Exploring Volume

Thursday, July 31, 2014

Scaffolding Comprehension Lesson

Teacher: Rebecca Pachuta Date: July 31, 2014

Subject: Exploring Volume Student Level: High School Geometry

Text: The Perfect Fit

1	This reading is intended for 9^th or 10^th grade geometry students. It is an activity that gives students the opportunity to take what they have learned in class and apply it somewhere else which is the ultimate goal of my instructional plans. In general, before this activity/reading the students should have learned general volume formulas. After the reading students can be directed to the bonus activity which involves using the volume formulas backwards, (for example, given the volume and height but need to solve for the radius).
2	"The Perfect Fit: Take-Home Activity 3." Teachers. Scholastic Inc., 2014. Web. 20 July 2014. <http://www.scholastic.com/content/collateral_resources/pdf/smp/actuarial/ actuarial4 _activity3.pdf>. This reading describes a take-home activity in which students analyze items they have at home and apply volume formulas. One example is having the students calculate the volume of their bedroom and closet. There is even a bonus activity included at the bottom that has students working backwards to find the height of a can of juice if they are given its radius and volume. Using Story Toolz I found that the readability of this text averages about a 6th grade level. While the reading is easy, the students will find this text more challenging if they are not properly focused and aware of the geometry/volume references being asked of them. On a personal scale I rate this a 3 for similar reasons to my 4th text above. Students are going to need some prior knowledge about calculating volumes before they can complete the problem set on their own. If I were to choose a grade level for this text to be used I think it would be best suited for a high school geometry class - so around 9th or 10th grade as mentioned above - because of what is being asked of the students. There are some visuals in the text which is helpful for giving the students an idea of what to do. The text also provides formulas for the students to use which helps to make it less complex than if the volume formulas were not given.
3	Guiding Questions: Why do we need to know volume formulas? Where do you think we could apply volume formulas in the real world? Think about how we might apply these ideas to finding the volume of our classroom.

LESSON

4	Time:	What teachers do…	What students do…
	Before (Day 1)	· Have students complete a taxonomy of terms related to volume as a warm-up. Individual work first followed by small group work. · Review different volume formulas with students using the volume formula handout⁹ and the volume formulas YouTube video⁷ visualizations. · Discuss different measuring methods and how a conversion chart¹¹ may be useful. Go through examples of conversions and give students time to work on a few by themselves.	· Complete taxonomy of terms as a Think-Pair-Share activity to discuss what they came up with and build their vocabulary with the help of others. · Take time to go over the different volume formulas – handout and YouTube video. Follow along with teacher and keep for future reference · Practice converting and understanding how to use the conversion table in the right way. Follow along with teacher and then try a few examples on their own.
	During (End of Day 1: front-loading of the activity that is to be completed at home in 1-2 nights)	· Discuss the components of the take-home activity and clarify student questions. Teacher asks volunteers to read the text¹⁰ allowed. · Guiding Questions: “Why do we need to know volume formulas? Where do you think we could apply volume formulas in the real world? Think about how we might apply these ideas to finding the volume of our classroom.”	· Ask questions and ask for clarification on the activity. · Have students discuss the guiding questions and make a list of possible real-world volume formula applications as a writing-to-learn activity.
	After (Day 2)	· Once students have had a chance to complete the assignment they will bring their findings to class and share with small groups. A few individuals can share with the class if they want. · Go over the bonus question step-by-step to prepare students to work backward with the volume formulas in the future.	· Share with groups and potentially the class. Discuss findings (peer collaboration). · Active listening and note-taking (perhaps use the double-entry note taking method with “knowledge” as one column and the other being “explanation/strategy”).

Bibliography

. 1 Daniels, Harvey, Steven Zemelman, and Nancy Steineke. Content-area Writing: Every Teacher's Guide. Portsmouth, NH: Heinemann, 2007. Print.

