Category Archives: Math

Frog Jumping

Gordon Hamilton is the amazing mind behind one of my favorite math sites, Math Pickle. (For a list of interesting math sites, check out this post.) Numberphile is an awesome YouTube channel for anyone passionate about math.  So, when the two collaborate, you know that it is going to be good.  “Frog Jumping” is one of Hamilton’s recent math challenges featured on Numberphile. I would definitely invite your students (probably 3rd grade and up) to try each problem he poses throughout the video – pausing for them to make their attempts. As for his final frog-jumping challenge, I may have to take him up on it, although it’s hard to imagine that I could solve something that eludes Gordon Hamilton!

Frog Jumping
screen shot from “Frog Jumping” video by Gordon Hamilton and Numberphile

5 Educational Mother’s Day Activities

I know that the readers of this blog live in many countries, so I try to write posts that might be applicable no matter where you are.  I was pleasantly surprised, therefore, to learn that many nations celebrate Mother’s Day in May, as does the United States. Here are some lesson ideas to consider that will simultaneously honor mothers as students learn something new.

  • GT Frames for Mothers (original idea from @jtrayers)
  • She Wears Many Hats (advanced students can use multiple meanings and think metaphorically)
  • Mother’s Day Trip (I am considering doing this with my 1st graders, who just researched different countries.  It would be funny to make the video sound like the mom just won a roundtrip vacation to the country on a game show or in a sweepstakes!)
  • Mother’s Day Shopping Spree  – Speaking of winning things, a fun math/writing lesson could be to have students “shop” for their mothers online with a budget. They would have to make sure they stay within budget as well as justify each gift they would purchase.  I would use one store site (such as Target.com) that offers many types of items, or curate some ahead of time for younger students.  Mothers may enjoy seeing what their children would buy for them if money were no (or, almost no) object!
  • Paper Circuit Greeting Cards (more examples here)
wearsmanyhats
My mom wears a “magician hat for when she magicly gets websites working again after I acedentely hit a button.” image from “She Wears Many Hats

15 Math Sites That Won’t Make You Fall Asleep

My students, especially my 4th and 5th graders, love math challenges.  If I can, I find ones that don’t show the answer so we can all try to figure them out.  I think it’s good for the students to see me struggling (and I really do!), and how I handle frustration over particularly devilish problems.  Last week, my 5th graders and I spent a good 30 minutes on this “easy” problem on Steve Miller’s Math Riddles page. (Technically, they had an excuse since they hadn’t exactly learned the math skill needed to solve the problem – yet.)

If you are looking for some unique math problems that will feel more like brainteasers than standardized test practice, here are some sites that I haven’t mentioned before:

And here are some that bear repeating (*sites include activities for primary grades, K-2):

With more and more articles coming out every day about the importance of modeling a good attitude toward math (like this one and this one), it seems kind of as simple as 1+1=2 to come to the conclusion that the people who have fun doing math will be more inclined to do it more often.

UPDATE 4/26/17 – I can’t believe I forgot to include this one: Estimation 180. So, there’s a bonus for you!

polyhedrons
image from: fdecomite on Flickr

The Hidden Secret to Understanding the World

In my 4th grade gifted and talented class, the students study masterpieces.  In addition to masterpieces of visual art, we talk about literary, musical, and even mathematical masterpieces.  When I saw the title for Roger Antonsen’s TED Talk, “Math is the Hidden Secret to Understanding the World,” I thought it might fit in well to the mathematical masterpiece section.  Little did I expect that it would tie everything together that we had discussed all year.

I should mention that this year’s 4th grade class has some very passionate mathematicians in it.  They worship Pi, see Fibonacci in everything, and sit on the edge of their seats whenever I mention that a math activity is imminent.  But I wasn’t sure they would find Antonsen’s talk as revolutionary as I do.  I was willing to overlook the mathematical examples that were over my head in exchange for appreciating the bigger picture, but would they?

Fortunately, Antonsen’s visualizations managed to maintain their focus, and even their awe at some point, as he gradually brought his audience around to the idea that mathematical equations and representations are actually different perspectives (a few heads raised a bit whenever he said this word, as we regularly talk about multiple perspectives).  The “a-ha” moment, however, was when Antonsen said this, “So let’s now take a step back — and that’s actually a metaphor, stepping back — and have a look at what we’re doing. I’m playing around with metaphors. I’m playing around with perspectives and analogies. I’m telling one story in different ways. I’m telling stories. I’m making a narrative; I’m making several narratives. And I think all of these things make understanding possible. I think this actually is the essence of understanding something. I truly believe this.”

