Lines and Polygons

What is a line? What are polygons? How are they related? – Those were some of today’s thoughts and investigations!

A polygon is a figure that is closed with straight lines, regular or irregular shaped.  A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

I asked the boys to find a polygon in the room. One answer was the rug we were sitting on, the walls, the windows and the best I thought was- the groove in the marble on the fireplace!

So why is this important and worth spending a morning on? Well, for starters it’s the beginnings of geometry and geometric terminology.  Polygons and lines are used in everyday life- mapping out land, engineers use them, painters use them, gardeners use them! They are applicable in almost everything that we do that requires the planning of materials for a structure or of a space.

We read two great books about lines and then I handed them each a large piece of yarn for them to create their own images using a line.

tracing his finger along- bonus for pre -writing skills!

a bird shape

it’s a man!

making loops

Then we did a few activities in our Kaleidoscope math book. Using a mirror and the images of triangles, in the reflected images, regular polygons were seen! Polygons can have 3 sides up to 12 sides.

After viewing several of these – What would happen if our mirror included more than one central angle? A heptagon was now seen!

We then took a break and read some poetry together and then I worked with Luke while Liam worked in him fraction workbook.

Sticking with lines; we did a tactile activity. I asked him to make lower case letters using the wiki sticks as we read an alphabet book.

He then went on to make his own cross-bow with them afterwards- came out cool!

Line and polygon art-

They used wave lines and then filled in the waves using as many lines as they could think of.

Then Liam ended his morning with a coding lesson, learning about artist sequence. Look- it’s lines and polygons! 😉

I understand this song- Right Brain learning!

What a morning filled with beautiful bird songs(Bird Biology) and a super math suprise gem(Right Brain Math)!

Learning and memorizing multiplication facts has been an ongoing struggle or perhaps a topic of boredom for my oldest. He would rather do fractions and decimals or measurements and graphs- Ahh, all of these are much more “visual” concepts… Now I’m starting to see why this topic was a broken record!

In researching yet another way to get him to memorize and get these down pat in a flash, I discovered:

MisterNumbers Pattern Play Math

A visual and structural approach to multiplication for Right Brained learners! I watched a couple of his videos and thought, WOW! this is so awseome. I signed up for the 3 free worksheets and had him watch the videos and do the sheets along with the video. He looked over at me half way through the video wide-eyed and said- this guy is a genius!

This is what one of the worksheets looks like, but if you’re at all interested watch the video to see the patterns of 3,6,9 times and the 7’s. It’s a simple tic, tac, toe pattern that incorporates all three tables.

We’ll be purchasing the workbook, it’s not expensive at all! Pattern Play Math-…… You’re playing our song!

Speaking of Songs; Bird Biology was the other highlight of our day! We headed over to The CornellLab of Orinthology to learn all about Birdsong! This was an interactive lesson with 7 steps.

What is a Songbird?

Songbirds learn too

Their reperetoires include songs and calls

Songbirds have local dialects

Songbirds are vocal gymnasts

They sing at dawn

Some sing two notes at once

Birds sing to defend and impress

Here a bird singing? It’s probably a male

After reading through these facts and hearing the Songbirds, we then played Songbirds in action and trained for Bird Song Hero!

Double sided voice box

Listen and match the visual

Then before heading outside we did a little watercolor fun art with singing birds!

Luke’s -Titled “The Bell Song”

Waldorf Inspired lessons today

I have always been one to be eclectic in our curriculum because I love so many different styles and philosophies- Montessori, Waldorf, Reggio Amelia, Charlotte Mason are a few favorites.

Waldorf Education is based on the work of Austrian philosopher Rudolf Steiner. Its premise is that the human being has three aspects: thinking, feeling and willing, and that education has to come from experiencing the world from all three aspects. Waldorf Education does not use textbooks. The children make their own based on their experiences.

After reading quite a bit this past weekend on Waldorf Education, I had a few ideas and was excited to try out a few things! My top favorite was the Math Multiplication  circle board- being understood that  the child thinks,feels and is willing to learn, the 3 aspects of Waldorf ed.  Here is a link to the video I watched on how this method works.

We made ours using foam board, nails and yarn. I also drew and colored in the 5 different circles as Liam used the board and went over his times tables.  He really loved it and did great! He first did each one orally then wrote down a few as well. We will continue using these as he enjoyed them- they are both visual and physical tools for success!

Luke did Waldorf watercolor art- I saturated the paper with water so he could just really focus on the colors and movement of the paints.

We then read a fairy tale- Jataka Tales- The Monkey and the Crocodile and we are going to draw an illustration to go with it tomorrow using pastels.

The next book was for Luke- called LMNO peas. Awesome visual letter story- followed by a math memory game that also had visual pictures that we stopped to view as we found each match. In Waldorf education, the letters are presented as pictures which appeal to the child’s imagination. In reality the letter is clothes in the picture…the picture is the key. All letters of the alphabet were once pictures themselves.

Here is a great reference site for Waldorf Introduction

As well as this one : Waldorfhomeschoolers

The I hate Mathematics! book

Today’s math lesson was taken from The I Hate Mathematics! Book by Marilyn Burns.

In keeping with our new routine of two Living Math lessons a week I have already noticed improvement in my son, as far as  understanding concepts, and better outlook/attitude all around as he seems to be actually enjoying math?! He even asked yesterday if we could do one more math lesson…What? I almost fell out of my chair. This is a significant turn around for him. So glad I did some research and have incorporated more story form math lessons as well as hands on, seems like we’re heading in the right direction.

