Make Valentine’s Day crafts to celebrate loving one another… in the context of mathematics!

Grow your math eyes on these little field trips inspired by topology, dynamical systems, and algebraic geometry for the young, the very young, and the young at heart.

Know another romantic math craft? Tell us in the comments!

**Make math:** Fold paper in two. Sketch a teardrop in such a way that the fold forms one side of its triangular top part. Cut it out, open, and decorate the heart-shaped greeting card. My teen and I decorated with a cardioid (see below).

**Grow your math eyes:** What interesting shapes can you fold or unfold into other interesting shapes? What if you fold more than once? Choose shapes to experiment, on paper or in your imagination.

**Topic:** Mirror Symmetry. **Inspired by Big Math:** #14 Algebraic Geometry, #53 Differential Geometry.

**Bonus:**

**Make math:** Cut out two strips of paper and glue them together to form the + sign. Attach the opposite ends, with a twist, as if making Mobius strips. Cut the strips through the middle, and Mobius Hearts will happen! Video instructions:

**Grow your math eyes:** Try twisting two or more times. Try cutting 2/3 of the way rather than through the middle. What other surfaces can you make by connecting, twisting, and cutting paper strips?

**Topic:** Surfaces. **Inspired by Big Math:** #54 General Topology, #57 Manifolds.

**Bonus:**

*Roses are red. Violets are approximately blue.*

* A paracompact manifold with a Lorentzian metric,*

* can be a spacetime, if it has dimension greater than or equal to two.*

By Sarah Kavassalis

From participants in the Multiplication Explorers course

**Make math: **Draw a heart. Mark two or more points around it, for example, up top. Draw smaller hearts there. Mark the same points on them, and draw even smaller hearts. Keep going. Decorate your heart fractal, put it on a wall, or use as a greeting card.

**Grow your math eyes: **How tiny can your hearts become? Will you run out of space on paper if you keep going and going and going? How many hearts do you add to your fractal at each step of the process? For more versions, choose how many hearts to add at each step, how much to shrink at each step, how to turn the hearts around – then observe what happens.

**Topics:** Fractals and exponential growth. **Inspired by Big Math:** #11 Number Theory, #37 Dynamical Systems.

**Bonus:**

**Make math:** Trace a plate on scratch paper and cut out the circle. Fold it in half a few times, as if for making a snowflake. Unfold; your circle is now split into equal parts.

Trace the same plate on cardboard. Then use your folded circle as a guide to mark your new circle. You may need to insert more dots by hand.

Image by Cory Poole/WonderHowTo

You can also print out a marked circle, or use a protractor to mark it. Then follow instructions from MathCraft for drawing, or Almost Unschooling for string art. The craft involves skipping the dots by one and two, again and again. The repetition feels meditative, and there is a beautiful surprise at the end. The heart-shaped curve emerges as if by magic! Decorate it and put it on the wall or use as a greeting card.

**Grow your math eyes:** What other curves can you make out of straight lines? Choose your own “recipe” for skipping dots around a circle, and see what happens. What if you used a triangle or a square instead?

**Topic:** Curves. **Inspired by Big Math:** #14 Algebraic Geometry, #52 Discrete Geometry.

**Bonus:**

**Make math: **Customize variables and make your own greeting cards out of pretty graphs. Go to **Desmos Math-o-Gram site** to play and share the love.

**Grow your math eyes:** Peek behind the scenes to experiment with the equations. Replace numbers or functions in them and see what happens. Young children can start experimenting without knowing much (or anything) about the functions.

**Topic:** Functions and graphs. **Inspired by Big Math:** #14 Algebraic Geometry, #33 Special Functions.

**Bonus:**

Posted in Make & Grow

Doing math with your children’s friends or a small math circle? Chances are your students are of mixed ages and levels. How can you have good dynamics?

- Don’t focus on activities that are likely to invite competition, such as problem-solving.
**Use open, collaborative activities**: hands-on maker activities, scavenger hunts for math, games, or puzzles. **Invite parents or adult helpers to be students too**, to participate, and to do activities for themselves. Now the oldest child you have is not the oldest group member anymore – the adults are! Guide adults to share their discoveries with one another, rather than overwhelming the children, unless the kids ask.**Try Notice-Wonder activities**: show a fractal, a math sculpture, a mandala, or any curious object to the group, and invite everyone to ask questions. Younger children ask weird and wonderful questions. Adults and older children can research the wonder.**Have tables children can choose**, as if you are doing a mini-festival. Check out examples from Julia Robinson math fest, Reggio Emilia provocations, or Montessori centers.

Posted in A Math Circle Journey

Our newest book for children ages 5 and up is out. Big thanks to the fabulous crowdfunders that made it possible! *Funville* is a math-inspired fantasy adventure by Sasha Fradkin and Allison Bishop, where functions come to life as magical beings. After 9-year old Emmy and her 5-year old brother Leo go down an abandoned dilapidated slide, they are magically transported into Funville: a land inhabited by ordinary looking beings, each with a unique power to transform objects.

