April 21, 2014March 29, 2017 by Beyond Traditional Math

Earth Day Water Pollution Activity: A Cross Curricular Inquiry Study

Today was one of those magical days at school. It was the kind of day that makes me LOVE my job, where all the pieces go together very nicely and the worldview expands for the students in the classroom. Today was one of those “teach like a pirate” days, where we took risks and immersed ourselves fully into an important issue.

We began our Earth Week (not just Earth Day) by learning about the Great Pacific Garbage Patch, something that is largely unknown to the general population. We read about the issue with a two page informational text today, while responding in writing with our new understandings.

Then we watched this video:

After lots of important discussion, I asked them a question, “How would you clean it up?”

That led to an awesome water pollution experiment, which ended up both engaging and frustrating the students. The groups had to try to clean up the water using the least amount of money possible. They had to write out their plan as a group together, figure out the cost and bring their proposal to my supply table to collect the materials they needed to clean the water. They had to be detailed and precise, use math in a very real way, and had to work under time pressure. Here is a peak into what it looked like:

Buckets were prepared with water and biodegradable items like coffee grounds, shredded paper, food that the kitchen hadn’t served but had to throw away, and soil.

Reused or recyclable items were for sale for students to use to clean up the water. (I wash out the cups and forks to reuse each year for this experiment! We reuse ziplock bags collected throughout the week. We recycle other plastics and aluminum foil.)

The students cleaned the water after “purchasing” materials.

Many methods were used to clean the water.

We compared water samples at the end, to see who was most successful. We also compared budgets, to see who was able to keep costs down.

We’ll continue this work for the rest of the week:

We’ll be writing a letter to explain what we learned today about the Great Pacific Garbage Patch and the difficulties of cleaning up water.
I plan to immerse them in lots of good Earth Day literature like: The Great Kapok Tree by Lynne Cherry, Oil Spill by Melvin Berger, The Lorax by Dr. Seuss, The Wump World by Bill Peet.
We’ll be learning about alternative energy to make wind powered cars later in the week, and we’ll even try to harness the sun by measuring and making solar ovens.
We’ve also got some tough math problems in the works as part of the Great Pacific Garbage Patch unit to help us think about conserving!

I love Earth Day…Earth Week, and more importantly introducing important issues to our young learners, encouraging critical thinking in meaningful ways. I’d love to hear what you do in your classroom! The more ideas we have to share, the more we can teach our children to be environmental stewards.

Learn more with these resources and dig deep into the issues:

March 30, 2014March 31, 2014 by Beyond Traditional Math

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.

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.

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.

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

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

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.

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. 🙂

October 27, 2013December 30, 2013 by Beyond Traditional Math

Problem Solvers Aren’t Born, They Are MADE

My first year of teaching, I was the queen of teaching problem solving. I would stand up in front of my students each day, and show them my beautiful strategies for solving the problems. Over and over, they would see my drawings, my number sentences and my solutions. I would ask them to copy them down if they couldn’t figure it out, so that they would have an idea for the next time. As I’d look at my data, I would notice that I had a top group of problem solvers who could always solve it, a big group of solvers that would typically get the problem correct, and a group at the bottom that would NEVER get the problem right.

I was foolish enough to believe that this was okay. I thought that some kids just weren’t very good at problem solving. I was SO wrong, and I am SO embarrassed to admit this now.

My second year of teaching, I heard this quote: “The person doing the talking is the person doing the learning.” I honestly felt sick to my stomach, because I realized that I was doing WAY too much of the solving, working and showing. I needed my students to take ownership, stand up, share their thinking in kid speak and start to GROW. I learned a lot that year, that students aren’t born to problem solve. It is something that requires an immense amount of practice.

I’ve come a long way since then, and would like to describe what I have done to be SURE that all of my students are getting this problem solving thing down before they leave my classroom. First of all, we take TWENTY minutes per day, every day to practice problem solving. This is something that is a priority during my math block. Then, I follow the steps below (UGH, I realize this looks like a TpT commercial, and I don’t mean it to be! You can do all of these things with your own resources.):

1. I assess what problem types the students can solve. Did you know that there are 9 problem types for multiplication and division in the common core? I use a series of multiplication and division problems, administering the first in the set to see how they do on each of the 9 problem types. I compile the results in a data table to see which ones the class struggles with as a whole. Then, we attack those problems one by one throughout the school year. I assess them again at the end with the last problem in the set to measure growth.

