Monday, August 18, 2014

Baking and Literature and Pi ~ Oh My! 6 Fun Steps from our Unit Study on Circumference ~

"Nature is an infinite sphere whose center
 is everywhere and whose circumference is nowhere."
~Blaise Pascal,
seventeenth century French 
mathematician, physicist and philosopher

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Welcome friends, to my little corner of the web!
In June, we completed a unit study on the topic
of circumference and I realized with wrapping the year
and preparing for our family travels,
 that I've yet to blog it---
for fun and for any who might find it a tad useful-----!
 Though the new school year's just about upon us
and we're thinking schoolroom set up
and curriculum choices,
here's our study......
For those mathletes among us who may be interested in  
 how we had fun bringing all things pi to life.

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For those of you who've not ventured into pi territory recently,
here's a refresher:
The number Pi is the ratio of the circumference 
of a circle to its diameter. 

The value of Pi is approximately
 3.14159265358979323846 or 22/7.

Sound familiar?
Sure it does!
Now let's have some fun....

1. Topic intro and derivatives~
We primarily discussed this brand new word, 'circumference,' in terms of its 
potential root. What word it sounds like, may be derived from, etc.
Yes, 'circle' can be derived and we know we're embarking on a study within geometry
of their size, measurements and all generally all things circular.

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2. Literature link~
Living books are huge around here. Our shelves, our window sills, our baskets
 strewn around the floor, in corners,
 by sofas and on counters are bursting with themed books.  
I know you'll agree that there's no better way to 
 begin learning a  new topic of study than
 by living it through literature and either extrapolating a deeper meaning
 through discussion or simply  learning this new topic, 
whether it be the Napoleon's demise, adverbs,  
the respiratory system or, in this case,  circumference.
Do you know  Cindy Neuschwander's clever mathematical titles? We adore her
 books for our math unit studies!  

We read and reread  Sir Cumference and the Dragon of Pi.
 Initially, just to enjoy and then, read  in succession,
 to jot in math notebooks, the following:
 the references to circumference usage,
 the "new" vocabulary, 
and to literally  write the formulas,
 working them with Radius, son of Sir Cumference, 
as he frantically follows clues given him about each circle's measure. 
Why the chaos, the rush and the need to figure exactly how big a given circle is?
 Well, you'll have to read that  for yourself and  work  each circle's circumference!

Needless to say, this math adventure is a superb and fun way to introduce circumference 
to a young kid ( grade 5)  and review the topic 
with an older child ( my other son, in grade 8) 
which is what we did here in
our homeschool, in June.

3.  Now, back to that vocabulary I mentioned above: 
We listed, defined and drew pictures of these words/concepts, 
specific to our study:

circumference
diameter
radius/radii
Pi
3.14 and 22/7
formula
geometry
angle
Review of these target words: 
perimeter
inch
centimeter
measurement
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4. Practice, practice, practice~
Around here, I'm known as The Queen of Drill and Kill. Sooooooooo this is just a tiny piece of the practical application.....We use the Math U See series and have, since...well,  forever.  While my kids no longer like the DVDs, (  I guess seeing the same math teacher day in day out since 2004 can get a bit redundant, no?)  I, frankly, like the program. The workbooks are user friendly  and the teacher's manual/DVDs are practical  if only to acquire background for myself and perhaps a different and more creative  angle on presenting a new topic. Especially as the kids get older and the demands of the math curriculum become more stringent!  


 My son was in grade 5 last school year and so, 
we  used the Epsilon level
(Circumference is covered in chapters 27 and 28)
And, do you notice how a cute little doggie notebook 
seems to make math just so much more fun??
If you are seeking  
additional practice to reinforce the concept, there's
always worksheet generators such as this.


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5 Find the D and the r! 
Working the formula forward and backward.~
Here's what I mean by that.....
I don't think that there's enough of a basis for understanding this
concept   if the only practice kids get is working the straight  
 C =  π d  
( or C = 2 π  r). 
Do  they really and deeply understand unless they examine
 the formula and they figure
from different "points of view?"
So we work the problems "backwards," creating our own "inverse" 
examples using  the ones provided in the book. 
The kids should not only know and be able to work formulas to find
 the C of a circle,
 but additionally,  given the circumference,
 they should be able to find the circle's 
radius and diameter as well using these formulas : 

For example:

The diameter of a circle is 3 centimeters. What is the circumference?

