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Oh My! The Progression of Multiplication

Well, I’ve watched this video three times now and I think I need to watch it at least five more times. I love, love, love how this presented to the audience.

 

My take aways for when I am teaching multiplication:

  1. I need to stop stealing the opportunity to let my students use concrete tools! They should be available every SINGLE DAY.
  2. Rushing to the traditional algorithm is a huge mistake. I am thinking we need to have some serious conversations about when to introduce this.
  3. I need to let the students explore. Let me say that one again, I need to let the students EXPLORE. So many times when they hit a struggling point I feel this need to jump in and tell…I need a muzzle for my mouth!

What did you take away from this?

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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.

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A Project On The First Day Of School? You Aren’t Crazy

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When I began teaching 8 years ago, I would prepare a lesson/project almost as a scripted piece of art. I wanted to be sure that every student had the same exact directions, the same materials to start the exploration and the same set of worksheets and questions to fill in when it was all over. I thought it was great because it was hands on learning. Students were engaged because of the nature of the experiment, but usually as they worked they became noisy, bored and restless. They weren’t interested in filling in the answers on the papers, they often missed steps in the directions and things felt messy. It felt like “play time” more than making actual discoveries, and it was hard for me to manage. I struggled time and time again, using this same method while searching for a way to get them to stay engaged.

So on the first day of school three years ago, I thought I’d try something completely different. It started with a problem: design a model/prototype of a vehicle that is powered by wind. (This eventually evolved into a longer project!) The materials they could use sat in a pile on a table: paper, scissors, straws, tape, lifesavers and paperclips. I set a fan on the floor and explained that they could use this fan to test out their prototype as they worked. I told them that I would not give them any other directions. I asked them to begin when they were ready.

The results of this method were astounding. Once they got over the shock that their teacher was not going to tell them what to do, they got serious. There were a few questions about how much of the material they could use, but then they set off to work. For a few minutes, the room was almost completely silent as they picked up their materials. Their little third grade brains were thinking, planning and wondering. I couldn’t believe the different types of things they were trying. There were 3 wheel bicycle models, sails going up, huge cars, small cars, students drawing sketches and then cutting, students testing and re-testing and testing even more. All of the talk in the room was centered around their designs. Even a few students took their materials and headed to a corner so that no one else could see their prototype. The floor by the fan became a busy place and students were giving one another suggestions to make their models better. Phrases like “It’s too heavy!” or “My sail is too small, it’s not catching the wind.” were followed by an excited run back to their work space to try it again. Mistakes were made and corrected.

The most amazing part to me, was that it was my first day of school. There were no procedures in place, no expectations laid out for how we should work on these types of activities. They were excited to learn, eager to try and left the room at the end of the day still talking about it. The next morning we wrote about the activity and they were eager to share their discoveries. As I’ve embraced projects more in recent years, I’ve found ways to structure the learning that still gives them free choice. I use a variety of formative assessments to be sure their learning is on track, and there is always accountability!

The best part is that learning finally felt right, authentic and exciting. It was a great way to start our school year.

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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.

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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.

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Problem Solving Boredom: Motivate Them With Real Life FUN

Problem Solving Boredom: Motivate Them with Real Life FUN

Third graders are so wonderfully and naturally creative. One day we were working through yet another problem of the day from our textbook (I could see the life from recess draining from their faces), and I just couldn’t take it anymore. I felt as though the problem was sucking the creativity right out of the room.

It was mid winter, which if you live in the northern half of the US or Canada, you know how loooonnnngg that feels. The students were restless and bored with problem solving. I needed to think of something, and of course, with student help I did.

I addressed the winter blahs right then and there. What would help us get out of this funk? We started to think of things that are fun. The first thing on the list? A party.

Of course a party would help!

That is when it clicked. Party planning is a very complex task, but requires basic math. This makes it a perfect problem for third graders to solve.

That was what started the Party Planning Awesomeness project.

First, we needed a budget. The students were so excited about the fact that we were having a party that everyone brought in a dollar. The budget was locked in at $25.

I spent a few days giving structured mini lessons (brainstorming, adding decimals, deciphering grocery store flyers) during our problem solving time. After that I turned them loose. I was floored by the thinking that happened. Here were some of the amazing things they planned:

  • They made sacrifices. One student skipped the paper plates for a few more Capri Sun pouches. “Who needs paper plates anyway? What a waste!”
  • They planned to save money on decorations by hanging student artwork in the room.
  • They wanted to play great music from their own iPods (as long as it was clean).
  • They planned great games and activities, even scheduling them down to the minute so that it didn’t go over the allotted party time.

Every student in the classroom had a plan, glued and colored up a piece of construction paper to communicate that plan…and we all voted on the best one. The best one turned into an actual party.

Giving them the chance to solve problems and think through complex life situations, all while having the motivation of a party was exactly what they needed.

And…don’t tell them, but it was fun for me, too!

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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.