The Surfoid: Making Geometric Solids Fun

Sometimes I use my job as a Mom as an excuse to test out adult education lessons. Recently I bought some geometric solids made for a Montessori lesson. This lesson is intended to be taught to 3-6 year olds, but adult students can benefit from a refresher on the names of these objects. And I ended up learning something really important about math in the process.


I love the Montessori method for hands-on learning, because it focuses on putting stuff in front of someone, then explaining what it’s called and what it can do. The introduction is a structured presentation, but then you let kids do what they naturally do: play with stuff. Montessori purists will call this a child’s “work.”

My well-planned idea went out the window when the box arrived. Before I could practice my presentation, my kids wanted to help take everything out. Then they started stacking the blocks and turning them into castles and guns while I struggled to remember the difference between the two egg-shaped pieces. My kids started to debate which one looked like a potato and which one was an egg. While I quickly re-read the Montessori Geometric Solids presentation, they organized the pieces into stacks with the same bases. All the triangles were stacked, the squares were stacked, and the circles were stacked.

I started by asking what makes certain blocks easier to stack on each other. The answer is that they have similar shapes on the bottom, called the base. I asked them to trace a base on paper to see that the shapes are the same. Then they wanted to cut them out, just for an excuse to use scissors.


Next I asked how many names of the shapes they already knew, and we discussed some new words. This is where things got really interesting, because again the kids started to see patterns before I even mentioned it. I drew an oval to show that the shape that looks like an oval is an ovoid. A shape that looks like an ellipse is an ellipsoid. We still couldn’t agree which was the potato or the egg.

Then my son drew a surf board. “And a surfoid!” my five-year-old proclaimed.

Sure! Surfoid. Why not?


This is where math can get really fun. Though Montessori’s methods are a century old, they have a lot of parallels with Common Core Math that parents are complaining about (another reason we hate it might be because over 55% of adults in the U.S. can’t do 4th grade level math). Why is this so different than the math most U.S. adults learned growing up?

Math like this shows us that geometry is just a way to describe the world around us. Instead of providing abstract equations to memorize with one right or wrong answer, we learn how to recognize patterns and use tools to manipulate our world using words and numbers. And when we learn to use mathematical tools instead of memorize equations, that’s when we learn how to create surfoids. That’s when math becomes play.

Beyond the Textbook: Additional Texts for GED® Test Preparation

Participants in my session on (Re)Writing History: Scoring GED® Social Studies Test Extended Response asked this great question:

In addition to published textbooks, where can I find quality non-fiction stimulus text and visuals as the basis for lesson plans and assignments?

For their (and your!) future reference, here is the list we generated:

Many newspapers also have lesson plans available for their content subscribers. This can engage adult learners while supporting journalism in our communities.

Newspapers to subscribe to for lesson plans/activities:

Do you have additional resources to add to this list?

Exciting Strategies and Technology for Detroit

Farrell Scholars, I hope you are staying warm and safe during this extended winter! I plan to spend an exciting day tomorrow with GED Test Preparation instructors in Michigan. We will spend the morning discussing changes we are experiencing with the 2014 GED Test and the implications for integrating technology in our classrooms. In the afternoon, small groups of instructors will create their own lesson plans and share them using Edmodo. With their permission, I will share their lessons with you on the blog as well.

Participants will choose between one of the following three sample lessons as a demonstration:

Six FREE Amazing Websites for GED® Test Prep

There so many websites for excellent, free content for GED® Test Preparation!

ProLiteracy Education Network

Free online resources and professional development for adult education students, instructors & administrators by ProLiteracy.

Example: 26 Tips for Working with Your Child’s Teacher

The Beehive

“Free help with money, housing, jobs, health and school. Available in English and Spanish.”

Example: Digital Basics: Learn How to Use the Computer and Internet Safely and Intelligently

Video: How to use the beehive


“TV411 is a collection of entertaining videos and engaging web activities, all designed to help you reach your learning goals. Pick a topic—reading, writing, vocabulary, math, science, or finance—and get started.”

Example: Fractions and Rhythm

GCF Learn Free

Quality online tutorials and courses for “anyone who wants to improve the technology, literacy and math skills needed to be successful in both work and life.”

Example: GCF Literacy Project

Khan Academy

Free videos and practice problems, mostly focused on mathematics but slowly expanding. The unique part of this site is not its content, but how students (and teachers) can track their progress using a free Facebook or Google account.

Example: The Beauty of Algebra

It can be hard to narrow your choices which content to use. This is especially true on sites like YouTube. Before you start, ask yourself this question:

What am I trying to teach or learn? What skill or piece of knowledge do I (or my students) need to know? Be specific!

Got it in mind? What is it? The Bill of Rights? How to find the lowest common denominator? Understanding poetry?

Now use your answer to focus your search through some of my favorite free websites for adult education & GED® Test Preparation. There are literally thousands of videos, tutorials and courses available here, so have fun searching:

YouTube…for Education!

Example: Why does a cat always land on its feet? A physics lesson from Smarter Every Day

Find what you were looking for on these sites? Please let me know!