 ( diagram ~~thanks to Math Goodies)
diagram for example 2 with diameter equal to 3 centimeters

Circumference equals Pi times diameter
circumference = 3.14 · (3 cm)
circumference = 9.42 cm

Now let's do that "backwards" too:
What is the diameter of a circle whose circumference is 9.42cm?

D= C/π

D = 9.42/3.14

D= 3 cm

Let's find the radius now by adding another step as we  divide the D by 2:
D = 3 cm, therefore  r = 1.5 cm.


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6. Invite geometry into the kitchen!
Chocolate chip cookies + math = fun!
At this point, after immersing in the activities, the practice and the measurement of all things circular ( ! )  while we definitely still needed to review, rework and revisit many examples around circumference using both 3.14 and 22/7,it was time to move on a bit.

We baked up a storm, using this recipe which is tried and true and oh-so-yummy! 
Click over the full description and step x step!
Here's what you need:

1 C butter
1 1/2 C sugar
2 eggs
2 tsp vanilla
2 C flour
2/3 c cocoa powder
3/4 tsp baking soda
1/4 tspn salt
2 c choc chips
1/2 cups chopped walnuts
 ( Walnuts optional, but we're big nut people, so I always throw them in!)


Here's my son having fun with PI:
We baked the above recipe and I took no shots of 
that kitchen adventure...drat.
So here he is a week or so later mixing up a quick and yummy



You know the drill, bake, enjoy and m-e-a-s-u-r-e!

We purposely baked many different sizes, so we'd
have the fun of measuring a variety of circumferences.....






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Hope you enjoyed some math fun around our circumference study!
I'd love to hear how YOU learned a math topic too...it's
always wonderful to get those ideas swapped!



Friends, as always,  
thank you for stopping over and 
spending some of your precious time 
here at my home on the web!

I'd love it if we could be in touch regularly.........
so please subscribe to Campfires and Cleats~!

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Until next time,

~Chris







14 comments:

  1. Oh this looks like so much fun and looks like everyone learned alot! I'll have to use this in the future for my own kiddos! I'm pinning it for reference! Thanks for sharing how to make such facts soooo fun! :) Have a blessed day Chris!

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    Replies
    1. Thanks Tra, for your kind words! I hope you can adapt a few ideas.....

      Thanks for visiting!

      Delete
  2. How very clever! I loved these ideas and I think they would be a great asset to our math lessons around here. I wish I had a math brain, but now maybe your ideas will inspire my kiddos to think creatively about their arithmetic.

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    Replies
    1. Hey Tara~~

      I'm not mathematically "inclined," either...... using Cindy's book gave me a lot of inspiration to out together a unit that was kind of fun!

      Thanks So much for stopping by and for your kind wods!

      Delete
  3. How fun!! I am going to look for that book and use it this year. Thanks for the great ideas!

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    1. Gina~
      Thant's great! I LOVE her math titles....they're just perfect to intro or review....happy you found something useful!

      Thanks for stopping by!

      Delete
  4. Chris, you're speaking my language. I used to teach math. LOVE math. Looks like you're having fun, too!

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    1. Rhonda!
      Well, great! So happy you stopped over and that you enjoyed a bit of math here.

      Thanks for visiting!

      Delete
  5. I wish I had learned about math using cookies! This sounds like fun. Thank you for linking at the In and Out of the Kitchen Link Party. Hope to see you again next week.

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    Replies
    1. Thanks Cynthia!! Hey, me too! And it's more fun teaching math in the kitchen as well!

      Thanks for visiting, ~~!!
      xoxox

      Delete
  6. Chris!!! This was the most viewed post in last week's Try a New Recipe Tuesday! Congratulations!!! :-) The post will go live with your post featured on Monday. Hope you can join us again this week. Much love to you!

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    1. Wow, thanks so much, Lisa! That's quite an honor! Very very cool!!

      No recipes this week, but I know I'll be back soon....I love your parties!

      Thank you for stopping by, friend!

      Delete
  7. Thanks so much for introducing me to sir circumference and the Dragon of Pi! What a fabulous book - and one that I must get! Your review is awesome. I am pinning this one. This is a must read!

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    Replies
    1. I'm really happy you like it..I have a feeling it will be a math staple in your HS! We love it !!

      Thanks for stopping by, friend!!

      Delete

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