Reflection: Developing a Conceptual Understanding Multiplication Models and Structure - Section 4: Let's Draw Together

 

When students use this type of mental model, they begin to develop a conceptual understanding of multiplication and equal groups. These models give a specific representation for groups, the quantities in each group, and the product.  Also, because this model is so different from any addition model, it helps students from confusing multiplication with addition.  

As factors change positions in a multiplication sentence, this mental model also changes and those changes "make sense".  The more students work with "thinking" models, the more practice they will have in analyzing the model rather than focusing on the product.  They realize all of the information of a multiplication and/or division sentence is represented in this type of model.    

I feel it is important to provide students with many different opportunities to draw out models, particularly to represent different missing factors.  The missing factors are represented in a way that my young 3rd grade students can reason through, as it partially abstract but concrete enough in its representation of the numbers being manipulated. This type of practice will reveal if they understand the concept of multiplication or if they have only memorized products.   

  Conceptual Understanding
  Developing a Conceptual Understanding: Conceptual Understanding
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Multiplication Models and Structure

Unit 1: Multiplication
Lesson 2 of 6

Objective: SWBAT solve for unknown variables using the structure of a multiplication sentence of groups x items in a group = whole amount.

Big Idea: Multiplication sentence structure using models to solve for unknown variables in multiplication.

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Subject(s):
Math, multiplication
  70 minutes
flowers for equal groups
 
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