember.  Now we're just going to add one more step, which is to color a certain number of sets after you circle them."  And they are on their way!  There are 3 levels of practice in my fraction of a set task cards.

In order to help them conceptualize fraction of a set without a visual, I came up with a quick review game you can do with your class, and all you need is masking tape!  

Here's how I explain and scaffold for the game.  Right before Morning Meeting, I used thin masking tape and divided the rug area into a large area and a small area.  That day I had 16 students.  I told them "I want 1/2 of the class in the large area, and 1/2 in the small area."  They quickly and easily got into 2 groups of 8. 

Next, I asked each group to line up in their section.  I wrote "1/2" on the board and explained that there were TWO lines, because 2 is the denominator.  I asked if they thought they could get into FOUR lines, with only 1/4 on the small side and 3/4 on the large side.  Once that was done, we determined that 1/4 of 16 is 4.  I asked them how much 3/4 of 16 was, and they counted 12.

The next day I pushed them a little further, asking for 3/8 of 16.  They needed some reminding about getting into 8 rows, but what most of them COULD do independently was to get 3 of those lines in the smaller side and 5 on the larger size.  I asked how many kids were in the 3/8 of 16 section and they counted 6.

The final variation of this game was to find a "mystery number."  In Math in Focus, Chapter 6 (Fractions) they have to basically "do fraction of a set backwards." 

In other words, I tell the class that I am thinking of a certain class size that is SMALLER than the number of students present today.  That number is a mystery.  However, I will tell them that 3/5 of that number is 9. 

Again, to start out they need reminding that they need to get into 5 rows.  They remembered on their own to have 3 rows on one side with 2 rows on the other.  Then I reminded them that there should be 9 kids on the side with 3 rows.  At that point, they remembered they needed equal sized groups.  

When there was a single student left over, not in a row, they determined that the class size I was thinking of was one less than 16:  15. 

In the end, we discuss 3 ways to find fraction of a set.  I had a few kids find the algorithm (method 2) on their own as they were working on the task cards!  They really feel like they "own" it when they "Find a method."  

Do you have any tips for teaching fraction of a set? 

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Number Line Frustration? Walk the Walk!

It took a while to really "sell" me on the idea of using number lines (and I'm a visual learner)!  However, since number lines don't seem to be going away when it comes to curricula and standardized testing, I knew I had to accept them, get comfortable with them, break them down for those kids who also are not initially "sold" on them either, and make them interesting for my class.  I've developed coloring worksheets and homework pages, but this year I wanted to "step" it up a notch and engage those kinesthetic learners.  So that's when I created "Number-line Tightropes!" 

The set up: 

While my fourth graders were at music, I broke out the masking tape.  I taped 2 horizontal lines and 2 vertical lines on the floor.

Next, I labeled the whole numbers with tenths at each intersecting tile.  I started on a vertical line with zero and worked my way up to 2.20.  Notice at that point, there was an intersecting horizontal line.  

On the horizontal line, I did the same thing, but instead of starting at the end with zero, I worked around the intersection.  To the left it says 2.10, and to the right (although you can't see it) it says 2.3.  Of course, I did not fill in every number; some of that work had to be for the kids!

Next, I drew smaller increments on the horizontal lines.  Those represent the hundredths.

 I followed the horizontal line to the left until I got to 1.3.  At that point I came to another intersection.  Just as before, I worked up and down the vertical line from 1.3, filling in the tenths, but saving some spots for the kids to complete.

Below, I followed the vertical line to 0.4, which brought me to the final intersection.  I filled in the hundredths on the horizontal line.

The activity:

When the kids walked in after music, they were "floored."  They could not WAIT to interact with the tape on the floor!

I had each of the 4 groups take a "line" to fill in some of the blanks.

Finally, a simple dice rolling game kept the kids engaged in studying the lines.  Roll a dice, move your "guy" that many tenths (for the vertical lines) or that many hundredths (for the horizontal lines). 

So much more fun than worksheets!

How have you turned number lines into fun?

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Have you tried Edmodo yet?

I recently had the opportunity to attend a workshop on Edmodo.  Whenever I heard about teachers talking about creating a class page with their students, Edmodo always came up.  And I'm interested in using technology more with my students;  I already had a classroom blog which I talked about in this post.  I just didn't know how Edmodo was different.