2. I introduce the Standards for Mathematical Practice. These standards are SO important for students to develop as math habits. They cannot be stressed enough. It takes us about a week and a half to get through them all, but it is worth the time. I post our work daily on the wall. The vocabulary from these standards becomes a part of our every day language.

3. I start small, with practice problems that are simple that they can relate to. Then, we go BIG. I have three types of problems that I use juggle through and use.

Simple Problems: There are so many problems out there about trains arriving and leaving on time, or other topics that students cannot connect to. I finally broke down and created problems over the years that would allow for practice of multiplication and division concepts. The problems are about things that students can understand. These are done on most days, with other problem types sprinkled in from my current math series. These simple problems are NOT done every day. That is not enough for students to become strong problem solvers.

Open Ended Problems: These problems require more reading, more steps and are much more complex. There are times that these problems require two 20 minute class periods to complete. These are the types of problems we will find on the Smarter Balanced Assessment next year.

Here is an example of an open ended problem:

Project Problems: These are always my student’s favorite type of problem. They spend several days on these problems and are a bit more out of the box. I always begin with the Book Order Proposal and go from there.

Book Order Proposal (Free to try out!)
Housing Market Analysis
Mini Golf Course Geometry
Party Planning Awesomeness
The Wind Powered Car
Elementary Architects

4. I make manipulatives available to them from the start, and I encourage their use. The idea that hands on problem solving is for young students only, or for struggling problem solvers is incorrect. Manipulatives are wonderful for any level of problem solver, it promotes deep thinking of the math concept you are working on.

5. I allow students to model their thinking in front of the class. More about how I do this you can find in this post. They solve it, explain it to the class and accept questions and compliments from the rest of the students. This is where the students do the talking, the questioning, the complimenting. They are seeing multiple strategies each day, they can “steal” ideas from each other and are held accountable for their work. I keep a tally chart right on the chalkboard so that students can see how many times everyone has been up. We try to make it equal, even though problem solving comes more naturally to some than others. This helps everyone know that they are ALL welcome up to the board, even if their solution is wrong.

6. I intentionally plan out which problems to do and when. I carefully monitor my students to be sure we are using our time effectively. I watch to see how we do as a class as we solve the problems. When the majority of the class is getting the problem type, I’ll switch to a similar problem type that requires a tiny adjustment in their thinking. I always incorporate a problem from the book that has to do with the concept we are studying from time to time as well. A two week plan might look like this (and it is always flexible):

Day 1: Equal Groups (Unknown Product)
Day 2: Problem from math series covering current concept.
Day 3: Equal Groups (Unknown Product)
Day 4: Equal Groups (Number of Groups Unknown)
Day 5: Problem from math series covering current concept.
Day 6: Equal Groups (Number of Groups Unknown)
Day 7: Equal Groups (Number of Groups Unknown)
Day 8: Equal Groups (Unknown Product)
Day 9: Open Ended Problem – Day 1 of 2 (complex, many steps)
Day 10: Open Ended Problem – Day 2 of 2 (complex, many steps)

7. I keep accurate records for myself. I have a class list so that I can see when students are getting the problem correct. I keep the problem as our daily focus until 90-95% of the class has mastered it. I have an answer key that allows me to check off when we’ve done the practice problems so that I don’t accidentally repeat the same problem.

8. I intervene with students when the problem type is a struggle. I pull small groups during our math work time, in the morning when students come in, during recess, during our intervention block time, whenever I can to get those students up to speed. Many times they just need more one on one support to be successful. I don’t wait any more for them to figure it out on their own. I intervene as soon as I notice the struggles.

It sounds like a lot, but once we get in the groove, and routines are in place things get ROCKING! I didn’t realize how much students love this process until we had a substitute teacher in for a day. The teacher worked the problem out on the board much to the anger of my students! The next day, they were SO fired up and upset that she didn’t give them time to work it out on their own. That is when I knew that the students in my classroom were finally owning their own learning.

October 13, 2013December 30, 2013 by Beyond Traditional Math

Just Make it Real World

I am not sure if you’ve ever had that “moment”. The moment where you are at a frustration level with why things aren’t working. I used to look for extra worksheets to give more time for tricky math concepts to “stick” with students. I looked online for further practice activities, I asked colleagues for their extra resources for more practice, I looked for games. I felt like I’d tried everything. That’s when I read some research that making math real world, connecting it to student’s lives was REALLY good practice. So a few years ago I started to create real world problem solving projects to help this problem.

