Reflection: Developing a Conceptual Understanding Checkerboard Squares Day 1 of 6 - Section 2: Exploration


Most of my students do not really understand what area means or represents. If they have learned to memorize what procedure to carry out for area and perimeter problems I have found that their learning is very fragile. Those who don't understand the concept or definition of what area is will not understand why the formula works and, subsequently remember it or apply it incorrectly. Students often come with the misconception that area IS multiplication.

This lesson helps provide a conceptual rationale for how the area formula connects to addition, because we are adding up multiple rows of the same number. The checkerboard makes it really easy to see, so I can point out that we have 8 squares in the bottom row and another 8 stacked on top of them, etc. in order to see that we have 8 squares eight times. 

Although this lesson seems like a really simple one, it provides so many opportunities for extension. But I also really like it because it helps provide intervention for so many of my students that didn't understand where the area formula comes from. I think it is important to meet students at their level of understanding. My students know there is a formula for calculating area, but they don't know what the numbers represent or why the formula works.

When I asked how many of the smallest squares on the checkerboard most of them added the 8 rows of 8 and didn't think of multiplying. This was fine, because it helped them connect meaning to the formula and helped them understand why multiplying works.

  Meaning vs. memory
  Developing a Conceptual Understanding: Meaning vs. memory
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Checkerboard Squares Day 1 of 6

Unit 2: Writing expressions
Lesson 1 of 7

Objective: SWBAT use the formula for the area of a square to find the number of single squares on a checkerboard and to look for patterns of regularity to find additional possible squares.

Big Idea: Students will begin to notice patterns of regularity in the checkerboard that they can use to determine the number of squares.

  Print Lesson
Math, tables of values, Expressions (Algebra), area of rectangle, pattern
  45 minutes
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