- Watch the 2-minute book trailer, read interviews, and get your copy.
- Start reading Chapter 1.
- Congratulate the authors and participate in our Facebook giveaway.

Heads up: our paperback prices will increase after December 20th. We may have a membership price range in the future; stay tuned. Meanwhile, now is the good time to stock up, because…

Shop for thoughtful and joyful gifts at Natural Math. Starting Cyber Monday November 27th and until December 20th, we have discounts on all paper and electronic books. You can mix and math different book titles for the following offer:

$1 off each book

$2 off each when you buy 2-4 books

$3 off each when you buy 5-9 books

$5 each when you buy 10+ books.

*See you online!*

*Dr. Maria Droujkova, and the Natural Math crew*

Questions? Email reach.out@naturalmath.com

Posted in Newsletter

*Math is what you make of it!*

Making math your own is the motto of Natural Math. Hundreds of your stories, interviews, and comments on chapter drafts went into Math Renaissance – the future readers, making the book address their needs. Many of you read Funville Adventures stories with your children and sent the authors feedback, art, and fanfiction inspired by the book. And now, **600+ of you crowdfunded** these two newest Creative Commons book projects. THANK YOU!

When you open a Natural Math book and see your name in the community credits, know that YOU made a difference in mathematics education.

There is still time to crowdfund Funville Adventures (until June 15) and Math Renaissance (until June 22) on Kickstarter. Even $1 makes a difference: it tells the world one more person cares. All funders receive insider updates from the authors, have their names listed in the book, get the book of course, and other exciting prizes.

Children’s fan art for Funville: the magic slide.

Rachel Steinig is the teen co-author of Math Renaissance. Are you seeking ideas for deep, meaningful projects for older students? Rachel’s book and her stories will help! At the age of 14, Rachel began a 3+ year journey of researching and writing the book. Her passions for journalism, mathematics, and student rights gave life to an incredible project. What does it take? Here is a quote from her college application essay:

If there’s one thing I hate, it’s injustice. I believe that all children deserve a good education. Educational inequality has been extremely apparent to me after attending an underfunded Philadelphia public school. This desire to eradicate injustice and to give all children access to the best possible education motivates me to engage in this writing and advocacy even when it gets challenging. I see writing this book as an act of sharing the pedagogical wealth by disseminating math circle practices to everyone.

What are these practices? For example, **meaningful work on complex problems**. Here’s a quote from the Math Renaissance FAQ:

Do kids as young as 6 or 7 really have sufficient motivation, attention spans, or capabilities to understand and solve complex problems, especially if the students are not yet firmly grounded in the basics?

In our math circles, children are motivated to learn because the questions are accessible mysteries. I have seen the intrinsic motivation generated in math circle sessions translate to more interest and motivation to learn the “basics.” Rachel taught a math circle this past fall on Rational Tangles (an activity designed by mathematician John Horton Conway) in which a bunch of kids were begging to learn how to manipulate fractions because they wanted to untangle a knot. When I taught The Unicorn Problem the first time, even though the kids were quite young, the pull of the narrative was strong enough to give them the extended attention span to solve the problem. We spent an hour a week for six weeks until we solved it because the problem felt alive to the students.

Do you get criticized for your dedication to teaching and parenting? Dr. Sasha Fradkin has always loved mathematics. She opened a frank, deep conversation on Reddit with her Ask Me Anything piece. “With a PhD in math from Princeton I chose to teach at an elementary school and write a math-inspired children’s book. AMA!” Her topic turned out to be one of the most popular this year, with **2100+ questions and comments**. Should mathematicians teach? Why and how to change careers? How does parenting come into the equation? These were the big themes. Here are a few sample questions Sasha answered:

How do you stay satisfied going over basic material year after year after exploring it in such depth in college?

At the university level, did you ever see common misconceptions or prevalent comprehension difficulties that you believe were rooted in educational problems that started as early as K-5?

Have you experienced a lot of people who criticised you over your decision/tried to stop you?

Dr. Allison Bishop, Sasha’s co-author of Funville, hated math as a child. She fell in love with it early in college, and is now a computer scientist. What was her secret? A good teacher, and… **storytelling**! Here’s a quote from Allison’s interview at Columbia University:

What really got me interested in math as an adult was the creative side of science research, and the human stories of how different people make different discoveries. Why them? Why that idea? What was it about that context and that time that sparked an insight?

Storytelling is fundamental to everything. Mathematicians and scientists need to think about storytelling as a way to get broader scientific literacy across to others. We as scientists don’t optimize the communication part; we spend so much time on the research. But we need to be able to explain science to someone who hasn’t spent years delving into scientific questions. People should be able to more easily see the creativity and beauty in science. So many people don’t get there.

*See you online!*

*Dr. Maria Droujkova, and the Natural Math crew*

Questions? Email reach.out@naturalmath.com

Posted in Newsletter