# Discovering Volumes of Known Cross Sections Using Play-Doh

My AP Calculus students had a tough time with volume last year. So this year I wanted an activity where they could actually see the cross sections. I have seen many awesome activities where students actually measure the base between curves, and then create cross sections using paper, like the ones from Bowman and Rebacka. I would love to do these with my students, but unfortunately we are very short on time this year because of our school schedule.

So, I decided to try it out using Play-Doh. I had students mold each type of cross section, and then let them slice it with either dental floss or a plastic knife. Once they cut their solid, I had them pull out cross sections so that we could develop the area and then volume formulas together.

First of all, kids loved playing with Play-Doh! It worked beautifully, and only took about 40 minutes to do the entire activity. Most of my students didn’t need to do all of the cross sections after the doing the first one. Doing the first one really helped them see and understand what was going on. So, if you are short on time, you could just do one cross section. However, my students really enjoyed trying to make the shapes for all four cross sections, and cutting them into the sections. And, again, they really enjoyed playing with the Play-Doh! They were so sad when I asked them to put away the Play-Doh for the quiz that I let them keep it out and play with it during the quiz. Sometimes I forget that high school students are still kids.

I pulled together a Desmos activity that I planned on using the same day. It is full of amazing graphs created by the amazing Suzanne von Oy. However we did not get to it as we ran out of time, and were just too excited about the Play-Doh! So I will share the Desmos with them when we do examples, and to remind them of what we did in class.

## Procedure:

• Class time: 45 minutes
• Materials
• Graph sheet and worksheet – I put the graph sheet into slip in sleeves, so I could reuse them for my classes. You could also use plastic page protectors or laminate the graph sheet.
• Play-Doh – I used one 4oz. can per every two students.
• Dental Floss (or plastic knives, but dental floss works better as it doesn’t squish the top of the shape).
• Rulers (they don’t need them for this activity, but it helps them see why they shouldn’t measure with a ruler).
• Desmos activity
• Directions:
• I let the kids just play with the Play-Doh first. Don’t skip this important first step, or you will never get their attention. lol!
• I had two students work together on one mat.
• While they are playing we talked about volume formulas. I found asking them how do you get the volume of a cylinder was especially helpful as they all knew it was the area of a circle time the height. I pushed them on this, and then they told me that you have lots of circles to get the volume of a cylinder.
• I told them to use all of their Play-Doh to make a solid out of the area between f(x) and g(x). Then, I had them mold their shape into the different cross sections.
• After molding, they sliced their solid, and took out two different sized cross sections, one from the middle and one towards the end. This was incredibly helpful as when I said, what is the base of the square? A couple of tables started measuring it with a ruler. (Rulers had been left on the table from the class before). This was accidental, but a great opportunity to talk about why measuring this is not the best method.
• This led to a discussion about how to get the base measurement we needed. And moved to the worksheet to write down the area and the volume.
• I did not give them the area of an equilateral triangle. We used our 30-60-90 knowledge to develop this.
• Once we finished everything we compared the volume formulas on their worksheet. We talked about how they were different and how they were the same.
• I planned on using the Desmos activity, but we ran out of time. So, I will use this the next day so they can see and manipulate the cross-sections of the examples we use in class.

# Blog Posts for the First Days of School!

It’s back to school time!!

Here is a compilation of posts that will hopefully help with all of your “Back To School” planning. Â I thought that putting them all in one place would be helpful. Happy planning and welcome back to school!

## The first CPM meeting is September 5th, register here!

My favorite session at theÂ #TMC18Â conference was the CPM Flex session that we had at the end of the day Saturday. Â (The Flex session is an open hour on the last day of the conference where anyone can propose and hold an impromptu session.) Â The CPM session evolved from meeting teachers who were also using CPM in other sessions. Â Once we discovered we were teaching CPM, discussions ensued, and it was obvious that we needed focused time together to brainstorm and discuss our experiences. Â Our discussions were incredible, and we all decided that they must continue throughout the school year!

### CPM Monthly Virtual Meetings

Typing on the document was great, but our conversations were even better. Â We decided that we would like to meet virtually once a month, to talk with each other and update the working document together. Â We will meet the first Wednesday night of the month, at 9PM EST. Â Our first meeting is September 5th, sign up here! Â I will update this post with more information once I know it, and then also post it on Twitter. Â If you want, sign-up to receive info here: Â CPM Sign-Up

I’m so excited to connect with an learn from other CPM teachers this year!

I loved using CPM this year. For my entire teaching career, I have not had a good curriculum to teach with. Â Sometimes I didn’t even have a textbook. Â So, with the help of the #MTBoS, I created (and “borrowed”) all of my material. Â This was enjoyable, as I loved creating the material for each day, but it was also exhausting, and at times, overwhelming. I’m at a larger school now, and working with other teachers across multiple subjects, so we needed a curriculum that we could all use. Â I was very happy when I found CPM two years ago, as many of the activities in their Algebra 2 book were things I was already doing. Â However, the CPM activities are written very well, with better scaffolding and questioning. Â And, CPM included things I wanted to do, like spiraling homework. Â It was also rated, scoring all greens, on EdReports. Â So we decided to try it out.

