Fraction Error Analysis (aka “Help Jane, Peter, and Sam!”)

It’s been a minute since I’ve come up with something I really felt compelled to share here, so…  guess this is a big day.

This year, my kids have math blogs – which they seem to be digging, which makes me very happy.  I’m aiming to have them post about 10 times this year to write about how they are making use of mathematical habits (thanks, Bryan Meyer), among other things.

This week, I had two goals: I wanted my students to do some error analysis pertaining to fraction operations, and I wanted them to do some for-real reflecting about their understanding of fraction operations. Essentially, I hoped to cement student understanding of addition, subtraction, and fraction ‘basics’ before jumping into multiplying and dividing after Thanksgiving break.

I threw together this sheet:

And then this one:

The conversations that ensued were great. (Students discussed in groups, and then we shared out as a class, prior to any writing on that second worksheet.) I loved hearing kids verbalize their conceptual understanding of fraction operations as they remarked upon what Jane, Peter and Sam did correctly and incorrectly. Additionally, my students seemed to take great pride in being able to locate the patterns. (If you haven’t closely analyzed the first sheet: Jane, Peter and Sam each have unique misunderstandings that reoccur in the three problems that they complete.)

I was pretty pleased with the writing prompts, too—which ask kids to think about and propose theories for WHY Jane, Peter, and Sam made these mistakes. (Thanks for the inspiration, Michael Pershan!)  So often, when I attempt to get kids analyzing wrong answers, they tell me, “Oh, it was just a careless mistake,” or, “That was a computational error – I need to slow down.”  I heard nothing of the sort today, which made me happy happy happy.

Each student will author two blog posts as a result of this activity (alas, each student must choose to neglect either Jane, Peter, or Sam). I’m hoping for good results and good dialogue in the comments.

One improvement I’d like to make, next time, would be to use real student work, in actual student handwriting.  If you have other suggestions, I’d love to hear them. I’m hoping to recycle this activity in the future.

PS – Come to think of it, this activity is kind of like an updated, much-improved version of another activity I wrote about here.

find the cost of your paper

Sep 13, Grand Remembrances

Today is Grandparents Day in the United States. Being a Grand is a special honor. I feel very blessed that my wife and I have two grandchildren. We were able to visit them today. Yes, we are still being cautious with the coronavirus, but we also find it very difficult to not see them when they live so close. So today we did drop by to visit Jacob (age 10) and Sophia (age 7) along with their parents. We brought donuts and caught up with them. Our grandchildren are still pretty young and this is a precious time in their lives – and ours!

I wish I had known my grandparents better. We never lived in the same place. Dad was a career Air Force pilot, so we moved around a lot. But we did get to see them once in a while when they would visit us, or we them.

A Plague of Giants

There are five known magical ‘kennings’ or types: air, water, fire, earth, and plants. Each nation specializes in of these kennings, and the magic influences the society. There’s a big pitfall with this diversity of ability and locale–not everyone gets along.

Enter the Hathrim giants, or ‘lavaborn’ whose kenning is fire. Where they live the trees that fuel their fire are long gone, but the giants are definitely not welcome anywhere else. They’re big, they’re violent, and they’re ruthless. When a volcano erupts and they are forced to evacuate, they take the opportunity to relocate. They don’t care that it’s in a place where they aren’t wanted.

I first read Kevin Hearne’s Iron Druid books and loved them (also the quirky The Tales of Pell), so was curious about this new venture, starting with A PLAGUE OF GIANTS. Think Avatar: The Last Airbender meets Jim Butcher’s Codex Alera series. Elemental magic, a variety of races, different lands. And it’s all thrown at you from page one.

But this story is told a little differently. It starts at the end of the war, after a difficult victory, and a bard with earth kenning uses his magic to re-tell the story of the war to a city of refugees. And it’s this movement back and forth in time and between key players in this war that we get a singularly grand view of the war as a whole. Hearne uses this method to great effect.

There are so many interesting characters in this book that I can’t cover them all here. Often in books like this such a large cast of ‘main’ character can make the storytelling suffer, especially since they don’t have a lot of interaction with each other for the first 3/4 of the book–but it doesn’t suffer, thankfully. And the characterization is good enough, despite these short bursts, that by the end we understand these people and care about what happens to them.

If there were a main character it would be Dervan, a historian who is assigned to record (also spy on?) the bard’s stories. He finds himself caught up in machinations he feels unfit to survive. Fintan is the bard from another country, who at first is rather mysterious and his true personality is hidden by the stories he tells; it takes a while to understand him. Gorin Mogen is the leader of the Hathrim giants who decide to find a new land to settle. He’s hard to like, but as far as villains go, you understand his motivations and he can be even a little convincing. There’s Abhi, the son of hunters, who decides hunting isn’t the life for him–and unexpectedly finds himself on a quest for the sixth kenning. And Gondel Vedd, a scholar of linguistics who finds himself tasked with finding a way to communicate with a race of giants never seen before (definitely not Hathrim) and stumbles onto a mystery no one could have guessed: there may be a seventh kenning.

There are other characters, but what makes them all interesting is that they’re regular people (well, maybe not Gorin Mogen or the viceroy–he’s a piece of work) who become heroes in their own little ways, whether it’s the teenage girl who isn’t afraid to share vital information, to the scholars who suddenly find how crucial their minds are to the survival of a nation, to the humble public servants who find bravery when they need it most. This is a story of loss, love, redemption, courage, unity, and overcoming despair to not give up. All very human experiences by simple people who do extraordinary things.

Hearne’s worldbuilding is engaging. He doesn’t bottle feed you, at first it feels like drinking from a hydrant, but then you settle in and pick up things along the way. Then he shows you stuff with a punch to the gut. This is no fluffy world with simple magic without price. All the magic has a price, and more often than not it leads you straight to death’s door. For most people just the seeking of the magic will kill you. I particularly enjoyed the scenes with Ahbi and his discovery of the sixth kenning and everything associated with it. But giants? I mean, really? It isn’t bad enough fighting people who can control fire that you have to add that they’re twice the size of normal people? For Hearne if it’s war, the stakes are pretty high, and it gets ugly.

The benefit of the storytelling style is that the book, despite its length, moves along steadily (Hearne is no novice, here). The bits of story lead you along without annoying cliffhangers (mostly), and I never got bored with the switch between characters. It was easy to move between them, and they were recognizable enough that I got lost or confused. The end of the novel felt a little abrupt, but I guess that has more to do with I was ready for the story to continue, despite the exiting climax.

If you’re looking for epic fantasy with fun storytelling and clever worldbuilding, check out A PLAGUE OF GIANTS.

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The Artwork Of Gary Choo

Gary Choo is a concept artist/illustrator based in Singapore. I’ve know Gary for a good many years ( 17, actually ), working together in animation studios in Singapore like Silicon Illusions and Lucasfilm. Gary currently runs an art team at Mighty Bear Games, but when time allows he also draws covers for Marvel comics, and they’re amazing –

The Art Of Gary Choo
The Art Of Gary Choo
The Art Of Gary Choo
The Art Of Gary Choo
The Art Of Gary Choo

To see more of Gary’s work or to engage him for freelance work, head down to his ArtStation.

The post The Art Of Gary Choo appeared first on Halcyon Realms – Art Book Reviews – Anime, Manga, Film, Photography.

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