Fraction Tile Strategy: Hide the Labels

I used to tell students WAY too much when introducing new concepts in math, and I neglected to let them discover things on their own.  When students are told what to think, I believe that it limits understanding. I used to stand up in front of my students and talk about fractions by telling them which ones were halves, thirds, quarters, etc. It is embarrassing to admit that I would teach that way, but now at least I can share what I’ve replaced that method with…lots of inquiry based hands on learning.

Today the learning target was: I can use benchmark fractions to estimate. After spending lots of days in a row with tangible real world concreteness, it was a big leap to move to representational models of fractions. We pulled out the fraction tiles (basically harder versions of fraction strips) that came with our new math series.

Fraction Tile Strategy

You’ve seen these, you may even have them, If not there are likely a dozen free ones out there that you can print and cut. Just try a web search for “fraction strips” or “fraction tiles”.

After we took them apart, I had them flip over the entire thing, putting the red whole number 1 at the top.  There were a LOT of confused faces, and even one student said “how will we know what they all are?” I asked them to trust me and luckily they do, so they flipped them over. Then, I asked the same question that the student had just asked. How do you know which one is which? Which one is 1/2, 1/4 or 1/3? A few students right away started to lay them on top of the red whole piece like this:

Fraction Tile Strategy

Flip over the tiles so that the labels are NOT showing.

After a little buzzing with their partner, they all pointed to the pink one immediately for 1/2.  It took them only a few more minutes to identify the 1/3 and 1/4 sections.  When we talked about how they discovered this, there were a couple of cool things they noticed:

  1. “I just counted, if there were two of one color, I knew it was two halves! If there was three, I knew it was thirds.”
  2. “I lined them all up below the whole tile to see how many could “fit” in one whole. Sometimes I didn’t need to fill up the whole thing, because I could just tell.” (Boom! Learning target met!)
  3. “I counted them and stacked them, as I they got smaller, they got taller.” (I really like the size thinking there.)
Fraction Tile Strategy

These students counted and stacked each one to figure out the fraction piece label. Then they noticed the sizes of their fraction tile stacks began to grow!

Giving them time to explore has made fractions way less intimidating. The models came much easier to them when they didn’t have confusing labels staring them in the face.  I am definitely a fan of using fraction tiles/strips with the labels hiding.  What an awesome way to get them to estimate using benchmark fractions.

Tomorrow, we’ll explore equivalent fractions with these same strips, and try to connect it to the real world.  I can’t wait to see their thinking!

3 Hands On Earth Day Activities that Integrate Math

Here are three really amazing Earth Day activities for your elementary classroom that all include math. I’ve done them all and they’ve been memorable, educational, and fun! The best part is they always lead to deep moral and ethical conversations.

1.  Hold a Trash Free Lunch Picnic:  This is a two day project.  The first day, you ask the students to keep track of how many pieces of trash they have as they eat lunch.  For the second day, you send home a note asking parents to pack a trash free lunch, (as trash free as possible) to see if you can cut down on the amount of trash.  On the day of the trash free lunch, you ask the students to count how many pieces.

Earth Day Activity Trash Free Lunch

Here is an example of a student’s trash free lunch.

 

We kept track on a tally chart and realized the impact we can have if we change one simple thing, how we pack our lunches!  Then, the students draw a bar graph or a pie chart to show the results of the tally chart.

Earth Day Activity: Trash Free Lunch

Record the data of a trashy lunch vs. a trash free lunch!

2.  Build a Solar Oven and Bake S’Mores:  Show a tutorial for how to make a solar oven a few days before Earth Day.  Here is one that could be made from a pizza box!

Tell the students to bring their own supplies from home (cardboard boxes, plastic wrap, aluminum foil, tape) and give them time to make them when they first get to school.  It took our class about 2 hours. The math involved is awesome, measurement, measurement and more measurement! I brought the graham crackers, chocolate, and marshmallows and they melted like crazy in the sun. It was super fun! Here are a few photos.

