Numberless Word Problems

So I first heard this while I was a guest on Derek Rhodenizer‘s Podcast. during the podcast he mentioned this idea about Numberless Word Problems, you can read about them here.  The idea is basically, to guide and scaffold students through the structure of problems by making them ask and rethinking questions.

Now this was my first attempt but I am going to attempt to share my thinking.

My goal was to get students to think about division. My students have already had practice at division but struggle to use their facts and thinking in a word problem. They just don’t seem to understand what to do or be flexible in their thinking. This is why I thought numberless problems would be amazing idea to try.

As the students came into the classroom I had this picture showing up on the screen.



Right away I had kids oohing and awing. One of the kids shouted out that is Niagara Falls! I figured I picked a good picture.

I then asked them What questions do you have? Do you wonder about anything?

This brought on an onslaught of questions:

  1. How much money did it take to build this?
  2. Why did someone want to build it?
  3. What is the diameter of this?
  4. What is the circumference?
  5. If you could divide the wheel into parts, how many parts could you divide it into?
  6. What is the environmental impact of the Ferris wheel on the neighbouring area? (they just came from science)
  7. what is the total cost to ride?
  8. How much money have they made since it opened?
  9. What is the distance between the mountain and the wheel?
  10. How many Mammoths tall is this? (Loved that question cause it was what I was going for)

I then told them a little more information: The Ferris Wheel is 175ft Tall ( I know I am Canadian but I needed the numbers to match Grade 5. They do 3 digits by 1 digit division so I couldn’t use 53m).

I then asked them does this change any of your questions or do you have any new ones?

Again this brought on an onslaught of hands.

  1. How many humans equal 175?
  2. How many V(student name) would be 175ft?
  3. How much more can the wheel expand till it reaches its maximum tipping point?
  4. Who would want to build a 175 ft Ferris wheel?
  5. If _(insert object)___ is (blank feet), how many of them fit inside 175ft?

I then added: The Ferris Wheel is 175ft tall and the Mammoth still looks kind of small.

Once again (I think you see the pattern) I asked what changes in your questions.

This time they all focused on the Mammoth and came up with two questions:

  1. How tall is the Mammoth?
  2. How many are needed to reach 175ft tall?

Which prompted me to ask them the real question:

The Niagara Falls Ferris Wheel is 175ft tall. The Mammoth’s look pretty small next to it. In fact, the Wheel is 9 times larger than the Mammoth. How tall would the Mammoth be?

What I really like about this approach is that it allowed my highly ELL (English as a Second Language) group to begin to understand how word problems are constructed. It also had them wondering about mathematics and seeing the world through a whole new lens. I am currently reading Jo Boaler’s book “Mathematical Mindsets.”  In the book, she mentions that many of our “math” problems stem from our children seeing math as a set of rules and the right answer. They don’t see the beauty in mathematics. Doing these “numberless” word problems allows the students to wonder, and think about mathematics. I know this post doesn’t do the justice and thinking that Brian has in his posts but I will post more as I go through them. If you have any advice or suggests please let me know or if you have any more ideas I would also love to hear from you.

What Should be Driving our Teaching?

20160803_082912I am not too sure if this title does my thoughts any justice but I hope at the very least it does touch on the topic.

I was recently watching a small clip about schools in Finland. I know Finnish schools have been all over the news for the last couple of years but this clip caught my attention.

Now I know Finland is small in demographics, they are largely Caucasian and they, for the most part, speak one common language (ELL not really a factor). However, as impressive as their scores are it was what the clip said that has always got me thinking.

We try to teach them to be Happy people, respect others and themselves.

I could not agree with this statement more. I fear that we have eliminated the human element out of education. Now please do not get me wrong I think there are many great teachers out there who really strive for this and I think we are getting better but as a whole, I don’t know if we do a could enough job, myself included.

For the last two years, I have really started to focus on my students as people (again not that I wasn’t before) but really trying to get to know them, who they are, what they like and help them grow as people first, students second. It’s interesting talking to them about their past experiences. But when I ask them what makes a bad teacher they tell me, when they fake listen to you, or play favorites, or don’t make learning fun.

I want to share a story with you. At the beginning of the year, I was talking with one of my new students, who I was told was a behavior, he told me in a quiet conversation that we had.

S:”You know what Mr.So?”


S:” Last year my teachers thought I was really annoying. They hated me!”

M:”Well I don’t hate you but I won’t lie, I do at times find your actions annoying.”

S:”yeah, I can be annoying sometimes” and we had a good laugh at that. But what was scary was his perception of himself and how he felt his teachers thought of him. 5 years of feeling annoying most likely mean you will just be that.

I see it with my own daughter who in JK decided that she hated school because the teacher didn’t like her. She told me that the reason why she acted out was that all the bad girls got friends. I asked her why she thought this and her answer was well the bad girls in the class do the same thing and never get in trouble and all the kids gather around them. What she failed to notice is how those girls got friends to stay or that they may have been talked to by the teacher.

Now I know this is student perspective and I am sure that we as teachers do not purposefully go out and do these things, this is not why we got into education but I also know and hear the stories. We all have had those frustrating days. We are all human and get annoyed at behavior and kids but it does have an impact on their learning and how they perceive school.  The problem lies in the perception that students have of themselves and how long that perception stays with them. The more that they hear you a problem the more they just say, “it’s easier to be one”.

Last year I focused on Collaborative Problem Solving by Dr. Green Ross. I have blogged about this before but basically, it was bringing the students together to discuss problems and situations as a class. I found this dramatically helped. One thing that I took from his book was there is no bad child. I know this may make many of you question the statement but I will say that ALL CHILDREN want to be good. Some may need more teaching than others.

Thanks to my good friend Pete Cameron and an amazing speaker Angela Maiers, I started a #Choose2matter board this year. The board started off with students feelings about themselves. I wanted them to be able to look at it when they felt down and think about a positive thought.


Updated Pic:


This board is now filled with compliments cards from the students to each other. I don’t have to ask them to add to the wall they just go ahead and do it.

I have also been reading about self-regulation and how students who may be deemed behavior really are just overstimulated or need help to regulate their behavior. Learning about Self-regulation has allowed me to see students stressors and remove them or calm them down before they happen. It also has allowed me to stay calm and not stress as much with those same kids.

I don’t have quantitative proof with my class but just hearing the comments from my fellow colleagues and principal about my students have made me see the benefits of what I am doing. They tell me that they have really grown up and matured. There doesn’t seem to be as much behavior from your class this year as last.

I really believe that focusing on students as humans and teaching them how to be kids, role models and believe in themselves is the key to changing our education system.

Now I know this is not a new concept that I am preaching and I know that we all want our students to be successful but reflect for a moment on a couple of things:

  1. How do you interact with your students?
  2. Do you listen to them?
  3. Would you feel comfortable with them evaluating you?
  4. Would you feel comfortable with them telling you how they want to learn and what they want to learn?

It’s not an easy transition or an easy path. As a teacher, I have had to give up control and let go of that “Oh I could have used that 40 minutes to cover curriculum” feeling. It is also not an instant success. It’s not some magical cure but it does and will work. Building trust and community takes time. Yes, students still get on my nerves and yes I still lose my cool and go five steps back but the difference is that the relationships I have built with my students allow me to make a mistake. They know that if I goof and yell or break a relationship it was a mistake and that I flipped my lid.

Now I know this may seem like more of a parenting subject than teaching but I will end with this thought.

Do unhappy children learn?

Love to hear from you.