2 Hibbing, Anne N., and Joan L. Rankin-Erickson. "A Picture Is Worth a Thousand Words: Using Visual Images to Improve Comprehension for Middle School Struggling Readers." The Reading Teacher 56.8 (2003): 758-70. Print.

3 Hillman, Ann Marie. "A Literature Review on Disciplinary Literacy." Journal of Adolescent & Adult Literacy (2013): PDF.

4 Lattimer, Heather. Reading for Learning: Using Discipline-based Texts to Build Content Knowledge. Urbana, IL: National Council of Teachers of English, 2010. Print.

5 Moje, Elizabeth Birr. "Foregrounding the Disciplines in Secondary Literacy Teaching and Learning: A Call for Change."Journal of Adolescent & Adult Literacy 52.2 (2008): 96-107. PDF.

6 Moore-Russo, Deborah, and Lynn E. Shanahan. "A Broader Vision of Literacy."Journal of Adolescent & Adult Literacy 57.7 (2014): 527-32. PDF.

7 Pachuta, Rebecca M. "Blog 3 Screencast: Exploring Volume." YouTube. YouTube, 16 July 2014. Web. 20 July 2014. <https://www.youtube.com/watch?v=Ke8n2ep4tc8>.

8 Smith, Antony T., and Robin L. Angotti. ""Why Are There So Many Words in Math?": Planning for Content-Area Vocabulary Instruction." Voices from the Middle 20.1 (2012): 43-51. PDF.

9 "Solid Geometry Wiki." Web log post. Solid Geometry Wiki. William K. Bradford Publishing Company, 2005. Web. 20 July 2014. <http://solid-geometry.wikia.com/wiki/Solid_Geometry_Wiki>.

10 "The Perfect Fit: Take-Home Activity 3." Teachers. Scholastic Inc., 2014. Web. 20 July 2014. <http://www.scholastic.com/content/collateral_resources/pdf/smp/actuarial/actuarial4_activity3.pdf>.

1 11 "Volume Conversion Table." Volume Conversion Table: Milliliter Liter Cubic Feet Pint Quart Gallon Barrel Cubic Meter. GlobeFeed, 2009. Web. 20 July 2014. <http://metricunitconversion.globefeed.com/Volume_Conversion_Table.asp>.

Friday, July 25, 2014

Disciplinary Text-Set

I have collected a text set of 8 different non-fiction texts related to finding the volume of different shapes. These texts could be used to build background knowledge and/or supplement any lesson related to volume in the geometry content area. (Note: For complexity info I used a resource called Story Toolz that I found easy to use and it mostly agreed with what I thought for each text's difficulty level.)

TEXT 1

Text Preview:

Bibliographic Info:

"What Is Geometry? When Do You Use It In The Real World?" TeAchnology. Teachnology, Inc., Web Access. 20 July 2014. <http%253A%252F%252Fwww.teach-nology.com%252Fteachers%252Fsubject_matter%252Fmath%252Fgeometry%252F>.

Summary:

This is an article I found online that describes the importance of using geometry in the real world. I began with this text in my text set because it focuses on the "big picture" of geometry that encompasses a wide range of ideas within. This article mentions the importance of volume and how it is used in the real world. "The most basic form of geometry is the so called Euclidean geometry. Lengths, areas, and volumes are dealt here."

Complexity:

The Story Toolz text complexity of this text was about 10th grade, although I think if properly introduced this text could be used anywhere from 9th-12th grade. Some of the main concepts of how geometry is used in the real world may be unfamiliar to students. While the wording and sentence structure is relatively easy, the concepts and main ideas are what make this text a little more challenging for some students. Additionally, there are no visuals included with this text which may have helped make it easier to understand certain topics.

Why Use This Text?

This text would be great as an introduction to any geometrical concept. It discusses where geometry can be seen in the real world and summarizes many different aspects of geometry. It would be great to use to get students excited and interested in the topic! That being said, it could also be utilized at the end of a geometry class to summarize what has been taught. With a better knowledge base of geometry students will be able to see how what they've learned is applicable. Either way, this text would be a great resource in a geometry classroom.

