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:
- How much money did it take to build this?
- Why did someone want to build it?
- What is the diameter of this?
- What is the circumference?
- If you could divide the wheel into parts, how many parts could you divide it into?
- What is the environmental impact of the Ferris wheel on the neighbouring area? (they just came from science)
- what is the total cost to ride?
- How much money have they made since it opened?
- What is the distance between the mountain and the wheel?
- 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.
- How many humans equal 175?
- How many V(student name) would be 175ft?
- How much more can the wheel expand till it reaches its maximum tipping point?
- Who would want to build a 175 ft Ferris wheel?
- 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:
- How tall is the Mammoth?
- 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.
7 thoughts on “Numberless Word Problems”
Awesome! Thank you so much for writing this up. I think you did a beautiful job of starting by letting each and every student access the situation however they wanted. They probably thought much more about ferris wheels from that discussion than if they had just been given a word problem to start. The beautiful pictured helped, I’m sure. I especially liked seeing how their noticings and wonderings shifted over the course of the reveals to the point that they were right in line with the type of thinking you’d like to see while solving the problem. By the way, how did it go when they finally had a question to answer? I definitely look forward to reading about future trials of numberless word problems. It’s always great to get perspectives from other teachers using them. Thank you again!
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Brian, thank you for your kind words. I loved the way that they students have started to understand how questions are posed. Their strategies where spot on division and multiplication. Just finished the problem today (I only see them one period everday). I want to throw these questions in more often. I will post their answers tomorrow when we debrief. Thanks again for all of the information.
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I like your energy in your articles and your passion for teaching math “not MATH way” is always evident. As an educator I feel Canada is not ready for open ended and creative math as boards are so much fixated on a certain pattern or way math has to be taught. I hope we have more teachers like you who can ignite math love in all the children equally and no one has to hear “Math is not your strong subject”.
Thank you for your comment. I do love math and think that it is one of the best topics to teach. I think math teaching is more about a balance. We don’t always do a numberless word problem but they are great for talking to students about how problems are made, as well as, what to look for in a problem. I find it interesting that you think Canada is not ready for open-ended and creative math. Can you explain more why you think this? Math teaching has changed a lot and I know our board has done a lot to bring this about. Just wondering what your thoughts on this was. Thanks again for the comment.
Thank you Jon for bringing up this conversation about teaching creative math or for that matter any other subject.Correct me if I misunderstood Canadian education system. This education system though is one of the best in the world (if you search rankings of top education systems of the world), is too Academic. If you look around yourself , how many creative spaces does a school have to kindle the creativity in children? Most of the play areas have old swings or probably couple of play structures. I am yet to see a very well designed play ground or an area in a school which gives children opportunities to spark their imagination. Secondly,as a teacher how many times do you integrate a core subject with Arts or Drama? How many times do you take your Junior grade out of the classroom for learning(excluding field trips)? Creativity has to be integrated with everyday learning for it to grow and not treated as a separate entity .I have tried to explain my observations though this discussion cannot be summed up in few lines.
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Meera you are very correct in your observations but at the same time I have faith that there are more then you think. I know there are more spaces in Peel who teach like I do. Arts and drama is integrated in a lot of areas (though I will admit there needs to be more). If you get a chance follow #enviroed and you will see a lot of teachers taking students outside. I know in Vancouver there are forest schools and even in ontario they have attempted this. I take my students outside whenever I can but -22 to -40 does stop many teachers as out kids do not have adequate clothing. That being said creativity is a must in today’s classroom and needs to be honoured more. What would you recommend to help facilitate this learning more? Thanks for the comments