Today was CUTTING SIDEWALKS.  We headed outside to the sidewalk and began following along with the book using chalk to cut up the sidewalk rectangles into pieces. Starting with one line, How many pieces are made? How about three lines?

Do the same number of lines drawn always have the same amount of segments? He tried drawing 5 lines in different ways to find out!

After gathering his data. We headed inside and I asked him to write down a few definitions as we talked about a Line, line segments and partitioning.

Next in keeping with the topic of partitioning, we used popsicle sticks and a round tray to begin cutting it up.  I asked questions like: If you had 4 guests how could you cut the cake evenly for all your guests? How about 6 guests? Ok, even numbers are pretty easy to divide. What about 11 guests? And so on….

Shel Silverstein Poetry Math

I did much research this weekend on Living Math.  How to apply it, what exactly does it mean and how to begin transitioning over along with a million other questions I had running through my mind! I’ve done lessons here and there that I’d consider Living Math, but not as a my typical method or style.  I found a ton of information and I have many Living Math books on their way. So with new knowledge, ideas and some much needed inspiration-  we kicked it off today with some Poetry Math using two of Shel Silverstein poems! (if interested, just type in a search, found many pdf’s) Under my Living Math tab, I have listed many books and links on this subject.

I also use Life of Fred for math and we did a Chapter in that book as well today. The lesson in today’s chapter was about seeing patterns in things. Such as a game of Which of these things is not like the others. Example: 7  36   8    1/2  in which you can see, could be any of them depending on your thought process!  He chose to say the 1/2 because it was a fraction, to which I said is correct, but it could also be 36, it’s a double digit, could be 7 it’s an odd number…and so on.

I took out a workbook for a Grammar lesson next and said there is a lot here, why don’t you just do the first column. He said “hold on” muttered to himself aloud….there’s 24 here, 12 in each row….cut that in half…that’s 6.…How about I do 6 in each column then? Absolutely! Great math buddy!

Free Educational Resources

Here are some free sites for books and other online educational freebies! I use most of these, some more than others.  A few are geared toward homeschooling, but can be enjoyed by anyone just the same! If you have   favorite that needs to be added, let me know! Check back often as I will update and add to the list as I come across new sites/resources!

Elementary Math:

Centre for Innovation in Mathematics Teaching- (MEP)

Fun for the brain-mulitplication

Math Fact Cafe

Mothmatic Math-online game

Book and Language:

International Children’s Digital Library

Magic Tree House

Shel Silverstein

Kids Literature

Usborne

Shakespeare for kids

Online Mad Libs- Wacky Web Tales

History:

Scholastic-colonial times

History for Kids

British Culture

Lego Castle

Civil War

The Middle Ages

Science:

50 Birds and more

Animals Myths and Legends

Nature Detectives

Kids Biology

National Geographic for kids

Space Place-NASA kids

Biology for Kids

Bats for Kids

Art/Music:

Olga’s Gallery

Classics for Kids Music

National Gallery of Art for Kids

Norman Rockwell Museum

Getty Games-Art Museum

Social Studies and Geography:

Heifer International-build a better world

Connecticut Kids

Social Studies for Kids

Foreign Language:

Spanish for Children

Foreign Language printable worksheets

Online Educational Game Sites:

Funbrain

Brainpop jr

Brainpop

Poptropica

Covers all Subjects!:

Some of these are not free, but can be used for ideas, resource and finding supplies. Easy Peasy is totally free and a complete curriculum.

Easy Peasy-

Simply Charlotte Mason

Queen Homeschool Supply

The Tanglewood School Supply

An Old Fashion Education

Documentary Tube

education.com

neok12-site that has videos on all subjects

Discovery Kids

Noodles and Marbles

What started out as a fun game, quickly grew into so much more! I was so happy to see the boys working together and taking the reins on this one.  Then watching it all spiral! A lesson for me- let the boys take from it what they will!

As Charlotte Mason said:

The child, though under supervision, should be left much to himself–both that he may go to work in his own way on the ideas that he receives, and also that he may be the more open to natural influences.
(Vol 1, Part V Lessons As Instruments Of Education, p.178)

I originally found the idea of this “race track and marble” game on pinterest, and my first thought was fun and we can make it into a math game! Let’s measure the tracks, time the marbles, try different layouts and compare.  So we set it all up.  All that is needed is a foam noodle cut in half, some marbles and a box to catch them at the bottom!

I gave my oldest the paper and pen and asked him to write down any data he thought was important as he played that would have to do with math skills (leaving it wide open to see his reaction). Well, he took that and ran with it, documenting so much more than I had planned. He made up his own chart and then the ideas for different things and ways to chart just came pouring out of him!  As an example, he thought to try using the large marble to hold a line of smaller marbles in place and let them all go at once to see what would happen.

My youngest son made up his own games as well, he’s two years old,  so it was pretty much him rolling the marbles followed by a  yell, then a chase after the marbles around the room! However, he kept manipulating his foam noodle as well and tried rolling the marble down it to discover if it worked or not.  We moved the noodles around to different places for variations of heights and had some competitive racing as well.

Finally, my older son asked ” now can we do marble painting?!”

and so we did….. with an impromtu Jackson Pollock lesson! (next post!) 🙂