after-MATH

As I was posting about Minnie Minus yesterday, the kids were off playing, pretending they were characters from our "Four Friends" story. Just about the time I hit "send", they appeared at my elbow and demanded "What is 'Multiply'?"

Trying to hit the balance between letting them make their own discoveries about the story as it relates to mathematical concepts, and providing them with information they need on that path, I queried, "You mean like Max Multiply?" They nodded, and I assured them that we would figure that out as we went. That wasn't good enough. "We want to know NOW," Zoo Boy demanded.

I sighed. This wasn't quite how I'd planned it, but the last thing I wanted to do was to squash enthusiasm for math! So I just offered "Well, what does Max do in the story?" "Cartwheels," J piped up. "Goes fast," Zoo Boy added. I nodded and asked, "And what's he doing while he's cartwheeling fast?" "Picking up gifts," J noted. "FAST," Zoo Boy added. I nodded again and commented, "Yeah, when you're picking up handfuls at a time, you collect more than just adding them one at a time." The boys looked at each other and headed back down the hall.

And here's what I came upon when I followed them a few minutes later:

I have to admit, I was a bit surprised. If you look at my actual lesson, while we DID work with the stones while doing word problems, they have never seen a manipulatives worksheet (which is what J created here on his magnadoodle), and I've never discussed the multiplication symbol with them. And yet, here was the very work I was going to introduce them to in another few weeks or so. Zoo Boy proudly pointed at the equation, and stated "2 multiply 4 is 8!" I softly corrected "2 times 4 equals 8", and the kids immediately shifted their language to reflect the proper phrasing as they played around with other equations.

Meanwhile, I started lunch. By the time I called the boys to eat, they had moved on to division, without ever asking me about it. I did hear J say at one point "oh, I know what divide is, it's where each gets his fair share" (a line from the "Four Friends" story). I watched as he worked through "12 divide by 6". He set out 6 of his Bakugan, then distributed 12 stones amongst them. At that point he realized I was standing there, and looked up at me with a smile and said "12 divide by 6 equals 2". I nodded my head at him, and we headed into the dining room to eat.

Later that afternoon, I found J writing out equations, asking them to Zoo Boy who was using his fingers to figure out the answers.

They've sort of rushed through 2 blocks worth of math on me. But that's OK. J already sort of knew this stuff before we started it -- the point of my bringing them the stories and the manipulatives isn't to teach them anything, it's to provide a stronger grounding in mathematical relationships and concepts, and provide the sign posts along the path to them making their own discoveries.

They're doing the learning on their own. I'm just here to document the journey.

3 + 4 =?

Did anybody catch my math error on the previous post?

Don't bother looking now, I already fixed it. But for about 12 hours, proof that I may not be well suited to teaching my children math was published for all to see.

Seriously, it was only the blog I made the error on, not the information I provided my children. That's some small bit of comfort for me, at least....

minnie minus

So for each creature grand and poor

I leave a gift at every door

Four, three, two, one...

Till everything I have is gone.

--from "The Four Friends Play", an Enki Education 1st Grade Math Story

Yesterday we began our work with subtraction, reciting the Minnie Minus verses from the "Four Friends" math story. Then we did a led-drawing of Minnie leaving her little gifts for all of her forest friends. This first drawing is J's. I would like to note that I did NOT draw a "minus" sign on my title, but both of the boys chose to do so, without me making any mention to minus signs. However, you will note that Minnie's arm purposely reaches straight out, it's own minus sign.

Zoo Boy's Minnie Minus drawing. He says there's a squirrel in the hole in the tree.











I then had the kids get their counting bags, which they were gifted with yesterday -- each bag has 12 glass gemstones in it. I also worked with a bag of 12 gemstones. I then gave them an oral word problem to work with, while I demonstrated how to work it out with my own stones. "Minnie had 12 gifts to deliver," I started, counting out my 12 gemstones. (Here Zoo Boy does the same thing with his gemstones, following my example.)

"She gave 3 packages to Paddy," I continued, pushing 3 of my stones to one side. "Then she gave 4 packages to Max," pushing 4 stones in another direction. (Here's J doing the same with his stones.) "How many gifts did Minnie have left?" I asked the boys. J immediately jumped in with an answer "5! 12 minus 7 is 5!" Zoo Boy counted his remaining gemstones to make sure he arrived at the same answer, and smiled. "It IS 5!" he confirmed.

(My Minnie Minus drawing. I really should have made her entire arm straight, without the bend at the elbow. Oh well. The kids' drawings are better, as usual.)

We worked through several more word problems in that way, then I left them to play with their stones as they desired for a bit before shooing them outdoors to get some fresh air.

farm animal class #3 -- sheep

I taught the third in my preschool farm animal series this week. Our topic was sheep, in particular lambs, like my adorable little Alice shown to the left. We started out singing the Old MacDonald song, with sheep, ewes, rams, and lambs (all sounding pretty much the same -- baa baa here, baa baa there). Then we sang Mary had a little lamb, followed by Baa Baa Black Sheep.


