Reflection: Diverse Entry Points Commutative - Concrete Representations - Section 1: Introduction


I think it's very important for 8 and 9 year old children to have plentiful opportunities to manipulate concrete objects while reasoning their way to an understanding of an abstract concept such as the commutative property.  (When I think back on my own experience with math in school, I think I would have been happy to have had more experiences with models and manipulatives even in middle school and high school!)  I suspect that for visual learners and kinesthetic learners, this isn't a strategy that we grow out of.  

Mathematical Practice 4, Model with Mathematics, speaks to the importance of supporting students in developing their mathematical thinking by using representations, including drawing and using objects. I'm excited that in the Common Core there is more room to address different learning styles instead of the previous exclusive focus on standard algorithms and abstract pencil paper reasoning.  

Some students immediately see the connection between the commutative property of addition and the commutative property of multiplication.  For others, this is something that has to be seen, felt and experienced many times before they believe it.  That's okay!  This activity provides an opportunity for the learners who need to see it and feel it to have that time, and in my experience those children who have a more ready grasp of the commutative principle still benefit from and enjoy the process of making the models.  It's good for them to have fun with math, and a comment I frequently hear when they are building different models, is, "This is fun!"

Meaningful fun cements learning in a more powerful way than something dogmatic and forced ever will! Isn't it great that we now have the support to go deeper in our mathematical explorations with our students?!  

Observing students in focused exploratory settings such as the one in this lesson gives me valuable anecdotal evidence that I can use to communicate with both families and the child about strengths and weaknesses, and notes from situations like this lesson also consistently give me relevant information about how to differentiate for both individual children and the group personality.  We all know how different some groups/cohorts can be from the previous years' students, and it's essential that we readjust accordingly.  

  Commutative Property of Multiplication- The Importance of Models
  Diverse Entry Points: Commutative Property of Multiplication- The Importance of Models
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Commutative - Concrete Representations

Unit 3: Multiplication
Lesson 7 of 11

Objective: SWBAT make a concrete model (with manipulatives) of a pair of math facts to demonstrate and explain the commutative property. REVISED 9/29/15

Big Idea: Students are able to illustrate the commutative property and articulate the differences and similarities between two models demonstrating the same pair of facts.

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