Math Monday:: “Simon Says…” Angles Math

In the spirit of Trampoline Math, our Math Club last week opened with some new Simon Says activities. Our exploration into square numbers and then the Pythagorean Theorem also led us into discussing angles and triangles.

The angles being: obtuse (bigger than 90 degrees), accute (smaller than 90 degrees), and right (90 degrees exactly). The triangles being equilateral (all 3 sides are equal in length), isosceles (2 sides are equal in length), and scalene (no sides equal in length). We also covered right triangles…the special kind of polygon where two of the sides form a right angle.

Was that as boring to read as it was to type?! Yes, methinks so. So, I’ll tell you how we talked about angles and triangles the fun way…using our bodies.

right angle, using your arms:

Acute angle, using your arms, arm, or fingers:

Once the kids got comfortable making angles, they started making them with whatever part of their bodies they could. Note that there are three different models of acute angles: Naturalist is using one arm and bending it way closed to make her angle…her friend T is using two fingers spread only a little wide to make his, while golfer is doing the two armed style. Later on they used legs, feet, wrists..anything with a hinge.

After a few warm ups to get everyone on board the angle train, we started Simon Says…Simon Says make an acute angle, Simon Says make an obtuse angle, Simon Says make a right angle with your leg, Simon Says make an acute angle with your arm…etc. etc.:

As you can see, this is multi-age friendly. Lots of laughs were had.

With only 3 angles, it didn’t take long for that part of it to be over with, so then we moved on to the triangle part of it. All the kids were in one group, and when I named a triangle they had to choose who would help make it with their body. For instance, I said, “Equilateral Triangle” and even though I’m pretty sure none of my kids could give the definition correctly, they knew that they had to find 3 kids that were the same height. It’s just another way of processing information…they don’t really connect to a triangle on a sheet of paper, and having 3 equal sides doesn’t really matter to them…until they have to construct one using their friends.

So here’s as close as we could get to equilateral:

They tried to build an isosceles triangle standing up, which didn’t really work…it looked more like a pentagon:

so they had to reform to make it on the ground:

I have to say, one of the most fun parts was rolling the younger kids into position…Sassy in particular is very ticklish:

Most interesting of all was making a right triangle. We knew, from the Pythagorean experiments we’d done the last week, that important numbers were 3,4, and 5…because if you take the squares of 3, 4, and 5 you end up with a right triangle. The kids set about finding a similar ratio that applied as a relationship to their sizes, and decided that my three would be perfect to make it:

Aren’t my kids simply and elegantly gorgeous? And photogenic?! Anyway, getting back to the triangle, sure enough, they were able to make a perfect right triangle:

would you like to see another angle of the right triangle? of course you would:

I found this fascinating to watch. The word ‘hypoteneuse’ doesn’t mean a whole lot to my kids until they started making their own body triangles, then they realized that the tallest person would always be the hypoteneuse, and that was always the line across from the right angle.

We did some other things, namely, building and playing with shapes:

but I’ll save that for another time.

For now, I’ll end with the observation that kinesthetic math is a powerful learning tool, and easily adaptable to most math concepts in a variety of ways. Math Simon Says has been a really versatile tool in our multiage gathering!

Indian Summer

Colorado is having a tough time deciding what kind of weather we should have this fall. Last week we were hit by a snowstorm that dumped 2 feet of snow, leaving our halloween decorations very confused:

This week, the last couple days have been in the high 70’s, low 80’s, leaving me very confused but very happy:

This schizophrenic weather is leaving me a bit off kilter…trying to enjoy Autumn while feeling like it’s Winter and at the same time bracing myself for winter while feeling like it’s summer. Very strange.

Summer is always a loud, boisterous season. Fall is a time to cycle back into a more quiet, subdued existence. Home and hearth, darkness and quiet. It feels like we only get 5 hours of sun. It brings with it more opportunities to spend time huddled together, but I also find myself wistful for the brighter moments. I loved reading this post by Tara about staying present and going with the changes. And then Amy over at On Bradstreet wrote a post about using November to ‘feather our nest’ at home. It brought out the simple and sweet comforts we can find at home going into the cold dark season. I appreciated reading that, too!

So, I’m off to feather my nest, as it were. I’ll let you know what I do once I decide what it is I’m doing. Which is sooo the story of my life, lol. I do know that we’ve started our weekly library trips back up, since it gets so dark so early now, and we have more time to cuddle up together to read. Maybe I’ll go fix up a book nook in a corner.

