More squares

Let’s make a square of area 21.

First, we find the sum of squares that is 21: 4+4+4+9.

We we will make a square of 8 from two squares of area 4

and then we will make another square of area 13 from a square of 4 and 9.

Then from those two squares of 8 and 13 we will make our square of 21.

Illustrations made with Geometer’s Sketchpad.


A square plus be square equals see square!

We’ve been going over the pythagorean theorem this week in my math classes, and I used this as an anticipatory video (along with some video with Darth Vader introducing the Pythagorean Theorem).

“And while it might seem like the only time that would be useful would be in say a high school geometry class, there are actually a lot of real life situations where the Pythagorean Theorem comes in handy. For example, say Jane is standing 30 feet away from a 40-foot tree and Paul decides to trim the tree 5 feet above the base. Is Jane safe from the falling tree?” Is Jane safe?! Dr. Amy Jeppsen Tanner proves the Pythagorean Theory by brownie 🙂

Featured in Creativiteach: The Lizzie Bennet Diaries

I wrote another guest blog on Dr. Starko’s blog on creativity: I had been planning on writing something on TheLBD but I was finally launched into play when Gigi hit the videos (Georgiana).  Anyway, it’s reposted in full here, but please follow the link to her blog.  There are weekly posts on teaching creatively and more importantly teaching for creativity.


Today, guest blogger Melanie returns with a post for those of you who teach English, love Jane Austen, are interested in video blogs or just want to see an amazingly creative riff on classic literature. Here’s Melanie.

Even if you don’t teach Pride and Prejudice in class, this web series presents a special opportunity for teachers and bookworms alike.  The Lizzie Bennet Diaries(LBD) is a modern adaptation of Pride and Prejudice told through a series of 5-minute vlogs (video blogs).  The LBD tells the story of Pride  and Prejudice over the course of a year, posting vlogs every Monday and Thursday.  Occasionally, when Lizzie has been away from home at Netherfield, Hunsford and Pemberly, Lydia has posted vlogs sporadically on Tuesday and Fridays.  (However, while Lizzie to-date has posted 83 vlogs, Lydia has posted 22.)

LBD2Not to spoil too much, but Lydia is a more sympathetic character.  Charlotte and her sister play a greater role in the story.   Mr. Collins is adorkable.  Mary is a cousin and Kitty is an actual cat that follows Lydia around everywhere.  Collins didn’t propose marriage to Lizzie but offered her a job that she did not want.  Wickham isn’t a soldier; that would be too respectable a job in our day.  Instead, he’s a swim coach.  Darcy’s the CEO of a media company.  The Bennet sisters have jobs and school but still face job uncertainty, financial distress and social pressures in their relationships.

Because the story is told through the limited frame of Lizzie’s videocamera, some action is re-dramatized in costume theater. Some characters are meta-aware of the camera and the vlogs (Caroline, Wickham) and others are not (Bing Lee).

LB3The writers have also created a transmedia storyline that enriches the vlogs (character twitter accounts, pintrest, linkedin and youtube channels).  Characters tweet in real time with plot-related tweets. For example, when Lydia goes to Vegas/Brighton,  Georgiana (Gigi) starts commenting on Lizzie’s videos when she watches them.  The show also encourages audience interaction.  You can connect to the transmedia in chronological order from the website: The creators announced that they will be adapting another story after this one.  However, they have not announced which story.

lb5Lizzie Bennett, and vlogs in general, offer a range of options for classroom creativity. Lizzie Bennett could be incorporated into classes as a weekly warm-up,  a lesson on modern adaptations, or even a focus on the Common Core outcomes regarding analyzing multiple versions of a story, or using technology to share writing.  Start by reading a short chapter (Mr. Collins’ proposal or Darcy’s profession of love and his letter) and then watch the segment from a period piece (BBC/Knightly) followed by the parallel LBD vlog.   Students can track the story differences in family dynamics, profession, and relationships.  Students should consider what parts of the story are left out because of the mode of storytelling.

