## Reflection: Developing a Conceptual Understanding Area and the Distributive Property - Section 5: Closure and Ticket to Go

I collected the tickets to go to see what students understood about perimeter, area, and the distributive property and what gaps in understanding they had.  While correcting them, I came across a few mistakes multiple times.

Multiplying only first value:

This student was able to determine the area of the first figure (24), but for the second figure labeled the area as x rather than 4x.  This is a common mistake thinking that 4(6 + x) is equivalent to 24 + x.  This students needs to have more practice using the algebra tiles.  This way she can see that when you multiply the quantity (6 + x) four times, you end up with 24 unit blocks and four x blocks.

Area as a Product:

This student was able to correctly identify the missing dimensions of the rectangle as 5 and 4x.  When he wrote the area as a product, he wrote 3(15 + 12x) rather than 3(5 + 4x).  My next question is to ask the student how he can represent the length of the longer side.  He needs to see the connection between writing the area as a product and a sum.

4^2 and 4+4:

This student was able to correctly create a perimeter expression of 4 + 4 + x + x.  She created another expression, 4^2 +x^2, that was not equivalent.  She needs more practice on the meaning of exponents and how to represent repeated addition and repeated multiplication.  I want her to see that 4 + 4 = 2 x 4 = 8, and that 4^2 = 4 x 4 = 16.  Once she understands this, she can apply this knowledge to variables like x.

Unit 6.17 4x and 4^x:

This student was able to correctly identify the missing dimensions of the rectangle as well as the area.  The one small mistake that she made was to represent the area in the diagram as 4^x.  I want her to realize that 4x and 4^x represent different quantities and to make sure she carefully labels her work.

I will pass back tickets to go to students during the next lesson.  I will bring up these common mistakes and ask students to talk through them.  I will push students to use the algebra tiles to support their thinking and help continue to work on developing a conceptual understanding of the algebraic expressions and the distributive property.

Developing a Conceptual Understanding: Common Struggles

# Area and the Distributive Property

Unit 6: Expressions, Equations, & Inequalities
Lesson 17 of 20

## Big Idea: The area of a rectangle is x^2 + 10x. How can you represent this area as a product? Students apply their knowledge of area and the distributive property to expand and factor algebraic expressions.

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Standards:
Subject(s):
Math, Algebra, equivalent algebraic expressions, Expressions (Algebra), distributive property, 6th grade, area, master teacher project, factoring algebraic expressions
50 minutes

### Andrea Palmer

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