Surface Area of a Square Pyramid - What shapes are the faces?

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Objective

Students will be able to calculate the surface area of a square pyramid.

Big Idea

Students unfold pyramids into their two dimensional nets in order to visualize all the faces and bases needed for calculating surface area.

Launch

10 minutes

OpenerAs students enter the room, they will immediately pick up and begin working on the opener – Instructional Strategy - Process for openers.  This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3.   

Learning Target: After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended targets are, “I can calculate the surface area of a square pyramid by finding the area of each face and base.”

Explore

40 minutes

Surface Area of a Square Pyramid Explore Narrative

Brainstorm: As a way to access prior knowledge, I give the students a square pyramid and ask that they discuss how they might find the surface area of it with their group (MP 3).  Groups will have two minutes to discuss their methods, and I will walk around to listen in and gauge understanding.  After two minutes, I will ask for a show of hands of which groups got 205 square inches as an answer.  

Surface Area of a Square Pyramid Notes: I will ask that students take out their foldable (we have been adding to the same foldable created in lesson 1 the entire unit) to jot down an example problem for finding surface area of a square pyramid. Students who do not have their foldable can do all of their work on their notes sheet, and file that in their binders. To make sure students have a good conceptual understanding of exactly what we are looking for, I will demonstrate finding the surface area of the square pyramid by breaking it down into its two dimensional net.  This way students are able to see the 4 congruent triangles and one square that make up the figure. At this time I will discuss the slant height versus the height of a pyramid.  Students are often frustrated that a pyramid has two heights, but I explain that the actual height is inside the pyramid – in “space,” and since volume is a calculation of space, we use the height for volume.  Since the slant height is on the surface of the pyramid, it then would be used to find the surface area of the pyramid.  Usually, that helps – although there are always a few students who have to hear that several times before it sinks in.  I will work out the example problem as well as one additional problem with the students, and then ask that they complete the remaining three problems with their groups.  I will walk around and provide assistance as needed during this time, placing most of my focus on the group that had the most difficulty with surface area in previous lessons. As groups finish up the example problems, I will ask for volunteers to go to the board and work out the examples for the class, explaining their work as they go.  For students who are not keen on explaining, I ask that they take a buddy to the board with them and one student does the explaining while the other does the writing.  

Table Challenge: I will conduct a table challenge using a 6 sided picture die on the smartboard.  Each side of the die has a square pyramid problem on it, and I will have students roll the die to reveal the problem.  For this challenge, I will choose a playing card A-8 to decide which table gets the problem (each table has a playing card taped to the center of it).  Though the cards will decide the table, I will choose the person from the table that goes to the board – by me choosing the student that goes up, it is more likely that students take responsibility for everyone at their table understanding the problem and the process of solving it.  This activity utilizes mathematical practice 1 by having students struggle with the problems, mathematical 3 because they will work together to come up with a solution, and mp 6 - because attention to precision regarding calculations and units will be very important. Instructional Strategy - How do table challenges work?

Summarize + Homework

10 minutes

Table Discussion: To summarize this lesson, I will ask that students turn to their shoulder buddy and discuss the three questions below.  I will walk around and listen in on the discussions, and then I will choose pairs to share what they talked about.  

  1. How many faces/bases make up a square pyramid, and what shapes are they?
  2. What is the difference between the height and the slant height of a pyramid?             
  3. How would explain to a 6th grader how to find surface area of any figure we have studied?

HomeworkI will then pass out the homework assignment and give students the last few minutes to look it over and get started. Philosophy on Homework