Free Math Practice for GED Test Prep: Khan Academy & More

Khan AcademyKhan Academy

About Khan Academy

Watch Videos

Practice Problems

Click on the links below to see Khan Academy videos & practice problems that you can use for GED® test preparation:

Arithmetic and Pre-Algebra


Probability & Statistics


More Math!

McGraw Hill's GED Mathematics Workbook
Get it now from

Math Practice #1 (GED for Free)

Math Practice #2 (TV411)

Math Practice #3 (GCF Learn Free)

Math Practice #4 (McGraw Hill Online Learning Center)

Math Practice #5 (

Math Practice #6 ( *Warning: lots of ads on this site*

Want More Practice?

Check out the McGraw Hill GED Mathematics book that goes along with Math Practice #4.

Get even more practice problems with the GED Math Workbook.

Practice with your own Casio FX-260 calculator using Calculator Power.

Khan Academy for Adult Learners

For the past couple years, I have been on the hunt to find or create a FREE online curriculum for adult learners to advance in adult basic 

Khan Academyeducation and study for the GED.  Last spring the name Khan Academy started popping up.  Here are some of the things I’ve heard from ABE and GED colleagues about Khan Academy:

“I think it’s a great way to reinforce lessons for those that need extra practice.”  Linda Letherwood, Adult Education Professional in Jackson, MS

“Excuse me if I sound too enthusiastic, but I can’t help myself when it comes to the Khan Academy. I think it’s the best thing that ever happened on the Internet!” Beth Lurie, Instructor at RSU#3 SPICE in Thorndike, Maine

“My overall assessment of the program is that it is excellent.  Sal is incredibly engaging and generally has enough video instruction that even the most challenging concepts become clear. The set up and integration between the videos and practice problems is very good.” Debbi Perkul, Workforce  Development Professional at University Hospitals in Cleveland, Ohio

“I, personally, am very excited about it and think it is a wonderful tool for anyone.”  Bob Stephenson, Executive Director of The Literacy Coalition in Kokomo, IN

Lots of enthusiasm, but several shared difficulties using Khan Academy in their programs.  So let’s hear more about what works and what doesn’t using this tool for adult education.  My major questions are:

  • What is Khan Academy?
  • What skills does an adult learner need to be successful on Khan Academy?
  • What does it take for an adult educator or tutor to start using Khan Academy?
  • Is Khan Academy the solution for a free online curriculum for adult basic education & GED preparation?

What is Khan Academy?

To summarize in one sentence: Khan Academy is a series of instructional videos and practice exercises where learners can earn points and badges for participation, and a coach or teacher can track their progress.

Founder Salman Kahn offers a funny and insightful explanation of the history and format of Khan Academy in this 20 minute TED Talks video on the “About” page.

(Beware: Don’t read comments on YouTube.  The language is filthy.  I can completely understand why schools filter it out.)

What skills does an adult learner need to be successful on Khan Academy?

Beth Lurie, Instructor in Thorndike, Maine says all it takes for a learner to be successful is…“Log on. You can’t miss learning what you need to learn about math. It’s fun, it’s math made easy, and you can log your progress.”

I don’t think it’s quite so easy.  However, it requires a fairly low threshold for basic computer literacy: learners need to be able to use a mouse, type, view a video, and navigate a website.  My biggest concern with getting anyone online is to explicitly teach and emphasize how to manage accounts and navigate the internet safely, especially advertising.  Online GED preparation scams are a big money-maker.

Specifically, learners need to be able to set up and manage either a Google or Facebook account.  They must be able to remember their login information!!!! (I find this a recurring problem with program administrators, let alone adult learners!)

Debbi Purkel, Workforce Development Professional in Cleveland, Ohio adds that adult learners “have to have the confidence to figure out how to navigate around the site. They also have to be motivated and self-directed.”  Personally, I think of these websites as just the next stage of textbooks. Just like with paper textbooks I think good tutors use good old-fashioned instructional strategies like modeling and scaffolding to use these tools to support adult learners in their educational success.

What does it take for an adult educator or tutor to start using Khan Academy?

It seems the major barrier to using Khan Academy is emotional.  Technology integration is as much about changing attitudes and building managerial support as it is about using the actual technology.  Debbi Perkul of Cleveland, Ohio said that to use Khan Academy, instructors need: “the ability to be flexible, and the lack of ego to allow another instructor [Salman Khan] teach math.”  Flexibility and lack of ego do not come easily for most of us!

If an educator is already using online materials to teach or practice math, then the only thing that I could see to prevent them from using Khan Academy is personal motivation and their organization’s internet filters.  Which leads us to our last question:

Is Khan Academy the solution for a free online curriculum for adult basic education & GED preparation?

Right now, sadly, NO. I have three reasons, and possible solutions:


Based on Salman Khan’s personal history as a hedge fund manager, the focus of the current content is math and finance, but math alone is not enough to pass the GED.  They recently added an entire section on Art History from the website smarthistory, which is very exciting, but not on the GED test.  I hope similar partnerships become a trend to round out their content.  He has a section for the math portions of the MCAT & SAT, so GED math could be next!