The instructors likened Edmodo to Facebook.  While I wouldn't "sell" it to parents in that way, the kids did see the connection right away and were excited about all the features:

1. Kids can personalize their account complete with avatar, learning style, career goal, and inspirational quote (they can even search by famous person within the system).
2. Kids can reply to posts.
3. Kids can write their own posts for others to reply to.
4. Kids can upload photos, links, and documents.
5. Teachers can post all of the above as well as polls and quizzes (very similar to using Google forms, but integrated onto Edmodo itself).
6. Teachers can enter dates and assignments into an integrated calendar.
7. There's an app for that (Apple and Android).

However, Edmodo is designed for children and therefore has safeguards against predators as well as cyber bullying. 

First, when you sign up for Edmodo as a teacher, you are given a "classroom code."  You will give that code to your students when you sign them up, and no one else can see the page unless they register with that code.  It's not the same as a password, in that the children will sign in with a username and password each time they log in, but the code is only used by them once when the register.  Once your whole class registers, you can "lock" the group.  If you get a new student later in the year you can reset the code to register that student (students who registered already don't need to re-register with the new code).  So the bottom line is, no one is getting on now or later without your help.

Second, unlike Facebook and other social media sites, there is no private messaging between students.  Anything a child writes will be seen by you and every other child in the class, and it will be logged under their real first name.  If a child was going to say something inappropriate, it would be as if they stood up in the middle of class to say it; it's all out in the open.  You even have the option (in case you do have a "bold" class this year) to "moderate" comments.  That is, you can set their posts to stay hidden from the other kids until you approve each one.   

Edmodo does not require an Email to sign up (unlike most websites that you create accounts for).  The only tricky thing about signup is that children need to tick a box that says their parent has read and agreed to the terms of use.  Out of respect to this rule, I sent home a permission slip that granted the children permission to tick the box in class during my introductory lesson.  [Update] A reader requested a copy of this permission slip.  I've added it to my TPT store for free for a limited time, so if you're interested, grab it now!

I've used Edmodo for 2 weeks now, and honestly I am not sure I love it more than the classroom blog.  Tomorrow over on Shut the Door and Teach I will be writing a pros and cons list for Edmodo versus Weebly.  So if you're interested in Edmodo, I feel it IS worth trying, but you might find a different platform suits your needs better. 

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Easy Decimal Game: This Means War!

Right before our February vacation, my fourth graders started decimals.  To start out, I always find it's easiest to equate decimals with money.  .50 is 5 tenths just as it's 5 dimes, and .05 is 5 hundredths just as it's 5 pennies.  They understand that; it's those pesky zeroes that throw them for a loop!  So to practice seeing decimals concretely (and relating them to fractions) we played Decimal War!

The game is easy if you have decimal cards.  Notice that in fourth grade we use units that are divided into tenths and hundredths (there are also thousandths in this set which are great for kids who like a challenge).

The basic directions for Decimal War are:

1. Shuffle the cards. 
2. Deal the cards so that each person has the same number of cards.  Note:  the number of red and green cards each person has does not matter.
3. Players should NOT look at their cards.  
4. Both players flip over their top card at the same time.
5. Determine who has the most shaded area.  That person wins both cards.
6. In the event of a tie, both players will place their next 3 cards face down, and choose 1 of those to simultaneously flip over.  The winner takes all 8 cards.
7. The object of the game is to finish with the most cards.

In this regard, the game is just like the traditional card game of War.  But now comes the math part!

Each player needs to create a T chart with their names at the top.  They write the card they flipped over in decimal form.  Finally, they need to write < > or = in the center to compare who had the greater amount.

This type of War Card Game is easily adapted to fractions, negative numbers, numbers of varying place values, coins, or anywhere that comparing or ordering numbers enters into your curriculum.  I love when I can reuse a format and save time teaching new directions (if the particular class loves it).

[Update: 3/16, I had a request through TPT's Q&A to make this a product.  If you would like a version that includes the cards and is ready to print, I have it for $4 here:  Decimal War Card Game]


If you're looking for more fun math games (or other resources) for your kiddos, you should know that Teachers Pay Teachers is having one of their HUGE sales this Thursday and Friday (2/27-2/28).  You can save up to 28% in most stores with promo code TPT3.  To help celebrate right here at All Things Upper Elementary, we're giving away TWO $25 gift certificates for TPT.  Just click the graphic below so you can enter.  That $25 will go a lot further this week, so don't miss out!   

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Organizing Literacy Center Materials

Yesterday over at my other blog, Shut the Door and Teach, I wrote about how I set up my Literacy Centers.  My school has been using Journeys for a few years now, and I'm more familiar with common core this year than I was at the beginning of last year, so I felt ready to really delve in.  You can see how I set up my rotation topics and schedule here.

