##
* *Reflection: High Quality Task
Step Into the 3rd Dimension - Section 3: Practice/Homework and Exit Ticket

In this lesson's exit ticket, students were required to determine the radius of a cylinder given information about a cone with the same volume. This is a challenging and higher-level question and asks students to have precise knowledge about each 3-dimensional shape and each formula. You may want to leave 5 minutes, if not longer, at the end of class for this question!

The following example shows one common misconception that many of my students had: Student Work #1. Many students simply divided the radius by three since the ratio of the volume of a cone to cylinder is 1:3. However, other students found the volume either plugged in for the radius or tried to set the two volume formulas equal to each other. You can see examples of these here: Student Work #2 and Student Work #3.

The next day, we revisited this question in class and looked at students' work to understand how to correctly solve this problem.

*High Quality Task: Higher Level Thinking in Exit Tickets*

# Step Into the 3rd Dimension

Lesson 2 of 4

## Objective: Students will be able to watch Simpsons' video and derive volume formulas.

**Do Now:**

Students will be asked to find the area of a circle when given the center and a point on the circle. Students will need to use the distance formula in order to find the needed information, the radius. You can then review the objective with students and perhaps, also, emphasis the importance of deriving formulas which will be our primary focus.

**Simpson’s Video:**

To engage and hook students into this lesson, we will watch an 8-minute part of a Simpson’s episode. You can find this clip in Season 3 of The Simpsons, Episode 2 called “Treehouse of Horror IV: Homer 3D.” You could buy the DVD but I bought the episode for $1.99 from amazon.com, and have this on my account which I can access whenever needed. I find that it’s well worth the money, and have shown this video not just in this lesson but also to my Algebra students, and asked them to identify the three names for each dimension.

You pre-read the questions with students and then show the video. I usually give students 2-3 minutes to write their answers, and then call on volunteers. This is a great opportunity to get “quieter” students involved in the discussion of math and Geometry. If teachers have time in this class or in another, you can discuss the writers of the Simpson’s experience with math; many attended Harvard University and studied math or related fields. Here is a great website from a math professor who connects math and Simpson’s videos.

Ultimately, students will see in this video how we have moved from 2-dimensional shapes like circles or triangles into a 3-dimensional world, featuring the z-axis. This highlights how we can model mathematics in both dimensions (MP 4).

**Introduction to Vocabulary:**

After the video, teachers can introduce key terms related to 3-dimensional figures like edge, face and vertex which will students identify how we classify figures. You can also emphasis the idea of a base, which will help students identify figures like cylinders later in the lesson. Then, students can work in pairs to brainstorm what they already know about volume. This is a great opportunity for you to establish students’ pre-requisite knowledge of volume, and then elicit from them a definition for volume using precise language (MP 6).

*expand content*

**Practice:** There are 8 practice questions for students. Some ask students to solve basic volume problems #1-5, while other are thinking questions, #6-8, that ask students to write or apply their knowledge to a more complicated question.

**Exit Ticket:** The exit ticket asks students to use their knowledge of how the volume for a cone and cylinder are related. Students may need to a hint to get started, which could be suggesting that they find the volume of the cone.

*expand content*

Hi! I love your lessons. However, you don't specify what part of the episode you show.

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