Fraction Number Line Tightrope Activity

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 games 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!" 

How I Set Up the Number line Activity

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 fun!  And for homework, I made these fraction number line worksheets. 

Then to reinforce the activity I created a follow up fraction number line game that can be played again and again during small group work or math centers.  Our custodians preferred this game.

How to Have a Decimal War Card Game

Right before our February vacation, my fourth graders start decimals.  To help them understand the concept of decimals, I always find it's easiest to equate them with money.  The Coin-Fraction-Decimal chart shows that 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!

To practice seeing decimals concretely (and relating them to fractions) we play 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 cards (tenths) and green cards (hundredths) 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).

If you don't own decimal cards, I had a request to create a printable game.

If you would like a version that includes the cards and is ready to print, you can get a Decimal War Card Game in my TpT store.

5 of the Best Fourth Grade Fractions Content Delivery Methods

 
If you've taught fractions before, you probably know that it's a tricky concept for a lot of elementary students.  But it's one of my favorite things to teach!  There are so many ways to explore and analyze fractions.  Here are 5 of the best fourth grade fractions content delivery methods.  Whether you're new to teaching fractions or you're looking to change things up a little, these activities will increase engagement and understanding with equivalent fractions, fraction of a set, improper fractions and mixed numbers. 

My Favorite Fourth Grade Fractions Content Delivery Methods

1.  Color.  When kids are ready to practice an algorithm, a coloring page is much more appealing than a worksheet of 20 examples set into a grid.  This post on 1/2 as a benchmark fraction breaks down the lesson and has a link to a free coloring page for finding fractions greater than, less than, and equal to 1/2.  
 

2. Make a real life connection.  I'm not talking about a worksheet with 10 completely separate word problems.  I'm talking about one overarching idea, such as meal planning, that can have multiple related math problems involved.  The more invested kids are in the topic, the more engagement you'll get.  Find out how I created an overarching fourth grade fractions lesson based on analyzing the sugar content in their favorite foods.

3.  Interactive anchor charts.  I've found there are 3 steps to making a great interactive anchor chart.  First, make an attractive title (bubble letters, rainbow letters, clip art if you don't feel artistic).  Then indicate a section for examples.  Finally, indicate a section for student explanations (definitions, algorithms, and so on).  Of course your role as teacher is to coach them on refining definitions and evaluating examples.  However once in a while a student creates a definition that is so well put that it blows my mind.  When you show your excitement about learning something new, your students will see learning in a whole new way.  You can see how I do this with after our fourth grade fractions pretest, introducing equivalent fractions for 1/2, other equivalent fractions, changing improper fractions to mixed numbers, and the inverse.  

4.  Manipulatives.  This one may be obvious, especially if you've worked with younger children (I've taught preschool, first grade and third as well as fourth grade).  However hands on learning is where it all begins.  One great instructional sequence I've learned in most areas of math and science is to start with hands on, then move on to visuals (worksheets, videos, anchor charts, and student drawings) before finishing with abstract (algorithms, definitions, and so on).  You can the progression that starts with fourth grade fractions manipulatives in this post.  

5.  Quiz the Teacher.  So one day the kids did NOT work well with their hands on manipulatives and games that I set up.  Hey, if one thing worked every time I wouldn't need a top 5 list in this post, right?  Sometimes group work is great for differentiation, but sometimes a whole class lesson is needed to get everyone on the same page.  In order to focus the thinking process of your class, try directing your students to "quiz the teacher."  In this post I describe how I facilitated a discussion about fractions that are equivalent to 1/2 using student generated examples and non examples that they "made" me sort in the form of a quiz.  

Bonus!  6.  Games.  I included this as a bonus because often manipulatives have a game component, but there are games you can play with the whole class using NO materials.  I walk you through a fun fourth grade fraction of a set game in this post.

Do you want more ideas for teaching fourth grade fractions?

If you are looking for a unit that has all of these content delivery methods for fractions, you get my entire Fourth Grade Fractions Unit in one download.  Otherwise, you can read my Fraction blog series here on Shut the Door and Teach.