Questions for Students to Consider:

Which of these examples are you already familiar with?
Likewise, which are you unfamiliar with that you would like described/clarified?
Can you think of any other real-world examples of where geometry is use? How about specific to the idea of volume?

TEXT 2

Text Preview:

Bibliographic Info:

"Solid Geometry Wiki." Web log post. Solid Geometry Wiki. William K. Bradford Publishing Company, 2005. Web. 20 July 2014. <http://solid-geometry.wikia.com/wiki/Solid_Geometry_Wiki>.

Summary:

This is a handy table that shows 6 important volume formulas including that of a cube, rectangular prism, sphere, right circular cylinder, right circular cone, and right square prism.

Complexity:

Some important things to consider in something like a table or image like this one are the font size and colors (since there are few words). Since volume formulas are typically learned in any grade from about 7-10th grade I am giving this a wide score for complexity. If I had to choose, it is about a 2 on my personal complexity scale of 1 to 5 (1 being the least complex). The large font and well-organized nature of this text are why I gave it a 2. Depending on when the students are learning these formulas, the complexity of this text would differ (according to the grades I mentioned previously).

Why Use This Text?

I think this text would be a great supplement for any geometry classroom that is learning about volume. Since it covers a number of common shapes it would be useful to have displayed somewhere in the room or for each student to have a copy of it somewhere with them. It is a quick and easy reference tool that is relatively easy to follow along with (see complexity rating above).

Questions for Students to Consider:

What are some similarities you notice between the different formulas?
Can you describe what each variable in the formulas stands for?
Do you see any references to AREA within these volume formulas?

TEXT 3

Text Preview:

Bibliographic Info:

Pachuta, Rebecca M. "Blog 3 Screencast: Exploring Volume." YouTube. YouTube, 16 July 2014. Web. 20 July 2014. <https://www.youtube.com/watch?v=Ke8n2ep4tc8>.

Summary:

This is the video I created and featured in my blog post from last week titled Visualizing Meaning via Screencast. It goes through 4 important volume formulas of a rectangular prism, cylinder, cone, and sphere. Each component of the formulas is mentioned and labeled. It also goes into detail about what exactly pi is and how it can be used in a volume formula.

Complexity:

I am giving this video a similar complexity rating to Text 2, above. Again, since volume formulas are typically learned in any grade from about 7th to 10th grade I am giving this a wide complexity rating. If I had to choose, it is about a 2.5 on my personal complexity scale of 1 to 5 (1 being the least complex). The large font, easy to see graphics (rotating figures, for example), and in-depth descriptions are why I gave it a 2.5. The additional .5 was because of the explanation of pi, which makes this text a little more challenging than Text 2. Likewise, depending on when the students are learning these formulas, the complexity of this text would differ (according to the grades I mentioned previously).

Why Use This Text?

This text is useful because it is something students can use on their own for clarification and further explanation. As a video, it is a little more exciting than simply reading these formulas in a text book. Each shape's volume formula is described in detail and would be a useful tool for any student learning about the different volume formulas one may encounter in a geometry classroom.

Questions for Students to Consider:

What are some similarities you notice between the different formulas?
What is the relationship of pi to a circle?
What abbreviation of pi is most common when utilizing these volume formulas?

TEXT 4

Text Preview:

Bibliographic Info:

"Volume of Mixed Shapes." Math Worksheets 4 Kids (2014): n. pag. Web. 20 July 2014. <http://www.mathworksheets4kids.com/volume/mixed-prism-level2-hard3.pdf>.

Summary:

This is a worksheet composed of 9 different 3D shapes in which students are to find the volumes of. The shapes are shown directly on the paper and all dimensions are given.

