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.