That was how the Book Order Proposal project started (for my gifted and talented students I’ve used The Housing Market Analysis). I knew that I needed to continually reinforce the concept of rounding/estimation, comparing numbers, and mental math addition strategies. I gave my students the chance to do just that by offering to buy books for our classroom library. I decided to coincide this project with my parent Scholastic Book Club order. Here is how it worked:

I made it my problem of the day for 4 consecutive days, giving 20 minutes each day for the project. The first three were days for them to work (with a mini lesson or two if needed), and the fourth day was the peer review day.
All students were given a budget of $50 (bonus points offset this cost-I was able to get all of our books free this last round) to look through three Scholastic flyers.
The students had to put together a proposal, thinking about their classmate’s reading interests, as well as thinking of what we currently have in our classroom library.

What happened was kind of interesting. The majority of the students got within $2 of the $50 budget. A few of the students tried to hand in proposals that were $1, $30 or $25. When we talked as a class on the second day, I asked my students if it was okay if someone didn’t get close to $50. The resounding answer was “NO!”. When asked why, they explained that it would be a waste of money if they didn’t spend it all, especially since they would become THEIR books for their classroom. I handed back those few papers and asked them to start again. (Now that is what we call peer accountability!)

At the end of the project we laid the papers out and did a gallery walk. Students voted on their top 3 favorite proposals. The proposal with the most votes actually got ordered! It was such a fantastic way to end the project.

My favorite part though, the very best part of the entire project, was the gallery walk and natural reflection. Students could see how others choose to put the proposals together. Some were neat and organized, others were missing information, some of them had a hard time with their handwriting, and other student’s numbers didn’t quite add up. It led to great discussion, and the students wrote goals on their proposals for the next time we have to present information to our peers.

It has been clear to me that making math real world, and connecting it to their own lives is a powerful thing!

September 7, 2013December 30, 2013 by Beyond Traditional Math

Two Projects That Created Authentic Dialogue About Work Habits

Well I did it again! I started the first day of school with a project, this one a little different than what I have done the last few years. I like to start the first day off with a bang. I asked the students to perform a complex task where I give them minimal directions.

First Day: Boat Challenge

The Task: Build a boat that could sail across a four foot channel of water in 30 seconds or less.

They could use a variety of materials that I set out: aluminum foil, paper plates, paper bowls, cups, straws, napkins, tape (almost all of these items were leftover from classroom holiday parties last year). They could also test their design as many times as they wanted before the “official test”. They were given 30 minutes to build their prototype.

Once the shock of learning that I was not going to tell them how to build it wore off, we began to see some pretty exciting stuff. They went back and forth from the supply table, many of them trying several different ideas.

There were so many feelings/things happening in the room, frustration, anxiety, excitement, nervousness, celebration, dismay, selflessness, idea “stealing/copying”, and not all of the feelings were good feelings. I took that moment to realize that sometimes we have to use these authentic experiences to help students identify ways to get better at work habits.

As soon as all of the boats had sailed, we sat down at the carpet in front of my easel to make the first half of my anchor chart. We came up with things to put under “I can work alone”. I was delighted by their thoughts.

This worked so well, that I thought I’d try for “I can work in a group” the next day.

Second Day: The Teddy Bear Challenge

The Task: Build a 12 inch or taller tower to hold a stuffed bear out of notecards and tape.

Each student was given a bag of materials: scissors, scotch tape, index cards, stuffed bear and a ruler. This time it was a group activity. Again, there was a wide variety of things happening in the room. Some groups worked perfectly together, others argued over supplies, some spent time doing individual towers, others fought over whose idea was best, I was most impressed with the group that gave each other jobs. The voice level in the room got louder, and louder, and louder. 5 of the 7 groups came up with viable options that worked after 20 minutes of building.

I realized quickly that third graders are not nearly as good at working in groups as they are working alone.

We met again at the carpet to discuss “I can work in a group.” Again, their frustrations turned into the positive on the chart paper. It was amazing to work through their negative thoughts, to turn them into goals for the next time we work in a group.