Today I thought I'd share how I organize my materials.  Let's face it; the best instructional activities will not engage students if the organization behind them doesn't work!  And if it's too complicated for us to manage, we're not going to want to use it either.  There was some trial and error when it came to different locations in the room and moving desks, which the kids HATED.  Who knew how nervous they would get about other people sitting at their desk!  

So I scrapped that first idea and instead created a file folder system.  It worked for my math games, so I shouldn't be surprised that it turned out to be the best solution for my literacy activities.  They know where to access the folders, how to distribute materials, and they can stay at their own desk.  There is only one activity in the course of the week that requires a single group to move to a separate spot in the room, and fortunately I have the space to accommodate that.

I keep the bin with 3 file folders right in the middle of my leveled readers.  My rotations are right above this set of bins as well, so everything is within reach.  Other than "read with the teacher," each of the other stations has its own file folder of activities.

Inside each file folder I can "preload" the activities for the week.  The Mentor Sentences page has 3 different activities in one, so it keeps them occupied in the "Editing" station for 3 days, and I load the spelling in on the final day.  The Vocabulary pages look different enough from one day to the next, so the kids don't mix up which one to do first, second and so on.  I clip the "not yet" pages to the folder as a gentle reminder, and their current pages are loose in the folder for them to take.  And finally, the Independent Reading Responsefolder has 3 separate envelopes.  These are clearly labeled for each Close Read slip they need to do, in order.  The kids know they need to tape the first into their notebook and complete it before they take the second.  This is the most time consuming center, so often they come back to it when they finish a different literacy center early. 

Considering that this is my first year running Literacy Stations since moving to fourth grade (and since Common Core began) I think they are going pretty well!  I plan to offer my Close Reads in my TPT store this summer, so if you are thinking about trying stations next year, stay tuned!

[Edit:  I've started to post my Mentor Sentences products in my TPT store.  There are a few freebies in the section I've linked to if you want to give them a try!]

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Practicing Long Division with Money

Do you find that the topics that you struggled with the most in school are the ones that you love teaching the most?  That's how I feel about math, and in fourth grade the math topic I remember struggling with the MOST was long division.

I remember when I was a kid, it would take me FOREVER to solve a page of 10 long division problems.  I was one of the last ones done, sitting off to the side to finish up.  I'd stare blankly at 658 divided by 7 and try multiplying every number by 7 in the attempt to get 65.  I felt so frustrated that I had to do all those "extra" math problems and hope that they were right too.

So when it comes time every year to teach my students long division, I've tried lots of ways.  I had them make their own mnemonic devices to remember the steps (similar to the Do My Scissors Cut Bricks type acronym for Divide, Multiply, Subtract, Check, Bring Down).  I've tried partial quotient.  But for me it always comes back to practicing the physical process of dividing.  Base ten blocks are a great way to do it, but my favorite manipulative when it comes to math is money.  There's just something about counting money that makes people happy! 

Last week I described how I introduce the concept of dividing hundred dollar bills, ten dollar bills, and one dollar bills into "wallets" over on Shut the Door and Teach.  This activity helps get the kids used to the manipulatives involved and has a high success rate; with numbers that are carefully chosen to be evenly divisable (such as 486 divided by 2) the kids are able to compute in their heads before long.  So to up the ante the next day, I give the kids numbers that are not as simple to divide.

In the example on the right, you can see that the child knew he couldn't divide a hundred dollar bill 4 ways, so he had to regroup it for ten tens.  He was then able to put 2 ten dollar bills in each wallet, and he had 2 ten dollar bills left as a remainder. 

Of course this does not complete the problem, however he is learning that 20 is a reasonable answer to 100 divided by 4, which is pretty powerful!  I'm much happier with him knowing this than memorizing DMSCB and not understanding what numbers to compute at each step. 


The child on the left is working on the same problem.  She also knows that the answer to 100 divided by 4 will be about $20.  However she is continuing the regrouping process.  She is trading in those 2 ten dollar bills for one dollar bills.  Although she has written a bunch of zeroes in the ones place on her place value mat, she will soon be able to refine her answer to include the ones place.

This child has completed the process of dividing 100 by 4.  She is also able to accurately record the steps she has taken to arrive at an answer.  She regrouped the one hundred to become ten tens (although she forgot to erase the hundred).  She also knew she could tally up the 4 twos in the tens place when writing out the long division algorithm.  She used the difference (10 - 8 = 2) to find how many tens to regroup into ones, and she divided the twenty ones by 4 to get 5.  Although it's difficult to read her paper, she transferred the process she used with the manipulatives to the traditional long division algorithm. 