Equivalent Fractions Lesson Fail (and Fix)

The week after vacation, as every teacher knows, is crunch time.  We know that the state math test is rapidly approaching and equivalent fractions lesson reviews are in order.  And we know that the pressure is ON.  As veteran teachers, the whole thing is old hat.

It's not old hat to our kids, however!

Usually my fourth graders tend to be well rested after a vacation (a benefit of teaching upper elementary kids; they don't forget about classroom expectations like the little ones).  But during Monday's equivalent fractions lesson, my kiddos were just not on their game. 

The Equivalent Fractions Lesson Fail

First, I was all excited to do an equivalent fractions activity involving stations and manipulatives and exploring different shapes and amounts of pieces that can equal one whole.  I was going to lead a discussion on patterns we notice and post photos of all their ideas and it was going to be collaborative and hands on and foster real mathematical thinking.

That is not what occurred.  At all.  

Similarly, my plan was to end the day with a fantastic board game I created that help kids practice how heating and cooling results in a solid, liquid, or gas.  I spent my vacation finding cute fonts for the game pieces, typing up directions, and looking forward to more thank yous like I got on 100s day for the fun activity that helped them practice a tricky concept until it was mastered.

Again...nope.  Most of the class was so off task that I called off the game.  I let the kids who had done focused work help me with some coloring/cutting prep, and left it for the next day.

It just confirms the fact that no matter how carefully you plan a lesson, no matter how fun you make it, and no matter how many classes it's worked for in the past, not every equivalent fractions lesson works for every group of children.  Otherwise there would be a single curriculum that everyone uses.

So here's how I turned a day 1 equivalent fractions lesson fail into a day 2 triumph!

Changing the Content Delivery for My Equivalent Fractions Lesson

The first problem was that the kids bicker, a lot.  Despite Morning Meeting and Responsive Classroom, and student generated rules and setting expectations for group work and reminders 5 minutes prior to starting, they still bicker.  

The second problem was that despite modeling each station, posting the model and directions on the board, and answering questions/the same question 10 times, lots of kids just did not understand concept and/or, more likely, the directions.  

So what I decided was to give them an extra day of break...from each other.  I love collaborative learning and I do lots of it.  Which is strange, because I'm an introvert.  Or maybe it's BECAUSE I'm an introvert, and it doesn't come naturally to me, so I want very much to impart the strategies I've learned in order to help other introverts in my class.  But when it's not working, there's no sense beating a dead horse.  When the concept is too hard AND they have to focus on collaborating well, it's too much for them to handle; one of those things has got to give, and today it was the collaboration.

The Equivalent Fractions Lesson Fix

So for Tuesday's equivalent fractions lesson reboot I came in with...a worksheet.  I know, I know, what a horrible teacher I am.  Antiquated methods and all that.  But you know what?  They did it.  They did focused work for the period, they noticed patterns during this revised equivalent fractions lesson, and they enjoyed the relaxing atmosphere that coloring patterns tends to evoke. 

Once they finished the worksheet, I pulled out the manipulatives once again with a different, higher level skill to work on.  But by starting out with a coloring worksheet (you can get it free from my TPT store) with the exact same skill that didn't come to them when they were collaborating with a hands on activity, suddenly they could do it.     

I continued to rethink the cooperative work hiatus in the afternoon.  I didn't let them play the science game in their groups.  Instead I told them they were going to "play with me."  I chose only 4 kids to get a game board, and I got one too.  I situated them so that kids could look on with those that got to play.  And then we each took turns, drew cards, read them aloud, talked about our move, practiced the good sportsmanship I was modeling, and applauded the first person who got to the finish line.  

I'd never tried a board game this way.

I liked it!

I'll definitely use this strategy at the beginning of the year, and whenever a class has a case of the "bickers."  Not only did it help, but the kids actually enjoyed it.  They started saying "us," instead of "her" for the person near them playing with the same board.  They formed informal teams.  It created a better atmosphere than having 5 separate groups with every man for himself.  Sometimes you just know:  It's time for plan B! 