Complexity:

As an exercise or assessment tool in the classroom I would rate this a 3 on a scale of 1 to 5 (same conditions as previous texts above). I had to rate this on my own scale because this text was composed mostly of images and the only words on the page were the values given for the dimensions. I am considering this text a 3 because students are going to need some prior knowledge about calculating volumes before they can complete the worksheet. If I were to choose a grade level for this text to be used I think it would be best suited for a high school geometry class - so around 9th or 10th grade - because of the number of different shapes used. As an assessment tool this text is easier to rate as a quantitative assessment of how much the student knows about finding volume.

Why Use This Text?

This text is a good practice activity for the students or can even be used as an assessment tool. This text would be used after the students have gained some knowledge about how to calculate the volumes of formulas. I like how there are different shapes represented and each is labeled well. This will give the teacher an idea of how much their students know.

Questions for Students to Consider:

What formulas are you using to calculate volume for the different shapes?
Is any extra information needed for the shapes in order for you to complete the problems? (Such as needing to know the correct volume formulas).

TEXT 5

Text Preview:

Bibliographic Info:

"The Perfect Fit: Take-Home Activity 3." Teachers. Scholastic Inc., 2014. Web. 20 July 2014. <http://www.scholastic.com/content/collateral_resources/pdf/smp/actuarial/actuarial4_activity3.pdf>.

Summary:

This is a take-home activity in which students analyze items they have at home and apply volume formulas. One example is having the students calculate the volume of their bedroom and closet. There is even a bonus activity included at the bottom that has students working backwards to find the height of a can of juice if they are given its radius and volume.

Complexity:

Using Story Toolz I found that the readability of this text averages about a 6th grade level. While the reading is easy, the students will find this text more challenging if they are not properly focused and aware of the geometry/volume references being asked of them. On a personal scale I rate this a 3 for similar reasons to my 4th text above. Students are going to need some prior knowledge about calculating volumes before they can complete the problem set on their own. If I were to choose a grade level for this text to be used I think it would be best suited for a high school geometry class - so around 9th or 10th grade as mentioned above - because of what is being asked of the students. There are some visuals in the text which is helpful for giving the students an idea of what to do. The text also provides formulas for the students to use which helps to make it less complex than if the volume formulas were not given.

Why Use This Text?

I think this text would be a fantastic activity and project for students to do once they have learned how to apply volume formulas. It is challenging in that it gets them to think outside the box. They are looking at real-life examples, not just 3D shapes drawn 2D on a piece of paper. It doesn't get any better than seeing what you've learned being applied to real life (Something a math teacher would definitely say!).

Questions for Students to Consider:

What other objects around your home do you know how to find the volume of?
Which part of the problem set was most challenging for you to complete?
Did you have fun figuring out the volume of places that you spend a lot of time in?
Using the methods and tools you had for these problems, what is the volume of our classroom?

TEXT 6

Text Preview:

(Note: I have added some information to the additional chart, specifically the fluid ounce)

Bibliographic Info:

"Volume Conversion Table." Volume Conversion Table: Milliliter Liter Cubic Feet Pint Quart Gallon Barrel Cubic Meter. GlobeFeed, 2009. Web. 20 July 2014. <http://metricunitconversion.globefeed.com/Volume_Conversion_Table.asp>.

Summary:

This text is a volume conversion table that includes milliliter, liter, cubic meter, cubic inch, cubic foot, pint, quart, gallon, and fluid ounce information. The volume conversion factors are not exact and some of them are rounded to limit the number of digits. The text also includes two examples that can be used to help one understand how to use the table.

Complexity:

According to Story Toolz the average grade level for readability of this text is "grade 15" or college, as I know it. One reason I think Story Toolz rated this text so high was many different units were used - both metric units and English units. It also might be challenging for students to figure out how to actually use the table which makes it more complex. I think with proper focusing and directions high school geometry students will be able to utilize the table. A teacher would have to go through a number of examples with them, perhaps, but it is definitely doable. When I was in high school I know we learned about how to "read" and interpret tables, so I have faith that other high school students can successfully use this text as a resource. Because of the complexity and different nature of this text I give it a personal rating of 4 - meaning it is challenging, yet learnable.

