Reflection: Developing a Conceptual Understanding Farmer John and Farmer Fred Day 2 of 2 - Section 3: Generalizing Patterns


The most valuable insights resulted from students continuing to draw a visual representation of what the fields might look like in each case. I would definitely suggest in subsequent teachings of this lessons that they draw to show what the fields referenced in the table would actually look like and spend more time on this. Their drawings really helped my students make more sense of the patterns in the math, especially when we came to the variable represention. It was much easier with the drawings to discuss what "n" represents or that "2n" represents the area of John's field and that "3n" represented the combined area. It also helped students see that n+n+n = 2n + n = 3n. 

The visual models, by providing something observable, helped students notice patterns visually. This was particularly helpful in illustrating and making sense of the numerical patterns in the table & expressions. A really important discussion popped up around one student's question that helped strengthen some knowledge gaps. One student, refering to the diagrams, pointed out that "two of Fred's fields always fit in John's field" and another student, who hadn't noticed that, asked if that would always be true. He proceeded to fill a page with possiblilities and I was able to ask the class why that made sense that it would always be true. 

I did a quick "number talk" to support this intervention that focused on math fact halves in which we did the following problem string: 7x10; 7x5 (half of 7x10); 12x10; 12x5 (half of 12x10). When a kid asked if it would work for numbers other then 5 and 10 I asked the math "family" groups to discuss it for 2 minutes then we tried it: 7x6; 7x3; 3x8; 3x4.

I followed up the next morning by asking students to draw, write, or show why it makes sense that this pattern happens. 

  Developing a Conceptual Understanding: Using visual representations to aid in sense making
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Farmer John and Farmer Fred Day 2 of 2

Unit 3: Equivalent Expressions
Lesson 2 of 23

Objective: SWBAT create diagrams of different rectangular fields with a given area.

Big Idea: Students will use factoring to discover possible dimensions for a given rectangular area and also become familiar with the area model to use in distributive property.

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Math, Factoring (Number Sense), Expressions (Algebra), distributive property, area of rectangle
  54 minutes
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