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?


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.


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.

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


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.

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.

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!

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!

Worksheets Aren’t ALL Bad: 5 Tips for Improving Their Practice

Let’s face it, we can’t all do projects 100% of the time, and we shouldn’t do them 100% of the time. Sometimes there is basic skill acquisition needed so that students can do a better job with project work. Worksheets have gotten a bad rap as of late, but I don’t believe they are all evil.  The way worksheets are used will determine if students will learn at the highest level.

Here are a few problems with worksheets in math (ahem…all of which I did at the beginning of my teaching career…ahem), and some possible solutions:

imgresProblem: Every student gets the same one, despite the fact that the sheet is too easy for some, and too hard for others.

Differentiation isn’t a buzz word, or a new thing coming to education. It is the BEST thing. We all know it, we all know how hard it is, and we all feel guilty if we can’t quite figure out how to do it for every lesson.

imgres-1Solution:  It will take some pre-planning, but you could write 2 to 3 problems on your Smartboard or easel for advanced students? For example: Perhaps your learning target asks students to compare numbers to the tens place. The worksheet may be full of what “on level” students should be able to do. They might be asked to order numbers like: 34; 54; 35 on the worksheet that came with the book.

A few problems for that challenge group could look like this:

Order the numbers:

1,000; 1,001; 1,100; 1010      or      3.54; 3.45; 3.544


Problem: The worksheets have 30 problems or more.  

Think about something that is really easy for you to do. Maybe it is adding numbers like 113 + 21.  Now, imagine if someone asked you to add those same types of numbers 30 times. (Boring right? Are you learning at the highest level?) If it is too easy for you, there is no reason why you should have to do it 30 times.

Now, if someone asked you to do a problem that was so hard for you, one that you don’t have the skills for, should you do it 30 times as well?  When you ask students who are struggling to do something 30 times, they might be cementing the wrong way to do it in their mind, making it harder to intervene when you need to.

Sometimes people worry that if they don’t give students 30 problems, it won’t sink in, and they won’t have enough practice.  That is what a daily math review is for. You can also embed those same skills into problem solving and other parts of your day. Maybe there is a morning message where you ask them to perform that skill once again.  It is our job as the teacher to continually bring those skills back.

imgres-1Solution: Alter the worksheet by cutting it in half.  You could also ask students to only do even or odd numbers. The pro to this, is that it’s so much easier on you in terms of teacher time.  You aren’t having to correct a student’s thinking who did it wrong 30 times, you don’t have to correct 900 problems (if you have a class of 30 students), and you can spend that valuable time pulling small groups over to re-teach or enrich.

imgresProblem: You correct the worksheet and hand it back at the end of the week.

There are two parts to this problem. First, if you correct it and put in the right answers, who is doing the learning? The student will have no motivation to learn if we put the answers for them.  Second, if you wait to hand it back a day, 2 days or even 3 or more…the true thinking that needed to be done on the spot is gone.

imgres-1Solution:  Correct those sheets as you walk around, as the students are working. Catch the errors immediately and re-teach.  Consider pulling back small groups of students to have them correct their own work and find their mistakes. Allow them to look at their own work and do an error analysis, as learning from our mistakes is very powerful.  If correcting on the spot cannot be done, consider returning the worksheet the next day and going over tricky problems as part of your daily review.

imgresProblem: Worksheets are graded, or add up in some way to count toward a grade.

I know right now that if someone told me that I had to learn how to carve wood, and that each day I’d be getting a grade on how I’m doing, I’d fail miserably at the start.  I’ve never carved anything out of wood in my life! Should how I perform at the start, before I have any experience or a chance to practice be the reason why I get a lower grade? Instead, I’d rather have the chance to practice wood carving, hone my skills, and show off my thinking at a certain point in time.

imgres-1Solution: Use worksheets as formative assessments. Form small groups based on what students need and what you see.  Talk to your co-workers and set up dates where you think students should have mastered a certain skill. Test on those days to see if they have reached the benchmark.  We MUST give them a chance to practice.  The parents in my third grade classroom LOVED it when I made the switch.


Problem: Worksheets are the only way students show their learning, every day.

Plain and simple, using only worksheets every day is just bad teaching. I don’t think many of us are still using worksheets exclusively. I know that growing up, that was what we did, and for some teachers it’s all we know.

imgres-1Solution: Beg for some professional development.  Along with worksheets introduce projects, problem solving, daily math reviews, mental math, games, flashcards, number lines, online activities and manipulatives. Blend them together and give the students a chance to learn the concepts in a variety of ways.

If you haven’t tried these tips, introduce yourself to them gently. You will notice a big change in how students learn.  If you have other tips, please feel free to comment below. I am always looking for ways to make things better, and we can all benefit from each other’s thinking!

Let Them Struggle: Raise The Bar In Elementary Mathematics

After reading this article, I was inspired to continue re-thinking how I teach math in the elementary classroom.  If you don’t have a minute to read the article, it explains that there is a healthy amount of frustration that is productive in mathematics instruction.

I absolutely love that idea. Last year when I did the Mini Golf Course Project during geometry, I saw a very healthy amount of struggling happening (though the students didn’t know it!). In this project, students designed mini golf course holes using specific geometric terminology that was introduced in earlier lessons. I knew I had to do something to connect those obscure words to something. After the first day students were so impulsive to hand in their sketches. After checking through all of the designs, only TWO students had approved sketches. I went back to the Standards for Mathematical Practice once again.

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

Where was their perseverance? When I handed back sketches that weren’t approved I got a few sassy comments like “Do we HAVE to do this?” and “This is too hard for me!”.  We sat down as a class and discussed why only 2 students in the whole class had approved designs.

After calming down, we came up with a list together:

  • We aren’t used to thinking this hard about things!
  • I’ve never done anything like this before.
  • I didn’t do very careful work.
  • I rushed to get it done because I knew money was involved.
  • I thought you would correct the parts that were wrong for me.
  • I am still not sure of what some of the terms are.


We realized that every single one of their problems on the list were things that they could solve.  We talked about how frustrating it felt to get their design back, with no corrections and without approval.  By validating their frustration, I was letting them know that I KNEW they were working hard, they just had a bit more to go. We talked about how to solve each of those problems on the list we had just made.

By the time the project was over and everyone was getting their payout, the students claimed that it was their favorite project of the year.  The frustration eventually changed to pride as they cut, glued and designed their little masterpieces. The frustration was worth it.

I need to remember how that frustration changed, because every project I do will likely have that moment.  Helping them work through that feeling is the key to their success!