This whole “*how** to teach math without numerals” *kick I’m on is blowing my mind. I tried this out in a 3rd grade class using one of my favorite problems. Here’s how two students solved this problem and what’s awesome about it is that they used completely different strategies and manipulatives! What a way to end the week!!!

If you have no idea what I’m talking about you might want to read a previous post http://wp.me/p2ESf1-35. What I found is that by removing numerals and “forcing” students to model with only manipulatives, it really gave them the opportunity to develop and verbalize their thinking. Without the use of numerals, the manipulatives helped students through their thought process when sharing their solution strategy!

Here’s the problem… but solve it without using numerals before checking the links:

*In total, there were 48 kindergarteners AND first graders in the cafeteria. The kindergarteners left and 26 second graders came in. Now there are 54 students in the cafeteria. How many kindergarteners were in the cafeteria? How many first graders are in the cafeteria?*

Two student solutions for the Cafeteria Problem:

1^{st} Lesson-Click here to view lesson 2^{nd} Lesson-Click here to view lesson

I saw something I never knew existed or was a “*look-for*” so I wanted to share. You probably already “*look for*” this so thanks for your patience on this one…

A lot of times when questioning a student about their solution strategy I have to repeatedly ask for clarification with the numerals on their paper: *what does this number mean? Where did this number come from? So explain what you did here. *Basically, I am continually having to connect the numbers back to the context. So here’s the kicker, when students explained their solution to me, while reenacting through the manipulatives, they used numbers in the context of the story and explained their solution strategies with minimal questioning from me. I absolutely love the fact that quantities were tied to units when explaining! Such great stuff!

As a side note…I found that I needed to be more creative in how I captured the student’s thinking. For these lesson I used educreations app for ipad and it’s FREE!!!! http://www.educreations.com/. It was like a mathematical storyboard and worked out better than I had envisioned. I asked students to take a picture each time they manipulated their tool and they went back and recorded their voice while flipping through the solution. I know numerals were used in the question of the task and that was done purposefully so that students would understand the quantities they were working with.

I’d like to get your thoughts and feedback on this idea or better yet…if you teach a lesson without using numerals and write it up, I would love to read and share your experience with others!

I am very interested in the lessons without numbers. I like the way you have presented the kids with a way to solve, record and be aware of how they are solving. I will be in a geom classroom next week with spec ed students. I think they would benefit from this- I look forward to more posts, and will share my exp as soon as poss, too!

AWESOME! Can’t wait to hear about it! I think I’m going to dive into a 5th grade classroom and try it with decimals. So it should be interesting…but I’m excited!

I agree with Cleargrace and I don’t think you answered the main question buddy…we need details on what the students did from the beginning when you gave them the problem without numbers.

I like to use lots of visuals in maths too, I taught a grade 5/6 class a fraction unit, and for the first three weeks all “calculations” were done with a fraction kit, equivelant, adding, subtracting, multiplying, simplifying etc. I didn’t let them write anything…while they got a little antsy thinking they were doing “baby” work, when I got to showing them the equations they had such great visual knowledge of what was actually happening they really understood the equation, not just rote learning of a formula. It was really fantastic, and taught me to make sure I work visually as well as with the equations.