Making Rice & Understanding Circumference
Rice and circumference go together? Why, yes, they do!
Yesterday, I was playing with the Going in Circles spark from the Inspired by Calculus class with my online class and my children. We did this activity.
We had so much fun verifying that the difference in the lengths of string was really the same no matter how big or small your original circle seemed to be. One student even did the activity in reverse. He noticed that drawing a new circle with a radius that was 1/2″ longer added 3″ to the string. When he did a circle with a radius that was 1″ longer, it added 6″ to the amount of string needed to go around the new circle (as compared to the original circle). So he guessed if he had a 9″ difference that the radius would increase by 1.5″ compared to the original circle. Then he tested his hypothesis! I was so excited by his thinking process! It was a bit challenging to use string and get accurate measurements.
Another neat question that arose, when we showed that the difference in circumference is always the same amount no matter the original circle size, was WHY!? Two of my students were really annoyed and wanted to know “Why! Mrs. Nash. How is that possible!” After racking my brain for a moment we settled on the analogy of making rice. It’s a proportion, and that’s where Pi really started to click (even for me!) Just like making rice is always 1 part rice : 2 parts water; circles are always increasing by 2π.
photo by Deborah Austin. CC-BY-2.0
So if I need 9 cups of rice I measure 3:6; if I need 24 cups of rice I measure 8:16; but no matter how BIG the amount of rice I need, the proportion will be the same. That’s when they got it—that’s when I got it! No matter how big my starting circle (even if it’s the earth), the proportion I add is connected to 2π . It’s a ratio!
Here’s a bit of my own math I did after the class.
- Original Circle: Radius of 10, circumference abt 60
- 1/2″ larger: Radius of 10.5, circumference abt 63
- 1″ larger: Radius of 11, circumference abt 66
- 1.5″ larger: Radius 11.5, circumference abt 69
Ta da! Can you see the 3 (or 3.14….) ratio! So much fun for my brain to see it!
If you’d like to try the sparks too, watch for our next Inspired by Calculus class.
Posted in A Math Circle Journey
Where’s math in this play? Open Minds book is out, and our new book bundle. Newsletter March 7, 2016
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Where is mathematics? Playing with blocks online, March 10
Sian Zelbo, a co-author and illustrator of the popular math circle and family book Camp Logic, is working on her next book, Playing With Blocks. Parents and teachers often tell us, “Yes, we see how your activities are beautiful and playful, and we want that for our children’s math. But we can’t find the math in our play. Help!” Sian’s book helps you to see deep mathematics in playful activities. And now, you have a chance to work with Sian Zelbo and Sally Bishop live, during a workshop we offer.
The activity you will explore in the online workshop is a joyful and elegant example of mathematics that starts easy, and then takes you far. The areas of math you will touch come from the subjects of geometry, number theory, and combinatorics.
You will help your children grow their math eyes, and notice unexpected links between concepts such as angle and area, minimum/maximum and perimeter, combinations that form a sum and types of triangles (equilateral, scalene, and so on). You will make bridges to other rich math activities, such as pentaminoes and tangrams.
As we talk, you will pick up good math terms for this exploration, and good search phrases for when you want to investigate these topics more. You will also collect questions you can ask about any problem, to learn deeper, more joyful math. For example:
- What makes Thing One and Thing Two similar or different? (For example, a triangle and a square.)
- What is the largest thing you can make? How do you measure your things? (For example, using a grid to measure areas.)
- What if you change your numbers around? What other things you can change? (For example, 10 toothpicks instead of 12.)
Check out a sample activity you can try, from our online workshop centered on the new book’s ideas. It runs on March 10 and 11, and is for parents and teachers with children ages 5-12.
A new Natural Math book is out!
The latest Natural Math book for parents, math circle leaders, and teachers is called Bright, Brave, Open Minds: Engaging Young Children in Math Inquiry. Go to the book’s page to try out several activities with your children, and get a taste of the inquiry-based approach to playful, deep mathematics.
In the introduction, the author Julia Brodsky writes:
I will share with you what I have learned as I tinkered with teaching problem solving to curious young children, ages six to eight. The purpose of this book is to invite you to experiment with your own children or students, without any preconceived notions of how the outcome will look. Instead, allow your personal taste and the children’s feedback to guide you.
