Area of a triangle= 1/2 bh
If you are a kid that formula can look like gibberish.
Let’s use geoboards to help that formula make sense!
The area of this square is 16. I can count those squares and that makes perfect sense.
Now I’m cutting the square in half and making a triangle.
What’s the area of that triangle? Half of 16 = 8
Booyah! I understand that.
1/2 of 4 X 4 = 8
1/2 of b x h
Let’s try this again:
I’m cutting up another triangle. Let’s find the area of that blue one.
Logic tells me that the blue triangle is half of the green one. The green triangle = 8. So the blue trianle should equal 4, right?
Let’s proove it!
If I use my imagination I can flip half of the triangle over and it becomes a complete square. Now I can “see” that the area of the blue triangle is four.
Or I can use the formula:
1/2 of b x h = 1/2 (4 x 2) = 4
Pretty cool, hunh?
Here’s a great starter lesson with geoboards: figuring out the area of squares and rectangles.
In the above picture I threw in some square inch tiles so that it is really easy to figure out the area of the rubber band square, just by counting. This also teaches early multiplication skills because we are looking at a 4 x 4 array.
Here’s another example, this time with a rectangle. To find the area of this rectangle kids can count the squares or…
…They can transition into just multiplying 2 x 4.
So now we’ve got an activity that teaches shapes, counting, area and multiplication all in the same lesson. You could do this with your four year old, or your nine year old, and they would both get something out of it.
I finally broke down an ordered a 7 x 7 geoboard. It was only $6 and now I’m thinking “Why didn’t I buy one of these sooner?” There are soooooo many cool things you can do with geoboards, that I thought I might create a new Pinterest board, all about them.
It’s really hard for classroom teachers to use math manipulatives “enough”.
Even when teachers have training in using things like geoboards, they might not have enough materials for all 30 students in their room. Then, even if they do have 30 geoboards, they are under enormous pressure by the state to makes sure kids learn computation skills like adding, subtracting, multiplication and division. Sometimes math manipulatives like geoboards sit on the shelf of a classroom, unused.
The sad thing is that geoboards can actually make learning easy.
They are kick-butt awesome at teaching geometry, fractions, division, multiplication, and logic. But to be fair to teachers (I was one of them so I know), managing geoboards, little boys and rubber bands, is really hard. The rubber band part especially!
That’s why using geoboards one-0ne-one with your child at home “for fun” is a great Afterschooling idea.
This month I’m going to be looking at some cool things you can do with geoboards at home:
- Area of squares and rectangles
- Area of triangles
- More area of triangles
- How many rectangles?
- Square numbers
- Area of circles
P.S. If you have never bought a geoboard before, be warned that there are two different types out there, 7 x 7 and 11 x 11. We happen to own both. But the 7 x 7 frame is what I’ll be using for these activities.
The last thing I would want to do on my blog is embarrass either of my children. So I won’t be sharing a second grade handwriting sample from my seven year old son Bruce. But suffice to say, it would be embarrassing.
I know from experience teaching K-4, that in a classroom of 20 there are always at least one or two kids who really struggle with handwriting.
More often than not, they are boys, lefties, or both.
Bingo on both counts!
So this past week I’ve been taking a hard look at Bruce’s handwriting and analyzing the heck out of it. The thing is, even when he is trying really hard, he still can’t write legibly.
That tells me something important: He actually can’t do it.
Could he try harder? Yes. Is that the source of the problem NO.
I want to say that again, because I think it will be helpful for parents of kids who struggle with poor penmanship to hear:
Effort is not the primary source of the problem!
So what is?
Well, it’s not that his teachers haven’t taught handwriting. Montessori kicks butt at teaching handwriting. His first grade public school teacher had him cranking out D’nelian practice sheets every day for a full year.
I think what we’re dealing with is underdeveloped fine motor muscles.
Bruce doesn’t sew. He doesn’t knit. He doesn’t play with play dough anymore. The only fine motor practice he gets is with Legos and Snap Circuits.
So what’s my plan?
Here’s what isn’t my plan:
- Encouraging him to try harder. (I’ve tried that and it doesn’t work!)
- Yelling at him to try harder. (Tempting but…no.)
- More D’nelian. (Why would I do more of what isn’t working?)
- Play Doug (blech! A little known fact about me is that play dough makes me want to gag.)
