Reflection: Diverse Entry Points Garden Border Sub Plan - Section 2: Warm up


This lesson is just screaming for manipulatives! I don't know why manipulatives are an after thought for so many of us secondary teachers, because they really help provide multiple entry points and a concrete springboard for discussion. The warm up provides an intriguing question that both kids and adults want to explore. Square tiles would make it so much more concrete and clear and I think I would ask students to build the two girls' rooms along with the original question.

Karla says that her room has a larger area than Nathalie's. Nathalie says that her room has a larger perimeter. What might both their rooms look like if they are both right? or Could they both be right?

Once the manipulatives are used to build the models they can be used to help students differentiate area from perimeter and focus on the mathematical structure (MP7) by answering questions like:

  • What part of the tiles represent the area?
  • What part of the tiles represent the perimeter? (just the outside edge)
  • Can you draw a diagram to show how the tiles represent the area?
  • Can you draw a diagram to show how the tiles represent the perimeter?

Sharing different student diagrams would be a good followup that might have helped my student notice more generalized structural patterns:

  • What patterns do you notice about the shapes of Karla and Nathalie's rooms?
  • What if both girls had the same area, could Nathalie's still have a larger perimeter?
  • If Karla's room has [a given area] what might Nathalie's room look like?

I would expect my students to notice that Karla's room is more like a cube and Nathalie's is longer and skinnier and I would ask them to explore why that pattern makes sense? or why it would be true?

If I were to give this lesson to a sub again, I would be more explicit with my intentions to let my students discover and that I didn't want them to be told what to do. I would be very clear that I want the sub to offer manipulatives and ask questions only. I also would let them know that respoding to questions with "I don't know, how could you use the tiles to help you  figure that out?" is perfectly acceptable. I struggle with whether or not to explain the math to a sub for fear that he/she might spill the beans. However, I also want my sub to feel comfortable with the content. 

  Diverse Entry Points: Manipulatives!
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Garden Border Sub Plan

Unit 10: Exploring Area & Perimeter
Lesson 4 of 16

Objective: SWBAT use a diagram to solve the border problem and write an expression relating it to the perimeter.

Big Idea: Students extend their knowledge of perimeter to a related scenario.

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1 teacher likes this lesson
Math, modeling, Geometry, areas, perimeter (Determining Measurements), perimeter, area, border problem, sub pl
  54 minutes
border problem solution model 1
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