Why Use This Text?

I think this text could be used as a great resource in the geometry classroom when learning about volume. It brings up great info about conversions and the different units that can all be used to measure volume. This text opens up many ideas and could be supplemented with different problems and examples to help students consider types of measurement they have not before. Additionally, this text could be used in other math or science classes. So by introducing this text to students and teaching them how to properly utilize it, a teacher would give them access to knowledge that they can apply elsewhere.

Questions for Students to Consider:

Which measurement types in this table are you unfamiliar with?
Can anyone show me how to convert ______ to ______. (Fill in the blank with any measurement unit!).
Where might you see similar tables to this? What other kind of conversion tables do you think exist for other types of measurement?

TEXT 7

Text Preview:

Bibliographic Info:

"Base (geometry)." Definition of Base (geometry). MathIsFun, 2014. Web. 20 July 2014. <http://www.mathsisfun.com/definitions/base-geometry-.html>.

Summary:

This text describes the meaning of a base in geometry. Specifically referring to finding the volume of 3D shapes. This text includes a short written definition as well as a couple pictures to aid in the description. (This resource can be used for other math-related definitions, I chose base because it is very relevant to volume and this specific text set).

Complexity:

The average readability grade level that Story Toolz gave for this text was 6th grade. I would have to agree that the readability of the text is at that level. That being said, you could easily use this in a high school geometry class to give students a reminder of this definition. It is a tool for them to use rather than a text for them to analyze and gain deep insight. For my personal scale I would rate this a 2. The pictures aid in understanding and clarification while the vocab is reasonable. If students had a little geometry background knowledge (such as the geometry they would learn in middle school) they would be able to use this text and most likely would not find it too complex.

Why Use This Text?

This text would be a great additional resource for students in a geometry classroom (or any math class, for that matter). Having access to these definitions that include picture descriptions along with the written description has potential to be very helpful. This text would serve as something supplementary to whatever is being learned in the classroom at the time and it is easy to use.

Questions for Students to Consider:

What other volume-related vocab words can you find on this website?
What other shapes can you think of that have 1 base? How about 2 bases?

TEXT 8

Text Preview:

Bibliographic Info:

"Volume." Wikipedia. Wikimedia Foundation, 22 July 2014. Web. 23 July 2014. <http://en.wikipedia.org/wiki/Volume>.

Summary:

This is the Wikipedia page for Volume. It includes some useful introductory material as to what volume is and why people use it. It contains a lot of information about the units related to volume as well as more about volume formulas and even volume formula derivations for the more advanced viewers.

Complexity:

The complexity of this text according to Story Toolz is a readability of grade level 14 (college). I think this is because of the dense information that encompasses a wide variety of volume. Derivations, for example, are very complex compared to just the volume formulas on their own. Though difficult, this text could be used in a high school geometry class if introduced appropriately. Perhaps even only utilizing the information that was relevant to what was being taught at that time. I would rate it a 4 on my personal scale (from 1 to 5) because it is a challenging text full of a lot of information.

Why Use This Text?

This text would be useful in giving students important background information on volume. It encompasses a lot of information and could be used in any way the teacher saw to be useful. Certain parts could be taken out of the text and analyzed on their own or the text in its entirety could be shown to an advanced class looking for a challenge.

Questions for Students to Consider:

What info in this text are you familiar with?
Does anything in this text strike you that you would like to learn more about?
What can you tell me about the different units used for volume?

These texts would work well together in a geometry classroom that was focused on finding the volume of any 3D shape. Together the texts act as resources, tools, and examples/problem sets for calculating volume. I hope that I was helpful in creating some ideas for a geometry classroom studying volume!