- Handwriting Without Tears (I’m keeping this one on the back-burner.)
Instead I poured over the Beyond Play catalogue. For those of you unfamiliar with Beyond Play, it’s a company that specializes in therapeutic toys for children with special needs. But you should check it out even if your kids are neurotypical because it’s awesome!
I’m planning a 3 pronged attack to the handwriting problem.
- DNA Balls. That’s the super cool ball Bruce is squeezing in the picture. We are going to keep one in the car for him to squeeze whenever we drive somewhere.
- Fancy Pencil Grips. I’ve ordered a whole variety of them. I’m going to write an I Brake for Moms blog post in the future about why pencil grips are like running shoes.
- Callirobics. 5 minutes of non-handwriting practice to music, every day for ten weeks.
I’ve never taught with Callirobics before, so Bruce is my guniea pig. But the cool thing is that it’s not concentrating on letter formation. Callirobics is about “eye-hand coordination, fine motor skills, and self-esteem”. At the end of every lesson kids are encouraged to doodle little faces into the lines of what they have drawn. If you know Bruce, then you know this is perfect for him.
Remember I said I was going to explain why I’m not going automatically with Handwriting Without Tears? That’s why! Bruce has already been hit over the head with letter formation. It’s not working!!! I want to come at this problem from an entirely different angle. I also want him to have fun.
So ask me in January how this plan works out. I’ll share some before and after writing samples in the future.
Croup? Slap cheek? The common cold? What haven’t we had this past month!
That’s why I’m creating a new Pinterest Board. It’s called Mommy Sick Days. The whole board will be about activites you can do with your kids when all you want to do is lay on the couch.
Beep Beep Woo Woo is the perfect game for Mommy Sick Days.
My sister invented it when she was two. All you do is lay on the couch and put your feet up on the coffee table. Then your kids run around the coffee table in circles. When they get to your legs they say “Beep Beep”. You say “Woo Woo” and lift up your legs for them to pass.
It’s ridiculously simple and yet ridicioulsy fun.
I came into Jenna’s room yesterday to find this. She had made her bed all by herself!
Which of course leads me to ponder…
I taught Bruce to read three letter words by two and a half. Jenna’s three and knows her letters and sounds, but still won’t blend.
Bruce on the other hand, is seven, and can’t make his bed.
I might as well sit on the couch and eat bon bons because I can’t take credit for any of this.
Hint! It’s because I used to be a charter school teacher!
Have you heard of Basher books?
I’m not actually a fan, but my 7 year old son Bruce is.
I bought Bruce the Rocks and Minerals book and Periodic Table edition a year ago, and they just sat on the shelf for about six months. Then, last summer he became obsessed. He read them over and over again and started asking me a bunch of physics questions that I had no idea how to answer.
So I bribed him.
I told Bruce that if he finished all of the Classic Start books we own, that I would buy him more Basher Books. (I love bribing kids with books!)
Now we own seven Basher Books, and the only one Bruce actively dislikes is the Grammar book. (That one might be sitting on the shelf for a while.)
For those of you who have never seen a Basher Book before, they use cartoonish drawings and funny descriptions to explain nonfiction vocabulary words and concepts. I don’t particularly find them very engaging. But maybe that’s because I’m not seven!
P.S. I’m adding Basher Books to my Grandma, Please Buy This page. Here are some links to Amazon so you can explore Basher Books for yourself:
When Your Parent Becomes Your Child by Ken Abraham is a book about losing a loved one to Dementia. But it is more than that. It would not be hyperbole to say that the author Ken Abraham has written his heart in book format.
His words were an honor to read.
This is one of those books that you can’t put down. It’s one of those books that make you feel like you know the author and that you should call him up right now. Don’t worry, I won’t! But I felt like the very spirit of his mother was living for me in those pages. It was a privilege to meet her.
I’ve read several books about Alzheimers, but none about Dementia. Mr. Abraham’s mother suffered from Dementia brought upon by a series of mini strokes. Lots of embarrassing and heart wrenching things happened to her due to her disease. It probably took a lot of courage for all of her sons to give their brother the go ahead to write this book. So I would like to say thank you to your entire family for sharing this story.
