##
* *Reflection: Developing a Conceptual Understanding
Length x Width x Height, Gives You the Vooooolume! - Section 3: Establishing Conceptual Understanding with Visual Thinking

Visual thinking is a powerful tool that I will be utilizing to augment conceptual understanding. In the video, students hear the narrator state, "Volume calculate the cubic units inside." As a teacher, I need to get them thinking about what that means. I really don't want them to give me the volume is Length x Width x Height response when I ask them to define volume. Rather, I want them to explain that volume is a measurement of how many smaller cubic units fit into a larger volume. To get my students to thinking about volume in a visual way, I ask them to draw how many smaller units make up the larger units in a prism. Later, when we are talking about liquid volume, I refer to milliliters in a graduated cylinder as hockey pucks. In that, when measuring liquid volume I want them to realize that by stacking hockey pucks, just like drawing how many cubes make up a whole cube, creates the final volume for the liquid. If students can describe their thoughts in a visual way then their conceptual understanding and confidence increase.

*Using Visual Thinking to elicit Student Thoughts*

*Developing a Conceptual Understanding: Using Visual Thinking to elicit Student Thoughts*

# Length x Width x Height, Gives You the Vooooolume!

Lesson 3 of 11

## Objective: SWBAT: Calculate the volume of rectangular solids.

## Big Idea: Students learn a fun song about calculating the volume of rectangular solids that they will be singing all the way home, and possibly in their sleep.

*55 minutes*

#### Do Now Activity

*5 min*

This lesson addresses 5.MD.C.3 and 5.MD.C.5a which cover volume of prisms and recognizing volume as a measurement.

Volume can be an abstract concept to students, so I like to start off by comparing area--a concept familiar to them from elementary school--to volume. I want them to see that there is a distinct difference between area and volume, but also see that there are some similarities.

I begin class by having a square drawn on the board and a 3-dimensional cube. I ask students to draw the shapes into their science notebooks. I then ask them to record observations about each one and record the similarities and differences. This enables students to establish that area is a 2 dimensional measurement (length x width), while volume--at least for the rectangular solid--is 3-dimensional.

Students will then think, pair, share with their partner, and then we discuss as a class. I want my students to understand that area is an aspect of volume, but the addition of another dimension makes volume a distinctively different and important measurement in science and in real life.

Once we establish, as a class, the difference between the two measurements, I ask students to explain why scientists and engineers might want to calculate volume of a rectangular solid. This ties in some "accessible" engineering -- shipping products that are rectangular solids. The summative assessment for rectangular volume will include students figuring the dimensions of smaller boxes to fit into a larger box.

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Since most students have varying mathematical computation and conceptual understanding coming into grade 6, I like to individualize the instruction as much as possible. I do this by having students watch a YouTube video that walks them through what volume is and how it is calculated. The author of the video has made the calculation of rectangular volume easier with a catchy song called 'Length x Width X Height'.

Students watch the video with the same partner from the Think, Pair, Share activity earlier and take notes in their science notebooks. The video is a good tool for students to work independently, and I stress to my students to watch it, pause and re-watch it if they need to.

The main concepts covered in the video include:

- What is volume?
- How is it calculated?

All bundled into a catchy tune, that won't get out of their (or your) head!

Alternatively, if you do not have access for 2:1 computer use in your classroom, just play the video on your projector. If you don't have a projector then you can play the song at the very least.

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My students are often great at calculating volume using L x W x H, but they have significant flaws in their conceptual understanding of volume. At the end of this lesson, I want students to explain that their calculations of volume determine how many smaller units fit into a larger unit and that volume can mean how much space an object (matter) takes up. This picture demonstrates how I want my students to demonstrate their understanding of cubic volume.

To facilitate this development of conceptual understanding, I ask my students to draw a visual representation in their science notebooks of what the narrator means when he says, "Volume calculates the cubic units inside."

This video shows how you can help student visualize volume using a manipulative.

This gets them thinking about the purpose of doing the volume calculation and adds a model to help them understand the concept of volume.

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Students should now have a sense that volume is a measure of how much space an objects takes up but they may still be struggling with the idea that they will be calculating the number of smaller cubic units that fit into a larger cubic volume.

To establish a deeper understanding of this, I first calculate a sample problem for them while thinking aloud to the class. I perform this on the board and ask students to listen closely to my thought process.

The modeling activity goes something like this:

I have a cube that measures 3 cm Long by 5 cm Wide by 2 cm High. I wonder what the volume of this cube is? How many smaller units, in this case cubic centimeters, fit into the larger volume.

I wonder what formula I could use to figure this out? Any ideas? Oh, that's right--Length x Width x Height! If you think ahead you can cue the music from the video to play at this moment and add a little excitement to the activity. I then plug in my numbers to the formula and then calculate the volume on the board. I then talk aloud about what my calculation means by discussing that the volume of the cube is 30 cm cubed. This means that in this entire area there are 30 1 cm by 1 cm by 1 cm cubes that make up the total volume of the cube. I then tie in the visual learning aspect from earlier in the class and draw a large cube and say that 30 cm cubed equals 30 1 cm x 1cm x 1cm. I then proceed to draw 30 cubes in the larger cube.

I also have a manipulative cube that helps kids visualize the idea of volume. It has a large plastic cube with smaller orange cubes that are 1 cm cubed. They can then see that another model of what I just drew on the board to help solidify their understanding.

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Students get more comfortable with volume when they practice calculating and communicating what their calculations mean. This portion of the class gives them ample time to practice individually and me time to circulate around the room to check for understanding and answer any lingering questions from students. If you notice that some students are excelling, while others are struggling, feel free to pair them together. We all learn best when we teach something on ourselves, so give students the opportunity to share their knowledge, too.

Students will be given a sheet that will be stapled in their science notebooks. All responses will be recorded in their science notebook.

Homework can vary depending on the individual classes ability levels. Options: 1) Find a rectangular object at home, measure its dimensions and calculate its volume 2) Give students more sample problems 3) Have students reflect on how their understanding of volume has changed compared to the beginning of class.

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- LESSON 1: Stairway to Learning! Moving Your Way to Understanding Metric Unit Conversions
- LESSON 2: Measuring Length
- LESSON 3: Length x Width x Height, Gives You the Vooooolume!
- LESSON 4: Measuring Liquid Volume
- LESSON 5: Measuring Volume of Irregular Objects Using Water Displacement
- LESSON 6: Mass vs. Weight: Using Concept Cartoons and Evidence-based Argumentation to Help Deepen Student Understanding
- LESSON 7: I Can Measure Mass, Not Weight, With A Triple Beam Balance!
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