One of the most successful math discourse routines that I have used this year comes from Turrou, Kazemi, and Franke out of the University of Washington. It is called Choral Counting, but it is much more than a class counting out loud together. Students do chant and count together, but they discover patterns in numbers, understand the number system, identify why patterns occur and discuss with partners.
When I introduced this routine to my fourth graders early on in the school year, we started by counting by 9's as this is a skill most students have mastered. As we counted by 9's, I created an array of the numbers.
We paused after about three rows of counting by 9's and I asked my students. What do you notice? Do you see any patterns?
"I see that it increases by 45 when you go down a column!" cried one student.
"That's because there are five numbers is a row and they are each worth 9," replied another.
I asked the students to turn to a partner and chat. "What are you noticing and wondering?"
The class erupted into discourse. Students saw the ones digits decreasing across the rows, and the ones digit alternating as you move down a column. Some students noticed that if you add the numbers in the digits together, you get 9 again and again.
I circled the patterns with various colors as the students chatted and shared their mathematical thinking. This is differentiated because all students can notice something, but other students can take the learning deeper by discovering relationships and explaining why those relationships exist within this structure.
I have created graphic organizers to help me with these patterns. If you are interested in checking them out, you can click here: Choral Counting.
Below is a picture of me circling relationships for a first grade pattern. I did this under the document camera.