I’ve taped the anchor charts to the wall, and plan to refer back to them often (especially in these first few weeks). I hope that it will lead to more risk taking when working alone, as well as more peaceful group work. I’ll let you know how it goes!

August 16, 2013December 30, 2013 by Beyond Traditional Math

Use Open Ended Math Problems to Raise Rigor in the Classroom

Use Open Ended Math Problems to Raise Rigor

This is a photo of our current math series and its Problem of the Day. This problem was solved in 10 minutes by my students. This is not rigorous enough, not complex enough, not inspiring at all, and just not good enough for my third graders.

Instead, I’ve been using Open Ended Math Problems for the last eight years about once per week. These problems require basic math, but complex thinking. They are multi-step, require more than one class period to complete, and are real world.

Here is an example, called The Museum Trip:

Some ways I’ve used them:

* as a “what to do when you are done” option
* as partner activities
* whole class discussions to talk about problem solving strategies
* small group gifted and talented students have tackled them
* parent volunteers have come in and used them with groups of students who are struggling with problem solving

Open ended math challenges present so many opportunities for dialogue and engagement in the elementary classroom. If we expect students to respond to the common core and the impending assessment that comes along with it, we must practice this type of thinking.

August 16, 2013August 16, 2013 by Beyond Traditional Math

Back To School Sale: Save up to 28% and Enter to Win 3 FREE Products!

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I am just getting started in my TpT store, and wanted to offer a give-a-way in addition to the back to school sale at my store. To enter just follow my blog by entering your email and I will add you into the drawing. (If you already follow me, you are automatically entered!)

Find my products at my TpT store (click the photo to see my store)!

You could win:
Open Ended Math Challenge (7 problems + rubric)
Housing Market Analysis Math Project (2 week unit)
Mini Golf Course Hole Math Project (2 week unit)
Float Challenge Math Project
Elementary Architect Area Math Project (2 week unit)
Party Planning Awesomeness Math Project (1-2 week unit)

* You can “save” your win for future products as well!

August 9, 2013December 30, 2013 by Beyond Traditional Math

Raising Rigor for the Smarter Balanced Assessment

In one year, our students will be taking the Smarter Balanced Assessment in place of our current state wide assessment system. You can click the logo below to find out more.

Our district participated in the pilot test of this assessment, and I was lucky to get a chance to see what we are up against. You can take that first part of the test here (there is not a performance task sample ready yet).

When I peered over the shoulders of my students, my jaw just dropped. The rigor of this test far exceeds what I’ve been used to for the last 8 years. There were two parts to the test that I was able to see; a multiple choice/short answer and then a performance task type of test. The first part was kind of standard, but included a lot of dragging, clicking and typing.

The second part was what really got me. Nothing in our textbook would ever prepare students for this! The first section of the problem was a full page of reading that they could go back and refer to over and over. The second section contained about 20 questions related to that reading passage that built on each other in difficulty.

Notice, this was a MATH test, not a reading test. If you can’t read you really can’t do well on this test. If you can’t persevere, you really can’t do well on this test. If you can’t sort through massive amounts of information, or use appropriate strategies and tools, or PERSEVERE when the going gets tough…you will not do well on this test.

In come the Standards for Mathematical Practice. If you aren’t familiar with them, you should get familiar. They are amazing, they are exactly what we’ve needed and wanted students to do since the dawn of time.

I have been thinking about some ways to prepare students. Here are some things I am thinking for the coming school year:

1. My plan this year is to incorporate deep problem solving DAILY. I will use mini lessons and structure to help them get started, and then get them working independently. We will do this every day for 15-20 minutes per day, I’ll even set the timer!

2. I plan to incorporate and embed those Standards for Mathematical Practice. I will explain that they are behaviors that great mathematicians do! I created a systematic way to introduce them to students.

3. I am going to let them struggle. Sometimes we learn best with our mistakes. Struggling can help us do our best critical thinking.

4. I will help them read for understanding, I may even incorporate reading math problems during Readers Workshop. We’ll talk about how math reading can be different than reading for enjoyment. I am going to use these open ended problems that are full of reading, encourage persistence, and are real world.

5. I’ll blend in reading, writing and math content into my problems so it becomes seamless.

To prepare them for the task coming (which they very well SHOULD be able to do), we’ve all got a lot of work ahead of us! I hope we can join together and re-ignite student’s passion for projects, hands on activities and rigor.

