Reflection: Developing a Conceptual Understanding Fancy Flooring - Section 3: Exploration


Even though (I think) my students know that opposite sides of rectangle are congruent, they don't tend to use that information when calculating the missing side lengths in irregular shapes like the ones they encounter in this lesson. I am still surprised by my students inability to apply their prior knowledge in a problem like this one. Consider, for example, Austin's explanation of how to find the length of the kitchen.  how much easier would it be to understand if he had shown us the two lengths that are equal?

So, when we discuss the floorplan diagram I like to draw their attention to the relationships between the segments that make up the shapes. I want my students to learn to make better use of the structure of geometric objects in their problem solving. Today, I asked questions similar to these:  

  • What does one side of the room have to do with the other?
  • What measurements do we have? What measurements can we infer using the given measurements? 
  • What do you see in the diagram that makes you think that?

I found that these questions helped my students to activate their knowledge of rectangles.

Today, I also decided to use our classroom as an example. I said, "Think about our classroom. If we knew the length of this wall, what other measurements would we know?" 

I think some of my students probably do make the connection to their prior knowledge of rectangles. Some may hesitate to share elementary knowledge in middle school. I often remind my students that understanding someone else's thinking is a really hard thing to do. I say, "The simpler and more detailed your explanation, the more convinced others will be."

  Developing a Conceptual Understanding: Making use of structure
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Fancy Flooring

Unit 10: Exploring Area & Perimeter
Lesson 1 of 16

Objective: SWBAT use the area formula for rectangles to help them calculate missing side lengths.

Big Idea: Students need to apply prior knowledge of area formulas and the structure of a rectangle.

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5 teachers like this lesson
Math, Measurement, areas, perimeter (Determining Measurements), Geometry, area irregular shapes, real world applications
  54 minutes
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