Reflection: Developing a Conceptual Understanding To Change or Not to Change - Section 2: Exploration

 

Today I observed that the Algebra Tiles helped my students to better understand the meaning of the coefficient of a variable. One mistake that my students sometimes make when substituting a value into a variable term is to not multiply by the coefficient. If x=5, for example they sometimes say that 2x = 25. 

I found that asking them how many of each type of tile are represented in the expressions was helpful. After they built and wrote the simplified expression, I asked them:

  • How many x-squared's do you have?
  • Where do you see that in the tiles?
  • Where do you see that in the simplified expression?
  • Where do you see that in the original (unsimplified) expression?

These questions helped my students see that combining like terms was like counting and that the coefficient represents how many of each type of term exist or 'how many times' we counted it.

Several of my students were still confused about how to calculate exponents. Some were struggling with the different between x^2 and 2x, for example. Because of this I like to avoid choosing 1 and 2 as values to substitute for for variables at this stage of the unit.

  Combining as counting
  Developing a Conceptual Understanding: Combining as counting
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To Change or Not to Change

Unit 3: Equivalent Expressions
Lesson 7 of 23

Objective: SWBAT distinguish constant from variable terms and combine like terms using algebra tiles.

Big Idea: Students learn that constant terms do not depend on the value of variables.

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Subject(s):
Math, Expressions (Algebra), distributive property, like terms, algebra tile
  54 minutes
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