Manipulatives Aren’t Just for Kindergarteners

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In our classroom we’ve been working through the math practice standards. We just finished number 5 today: Use appropriate tools strategically. Last year I researched the math practice standards, re-wrote them to be kid friendly, and turned them into learning targets.

I can use the right tool for math, and explain why I chose it. 

We talked about the kinds of tools that mathematicians use, and they came up with a healthy list. After that, I read the problem, made sure to show them where to find the manipulatives, and turned them loose to work. I thought this math practice standard would be a breeze!

Some of the tools I put out:

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In the past I’ve always offered the appropriate math tool for them, taught them how to use it and that was that.  This is the first time I’ve ever asked THEM to choose a math tool from a bunch of options.

I learned today that math tools are much more complex than I expected. The result of today’s lesson was a total surprise.  (I LOVE that even after 8 years of teaching I can still be surprised.)  Every student in the room was comfortable with using the manipulatives, but only about 5 out of 25 were using them effectively.  Rather than thinking about what tool might help them solve the problem, many of them chose tools based on their shapes.  For example, the problem was about cookies, so they picked the fake money manipulatives because they were round and they could trace “cookies” on their paper.  They were using a math tool (clearly not the right one), they could explain why they were using it, but their use of it was not exactly accurate for the problem type.

I took this moment to reflect and think about how I can incorporate math tool use more intentionally. I think that there are many tools appropriate for third grade. I used to think that math manipulatives were just for kindergartners or the early primary grades, but I have realized quickly today that their complexity is vast and allows for deep thinking.  I am excited for the challenge of exploring each tool’s unique properties!

3 Step Process to Strengthen Problem Solving in the Elementary Classroom

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Problem solving seems to be an issue time and time again every year in my classroom.  When the math practice standards came out, I thought that they paired nicely with problem solving. These standards are deep thinking math habits that students can try to develop for all areas of math, but I noticed specifically how they were helping my students problem solve. I developed a way to introduce these standards in the beginning of the year as a way to start up my math workshop. There are 3 components to how I do this.  It takes 20-25 minutes per day of my math workshop for this process for my third graders. That means I can introduce all of the math practice standards in about a week and a half.

1.  Students solve a problem and model their strategy for the other students:

The photo above is a screenshot of my SMARTBoard today from the Guide to Introducing Math Practice Standards.  We’ve been introducing the math practice standards each day during math by working out a problem that is related to the standard.  I am a firm believer that students can become better problem solvers by seeing each other’s strategies and by describing their thinking. Every day when we work out a problem I choose two people to go up to my chalkboard, and one person to go up to the SMARTBoard. They write their strategy out for others to show how they solved it.  While students show their strategy, and explain their thinking to their classmates…I start to see the lightbulb go on for those students that day who did not understand the problem.

2.  Allow the students in the “audience” to interact with the students who are modeling:

I allow the students who did not get to go up to the board to ask questions and give compliments using the math practice standards in their language.

Today was an awesome example of that happening! After they explained their thinking the students complimented the people at the board for not giving up, noticed how the young man underlined the question to the problem, asked how they knew to multiply instead of divide…it was just beautiful. The math dialogue flying around the room was amazing.  It gives confidence to the students in the spotlight, and clarifies the problem for the people at their desks.

3. Close the lesson by asking the students to rate themselves on their problem solving for the day:

As an example, I closed the lesson today by asking the students to rate themselves using Marzano’s Levels of Understanding. We hung up the math practice standard poster with a student’s sample paper.  We talked about how we can continue to use that standard every day, and as if on cue one student shouted “especially the part about not giving up!”  If anyone had a less than 3 rating, we talked about what we could try next time.

Seeing how far the students come from the first week of school to the end of the year is very motivating for us all!

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.

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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.

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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.

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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.

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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!

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Don’t Be Scared of Those Math Practice Standards!

Don't Be Scared of Those Math Practice Standards!

I will never forget my first reaction when I read through the Standards for Mathematical Practice.