Enjoy the gifts of the season…I’m trying!

2e Tuesday::Dancing With Words.

Don’t you hear it? she asked & I shook my head no & then she started to dance & suddenly there was music everywhere & it went on for a very long time & when I finally found words all I could say was thank you. –storypeople

______________
I’ve had this post in my head and in my heart for a long time, but sometimes I just have to sit and stew with the ideas for a while…either to let them form completely or because they bring up some pretty strong emotions in me that I’m not ready to deal with yet. I think because when I talk about Out Of The Box Thinkers I’m talking about my kids mostly, nothing gets my heartstrings all bunched up like good ‘ole Mama love. And also Mama fear, and Mama anger, and Mama confusion. All of which apply when speaking about kids that don’t fit into any mold or pattern or curriculum or…or…or…well, just don’t seem to fit, period. I have a feeling that if you’re reading this, you know what I’m saying. If we ourselves remain in the box, then all we see is the many ways our kids aren’t fitting in. If we can get out of the box ourselves, then it’s possible to see that the world our children can create is something so blindingly unique and valuable, it’s something to be encouraged and treasured. Protected, even.

I’ll take a specific example from Naturalist, and her writing. In school, writing was a source of constant trauma for her. Hell, for both of us. I would sit there at night, watching her painstakingly work over writing down words and sentences and paragraphs correctly. And when I say painstakingly, I’m emphasizing the PAIN part of it. I wish I had some work to reference, but as I shared last week, I threw all of it away. But a good example of one of her sentences is something like this:

eny boDe wil wont! to Et choclt

which is…translated…

Anybody will want to eat chocolate!

Her dyslexia made it a struggle to remember spelling, punctuation, capitalization, and even word order correctly. She is an extreme example of this, but any creative, right brain kid…even if not dyslexic, will struggle with this.

If you are dealing with someone that thinks visually, in pictures, then their thoughts are not in words. When you give a writing prompt about “Think about a time you were at a Fair”, then the verbal, left brain kid will think and write in the exact same form…

“First I walked in and ate a pie. Then I saw a big horse, and next I rode on some rides. It was fun!”

Visual kids don’t think like that. If you have them remember about a time they were at a fair, they see it all in their minds eye. Vividly! It’s not a sequential though process, it’s more like a snapshot or a movie…they can taste the pie, smell the horse, feel the bumpy ride, hear the laughter. How do you order a picture? How do you get all the detail of a movie down on a blank page? It’s overwhelming.

I can always tell a visual thinker from a sequential thinker by watching their eyes. If you ask a visual thinker a question, they tend to see it in their mind and then you can watch their eyes track what they’re seeing. So, they tend not to maintain direct eye contact but look around a bit before answering the question. A sequential left brain thinker doesn’t have a picture in their mind to ’see’ so their eyes don’t move around that much. Sometimes my visual picture is so strong, I start gesturing and pointing in the direction the image is in my mind, even though no one else can see it.

So how to protect this kind of thinking, because I’ll tell you, Naturalist became anxious and depressed when she had to write. She grew tired of getting back ‘zero’s’ on her spelling tests, and low grades on her homework for misspellings, lack of punctuation, and very little form to her sentences. She began to shut down at school, and would rather get yelled at for not doing an assignment than trying 1,110 percent and getting it back marked up with red corrections and a low grade.

However, at home she was a very expressive kid. She was always writing me poems, notes, and stories. I was so tired of working with her on her homework, that when she did stuff at home (full of errors!) I didn’t have the heart or energy to correct her. So, I just let her create without saying anything about the technical parts of writing.

When we stopped public school and started homeschooling, we followed a curriculum for writing (since I felt I had to get her to ‘catch up’ with all the other normal kids she was so far behind, right?! right?! It makes sense!). I drilled and tested and tried to force her to learn all the spelling and punctuation rules.

It didn’t take long before I realized that she had stopped all forms of writing…even the illustrated poems that I loved so much.

When we started unschooling, the writing lessons were the first to go. Slowly, her writing passion returned. Like so much about these kids I noticed a dual nature to her. I realized that while her visual thinking made the act of writing extremely difficult, it also had the opposite affect and made her a fantastic author. For the past 2 years, she spends the time at night when she’s awake while everyone else is asleep (also another indicator of an OOTBThinker…wacky internal clock) writing fiction. She’s written hundreds and hundreds of pages of fiction by this point. Currently, she has a story that has taken on a life of its own, and she writes probably 4-5 hours a day, plus whatever she writes at night. It’s a novel. She prints off the Chapters for Todd and I to read as she finishes them.

