Category Archives: 3-12

The Beauty of Spirals

My 4th grade students are currently studying mathematical masterpieces.  I love showing them examples of the intersection of math and art.  When I saw a tweet yesterday morning from @TheKidShouldSeeThis with a link to the video of John Edmark’s spiral geometries, I knew right away that they would want to watch the video.  It weirdly connected with the magical drawbridge from yesterday’s video, so I showed that part to them first.  We have already talked about Fibonacci and the Golden Spiral, so they immediately found ways to connect both videos to their learning.

Since the students have also been using Scratch coding, I found a Scratch project for making spirals.  First we looked “inside” to decipher the code.  Then the students explored running the program.  After that, I talked about creative constraints, and gave them the challenge of changing one and only one part of the code to see how it made the program run differently. They recorded the results of their new programs and the class tried to guess what variable each student changed based on the videos.  Then I gave them time to freely remix however many parts of the program they liked.

This was one of those times that the students could happily have explored all day.  It was their first time remixing a program, and they delighted in trying to take it to the extremes by putting ridiculous numbers in to see how large or small or non-existent their spirals became.  Some of them created spirals so tiny that they appeared to be flowers blooming as they popped on to the Scratch stage.

And I still haven’t blown their mind with this Vi Hart video yet.  With the school year almost over, we may have to take this unit into their 5th grade year.  There is so much beauty in math, and we have barely scratched the surface!

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image from Marco Braun on Flickr
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Our Magnificent Manifestos

As my 5th grade students wind up the school year, I begin to worry that they will go to middle school next year and forget everything they learned in our GT classroom.  Some of them have been with me for 6 years, so I’m hopeful that a few things will “stick.”  Nevertheless, a visual reminder can be helpful.  Rather than make them all stick pictures of me on their walls at home, I started this project with last year’s 5th graders.  It seemed to make an impact so I decided to repeat it this year.

You can read a little more about the process I used to jump start this year’s manifestos here.  Once the students did quite a bit of brainstorming, I let them jump on to Canva to design their manifestos.  Things were going merrily along until I noticed that many of them were using famous Pinterest quotes on their documents instead of their own words.  There was a bit of groaning when I insisted the manifestos needed to be in their own voice – not someone else’s.  I’m still not sure if that was the right thing to do, but I just felt like it would be more meaningful.  One of my students was quite satisfied with one her rewrites, “Life’s a llama with a neck full of opportunities.”

Another mistake I made was to let them design to the edges.  Last year, the students downloaded their manifestos as images, and we printed them on t-shirts.  The quality was not very predictable, though.  This year, I went to the dollar store and bought each of my 11 students a frame.  When we tried to put some of the manifestos into the frames, though, words got cut off.  (That’s why you won’t see 11 in the picture below; I’m still re-printing some.)

For an investment of $11, I got more than my money’s worth when the students framed their manifestos.  The students were proud of their work and I got the impression that at least some of them might display those manifestos in a place of honor when it goes home.  I also really like having them in the classroom for all of my students to see. (We can’t hang them up because I am in a borrowed room at the moment.)

The next part of the project is for the students to design their “Dream Teams.”  They are using the “Find My Role Model” tool from The Academy of Achievement to find 5 people they admire who embody the statements on their manifestos.  You can see some ideas for how to publish your Dream Team here,

Photo Apr 24, 12 59 09 PM

Scholastic Beasts

I am currently offering an online Google Classroom for some students in our district that assigns them one Digital Breakout (Math) a week for 5 weeks.  “Scholastic Beasts” is the 4th one in the series.  For the first three, you can see:

All of these are designed for 4th grade gifted and talented students.  As with the others, you can e-mail me at engagetheirminds@gmail.com with the title of the Digital Breakout if you need the answers – but I find that it’s better to not help your students too much!

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Click here to go to the Scholastic Beasts Digital Breakout!

CommonLit Poetry

Back in 2015, I found out about CommonLit from Richard Byrne and pointed people to his post to learn more about this free resource for teachers.  Since then, CommonLit has added a Guided Reading feature that can really be helpful for differentiation in your classroom, Book Pairings, and probably a few other tools that I haven’t mentioned – yet it has continued to be free.  This is huge in the world of EdTech, where teachers often find ourselves priced out of “free” programs.

Since it is National Poetry Month, I thought I would remind you of CommonLit, which does have quite a few poetry offerings.  Once you log in and go to the library page, you can see some of the featured poems selected by the staff for this month.  You can also go to the “Browse all Text Sets” page in order to search for particular genres, themes, grade levels (3rd grade and up), and lexiles.

I love looking at the Book Pairings, which offer supplemental short texts to accompany novels.  For example, my 5th graders read The Giver, and CommonLit links to 4 poems that nicely fit with the themes of the book (along with some news articles and informational texts as well). The search page helpfully identifies the genre of each link, its lexile level, and grade level.  CommonLit even gives you advice on which point in the novel would be a good time to add the paired text.