So how do you use this in your own teaching?  My vignette was one example, but here are more general ideas.  

5 Switcheroos for Plan B Activities:

1.  If a competitive game creates tension, take out the competition. 
2.  If a cooperative activity creates tension, try an individual activity (worksheets including coloring often go down well).
3.  If individual activities (like worksheets) create frustration, try a partner activity (Pick partners by personality, then sit with a couple partnerships who struggle with the content area).  
4.  If you don't have good working partnerships, play a teacher vs kids game.
5.  If a modality displeases the majority, pick a new one (drawing as opposed to music as opposed to acting out).

I originally posted this on All Things Upper Elementary.

Playing with Our Food, Nutrition, and Fraction Line Plots

Fraction line plots did not come naturally to my learners or my teaching.  Then I found a way to relate it to food, and suddenly it made so much sense!

It all started when I discovered the Smash Your Food site.  It's not only educational but also really gross.  So of course, my fourth graders loved it.  We affectionately referred to it all week as "Squish My Food Dot Com."

Originally our Health teacher (yes, my kids have health as a special, which is pretty great) told my class about it.  As you can guess, (sadly) our specialists don't get time built in to bring kids to the computer room, so he could only talk about the site.  He said it was a fun way to see how unhealthy various foods really are.  "You might be surprised to see how much sugar is in some foods."  I was waiting at the door to pick up my class when I heard him so I offered, "Hey, our class has a blog (besides this one).  I can put a link on there and even introduce it during our computer time."

He was so grateful.  :)  I put the link on our blog, and a couple kids tried it that evening.  Then on Friday, during our computer lab time, I set up the program on the big screen for everyone to experience the messy info.

With a quick poll for the median age, majority gender, and the law of central tendency dictating that the majority activity level should be moderate, we looked at the selection of foods available for squishing.

The first vote was for a slice of pizza.

The kids guessed there would be 1 cube of sugar, 3/8 tablespoons of salt, and 3 teaspoons of oil.

Next we watched the press come down and pulverize the nasties out of it.  There goes that oil.  Ewwwwww.

The next screen showed that one of their guesses was correct, but one of them was half of the actual amount!

Although we did spend time on other activities in the computer room, I always give my kids some guided choice time (sometimes they are allowed to read and comment on the blog, other times they are allowed to play any math game I've linked from the blog, and so on).  This time playing on Smash Your Food some more independently was on the agenda, and it was a "smash" hit.  Most kids happily watched every available food get smashed, then went back and watched their favorites on repeat. This was key to give them background information about the nutritional information of foods before reducing them to numbers on fraction line plots. [Update:  This site seems to have vanished and possibly became an app.  The good news is you can still watch a Smash Your Food video on YouTube.]

Investigating Nutrition Information on Fraction Line Plots

In order to capitalize on their excitement, I carried the subject of nutrition into our study of fraction line plots.  You know that pesky common core standard that math textbooks don't cover at all (CCSS Math 4.MD.B.4)?  Yeah, that one.

I plotted some nutritional information I got from the website, plus a few other popular foods.  Having various data points plotted on a fractional number line became more clear to them because they already had some background on the subject matter.

Further Practice with Fraction Line Plots

I created a couple worksheets to help kids practice reading and interpreting line plots with fractions.  One of them is based on the sugar content of the foods we researched.  The other worksheet uses a novel context, which was perfect for homework.

You don't have to do one in order to do the other, but this math concept worked really well in conjunction with the site.  Have you smashed your food with your class?

Update: Due to popular demand, I've created a fraction line plots resource with even more practice! This new resource is perfect for you if you want:
1. Additional practice for your fourth graders
2. Task cards instead of worksheets
3. Differentiated materials for learners who struggle to get started or recall directions.

Here's how I like to use both.  I start with the sugar lesson with the whole class.  I assign the plant worksheet for homework.  Then I use the fraction line plot task cards in small groups/centers on days that we are doing spiral review.  Click to take a look at the preview and see if these are right for your learners!  

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 review with the concept of arrays 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? 

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.