Her spelling? horrible. Sentence structure? a little better, but still shaky. Paragraph form? not so good.

But the story? the characters? the development of the world in the book? Amazingly detailed, descriptive, and amazing. The worlds she sees in her minds eye are incredible, and the beauty she shares in them sometimes makes me cry….simply because I remember a time when she was so traumatized she never wanted to pick up a pencil again. All this expression would have been lost. Lost! And why? Because of spelling? rules? What a waste.

If it’s a question between expressing thought and feeling, or proper technical writing, always err on the side of expression. Whether in public school, homeschool, or whatever, protect your child’s freedom of expression. Work with the teacher or with yourself to give grades that can allow the technical, tricky parts not to count. It is a shame when these kids are silenced from sharing their own beautiful dance with words because rules, forms and conventions get in the way.

_____________
Other stories and resources:

Stories of other dyslexic authors and their struggles here

Terry Goodkind, dyslexic author, bio here

Interview with Jonathon Mooney, great stuff in here about reading, writing, and being an Out Of The Box Thinker.

“Learning Outside The Lines”, the book Jonathon wrote. It goes into greater detail about being an OOTBThinker in school. A must read!

Math Monday::Pythagorean Theorem

For our latest Creative Math Club, Sonja (who I’m happy to say is rested and recovered from her family’s bout with the flu!) prepared some activities having to do with the Pythagorean Theorem. We geared this one towards the older set of kids, those between the ages of 10-15. We had an amazing turnout for the day so ended up splitting off into groups arranged by age…the under 6 set of kids, the 7-9 set of kids, and then the 10-15+. There were kids and parents everywhere!

We had lots of inch squares for everyone to play around with and mosaic for the first 10 minutes or so, just to get in the mode of squares and numbers. Once the older kids had settled into the routine, Sonja wrote out a number line from 1-10 and then had the kids square each number:

Sonja was starting to teach them the Pythagorean Theorem, but in a backwards way. Or, rather, in an investigative way. So instead of giving them the formula a(squared) + b(squared)=c(squared) she led them in an investigation to discover that using squares. Once they had squared all the numbers between 1-10 (some kids knew the answers by doing it mentally, other kids made a square using the square pieces of paper…)

Sonja challenged them to find a sequence of 3 numbers where the square of that number plus the square of the next number equaled the next number squared.

I hope I’m explaining that clearly, lol. So, looking at the numbers 1-10, they were to find the sequential numbers where the first number squared plus the second number squared equaled the third number squared. Lots of number crunching ensued. They were using their mental math skills, or the square pieces, or calculators. They were also, because they are in fact creative kids, taking larger square sheets of paper and constructing paper houses out of them. Which is totally off topic, but I figure that any kind of investigation (on or off topic) is better than no investigation at all. And with creative kids, it’s the most random experiences that can lead to the best kind of learning. So, all forms of square ‘play’ was allowed, whether it was a direct contribution or not.

In any case, they eventually discovered that the numbers 3,4, and 5 are the only consecutive numbers where the squares of the first two numbers equals the square of the third number.

Sonja had prepared some new squares…not the square inch shapes, but 3 inch squares, 4 inch squares, and 5 inch squares. Each kid got one of each, and were asked to construct a triangle with them.

What they came up with was a right triangle:

At this point, we had a discussion about angles and triangles. The definition of ‘right angle’ was important, and then Sonja was able to tie the triangle they had made with squares, into the Pythagorean Theorem. Which is to say, anytime there is a right triangle, the Pythagorean Theorem of a(squared) + b(squared) = c(squared) applies. This also introduced the idea of the hypoteneuse being like the third number, or, the c part of the triangle.

By this time, the kids were starting to get antsy from sitting at a table, so we ended that part of it without doing much application of the formula as far as plugging in numbers and measuring–we can do that another math club. What we did was one last cool application of the idea by using a 12 foot long piece of string.

