Number Talks Modeled Multiple Ways: A Sure Fire Win!

    If you are ready to start using number talks in your secondary math classroom, it's time to start thinking about how you will represent different strategies as students describe them.  Personally, I like to use a variety of strategies including equations and visual models such as number lines and the area model.  I feel that seeing the connections between different models can be very powerful for student growth.  Here are a few reasons why I like using different representations of student strategies during number talks.

1. Help students see connections between their thinking and formal equations.  Using equations to model thinking from number talks helps students get used to seeing equations with many steps to represent their thought process....and what better preparation could there be for more advanced math?
2.  Help students see that things we learn in math class (like math properties) really are useful!  Numbers talks represented as equations are an excellent chance for students to see how much their thinking actually relies on mathematical properties.  As you use equations to represent thinking, time and time again you will find instances of the commutative, associative, substitution and distributive properties. How powerful for students to understand that they really are using these properties we keep talking about!
3.  Students get a confidence boost when they see their strategies represented as equations or visual models.  In reality, the strategies students use are based on understanding some very important math concepts.  Don't miss out on this chance to build student confidence by pointing out just how complex their thinking looks when you write it out with equations or a model....and to think that they did all that in their heads! This can really be a chance to build up our students and help them understand that they know more than they even realize.
4.  Use of models such as open number lines and area models can be great preparation for future algebraic learning.  Students use open number lines in algebra to graph inequalities and other types of equations.  As students learn about polynomials, area models can help students understand the process of factoring. Previous exposure to open number lines and area model will certainly help students learning these advanced concepts.
5.  Multiple representations help build an understanding of how strategies are related to each other.  Many times, students will use strategies that are mathematically related.  Visual models and equations can help students understand these connections.  For example, to solve 28 x 6, here are two strategies that students might use:
             Strategy 1:  28 x 6 = (20 + 8) x 6 = 20(6) + 8(6) = 120 + 48 = 168
             Strategy 2:  28 x 6 = (30 - 2) x 6 = 30(6) - 6(2) = 180 - 12 = 168

The connection between the strategies becomes clear with the use of the visual model and equations.

     With all of these great reasons to use number talks, what are you waiting for?  If you need some more information about number talks, check out these other blog posts.  Or grab these free number talk resources!  These number talks incorporate equations and visual models!