Clip 7/11: Problem 2 - Area & Perimeter Part B
In this section, Patty and I begin to move students to the core mathematics of the Pizza Crust problem by looking at the relationship between area and perimeter.
After part A where we helped students develop some new academic vocabulary, Patty and I went further into the justification portion of our objective for part B of this problem. Little did we know that going five minutes further into developing this vocabulary would push us later in time with getting to problem three. During the lesson, we privately conferred about what to eliminate and what we wanted to complete in the time remaining. Like all teachers, I get anxious reading through this part--even after all these years. This still happens all the time -- based on students' unanticipated questions, or concepts that require more depth and enrichment, such as vocabulary. Teachers often have to think about how to modify a lesson in a given moment when time is a consideration. In this clip, we were forced to consider what to move to the next day and what to assign instead as homework.
When we finally do go into the justification portion of this problem, we had students calculate the perimeter of a square based on an area of 36 inches. Our posters showed different ways that students had attempted to solve this from the first attempt at the MARS task. We planned it so that there was a progression of ability--it started out with someone believing that the 36 came from perimeter. When we analyzed student work and re-engaged the students with effective and ineffective strategies, this was a common misconception. Then we progressed to a problem where a student thought that the 36 was not the area but the edges--which leads to an answer like 1296. Then we finally got to a problem where students could see that each side was 6, and to get a perimeter, they would have to multiply it by 4. By putting up the strategies one at a time, we could ask the students if they agreed with the strategy and why. Asking students to do the work of analysis was the foundation for this part of the lesson, which is why it's called a re-engagement. Essentially, we are asking students to act as the teacher and learn to analyze students' responses. Ideally, when they learn to do this, they can eventually evaluate their own responses on future math problems and assessments that they encounter.
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