August 7, 2013December 30, 2013 by Beyond Traditional Math

The Float Challenge

The amount of vocabulary that is embedded in the measurement and geometry Common Core State Standards is staggering. Along with most things in math, I feel that more than ever students need to see it, use it, or touch it in the real world to connect to these words.

This occurred to me halfway through our measurement unit, as I was teaching metric units to measure mass. The day before, we had covered customary units for mass. Adding more vocabulary the next day felt like I was pushing too much information into their brain.

So I tried a little something. A Float Challenge.

I gave the students a 1′x 1′ piece of aluminum foil, and asked them to create a flotation device. This device had to float/carry the amount of mass weights (in grams) as high as they were willing to bet. The person who could successfully float the greatest mass (had to stay afloat for 5 seconds) would be the winner, but if they bet TOO high and their boat sank, they were disqualified. The mass weights that I had came in increments of 1, 2, 5, 10, 20 and 50 grams. They could decide how they wanted to distribute their weight.

The bets came in slow and steady. Some students wanted to see how others would bet. Others worked on their flotation device right away. A few students went for it all, hoping their flotation device would carry 80-100 grams. Every student came to the table at some point in the design process to feel what the weights felt like in their hands. After about 15 minutes of engineering we began the floating. It seemed like every student was hanging on the edge of their seat as the flotation devices came forward. Near the end they were trying to stand on chairs to see the final two. The results as we proceeded were recorded on our easel chart.

The reflection that followed was powerful and meaningful. Many wished they had bet more weight, others expressed an interest in changing their float design. Some explained that they would have liked the opportunity to test their float ahead of time. Other students felt that they had over-thought their design, and wanted to do it all again.

By the end of the lesson, every student in the room could tell me what 1 gram felt like. A week and a half later, they could STILL tell me what 1 gram feels like, AND they are connecting it to other things in the world around them. Seeing the success of something that was so simple, and that truly took only 25-30 minutes makes me see that I need to do this more. I need to connect it more to their lives, allow them to see it, touch it, (maybe even taste it!) to make it meaningful.

You can check out my Float Challenge in the Resources for Educators section, or just click here! In it is the lesson in GANAG format (Jane Pollock’s amazing lesson planning format) and includes goal setting, the guidelines for the contest, and formative assessment at the end. Happy Floating!

August 3, 2013December 30, 2013 by Beyond Traditional Math

REAL Problem Solving at the Elementary Level

One of the things that I struggle with as an educator, is how to incorporate real problem solving in mathematics instruction. As an adult, I don’t sit down and think about how if Johnny gave me 3 apples and Julie took 1, how many I would have left. That type of simple math is probably useful for K-1, but not for 2nd grade and beyond. The intermediate grades are READY for multi-step, complex problems that require creativity and critical thinking. The problems that are part of our math series are not deep, nor are they relevant to student’s lives. They don’t differentiate for gifted and talented students, and they definitely aren’t always appropriate for students with special needs.

Last year when I handed out the Problem of the Day book, supplied by our math series, I cringed a little. Students didn’t open up these books the same way they open up a book like Harry Potter. There was no excitement, the general feeling was very “blah” in the room. I know that there has to be a better way.

So, like any teacher, I turned to Google to solve my problems.

“elementary problem solving”

“project based problem solving”

“motivating elementary problems”

There is really not a lot out there. There are suggested ideas and a few projects here and there, but the majority of the problems are for middle school and higher. With the new Common Core State Standards and the up and coming Smarter Balance Assessment, I knew that what we currently have isn’t enough.

I have introduced some problems each year, and each year they get better and better. I will keep on searching for more, as well as continue to tweak what I have. The best place I have found ideas has been on Twitter, where someone’s language arts lesson prompts me to think of how I could do a similar project in math. Here are some of the problems I currently do, and I am slowly uploading them to share in Resources for Educators:

Book Order Analysis
The Float Challenge
Housing Market Analysis
Mini Golf Course Geometry
Wind Powered Car
Classroom Economy
The Great Air and Water Craft Extravaganza
Desert Hike
Elementary Architect
The Last Summer Picnic
Restaurant Dreams
Family Reunions
Desert Island Playlist

We’re getting there but it’s coming slowly. Join me by posting any of your ideas and products in the comments area!

Beyond Traditional Math

Fostering conceptual understanding with real world connections.

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