Add GED to Khan Academy PLEASE

To get the ball rolling, I organized a campaign to add adult basic education and GED preparation to Khan Academy. There are two quick “one click” solutions to help out the cause!

Update (11/12/2012): The campaign has closed, but you can still go to and request the addition of GED content!


All Khan Academy videos are organized by playlist on YouTube (their channel has over 200,000 subscribers).  This caused a major issue for Linda Letherwood, Adult Education Professional in Jackson, MS, who said, “I would love to use it with my students. However, we are in the public school system and they block You Tube videos.  I can only suggest they do it at home or in the library.” There’s also filthy language posted in the comments on videos all over YouTube, so I would include in-class mini-lessons on netiquette.

One solution to this problem is to search individually for the Khan Academy videos on TeacherTube, which is a district-web-filter-friendly version of YouTube.  As a user, you can download one of the YouTube videos then upload it into TeacherTube for use in the classroom.  Some of the users there have already begun uploading Khan Academy videos to TeacherTube, but then you lose all the tracking capabilities.

Another solution is for Khan Academy to create an official channel on TeacherTube or another filter-friendly site (hint, hint!!).  In the meantime, disabling or at least moderating comments on YouTube would be very appreciated (are you reading this, Khan Academy?).

Update (11/12/2012): Teachers can now find appropriate educational videos on You Tube EDU and schools can sign up for You Tube for Schools.


My biggest professional hurdle is not getting people to do things they don’t want to do…it’s helping volunteers to follow through on the good projects they do want to accomplish.  Khan Academy is no exception.  Bob Stephenson in Kokoma, Indiana shares a possible solution: “I introduced the Khan Academy to my math tutors this summer. Although they were interested I am not sure anyone is using it at this time. I think I will begin tutoring a student in math using it to work through any problems and develop teaching strategies. After that I can present it to them again during a tutor in-service training and have results to back up my experience.”  Bob sounds like a guy I would like to work with!

As with any change, there can be anxiety, frustration and confusion starting something new.  But the potential benefits in terms of learner engagement and profile tracking mean the investment of time and energy will be paid back with interest once classes, tutors, and programs get started.

Are you using Khan Academy to learn or teach?  Comment and tell us your story!

Staying Safe in a Toxic World

Announcement: New Issue of the Change Agent The Change Agent Issue 32 Staying Safe in a Toxic World
Staying Safe in a Toxic World, Issue #32 of The Change Agent

“This issue of The Change Agent, produced in collaboration with TERC’s Statistics for Action project, will explore the local environment and will tell our stories of environmental clean-ups and community efforts to identify pollution sources and deal with them. With an emphasis on math and science, activities help students think about large and small numbers, percents, ratios, and scale. A one-pager on “Smart Moves: Take Control of Math” offers strategies for confronting difficult math problems-while avoiding an attack of brain freeze.

Using short narratives, interviews, cartoons, illustrations, and photos, this issue roots reading, writing, and math lessons in content that is relevant to adult learners. Background pieces and interesting facts provide opportunities for students to extend their learning. Lesson plans and discussion questions give teachers classroom-ready material that will engage students and provide an important forum for critical thinking, sharing, and achieving understanding across diverse experiences.

The magazine is free online at .”

For more information, please contact Cynthia Peters at

Forget Flash Cards: Try Math War

Back by popular demand is my most popular post of all time, original linked here:

Use an ordinary deck of playing cards to relax with math. Try Math War to practice basic math operations:

Playing Cards
  1. Take out the Jokers, Kings, 10s, and Queens.
  2. Deal the remaining deck between two players.
  3. One rule: Aces are One, and Jacks are Zero.
  4. Each player flips up a card and the student has to add, subtract, multiply or divide the numbers.
  5. When the student is right, he or she keeps the cards until the whole deck has been won!

You can use this method of playing cards to practice any type of math, all the way to the high school or GED level and beyond. This includes algebra and geometry! But how, you ask? First of all, you will need to grab a pencil and paper for these brain workouts.  I suggest starting with a round of the lighter stuff before getting started on the heavy lifting. Because of the element of chance, these problems often don’t work out to have easier answers…just like numbers in real life.

  1. More numbers: each player flips up more than one card at a time.
  2. Mixed practice: flip up a card and the tutor randomly chooses between add, subtract, multiply, or divide.
  3. More mixed practice: Take a blank piece of scrap paper and fold it in half 4 times. Unfold the paper and cut on the lines to make 16 pieces. Make one of the operation signs (+ – x ./.) on 4 pieces each.
  4. Fractions: one card (or more) is the numerator and one card (or more) is the denominator.
  5. Decimals: use a face card or a piece of scrap paper to make the decimal point.
  6. Percents & ratios: use a face card or piece of scrap paper to make the decimal point.
  7. Algebra: add the face cards back in to become your variables. You might also want to make pieces of scrap paper with (parentheses), square roots, and positive or negative signs.
  8. Geometry: start with your formulas and use the flash cards to get the numbers.

LOL FUN: Return to the simplest version of Math War. When each player flips up a card, make a real life word problem using the numbers. And since this article is meant for adult literacy tutors, you don’t have to censor the results. Trust me, this will hold your students’ interest and make math much less intimidating!

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