SWBAT decompose an irregular figure, & calculate its volume.

Determine which student's model is the most cost-efficient for a business to build.

10 minutes

My motivating to create this lesson stems from one of the policies/understandings within our district. It's very important for us to promote lifelong learning, and college/career readiness. With this lesson, I end up empowering students to use analytical skills, workforce skills, to use their best judgement to make a decision that will affect their employees and ultimately their business. If you've followed my other lessons, then you know that I need to "hook" my students very quickly this year, due to ability levels, and provide extremely motivating scenarios.

Since we've discussed volume before, this is a review; to quickly review we use the Ixl website. Here, we practice answering questions. If we get an answer wrong, then we see the following sections: Review, Remember (This shows a tip.), Solve (This shows steps on how to solve.) We are given various rectangular prisms and cubes with dimensions, and we practice calculating the cubic units. Today's lesson will be be complicated than this; students will have to break about a bigger shape into two shapes, and then calculate cubic units. I want my students to feel successful first though, so I start with this somewhat simple game.

10 minutes

(a) Uses MP3 (Construct viable arguments & critique the reasoning of others), and is a Level 2 DOK; here students critique a method for solving a problem and find the error in the method.

(b) Uses MP7 (Look for & make use of structure), and is a Level 2 DOK; here students decompose an irregular figure.

(c) Uses MP3 again, and is a Level 3 DOK; here students explain how to solve a problem using a formula.

(d) uses MP6 (Attend to precision), and is a Level 2 DOK; here students calculate to find the volume of an irregular figure.

15 minutes

In the (a) section, students are given a new model. I'm looking for them to accurately re-draw the shapes with the correct dimensions.

In the (b) section, I'm looking for students to draw the line segment correctly. For struggling students, I suggest drawing a picture of a right rectangular prism to see how to decompose the figure.

In the (c) section, I'm looking for students to correctly explain their reasoning clearly. Students should be able to explain that they can find the volume of each decomposed figure and then add the volumes.

In the (d) section, I'm looking for students to determine which model would be the most cost-efficient model for a business to build. Here in comes the discussion, and "business sense". One of the most important parts of teaching is coaching your students to expand their knowledge, and extend their thinking. Sometimes my students take things even further than I anticipated, and I most definitely use those teachable moments to every advantage. Then, I'll "brag on them" to the whole class either anonymously or not...depending on the student(s.) I intentionally included this last question to extend my students' thinking. Some of students immediately thought about less bricks and less metal, for building materials, mistakenly thinking about the perimeter of the buildings, and not the volume. This was important for me to note, and review when we review volume before the End-of-Grade test.

In this video clip, you'll see how I paraphrase and reiterate the strategies that students have used to solve this problem. My students have learned from my modeling, and have used the color coding model to color code their own models and appropriate math on either side of their paper. You'll hear me refer to the shapes as "boxes", which is what I heard a few times while I was walking around facilitating. I bring this up during the teacher-talk, and ask what the appropriate word is for the shapes.

15 minutes

To close out this lesson, I have students take on the role of being an entrepreneur. Throughout the year, we've discussed this word many, many times. My students are very familiar with what this word means because we've read passages and biographies of entrepreneurs.

Students design their own building, using what they now know about cost-efficient businesses (having less square footage may be the best). This takes just about ten minutes, and then students share out with their partner to discuss why they designed their building like it is. (I have to limit the time spent on creating a business for some groups, in order to make the mathematical practice the most important idea here.) I also ask my students what the purpose of an architect is; and relate that back to building design. Some of my students even "went green", with their hybrid car in a parking space. (We previously designed hybrid cars for Earth Day in April.), and included solar panels, and many trees, and shrubbery. What I'm looking for is if students designed a compact building with realistic dimensions, and described 1 or more money saving practice that they would use.