Earth Day Activity: Build a Solar Oven

Students bring in their own materials, but you may want to have some extras on hand.

Earth Day Activity: Build a Solar Oven

This student even put a skewer in the middle of the oven, too bad they decided not to use it in the end.

Earth Day Activity: Build a Solar Oven

Some students learned the hard way that you need to CLOSE the solar oven!

3.  Study an Important Environmental Issue and Act on it: Perhaps the best Earth Day activity we’ve done is something that felt meaningful, like we could make change happen!  We studied the Great Pacific Garbage Patch by watching videos, reading about it, doing some math problems surrounding conservation, and by writing persuasive letters.  We ended the project by doing a water pollution science experiment.

Here is a video about the Great Pacific Garbage Patch if you haven’t heard about it (Depending on the age of your students, you may be able to show it to your class.):

Here are some photos of us trying to “clean” water, so students could find out how truly difficult it was.  As they work, each tool they borrow from me costs them money. They have to keep track of the cost of their clean up.

Earth Day Activity Water Pollution Experiment

Students are trying to clean out a polluted basin of water using different tools (all of which cost different amounts of money). They keep track of their successes and the cost of cleaning out their basin of water.

Earth Day Activity Water Pollution Experiment

A student is trying to remove vegetable oil from their basin of polluted water. NOT easy!

The bottom line, is there are so many things that students can do to learn about alternative energy, and to study current environmental issues. Instead of encouraging them to recycle with a coloring sheet or a worksheet, engaging them in these issues will help them feel an authentic push to do it!

I love Earth Day and the awareness it brings to young people! What kinds of things do you do with your class on Earth Day? Share below in the comments. 🙂

Discovering Numerator and Denominator with a Pan of Brownies

The way to a child’s stomach heart brain is most definitely with sweet treats. While I don’t like to sugar up my students, I do like when they can connect math to the real world.  That was exactly my mission when I brought in a pan of brownies.

Example of Real World Fractions

If all else fails, capture their interest with food!

So far at this point, we had examined the definition of a fraction, and thought about things that come in halves and quarters.  It was time to move into some more new vocabulary, the numerator and denominator of a fraction.

In came the pan of brownies.  I brought it over to a large rectangle table and had them all gather around me.  As they were salivating I asked them how I could split this pan into fractions so that we’d all get an equal amount.  I asked them to draw what that looked like in their math journals knowing that we had 25 students in the room.  This was easier said than done.

For some reason, a bunch of them abandoned the hard work we’ve done with arrays, and started drawing diagonals and squiggly lines all over their papers.  It was like they heard the word “fraction” and felt they needed to abandon everything they knew for this brand new concept.

*Sigh*

Then, I asked them to start sharing solutions, and we started to get somewhere. Arrays popped up on the chalkboard, 2 x 13 arrays (“I didn’t want to leave the teacher out!”), a 5×5 array and a 3 x 10 array.  I asked them which one would get them the best deal.

The settled on the 2 x 13 model so that I could get a brownie (how kind!).  That was when I began cutting.  I handed out the first one and asked them to think about what fraction of the brownie pan they were getting. That was when I introduced the fraction in number form and explained the difference between the numerator and denominator. The numerator was the number of pieces they were going to get to eat, and the denominator was the total pieces in the pan. For example (Hint: This is not the actual pan of brownies I used, since the cuts became VERY small and very messy…they were super gooey! So…I had to whip up another batch tonight for this picture, YUM!):

Real World Examples of Fractions

The numerator and denominator suddenly became clear!

They didn’t REALLY get it though, until the last person got their brownie. At that moment, I gave her my piece, telling her how proud I was that she was so patient to wait and be last. That was when the numerator part really sunk in, because I announced that she was getting 2/26 of the brownie, while everyone else only got 1/26. It was a lesson in patience as well as a lesson in math.

It was a pretty sweet mini lesson!