Then, students can propose their own vlog adaptation of a period story they have studied, creating a short script or storyboard–or even a vlog of a particular scene. Imagine Huckleberry Finn or Oliver Twist as contemporary characters. Perhaps Huck would really like to skateboard and film his boarding tricks, but be in and out of schools.  King Arthur might interview and vet the resumes of his knights. Or what if you are reading Treasure Island: who will be voted off the island first?  Lewis and Clark could have a travel blog!

Here’s Alane again. Isn’t this fascinating? And what better way to hook technology-saturated students into the complexities of period literature than doing what any good teacher does–tie it to what they know. Of course, the key that will move this from a motivating-but-tangential activity to one that leads to in-depth understanding is the degree to which it is structured to require students to create and justify real parallels. If Huck Finn is a skateboarder, why? What characteristics from the novel support the decision? How are the relationships and struggles in the Lewis and Clark travel vlog representative of what happened to the original explorers? Helping students make and justify such decisions can lead to critical analysis of literature, boundless opportunities for creativity, and a lot of fun.

I’d love to hear about your experiences in the world of vlogs.


Featured in Creativiteach: If the teacher is bored…

I wrote a guest blog on Dr. Starko’s blog on creativity: It’s reposted in full here, but please follow the link to her blog.  There are weekly posts on teaching creatively and more importantly teaching for creativity.  I feel very honored to have Dr. Starko as a friend and a mentor.

 It is a classic line: If the teacher is bored, we have a problem! In this guest post, Melanie Carbine describes a math lesson that is an example of both creative teaching, and teaching for creativity. Like many creative activities, it emerged from a moment of need. Here’s Melanie.

I had a month substituting for what I thought was my ideal teaching position: 8th grade pre-algebra and Algebra 1.  Coming into 8th grade after spring break would have taxed my planning abilities even if I hadn’t been the substitute.  The teacher had left plenty of basic lesson plans that I could use, and it sounded as if they had gone over geometric constructions before.  So, I let them have at it… epically overestimating their abilities (to self-manage)–especially with pointed implements in hand.  Then I sat down and started over.

From the start when I was looking at the week’s flipcharts and worksheets and quz, I just sighed: BORING!  You know you have a problem, when the teacher’s bored.  When are these kids ever going to need to construct a square free hand??  Carpentry.  Ok.  Architecture.  That’s a cool profession.  Photography.  Yes.  And comic strips and graphic novels.  Jackpot!!  They’ll learn how to construct squares as the means to do something cool. And creative.

With that in mind, we started the week off constructing lines again.  We copied a line segment, bisected a line segment, copied an angle, bisected an angle.  I did the first example of each and then had a volunteer give it a try.  Then, there was some independent practice.  Next day: copying triangles.  And, more practice.  Then we hit squares.  I was using the teacher’s flipchart and thought we could certainly get half way through the process.  Ha!  There were so many circles I was getting lost!

I let the kids do some problem solving and they developed a strategy that built on the skills they had previously developed.  Using their strategy*, I set them on the task of creating either a four-panel comic strip or constructing a Mondrian square, modeled on the geometric art work of Piet Mondrian. This easily took two 40-minute class sessions, especially with coloring the final products and some students completing both options.  Considering my open-ended directions, I thought the students still did a very nice job.

*Student Strategy: Double a line segment.  Bisect that line to create a right angle.  Measure off an equal distance.  Work as if finding the angle bisector, and connect the four points to make a square instead of drawing the diagonal.

Afterward from Alane: I particularly like this lesson because students had a double opportunity for creativity, while also practicing required math activities. Designing the Mondrian squares allowed for artistic creativity, and designing their own strategy for constructing squares provided a chance for flexible thinking in math. And as an added bonus, required math had a clear real-world purpose. Such a deal!

Think about a time you’ve incorporated creativity in one of your lessons–perhaps because even you were bored. I’d love to hear from more guest bloggers. Just go to the “About Creativiteach” link at the top of the page and tell me about it.