There were audible exclamations in my class when the word, “metaphor,” was used.  We started the year by learning about figurative language.  And the concentration in 4th grade in Texas is on Writing as it is tested at this level for the first time.  So, looking at math as a way to tell stories and show different perspectives really captured the attention of my students.

I often tell my students about my childhood struggles with math, how I was often congratulated on my writing skills but made holes in my math assignments due to all of the erasures.  It wasn’t until high school that I had a few great teachers who taught me to love math and helped me to see that my only obstacle had been my own fear of the subject.

Screenshot 2017-04-04 at 8.35.25 PM
from Roger Antonsen’s TED Talk

If I had seen Antonsen’s TED Talk when I was in 4th grade, things could have been different for me far sooner.  Instead of feeling like math divides people into those who can and those who can’t, I might have realized that math is actually the language that brings us all together.

Visualistan

Perhaps my interest in the infographics on “Common Mythconceptions” led me to Visualistan, which I bookmarked in my Pocket account awhile ago.  The specific infographic I thought might be useful for my students was, “How Long Did Famous Structures Take to Build?

How Long Did Famous Structures Take to Build? #infographic

Having time during this Spring Break, though, I found some others that might be of interest in educational settings. For example, if your students are doing animal research, you might want them to take a look at, “Travelling Speeds of Animals,” or “Sleep Habits of the Animal Kingdom.”

Travelling Speeds of Animals #InfographicYou can also find more infographics at Visualistan

Sleep Habits of the Animal Kingdom #InfographicYou can also find more infographics at Visualistan

Another one that I find intriguing is, “Cultural Differences in Teaching Around the World.

Cultural Differences in Teaching Around the World #infographic

Like “Common Mythconceptions,” I would not recommend the entire site of Visualistan for elementary students, but single infographics from the site could certainly be used at all levels.  There are many real-life math applications and engaging topics, from “Lego Bedrooms,” to the “Evolution of Video Games.”  You could create your own questions, have students create questions, and eventually allow students to create their own infographics!

Some Rational Ways to Celebrate an Irrational Number

Pi Day (3/14) always falls during our district’s Spring Break, so I try to celebrate it with my students the week before, if possible.  After looking back at my Pi Day posts from past years, I see that I can add a few updates, so here are some of the ways we honored it in my classroom this year:

Some other resources you may want to try that I haven’t mentioned before are:

The number of ways to celebrate the number seem to be almost as infinite as the number itself!

piday
image from: Amit Patel on Flickr

Prodigy

This year I seem to have a group of students in each of my grade levels who are passionate about math.  Every time I pull out a math activity, they devour it with glee.  It has been a challenge for me to give these students assignments which maintain their excitement for “hard” math without discouraging them with work that is too difficult.  Their classroom teachers are facing the same dilemma.

A couple of weeks ago, I decided to see what my 4th and 5th grade gifted students thought about Prodigy.  Prodigy is an online math game that is free.  (It is also available as an app.)  Teachers can add classrooms of students, and can manage the math topics students practice, as well as the levels at which each student plays.  I immediately assigned all of my students to topics above their current grade levels.  After introducing it in class, I gave them their individual passcodes, letters for their parents, and the caution that playing Prodigy was completely optional.  I also notified their homeroom teachers, and made it clear to the students and the teachers that it was completely up to the teachers to decide if the students could play the game in class.

My students say that the graphics are apparently reminiscent of that popular game, Pokemon.  The students create avatars and can battle each other by doing math problems. They can also earn different abilities as they progress through the game.

There is a paid option for Prodigy, where parents can buy memberships.  This allows the students to access a few more features than the free version.  I have one student who asked his parent for permission to get the membership so far; everyone else seems satisfied with the free game.

I like that I can see individual student reports with Prodigy and that I can differentiate for each child in my class.  I am also pleasantly surprised to see how excited the students are about playing the game.  In addition, the privacy aspect seems fairly good, as the avatars do not give away any student information.

Prodigy does not teach.  It is not a substitute for engaging classroom lessons that include higher order thinking skills.  I enjoy using it as a formative assessment as it gives me reports on the strengths and weaknesses of each of my students in the skills they are assigned, but I would be appalled by any teacher who used Prodigy as their only method of assessment or differentiation.

As long as my students continue to be excited about math, I will view Prodigy as one of the many tools at our disposal that supports their learning.  But I will also continue to provide them with real-life opportunities to use math in relevant ways.

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