If you need more examples of numbers that increase in difficulty when it comes to long division, I have 3 different levels of long division task cards with numbers similar to these two examples available as a bundle (they will be 28% off on Cyber Monday and Tuesday, 12/2 and 12/3 with promo code CYBER).  I use the cards as review throughout the year because long division is one of those concepts that kids need to see many times before they can master it.  I never feel guilty leaving these in my sub plans because the kids know what to do and actually enjoy long division when they get to use the money. 

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Free Educational iPad App: Educreations

Have you tried Educreations yet?

At the beginning of last year I started a classroom blog that was tailored more to my fourth graders than to their parents.  I posted photos of anchor charts as well as educational online games to keep them coming back to it on a weekly basis.  Then, later in the year, when the PTO bought all the teachers at my school iPads, I was determined to put mine to good use.  I wanted an app that was going to enhance my instruction in a new way, and that's when I found Educreations. 

Educreations is like recording yourself teaching a whole class lesson on a white board, except your audience won't see you.  They'll hear your voice and see what you draw.  You can also embed pictures into your presentation, and on the iPad you can add text (typed) instead of writing words. 

It takes a little bit of practice to find the possibilities and limitations to the program.  For example, I love that it lets me pause my recording so I can collect my thoughts after each slide.  However I don't love that if I make a mistake in the recording I can't go back and redo it!  There have been a few updates to Educreations, such as the addition of an eraser tool (because users begged for it) and you can now use Educreations on your computer as well!  I love a product that is regularly updated based on user feedback.  It's rare when a product is FREE.  That's right, it's a free app. 

So how has this changed my teaching?  Well, although I'm not sure my district would approve of going the flipped classroom route (hard to do when not every child has internet access at home) it really has helped my kids learn some tricky, multistep processes in the following ways:

1. Kids love anything novel.  Sitting in front of the computer (no, I don't have a projector either) for 4 minutes to watch a video is more interesting than the other 179 math lessons at the rug listening to me.  Suddenly no one needs to go get a drink of water!
2. If a child needs reteaching, all they need to do is go back over to the computer with a small group of students and rewatch it.  Obviously I am available to answer questions, however sometimes, as one boy told me this week, "I just want to watch it a bunch of times until it REALLY sinks in!"
3. Two words:  Sub Plans!
4. Two words:  Homework help.
5. If a student is absent of course they can watch it at home and learn without spreading their germs around!

If you're not sure you're up to creating videos, keep the following in mind:

1. Don't feel you have to make a video on EVERYTHING.  I started out with the idea of 2 math procedures that I really wanted kids to see in action because historically their written notes just weren't enough.  This year I added another video for a third concept.
2. You don't have to make videos for your class to benefit from Educreations.  The site is searchable, which means there are TONS of free, public presentations available.  You can show them in class or link up on your classroom website.  Once you start finding great videos you'll get a good sense of what you really want in a video, and then you can rethink the idea of creating your own.

To get you started, here is a video I created to help my fourth graders multiply 2 digit numbers by 2 digit numbers.   

It's a nice lead in to some hands on practicein class (this is a paid for product).  By keeping the direct instruction short, sweet, and engaging, we can get into the practicing quicker, which I love.  The work you put in creating or researching videos will make your job during class time much easier; you can focus more on the kids' learning than the subject matter itself.

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Estimating on Number Lines

I have found that estimating on a number line was a big shift for my class.  At first, they looked like EXPERT estimators; I was ready to hug their third grade teachers.  But then problems kept cropping up.  Why were they suddenly struggling?  Everyone knew that 48,053 rounds to 50,000 and everyone knew 21,923 rounds to 20,000. 

It was pretty clear that when I asked them to round 34,356 to the nearest hundred and suddenly they looked like deer in the headlights that place value was the issue.  Oh, they all whizzed through chapter 1 and knew their word form and expanded form and lined up numbers in columns like pros.  And we've practiced regrouping on a daily basis in our Every Day Counts routine.  But they are still not able to put it all together to really conceptualize how numbers differ.

To fix this I designed two activities.  The first was "Pin the Number on the Number line."  I started out with a single sticky note with the number 35,421 on it.  Then I created four number lines on sentence strips based on that number.  Each number line represented a different place value:

Ten thousands:  10,000  20,000  30,000  40,000 and so on.

Thousands:  30,000  31,000  32,000  33,000  34,000   35,000  36,000 and so on.

And so on for the hundreds and tens...notice that the original number will fit on both of the number lines.  All the number lines were designed to have a space where the given number would fit into. 

Next I wrote 7 more sticky notes that could all fit somewhere on the tens number line, since of course that line would have the most limited choice.