Sonja asked, if we are building a house, and we need all the corners to be square, or have right angles, so our house is a perfect square, how can we do it using only this rope and our knowlege of the Pythagorean Theorem? The kids gave different ideas, and then Sonja had them measure and mark the rope off into sections of 1 foot. They ended up with a rope marked off at every foot. She told them to think about what consecutive numbers made up the answer in the first part of the lesson, they replied “3,4 and 5″ so she had someone grab hold at the 3 feet mark, then had someone grab hold 4 marks after that, and the last person grabbed hold 5 marks after that which happened to be at the 12 foot mark. She then had them take it down to the floor and make a triangle out of it. This is what they saw….a right triangle appeared!:

So. Freaking. Cool!

So, that was our brush with the Pythagorean Theorem. Personally, I remember learning the Theorem as just a string of numbers to memorize without any connection to why or how it works. I really enjoyed re-learning it this way!

My Soul Is In The Sky–William Shakespeare

I’m working on my Math Monday post, in the meantime I thought I’d share that if you head on over to Shutter Sisters today, you’ll see my picture featured on their blog! I’ve been inspired by the Shutter Sister website and by the amazing women that form the Shutter Sisters group on Flickr, so it was a fun surprise to wake up this morning and be a part of it!

Halloween is upon us!

And I’m soooo not ready.

It’s just not right when Hubby has to shovel the sidewalk so trick or treaters can make it to our front door. It’s actually reminding me quite a bit of ‘Nightmare Before Christmas’.

We haven’t even carved pumpkins! In fact, I don’t even have pumpkins! All the pumpkin patches around here have not fared well through the last couple snow storms.

As with all holidays, my focus is on the food we’ll eat. Last year we did this:

And this year I’ll do the same but maybe switch out the chicken pot pie for a gruesome meat hand from Not Martha.

Today will be lots of scrambling to do all the errands that I needed to do when we were snowed in, and lots of crafting with the kids. One thing we’ve got going for us is that this year, unlike last year, none of them have the chicken pox!

Are you ready for Halloween?!

2e Tuesday::Jonathan Mooney

Every parent of a 2e or out of the box thinker should know the name Jonathan Mooney. Labeled with ADD, dyslexia and severe learning disabilities, he is, in fact, a 2e Out of the Box Thinker himself and he’s written two books on the subject: Learning Outside The Lines: Two Ivy League Students With Learning Disabilities And ADHD…
and The Short Bus: A Journey Beyond Normal It’s worth noting that while he struggled to make it through school and dropped out for a time, he since went on to Brown University and holds an Honors degree in English Literature.

I’ve written about Jonathan Mooney a couple times before, specifically here:
About when we met Jonathan Mooney and here: About the book “Learning Outside the Lines”

His website is a fantastic place to go for more information, understanding, and resources about and for Out of the Box Thinkers. His books and media interviews continue to spread the message that thinking outside the lines (or, out of the box ) is not a disability and shouldn’t be treated as such. He’s a hopeful guy with a strong message for educators, parents, and kids, and I’ve enjoyed both meeting him and exchanging emails with him. He’s been one important step on the path towards helping my Out of the Box thinkers thrive.

He is embarking on a cross country tour for the next couple months, I thought I’d post the dates and locations in case any of you are close to one of them. If you are, go go go!

Nov. 4
7:00 p.m. – 9:00 p.m.
The Ross School
9 Lagunitas, Ross, CA
Neurodiversity
Free & open to the public

Nov. 9
6:30 p.m. – 9:30 p.m.
Floral Park Memorial High School
210 Locust Street, Floral Park, NY
Book signing and parent meet up
Free & open to the public

Nov. 10
8:00 am keynote for parents and teachers
Floral Park Memorial High School
210 Locust Street, Floral Park, NY
Free & open to the public

Nov. 11
Washington, DC

Nov. 20
University of Washington, College of Education Community
The Short Bus Stories

Dec. 1
Special Education Conference
Oklahoma State Department of Education, Oklahoma City
The Short Bus Stories

Dec. 5
10:00 a.m. – 3:00 p.m.
National Alliance on Mental Illness Transition workshop
Holiday Inn, 172 North Main Street, Concord, NH
http://ent.groundspring.org/EmailNow/pub.php?module=URLTracker&cmd=track&j=296380029&u=3289773

Dec. 14 & 15
The Lab School, Washington, DC

Dec. 15
The Lab School, Baltimore, MD

A brief look ahead:
Jan. 23
El Paso, TX

Feb. 4
El Paso, TX

Feb. 4 & 5
Oakton, VA

Feb. 8 & 9
Charlotte, NC

Feb. 12
Bethalto, IL

Feb. 20
Santa Barbara, CA

Feb. 26
Santa Ana, CA

March 5
Salt Lake City, Utah

March 11 -13
Diamonds in the Rough: Smart Kids Who Learn Differently Conference
http://ent.groundspring.org/EmailNow/pub.php?module=URLTracker&cmd=track&j=296380029&u=3289774
Rockville, MD

March 16
Northridge, CA

March 20
Fairfax County, VA

April 17
San Francisco, CA

April 29 & May 1
Philadelphia, PA

June 19
Tokyo, Japan

June 20
Osaka, Japan

Please spread the word to your friends and colleagues and I hope to see you all soon!