Wednesday, July 16, 2014

Visualizing Meaning via Screencast

Part I:
Screencast about different volume formulas that are important to be aware of.

https://www.youtube.com/watch?v=Ke8n2ep4tc8&feature=youtu.be

Part II:

Since I am exploring volume I thought it would be useful to have a summary of some important, and frequently used, volume formulas. I was not quite sure how I wanted to get my message across or what details I wanted to include so I got started with 4 formulas. I wanted my visualization project to go beyond words on a page (since volume formulas can easily be found in a geometry textbook!) which lead to me using a video of some sort. I liked that PowerPoint had tools that I knew how to use, such as shapes and lines I could use to make the 3D figures, as well as interesting layouts. One thing about PowerPoint that I was unfamiliar with was timing and recording which something I figured would be useful and cool to learn about.

First, I knew it would be important to have a visual of each shape that I was describing. Since it is a video and I was looking at 3D shapes I thought it would be interesting and attention-getting to have the figures rotating. My next step was to write each formula with the corresponding shape. This was about all I thought about up until that part of the project. I realized that there were many aspects of each of these formulas that may be unclear which is why I labeled each figure. My biggest thought that I had mid-project was that not all students would be aware of certain details, such as pi, which is why I added an extra part to the video describing pi and how it is used in this application. At this point I thought the video was coming along fine but needed something else to help get my message across and something that made the video a little more personal and interesting. This is when I decided that recording my voice describing what was going on in each part and explaining the different aspects of each formula would be very helpful. I thought that this would not only help the visual learners but also the auditory learners as well.

I definitely did not consider certain details about volume formulas when starting this project. I think since I know geometry fairly well myself I thought that these formulas were “easy” and self-explanatory. Once I began drawing out the figures and labeling each part I realized that more explanation was needed for people who were beginners/students. I also did not really consider that some students may not know what to do with pi (such as round it to 3.14) which is why I added that portion of the screencast. Through visualization my understanding of the complexities and components of volume formulas increased. I think if students were to do a project similar to this it would help them feel more comfortable with these formulas. It would also help them visualize the shapes and solidify those in their minds as well. Simply reading these formulas may not be effective for some students. Going beyond the textbook seems like a good way to get the students thinking in a different way. It should also help them with motivation for learning the formulas as well as with remembering them in the future.

Sunday, July 6, 2014

Where I Am, and Where I Want To Go

What do I already know about teaching volume?

In the state of Wisconsin volume is discussed throughout 6th-12th grades. In middle school, students learn about right rectangular prisms and are first introduced to the formulas for that shape. 7^th graders begin to look at other shapes including those composed of triangles, quadrilaterals, polygons, cubes, and right prisms. In 8^th grade they are introduced to cylinders, cones, and spheres. High school students go a little deeper and are supposed to be able to explain the volume formulas and use them to solve problems. They should also be able to visualize relationships between 2D and 3D objects (a challenging task, as discussed in my previous post: About This Blog). High school students are also introduced to modeling with geometry which can only happen if the first topics, such as volume, are taught effectively.

I know that there are many methods in existence that can be used to teach volume. One example are CMP (Connected Mathematics Project¹) lesson plans that use hands-on activities and visuals to help students see what is going on. While this seems like a great start, I think there is a way to incorporate literacy into the hands-on activities in order to help solidify what the students are learning.

What more do I want to know about the topic?

I want to learn what kinds of questions can be asked of my students in order to increase their literacy in the topic of volume.

I want to know the different methods that are currently utilized to teach volume in secondary classrooms.

What kind of info, beyond the formulas, should be taught about volume in a geometry classroom? Further, in what ways can you get the students to be able to effectively explain the volume formulas?

Resources for Further Research and Classroom-Friendly Texts

Here are some great resources for teaching volume. Check them out below!

1. http://connectedmath.msu.edu/the-math/math-goals-by-unit/grade-7-goals/

2. http://jmathpage.com/middleschoolmath/jmsmgeometry.html

(http://www.interactivestuff.org/sums4fun/3dboxes.html)

This resource has some interactive features and examples using visuals that the students can also use in the classroom for a hands-on experience.