As all our books, Open Minds is available in paperback as well as electronic formats and name-your-price PDF. To celebrate, we offer a limited-time sale on our book bundle. Check it out!
Dr. Maria Droujkova and the Natural Math crew
Questions? Email reach.out@naturalmath.com or ask in comments to this page.
Posted in Make & Grow, Newsletter
Playing With Blocks: Newsletter March 2, 2016
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Playing With Blocks ideas, and a workshop on March 10
Sian Zelbo, a co-author and illustrator of the popular math circle and family book Camp Logic, is working on her next book, Playing With Blocks. You can grab this Math Spark and play-test an activity from the book with your children: easy, addictive, smart toothpick puzzles!
Sally Bishop, an enthusiastic Natural Math leader, has joined Sian to offer an online workshop centered on the new book’s ideas. It runs on March 10 and 11, and is for parents and teachers with children ages 5-12.
What do you get if you join Playing With Blocks workshop?
- A highly interactive experience where you make models, talk, and collaborate with 24 other parents and teachers. We keep our groups small.
- Leading your children or students on playful math adventures.
- The first meeting in a math circle format (you as a student!) to see how to run these activities, and to get inspired.
- A day to try activities with children and friends
- The second meeting to answer your questions, overview other activities, and prepare to do more with children.
- Insight on how to adapt puzzles and problems to facilitate endless math exploration.
- Make an impact on another Natural Math book by sharing your ideas directly with the author
- (The crowdfunding option) Your name as one of crowdfunders in Sian Zelbo’s new book, Playing With Blocks, and the paperback and ebook copies (~Fall 2016)
- Most importantly, you’ll get the confidence in your own ability to do math differently in your family or group!
Dr. Maria Droujkova and the Natural Math crew
Questions? Email reach.out@naturalmath.com or ask in comments to this page.
Posted in Make & Grow, Newsletter
Calculus for 5-12 yo (grown-up workshop) on March 2, samples to try, shenanigans: Newsletter February 26, 2016
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Inspired by Calculus on March 2
We had a lot of requests to repeat the Inspired by Calculus online workshop for parents, teachers, and their children ages 5-12. We will run another session with three live meetings, starting March 2. Check it out!
We’ll have a calendar of all upcoming courses very shortly. Please stay tuned.
What do you get from Inspired by Calculus?
- A highly interactive experience where you make models, talk, and collaborate with other parents and teachers. There are only 25 spaces in the course.
- Leading your children or students on playful math adventures.
- The first meeting in a math circle format (you as a student!) to see how to run these activities, and to get inspired.
- A day to try activities with children and friends
- The second meeting to answer your questions, overview other activities, and prepare to do them with children.
- Three weeks of mentoring and peer discussions on the forums.
- The third meeting to recap, ask more questions, and stay inspired by calculus!
- A dozen reference cards (math sparks) to help you try out the activities with your children.
- Access to the Natural Math online forum to ask questions and share resources, even after the class is over.
- Most importantly, you’ll get the confidence in your own ability to do math differently in your family!
Go to the course page to try two short, sweet math spark activities with your children, and learn more about the course.
Socks Are Like Pants, Cats Are Like Dogs… Wait, what?!
The pre-orders and crowdfunding prizes are on the way, and our new book that makes bold claims about similarities between different things is out! Get the new preview of the book, read the intro on how to play algebra with children, and then try two activities from the preview:
As always, this book is Creative Commons and name-your-price PDF is available.
Discussion Group Shenanigans
Once in a while, when a new member joins our FB discussion group ‘1001 Circles’ we make a number theory greeting card like that. Every number has cool features. Every one!
And every Monday is a PunDay. From this week:
But mostly, the 1001 Circles group has discussion about family math and mathematical circle activities. Check it out. We have plans to produce digests of discussions – if you’d like to help, let us know.
Dr. Maria Droujkova and the Natural Math crew
Questions? Email reach.out@naturalmath.com or ask in comments to this page.
Posted in Make & Grow, Newsletter