For the activity, I put a number line at each table and had students rotate through, working with a partner to determine where to place the sticky note would go each time, and record it onto their sheets.  As they finished they switched sticky notes with others to get more practice. 

This activity was simple enough for all students, yet it gave them the practice they needed to start looking at a number more than one way.  They had to switch the focus of the place value at each spot.  Since they already had the concept of the 5 determining if a rounded number is larger or smaller than the original, I didn't even focus on that in this lesson.  It was all about find the place value and determining what the higher or lower value was.  In fact, when they sat down and looked at their recording sheets with the higher and lower value their number fell between, they automatically made the connection to circle which of the two the number rounded to.

I had an extension activity that I cycled students through, which I wrote about on my other blog.  This estimating activity was also hands on, but instead of using number lines as a tool I used money to help us estimate!  

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Creating Classroom Rules

Every year I start out by talking to my fourth graders about rules.  But by fourth grade, they already know, on paper, what classroom rules should be.  So I've always asked them what they think the rules should be instead of telling them "these are my rules." 

And yet until last year, I would alter those rules, combine with other ideas, throw out "obvious" rules, until lo and behold, their rules were the same as I happened to have on my poster that I'd secretly kept from the previous years.

I don't do that anymore!

Of course, when my students list rules, some are too general, some are more motivational phrases than actionable rules, and a couple are rules that I feel are actually unnecessary.  They also used to be an overabundance of "Don'ts," however once this went out of fashion a few years ago, it seems that by the time they get to my class nowadays they've had enough models of rules phrased as a positive ("stay quiet" instead of "don't talk") that I don't even have to "fix" those (I allow some, I just keep them in the minority).  So of course I still need to "tweak" their rules, but I do NOT put up the same poster every year.

The trouble we DO run into is that we can end up with nearly 50 rules.  So I tell them, "obviously we are never going to be able to remember every single rule on its own.  So it's going to be very hard to follow them!  Are there any we can throw out?"  Once we realize that they are in fact all important, I promise them, "tomorrow I'll teach you a way that we can group these rules to make them easier."

This is when our discussion about rules turns into a reading/writing/executive functioning lesson: sorting details from main ideas.  This is usually SO difficult for kids to grasp, and I used to think it was so hard to teach (since I used to be bad at it when I was their age).  So I model it in the easiest way I know; so simple that many preschoolers would have some success: relate it to animals. 



I start sticking these cards on the board, and at the end I write the sentence in blue.  They're all yelling out the answer before I can even finish the question.  

Next I tell them to think about ways they're alike, and tell me what groups to put them into.  I draw 3 columns as a hint, and listen in as they "turn and talk with a partner."  When they answer, they will usually say, "These 3 are all birds," I'll ask, "How do you know?"  This is because we'll be talking about "finding evidence" a LOT this year.  And finally we name the groups.

Next I ask if there is any other way we can sort these words.  I move "eagle" over into the middle column and ask if the animals are all related in some way.  Kids might see that they are all wild animals.  I ask if robins and blue jays are different; are they not wild animals?  We start to find that there is more than one way to name the groups; sometimes it results in the cards being in different columns, and there is no one right answer.

Next, I gave each group a set of sentence strips.  Last year I "fixed" the strips so that each group would come to a single main idea.  I even threw a main idea strip into the mix to see if they could find it and check if the rules below it "fit inside it." 

This year I mostly fixed the strip distribution it so that each group would have 2 sets of details, and they had to figure out the main idea on their own.  They still have plenty to learn when it comes to compromise and hearing all voices, but I was able to point out some positive behaviors for others to watch and learn from.

In the end, we were able to come up with 5 topics.  Some groups realized their main ideas were synonymous so we needed to combine their piles into one.  Some strips needed resorting the next day, and another lesson was needed to change the topics into main idea sentences (the model I gave them was "Learn as much as you can.") 

There are some rules that I think fit better on a different poster, and the "talking rules" makes me cringe because it's not a fantastic main idea sentence, however the class feels a sense of ownership over these rules.  When we had a fire drill today they pointed out that we needed to add to the safety rules.  Having 5 main ideas to focus on, especially when they were all their own ideas is very manageable.  And yet for those "black or white" thinkers, having the sub-rules that help clarify and define the general rules is helpful.  

We still have more work to do such as talking about how it feels when others break the rules that the rest of us are following (using role playing) as well as talking about their rights as students in our class (which will lead into our unit on government and the Constitution).  But for the most part, after a week and a half our rules are finally finished!  

How do you get kids to "buy into" rules in your class? 

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