CommonLit offers a Teacher Dashboard so that you can assign passages within the site.  There are also short assessments and suggested discussion questions for each assignment.

Because CommonLit is a nonprofit organization, it promises that its resources will always be free for teachers.  Take advantage of this site to encourage deeper reading, discussion, and connections.

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Go to CommonLit for more information.

Counties Work

The iCivics website is an incredible free resource that I have blogged about in the past.  Recently, the site added a downloadable, printable resource called, “My County Works,” for elementary students that gives an overview of the way county governments work here in the United States.  There are other links to lesson plans and activities for middle and high school on the “Teach Local” page of iCivics.  My 3rd graders, who have been studying Systems Thinking, enjoyed playing the “Counties Work” app, which allows the user to be in charge of a fictional county and make decisions about the appropriate ways to spend the budget.  The students had to learn which departments would be assigned particular projects, how spending money and charging taxes would affect their popularity (since they were in an elected office), and the importance of keeping a balanced budget.  Although the game is, of course, a bit simplistic, it does give students an idea of many factors that need to be taken into consideration by officials before approving citizen requests.

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Counties Work app from iCivics available on iOS and Google Play

Kaled It!

I overheard some of my students talking about a cooking show called, “Nailed It!” and decided to make my next Digital Breakout based on that title.  Because we have been having a few glitches with Google Sites in our district, I decided to use Weebly to create this one.  “Kaled It!” is a bit harder than my 1st and 2nd Digital Breakouts.  Therefore, I thought I would give you some of the clues I just posted for my Google Classroom students: Lock 1 can be answered with “The Milk Dilemma.” Lock 2 will be found on “Shopping.” Lock 3 is answered using “Kale Pesto.” If you want to answer Lock 4, then carefully explore the “Meet the Contestants” page.

As with the first two Digital Breakouts I designed, teachers can e-mail me at engagetheirminds@gmail.com to receive the answers. (Please put the name of the Digital Breakout in the Subject line.)  However, I agree with the one teacher who told me that she enjoyed not knowing the answers because she didn’t help her students too much!

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Click here to go to the “Kaled It!” Digital Breakout

Causal Modelling

I’ve been lately trying to use more Integrative Thinking in class.  It bring about really deep discussions, and I like to see the students make visual models of their thoughts.  In the past few weeks, I have been working on “Causal Modelling” with my 3rd-5th graders with varying degrees of success.

You can see a short video of Causal Modelling in action here.  Basically, students try to consider all of the possible reasons for a particular situation or problem.  In the video, the topic is, “People Struggling to Afford Food.”  With student input, the teacher makes a web with this topic in the center and several nodes that name possible causes.  It quickly develops in complexity as the students volunteer causes for the causes and begin to see connections among causes.

This blog post by Heidi Siwak shows several examples of causal models diagrammed by her 7th graders for issues varying from gun violence (very topical!) to unfinished homework.

To start causal modelling with my own students, we worked on creating a class causal model about why Nemo gets lost in Finding Nemo.  Then I put students in groups to generate causal models about the fiction we were reading in each grade.  For my 5th graders, this meant they explained an event from The Giver.

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After doing group causal modelling about fiction, I asked each grade level to apply it to “real life.”  My 3rd graders brainstormed recurring problems, such as a sibling interrupting them when they are playing with friends, and came up with multiple causes.  After breaking it down this way, they could see potential ways to avoid some of the precipitating events (sibling needing attention, for example), and potential solutions.

With my 5th graders, I had a different idea.  After reading this post from Heidi, I realized that the personal manifesto activity they were working on was the perfect opportunity for them to get a picture of why they believe what they believe.  Since we were about to have a 3-day weekend when many would be visiting with extended family, I sent them home with a rare homework assignment: pick one of your belief statements and do a causal model for why you believe it.  Think about your own experiences, what your parents believe, and even ask your grandparents and parents why they believe it (if that’s where it came from).

One student said to me, “What if it’s not from your parent?  What if it’s from you?”  I asked, “What’s the belief?”  She said, “Taking risks.”  So I explained how, when I was young, I had volunteered to do a monkey bar race at an amusement park.  Sneakily, the proprietors had greased the bars, so I fell off when I reached for the 2nd bar, landing in a pool of water.  I was humiliated.  Afterward, my mother bought me a coveted stuffed animal in the souvenir shop – not to make up for the embarrassment, but to reward me for trying.  That’s when I learned that it’s more important to try and fail than to do nothing at all.

The students came back from their weekend, nearly all having done the assignment in one form or another.  Some wanted to share it publicly, and some wanted to have a private audience with me to speak about the personal reasons for their beliefs.  I would definitely say that I learned a lot about each of them, and I hope that they learned more about themselves.

Overall, causal modelling helps students to grasp that “wicked problems” (as Heidi calls them) cannot be solved with sweeping generalizations.  “Why don’t they just…” rarely addresses all of the causes, or all of the deeply held beliefs that led to those causes.  It might help a few of our current leaders to keep this in mind. 😉