If I could give this book six stars I would. But if I had one criticism it would be that I think the family is too hard on itself. In the beginning of the book there is a lot of “If we only had realized….In hindsight etc.” As an outsider looking in it seems to me that each family member had a different piece of the puzzle. A son in Tennessee knew “A”. A daughter-in-law in Florida knew “B”. A neighbor in Pennsylvania knew “C”. If you put all of those puzzle pieces together sure, you might have recognized what was happening a whole lot earlier. It’s not your fault that you couldn’t. That happens a lot with aging loved ones and the family members who try to take care of them.
But maybe by sharing your story it will help young people like me know what to look for when it becomes our turn to be the sandwich generation.
Thank you for your courage.
P.S. I received a free copy of this book from Booksneeze in exchange for my honest opinions and reviews.
Welcome to the October 19, 2012 edition of Carnival of Afterschooling!
Liz E presents Books and Resources.
Courtney Sperlazza presents Well Wise Happy | Homeschool Books for Kindergarten saying, “Kindergarten curriculum books list we use. This list can stand alone as a homeschool kindergarten curriculum, or any combination of books can be used to supplement a kindergarten student’s education at home.”
I’ve never organized a blog carnival before, but it was pretty easy. The only problem was that a lot of the submissions were from SPAMers. I’m sorry, but I’m not going to use my blog to advertise for your nanny business!
If you have an actual Afterschooling link you would like me to include next time, you can submit your article to the next edition of Carnival of Afterschooling using the carnival submission form.
For my non-Pacific Northwest blog readers, I have to explain that there is an insurance company up here in Seattle called PEMCO. They have an advertisement campaign called “We’re a lot like you” which is super funny. I think the “Mom in Clogs” definitely deserves a profile!
Is there one right way to harvest all of these tulips?
Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?
Now look at this addition problem:
Is there a “correct” method to solve this problem?
Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?
If you have never had formal or informal instruction about teaching math you might be thinking “‘Yes Jenny! You are asking crazy questions! Just start from the right!”
That’s what I used to think over ten years ago before I first started learning about teaching math from a Constructivist point of view. Ten years ago I would have taught children to draw a bunch of lines and junk and crank through the traditional algorithm. Yes, they could learn to do that. NO WAY would they ever be able to solve a problem like this quickly and accurately in their head.
It took me almost ten years as an adult to unlock my brain from “the right to left method”.
But kids can learn multiple methods with high accuracy in just a few years, if they have a good teacher who holds off on teaching traditional algorithms until the students actually understands math.
Here is what that type of teaching might look like. If this is new to you, hold onto your seat and prepare for the crazy.
Notice that the problem is written horizontally instead of vertically. If you want your kid to be good at mental math then you have to present problems to them horizontally at least as often as you present them vertically. If you think that the best way to solve problems is by stacking them vertically, then that is your first problem! Maybe the best way is to stack the problem vertically, or maybe not. Strong mathematical thinkers could do the problem either way.
But if horizontal is hanging you up, let’s go vertical:
I’ve seen this method called the “Sum All Totals” way and I think that’s pretty cool. Kids who learn this method really understand that the “4” is really 4,000. That “3” is really 300. etc.
Now let’s go mental:
Start at the left, look to the right, reassess your answer, and keep moving.
If this is new to you, you might need to stare at that last picture a really long time.
Now for the sad part…
Remember how I told you it took me about ten years before I learned to unhook my brain from borrowing and carrying and get good at other methods?
That’s because traditional algorithms are like row-boats. They help you get over really big waters.
It’s super easy to teach a swimmer how to climb into a rowboat. It’s super hard to teach a non-swimmer how to climb out of the rowboat and learn to swim.
No mom would send a non-swimmer into the ocean on a rowboat and say “Look! My kid is water safe!” But lots of people mistakenly think that children who can crank out algorithms “know math”. Maybe they do, maybe they don’t.
I’d like to close with a comment Crimson Wife left on my blog earlier this week that illustrates a lot of what I just said. She’s in the enviable position right now of teaching her super swimmer son how to climb on the rowboat. I’m guessing it’s not going to take Rusty 10 years to learn, like it did me!
Crimson Wife says:
The funny thing is that I’m currently fighting with my almost 7 y.o. to NOT use mental math because he’s working through a section in his Singapore math book where they are having the student practice the traditional algorithm. I finally had to pull a worksheet from my older child’s pre-algebra program where the task was to add three 5 digit numbers. The numbers were so big that my DS couldn’t just use the mental tricks but had to use pencil & paper.