Before using CPM, I never realized the importance of a cohesive, comprehensive curriculumÂ (note: not a textbook series). Â  The CPM series threads together concepts from chapter to chapter, always including past material and going deeper each time. Â It is really enjoyable to experience it unfold throughout the year. Â Additionally, concepts are taught in a consistent way, with consistent ideas and terminology, in subsequent subjects. Â  No longer do I hear, “That is not the way that Mrs. X taught it last year”. Â This consistency has allowed students to build on their previous learning, instead of feeling like they are learning entirely new and different math each year.

# Making Groups Work

It’s not Sunday and this post is a week late!Â  I just finished up the first trimester at school so I’ve been swamped!Â  We have also experienced a blogging slow down.Â  It’s the busiest time of the year for most people!Â  So instead of a weekly posts for the month of December, let’s do one blog post this month.

The topic for December is “Observe Yourself:Â Â Phone Pocket“.Â  At Twitter Math Camp this year, Peg Cagle encouraged us to all “Phone Pocket”.Â  It is when you put your phone on audio record in your pocket for 10 minutest to record your conversations with students.Â  She said you can learn so much from this practice!Â  So you don’t get overwhelmed, don’t try to observe everything about what you say and do, but pick one or two things you would like to watch for when listening to the playback.Â  Then, blog about what you discovered.Â  Tell us what you do noticed, what you do well, and what you would like to improve.Â  It is due December 16th.Â  Â Submit your blog post here.Â  Then, you can start working on yourÂ Â “New Year’s Resolutions!” blog post,Â due January 7th.

Blog posts appear in the order they were submitted.Â

# Our topic for next month is, “Observe Yourself:Â  Phone Pocket”

Due: Sunday, December 16thÂ Â Â Submit your blog post here.

• Submit your blog post (below) to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

# Self-Care Tips

The topic for next week is “Group Work:Â  How Do You Make Group Work WORK?“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “Group Work: How Do You Make Group Work WORK?”

Due: Sunday at 6AM

What do you do for group work?Â  How do you make it work?Â  Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

# Photo of the Week, #MTBoS

The topic for next week is “SELF CARE TIPS – How Do You Take Care of YOU?“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “SELF CARE TIPS: How Do You Take Care of Yourself?”

Due: Sunday at 6AM

We are deep into the school year.Â  Please share some ways you take care of yourself!Â  Â Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

The topic for next week is “Photo of the Week!“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “Photo of the Week”

Due: Sunday at 6AM

Take a picture of something that happened this week and share it with us!Â  Tell us all about it!Â  Â Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

# Math Games!

The topic for next week is “Your Teaching Story“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “Your Teaching Story”

Due: Sunday at 6AM

Tell us your teaching story!Â  How did you get where you are?Â  Who inspired you to be a teacher?Â  Â Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

# Our Favorite Education Books

The topic for next week is “Math Games!“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “Math Games”

Due: Sunday at 6AM

Blog about your favorite math games that you play in class! Â  Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend

New to Blogging?

If you are like, “Wow! Â This sounds like so much fun! Â I want to blog but don’t know where to start!” then you must read “Mission 1: The Power of the Blog” on the Explore the MTBoS site.

** The hardest thing to do week after week is come up with great prompts. Â Please help us out by telling us what you would like to blog about (or even read about) here!

* The Math Twitters Blogosphere is not an organization. Â Rather it refers to ANYONE that is involved in MATH in ANY way! Â You do NOT have to Tweet or have a blog! Â But, you can find many teachers that do tweet and blog by searching the hashtag #MTBoS on Twitter. Â All are welcome, no invitation necessary! Â Please join in the conversation! Â Just #PushSend! Â

Thanks so very much to @DruinOK for getting this all started and Jessica, Â @Algebrainiac1, for creating our awesome logo!

# #ClassroomTour

The topic for next week is “Your FavoriteÂ Education Books“. Â Â Submit your blog post here.

Blog posts appear in the order they were submitted.Â

# Our topic for next week is, “Your Favorite Equation Books”

Due: Sunday, October 1st, 6AM

What have you read that you love, or even live by? Â What books would you like to read when you get the time? Â Â Submit your blog post here.

• Submit your blog post (below) by Sunday at 6AM to have your post included in the weekly summary.
• Tweet out your post! Â Use the hashtags #MTBoS (Math Twitter Blogosphere)*, and #SundayFunday to get more traffic to your post. Â This is especially important if you are new to tweeting because only your followers will see your tweets unless you include a hashtag.
• Additional Hashtags: Â Of course you can always add more hashtags to your Tweet so more people will be exposed to your post! Â You can search any keywords to find a hashtag, and here are some of the more popular ones:
• #ElemMathChat (Elementary Teachers)
• #MSmathChat (Middle School Teachers)
• #GeomChat (Geometry)
• #Alg1Chat (Alg1 Teachers)
• #Alg2Chat (Alg2 Teachers)
• #PreCalcChat (PreCalc and Calc)
• #MathChat
• JUST Â #PushSend! Â ðŸ™‚

Submit your post using the form below by Saturday at midnight! Just #PressSend