Making Number Talks Happen

I mentioned in my post Does Automaticity = Timed Tests? that number talks are a great tool for building number sense.  Number talks can be used regularly to engage our students in mental math that puts the focus on developing efficient strategies.

In the past month, I've had the opportunity to facilitate number talks in a few different schools with teachers and with students using the visual cluster of dots shown to the right here.  I am excited to report that teachers have been having success using this strategy with their classes.  In this post, I'll share some general guidelines (nuts and bolts) for facilitating a number talk, and share one teacher's experience using them with her third grade class. 

Guidelines for Facilitating a Number Talk:

• Pick a skill focus - Are you working on making ten, repeated addition, the multiplicative inverse relationship, understand fractions as part to whole?
• Show students a math representation that targets the skill focus -  It could be a visual (like the cluster of dots above, a Cuisenaire model or a diagram) or a symbolic expression (like 13 or 5 - 3 = _ - 4 or 15 x 19). 
• Start out with independent, mental work - Set pencils and paper aside.  No call outs, raised hands, turn and talks, etc.  Tell your students that you are focusing on highlighting all the different ways to see the representation, and it's about stamina rather than speed.  Initially, your students may only have the stamina to do this for 15 seconds before becoming antsy.  You can focus on building up this independent focus time.  Celebrate progress.
• Have students record their ideas and collaborate informally - Have manipulatives, notebooks, pencils, paper, etc. handy and encourage students to express and record the ways they found to see the representation.  Have them share and explain informally to one another.  Then share out a variety with the whole class.  
• Share Out - Record and post the different ideas that come out.  Be sure to rely on a diverse range students for this.  Emphasize equivalence ("Can these ideas both represent the same number?  How do you know?").  Have students explain and restate others' strategies.  This may take some stamina building, too.  Recently, I saw a second grade class sustain this kind of sharing for 30 minutes, but you may find that your students have the attention for only two examples initially.  Track and celebrate improvements in stamina for sharing out.

A week ago, when I was facilitating a second grade number talk, Mary - who is a third grade teacher - was able to come and observe.  To my delight, she took off with the idea, and sent me all of the details...

The first day, she facilitated a number talk in much the same way she saw me do it: flashing this cluster of dots for two seconds, having students use Cuisenaire rods and paper to record the patterns they saw, then summarizing and recording the different patterns using diagrams and symbolic expressions.

Then, later in the week, one of her students (whose parents were willing to let us share this with you) came in with his own dot pattern...  

And Mary sent me pictures documenting their number talk with this explanation: 

He came up with the pattern with no input from me, and I was pleased that he did such an interesting pattern, and that he put dice patterns into it.  I showed it first for two seconds, gave them some time to draw what they saw, then showed it for another two seconds, gave them a little more time, and then posted it and asked them to build it, with no specific directions for how to build. We did something similar but much simpler yesterday.They went to town with their building!  I'm amazed at how quickly they have become very flexible with the building and how quickly they moved from building with ones to much more sophisticated representations.

Here are a few of the pictures that Mary sent me:

One student's view of the clusters.

Another student shows more than one way to see it.

A student translates the cluster from the concrete model to a pictorial and symbolic model.

Various interpretations recorded on the board.

This number talk took about 25 minutes.  Since Mary is teaching third grade, she is focusing on firming up her students' additive reasoning while pushing them to start seeing repeated addition as multiplication.  She notes:

We spent the rest of class today building ways to make 10 with two rods, and some kids got started with building 10 with three rods.  One of them realized that she couldn't use the 9 rod if she was using three rods.  Moving into using three rods will be interesting.  Some kids wanted to do this without building, but didn't get very far.   Of course they had a blast!

Thank you, Mary, for your sense of adventure and your willingness to document and share your experience!  If anyone else out there wants to share or has questions about how to use number talks to build number sense, please send me a note or comment below.