Cheers,
Jonathan

I hope some of you can make it!
And, if you haven’t already, come join us over at the Out of the Box Thinkers group!

2e Tuesday: slight delay….

Not that I’ve been great at getting these out on Tuesday, anyway, but this week I was really trying hard!!

However, today I’ve been running around preparing for some nasty weather. And on the foothills of the Rocky Mountains, nasty means we’re holed up in our house for the next few days, with or without power. The kid in me is excited! The mom in me is freaking out a little bit, wanting to make sure we’re prepared for this:

They give us an 80% chance that it will hit, which are pretty good odds. So…if we are holed up here together then I’ll just write it tomorrow while we watch the snow fall. Unless there’s no power, in which case I’m putting everyone in the car and driving south until we hit Mexico. In that case, it may be a while before you hear from me again. I don’t think they have internet access on the beach.

Math Monday::Halloween Symmetry!

With Halloween being not to far away, at least for us here in the USA (which reminds me of a hysterical story involving our attempt to trick or treat with the kids when we lived in Budapest…but I’ll save that for later…), we’ve been crafting like crazy. Also, the leaves are almost all off the trees, so I thought I’d post a Math Monday using symmetry before all the leaves are gone, baby, gone.

First, paper cut symmetry…it’s the same principle as making paper snowflakes…the idea that you can fold paper, cut it, and it creates a symmetrical pattern. This is a fun one–take square pieces of paper, we used 8 by 8 decorated pattern paper, but even construction paper will work. Since this is symmetry, you’ll fold it in half. On one half of the paper, draw half your shape:

We drew:
pumpkins
ghosts
cats
spiders

Then, once you’ve done that, you can cut around the mark:

…and open the paper up again to see how it looks! Here’s a bat…

and a cat from Naturalist:

There is something called a ‘line of symmetry’ which is illustrated perfectly when the figures are unfolded. It’s the line in the middle that divides a shape where the two sides on either side match.

A great video to watch with your kids on symmetry and line of symmetry is through this link.

A quick note: if your child struggles with writing, it may be frustrating for them to draw the image and/or cut it out. Golfer didn’t enjoy that part at all. So I let him direct me in the drawing and cutting, and then he got to take our images and tape them to all the windows:

Something else we’ve been doing is the good old leaf rubbings. Everyone goes outside and pics a few (or more!) of their favorite fallen leaves. They can’t be too brittle, or it won’t work…so, leaves that aren’t too dry yet.

Bring the leaves inside, lay them on a piece of paper and place another sheet of paper over the top. Get a crayon in a nice fall color, unwrap it, and use the side of it to gently rub over the paper. This will give a nice rubbing of the veins and outline of the leaf. Point out the lines of symmetry and talk generally about how one side of the leaf is so similar to the other. Do this for every leaf, varying the fall colors you use, then cut them out and tape them everywhere.

This may lead to an interesting observation about all the symmetry there is in nature (if the video hadn’t already sparked this discussion!). If you child is interested, go on a photo safari for nature symmetry. (Symmetry in Nature) Sassy and I did this, but my card reader is about 2 seconds away from not working anymore, and it failed to upload any of those pictures. But I’m sure you know what I mean! Snap a picture of everything that you see outside that is symmetrical.

This is a perfect ending to a fun time…especially if you’re coming in from outside where it may be cold–a great excuse to put on a pot of hot chocolate and look around at all the lovely decorations you have scattered all over your house!

True Love

True Love

I love Coke. Especially Cherry Coke. I’m trying to cut back and drink more water…it’s smooth sailing until about 4:30 hits and I realize I still have 6 more hours of awake time where I need to cook, clean, read to kids, organize stuff, and all other manner of ‘awake time’ things.

You can imagine my glee when I spotted this enormous coke bottle at Universal Studios in Florida last year. We were obviously made for each other.