Huh?

I think it took me another 5 reads to even scratch the surface of what they meant. The rest of the common core seemed like a piece of cake in comparison!

I really tried hard to understand them, but truth be told, I wasn’t sure how they fit in to my classroom. How were elementary students supposed to understand this stuff when I barely could?

As we began to implement the common core, I noticed my students struggling with the deeper problem solving concepts. I was so frustrated. I tried everything…I looked for strategies online to see if there was some kind of magic answer, I asked colleagues what they had tried and began to pull my hair out.

That was when it dawned on me…why don’t I try to incorporate the Standards for Mathematical Practice?  So I dug deep and did some research. One of my favorite things I found is from our friend Marilyn Burns (if you don’t know who this is, get to know her!). Her site is amazing, and the video series is really great.

All of the research allowed me to create a guide to introducing the standards for my students. I started with putting them into kid friendly I can statements. I added some sample problems and allowed the students to see each other’s work habits.

Voila! It was like a revolution was born. One of my students had the idea that we should post the standards on the wall, and get a point every time we had a question or gave a compliment with the language of the standard in our comment. Done! We had points like you wouldn’t believe by the end of the school year. (Incidentally the points counted toward absolutely nothing, they were just points for the sake of getting points!)

Intentionally putting the language of these math practices in our every day commentary did the trick. Students gained confidence, it was fun and best of all problem solving was no longer a stress in our classroom.

Winner! Winner! Winner!

Congratulations to 4th grade teacher Jen Jones on winning my Back to School contest. She chose the following products from my store for FREE!

Mini Golf Course Geometry
Housing Market Analysis
Open Ended Word Problems 

Thanks to all for the follows.  If you have a blog that you’d like me to feature or publicize, please contact me so we can all learn together!

Anchor Charts = Google for Kids

Anchor Charts = Google for Kids

If I were to count how many times I use my Smart Phone to look something up every day, it would be at least a dozen…maybe more! I use it to find out random facts, convert numbers, convert languages, remind myself of an interesting article I read 3 months ago…I could go on and on.

Anchor charts are truly “Google” for our students. I’ve seen it time and time again. The students are sitting at their desk, drawing out something for their latest project. When they can’t remember what an equilateral triangle is they simply look on the wall where the lesson they just learned about (but haven’t memorized yet) is hanging nicely there. Whenever I have massive amounts of students coming up to me to ask me what something is, it never fails, I’ve forgotten to hang the anchor chart.

So hang those anchor charts! Give them the tools they need so that they can use and remember these important concepts.

Their Formative Assessment = Your Anchor Chart

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One of my favorite practices that has really caught fire in education is the formative assessment.  I love it because I know that the “check” I am doing will help me figure out what to teach next, who knows the information and who needs help.  I’ve taken formative assessment a little further by allowing their handwriting, work and calculations to become our classroom anchor charts.

In this example, I introduced the students to different types of angles to prepare them for the Mini Golf Course Project.  It is one thing to be able to identify them, but a completely different skill is needed to draw them! As a morning message the following day, I asked them to draw me three types of angles: acute, right, and obtuse.  It was interesting to see who was most confident, they posted their note up immediately. Others were cautious and wanted to make sure they had it right first.  Then, there were those few who were completely baffled. On the spot I was able to guide their thinking, it took only 5 minutes as the rest of the students were getting ready for the day.  It was a neat way to slip in a quick intervention. As another review during morning meeting, we looked at how the figures were similar and different.

The best part was, these beautiful angles they drew became an anchor chart for the project! They were able to reference it during the entire project.  Their pride in seeing such a simple thing on the wall was simply priceless.

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:

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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.

What Math Project Work Should Look Like

What Math Project Work Should Look Like

You know students are learning when there is an abundance of glue, scissors, pencils, markers and writing about math at the table.

Sometimes it is okay to abandon the quiet, sometimes they learn more from each other.

Let it be a hot mess!

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.

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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!