Billy Bug: Coordinate Graphing Game

I am a huge fan of simple games for upper elementary students. Sometimes the less flashy, the better, so that students can understand the purpose and the math behind them. One of my favorite games to have available for students to play is Billy Bug. It is a coordinate graphing game and it’s super easy and fun.

Billy Bug Coordinate Graphing Game

Usually I do a “game talk”, similar to a book talk, where I introduce how to play the game.  Showing just a few examples, even my third graders catch on. It is a really fun introduction to coordinate graphing, the concept of negative numbers in the advanced version, and the x and y axis. (Click on the photos below to go to the two versions.)

Billy Bug Coordinate Graphing Online Game

Basic Version (without negative numbers)

Billy Bug Coordinate Graphing Online Game

Advanced Version (with negative numbers)

I’ve also used this with 4th and 5th graders as a short warm up during a summer school educational games online class.  It is simple enough that it can be played for 5 minutes.  That is really all you need!

A great review of coordinate graphing in a simple and fun way!

Third Graders are Googling the Answers to Math Assignments?

My jaw literally dropped when I received this email the other day:

Assign Rigorous Problems

Let me explain two things to give you a little background:

First, I have a “contact me” section on this blog, for anyone who may need to get in touch. I received this email through that form.

Second, I recently put out a free resource called Doggy Dilemma for teachers.  It is an open ended problem that requires a lot of reading, writing and thinking.  There is no immediate answer, and all students would have a different answer in the end.

So…by the powers of observation and inferencing I can only conclude:

  1. This person who contacted me is a child that has received the assignment in class. (I am thinking this due to the lack of punctuation, capitals and misspellings. The “voice” of the writer seems very young, also.)
  2. This person is likely a 3-5th grader (since that is the target age group of the problem).
  3. This person is incredibly resourceful and bold. Not only does she google the problem, but she thinks to contact the author of the problem for an answer!

After I got over the shock of receiving this message I thought to myself, THIS is why I create what I create. No child should be able to google the answers to a great math problem.

What do you think about this?! I would love to know your thoughts.

 

Things That Come in Halves and Quarters: The Real World Connection

Whenever I have connected math to the real world, I’ve seen a boost in achievement in my classroom. Fractions are REALLY important concepts that must be connected to student’s lives. When I first started teaching, I would just plod along in the book. I would hand out worksheets with rectangle boxes that students would just fill in.  They’d write the numbers without really connecting it to much of anything. It was kind of a disaster!

Now, I love to collect real world examples, and put them on an anchor chart.  Because fractions are so abstract, we put this anchor chart together after brainstorming with a partner first:

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On the student planner that day, I put an assignment to look for things that come in halves or quarters at home as well. We can always add more! Now, each time we talk about a fraction, we try to picture something from this list.

I am hoping that these concrete examples will really help them understand when I move them into representational symbols and numbers.

What Exactly is a Fraction Anyway?

When I was a student in elementary school, I dreaded learning about fractions. It was a very tough concept for me. All I remember is shading in boxes and finding common denominators. I never understood what I was doing.

I decided as a teacher that my mission was to help fractions make sense to my students.  So I introduce the concept very slowly and very carefully.  Because this is so abstract for students, it must be connected to the real world the whole way through the unit.

We started learning about fractions by trying to figure out what a fraction actually is.  I know that sounds obvious, but I need to find out what my students know. So I posted the question, What is a fraction?

I gave a large piece of paper to small groups and asked them to write everything they know. They all pretty much came back with something along these lines.  There were a lot of I don’t knows, and a lot of blank stares. The people who did write something just wrote symbols or numbers.

IMG_8436

Not one student could tell me what a fraction really was. So I tried to clarify it for them with a simple drawing.

IMG_8435

 

Now that the definition is out of the way, maybe we can move into the conceptual understanding part! I make it a point to say those words daily as we talk about what we learned the day before. The emphasis in the Common Core State Standards for fractions in third grade is on parts of a whole, so that is what we’ll focus on!

How do you help your students know the meaning of math vocabulary?