The book I read was the lovely Little Baa, by Kim Lewis. In the book, Maa looks all over for Little Baa, who fell asleep, and is found and reunited by the shepherd and his sheepdog. We then went outdoors and played a game of "Sheep Tag". Most of the kids were sheep. Two of the kids were wolves. And one was the shepherd. The shepherd went across the field to the "barn" and called the little sheep to come home. As the sheep ran for the barn, the wolves tried to tag them. If they were tagged, they went to the "wolf den". Basically it was an excuse for the kids to run around screaming in the sunshine. It worked well!

Then we went back indoors to make our craft -- this cute little magnetic note-holder with a sheep on it. This one wins the prize-of-the-series for being the most simple craft -- all we had to do was glue on the sheep and stick on the self-adhesive magnet to a clothes pin. I did pass out markers so the kids could color their clothes pins first if they wanted to. (Zoo Boy chose not to, but I think everyone else did.)

And of course I gave them each a coloring sheet to work on at the end of class. As you can tell from the past three weeks worth of coloring sheets, coloring just isn't Zoo Boy's thing.

We have a week off from classes next week, then three weeks in a row to finish up the series. Still to come, horses, ducks, and cows!

four friends

This week we started a math block about the four computational processes (addition, subtraction, multiplication, and division). As with all conceptual learning, Enki Education approaches this through story first. So on Tuesday we read the Enki 1st Grade Math Story "The Four Friends", about Minnie Minus, Paddy Plus, Max Multiply, and the ever equitable ruler of the kingdom in which they live, King Dominic Divide. (This first photo is my beeswax sculpture of the four friends.)


Both kids were very taken with the story. J in particular was getting more excited every time a new character was added. As soon as I finished the story, he immediately jumped up and yelled "I know who those guys are! They're math guys!" and then rattled off their names with an emphasis on the character's process as proof of his understanding. I smiled as they boys ran off to recite lines from the story and pretend to be various characters. (Second photo is J's interpretation of King Dominic Divide, sculpted in beeswax.)

Yesterday we recalled the story, and I chose beeswax sculpting as our artistic digestion. We'll be working with each character/process individually in the coming weeks, including led-drawings of them, so I felt something other than drawing would serve my children's interest best. (Third photo, Zoo Boy's representation of Paddy Plus.) The kids were given no instruction, just a pile of colored beeswax, they chose what they sculpted and how they looked on their own. I found it very interesting that Zoo Boy's Paddy wound up looking like a plus sign, and J's King Dominic wound up looking surprisingly like mine even though we each worked individually on our own creations without referencing the others.

back to walking

With the weather warming up (ever so slightly), we've been able to resume our morning walks. J wanted to focus on finding and photographing signs of spring this morning, so we brought my camera to see if we could capture some signs that life really IS going to return around here at some point. We've had some pretty good luck finding spring signs in the places we visit, but here in our own neighborhood things are moving a bit slower thanks to it always being about ten degrees cooler than it is anywhere else.


We discovered the first of the skunk cabbage coming up in a marshy area. Didn't seem like there was much else in the way of greening up going on there yet, though.





J stopped to examine the buds on a Sugar Maple. They are still small without much sign of leaves, but at least they are red and adding a bit of color to the gray landscape. The grass in the pastures is also starting to green up, although it hasn't begun growing yet. Soon, I think. (And our sheep hope!)

The forsythia are trying really hard to push some blossoms out. They are all showing the slightest yellowing now, and I suspect by the weekend we'll see a burst of yellow flowers.

Zoo Boy examines a vernal pool for signs of life. No frogs or salamanders seen today, still too chilly. He and J are both looking forward to a nice warm, rainy spring night so we can drive around and look for amphibians moving to their breeding pools to lay eggs.

Grace poses by some emerging Horsetails. I love Horsetails, they're just such primitive plants, they seem out of place growing along a New England stone wall.

local wildlife

The boys had a museum class yesterday about the types of wildlife that live right here in Connecticut. They discussed various species of wildlife and examined their tracks, scat (poop), claws, fur and quills. They learned about White-tailed Deer, Porcupines, Beaver, Cottontail Rabbits, and Painted Turtles, amongst other species. In this photo, Zoo Boy shows some of the class materials to The Map Man after class.



The class prepares to go bird-watching. This morning Zoo Boy told me that bird-watching is his favorite thing to do in the spring. Nice coincidence, as bird-watching is one of MY favorite things to do, any time of year.








Some of the identification tools they used while out bird-watching.









J works on a diorama in class. The kids built a model of their backyards and covered the ground with footprints from the animals that are found there. J chose to have a bear walk across his backyard. Not totally unrealistic, we do have Black Bears in our neighborhood, and no doubt they traipse across our property on occasion, although we've never seen one in our actual yard. A neighbor did see a Mountain Lion in our yard once, however.


Zoo Boy shows off models of the scat from a beaver and a porcupine, two of his favorite mammals, or so he tells me. (Black Bear is his third favorite.) Not surprisingly, this class was a HUGE hit with The Boy. Right up his alley, so to speak.