Open Ended Math Problems Promote Reading, Writing AND Math

Last spring I had the opportunity to take a practice version of our new state assessment (the Smarter Balanced Assessment). In some states in the U.S. the PARCC is the new assessment which is similar in nature.

Talk about a jaw dropping, sweat on my forehead, instant anxiety through my whole body moment.

What the students are being asked to do is way more than a few math problems. They are expected to read, write and use appropriate grade level math in VERY complex ways. I realized that I needed to add some deep problem solving to my math instruction.  So I began to make open ended problem solving problems to introduce regularly into the classroom.

I decided to create Doggy Dilemma, a free problem for anyone to try out.  It is a highly motivating, real world problem in which students must read through information to decide what dog they must adopt. They draw a diagram of the dog pen, calculate the cost of the fencing, and write a letter to their parents explaining why they made the choices they did.

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My third graders have gone crazy over it.  They love it!  There are two full pages of reading involved which mimics the new assessments.  I have enjoyed creating it and want to make it available to anyone who teaches elementary math so that you can give your students the experience they need before the real assessments begin. You can get it by clicking on the picture below:

Open Ended Problem: Rigorous Problem Solving for Elementary Students

I’d love to hear how other teachers are encouraging this type of thinking in their classrooms. Please feel free to share in the comments!

I am happy to link up here:

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Concrete Number Lines Teach The Value of Numbers

During one of my recent 20 minutes of math play sessions with my 5 year old daughter, we played around with a number line.  A number line is a really abstract thing, and without something to connect it to, it is nearly impossible for a young learner to understand. So we built this fun thing:

IMG_4775The conversation afterward was awesome! She could see that the more legos we had, the longer the line got, which meant we could talk about the value of the numbers.

That got me thinking that maybe we could build one that didn’t use similar sized objects for a number line, to help her understand that a number’s value will still be the same even if the object is a different size. That was when we came up with this one:

IMG_4772

All of this building led to talk about sizes of things, grouping things, ordering and reordering, the value of numbers and so much more.  It was a ton of fun to make both with the number representations and actual concrete objects!

Concrete Learners: Hands On and Real Life…Every Day

In teaching division this year, I’ve never before used so many counters for so many consecutive days in a row.  I’ve got a core group of students who feel really great about division, some of them have even been memorizing multiplication at a very fast rate, which allows them to make better sense of division.  But I also have the exact opposite end of the spectrum as well.  As soon as they see that division symbol, their eyes glaze over and they become fearful of the problem. They worry about what to do and they think they cannot divide (even through they’ve been dividing all of their lives, they just haven’t seen the number sentence for it).

To help struggling learners, I’ve been trying to make it more concrete. Our youngest learners often need to see visual representations of numbers so that the concept is not so abstract.

In this set of problems, fruit was being divided equally into bags. I decided to lay out paper bags for this student.  The problem was 14 divided by 2, and he could easily solve it. He was both proud and excited to write his answer.  Win!

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Another student though, had a little more trouble. The problem was 8 divided by 4.  Because she had done 10 divided by 2 right before this one, she forgot to put away the 2 counters to start. She hit a wall very quickly and gave up. Instantly, she had her hand up for more help.

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To help her, we re-calibrated a bit by checking the problem again.  She very quickly realized that her counters started out wrong, and she was able to fix it. That check back to the problem is what I want her to do in the first place, great mathematicians do that without any prompting.  It was clear to see that she wasn’t connecting the number sentence with the manipulatives at all. It was a quick 1 minute conference on the importance of paying attention to detail/being precise, a math practice standard that many students struggle with. I told her that the next time she should try that strategy before asking for help.

Giving these quick teaching tips while conferencing with students makes WAY more sense when those tools are right there in front of them.  I used to try to draw on student’s papers, help them extend patterns etc… but the most struggling students need those tools in their hands to actually act out and see the problem. That is when I’ve noticed teaching tips given to them have become ultra powerful!