Holiday Math and More: Math Teachers at Play #114

Do you enjoy math? I hope so! If not, the links in this post just may change your mind.

Welcome to the 114th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of articles by bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

By the way, I found a cool, semi-self-referential trivia tidbit about our carnival number: 27 − 14 = 114. And if you put 114 dots into a 1←7 Exploding Dots machine, you’ll get the code 222. Pretty neat!

As you scroll through the links below, you find several puzzle graphics from the wonderful Visual Patterns website. Use them as conversation-starters with your kids: What do you notice? How does each pattern grow? For older students: Can you write a formula to describe how each pattern? What will it look at stage 43?

Pattern #7, Trees

A BIT OF FUN

Setting the mood: Enjoy this bit of seasonal fidgeting from Vi Hart (@vihartvihart).

If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and enjoy the fun of learning something new.


TABLE OF CONTENTS

And now, on to the main attraction: the blog posts. Some articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

Let the mathematical fun begin!


SEASONAL MATH ACTIVITIES

You don’t have to celebrate Christmas to enjoy many of these activities — but really, I couldn’t find much for the other winter holidays. A few calculation worksheets with clip art, which is not my idea of playful math.

Do you know of any great math-related seasonal games, crafts, or activities I missed? Please add them to the comments section below!

Pattern #9, Snowflakes
Pattern #152, from John Golden, Circles
  • Clarissa (@c0mplexnumber) demonstrates how to make beautiful, challenging origami snowflakes. She recommends beginners try the first few folds — which create a pretty cool design on their own. Let it Snow… You may also enjoy her other Christmas projects.
Pattern #8, Penguins

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TALKING MATH WITH KIDS

Pattern #20, Helmets

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ELEMENTARY EXPLORATION AND MIDDLE SCHOOL MASTERY

  • If you’ve followed my blog for long, you know I like to play with dot grid paper. So of course, I was delighted to find Spatial Learning’s Isometric Dot Paper Activities, and the follow-up Cube Stack Activity. What a great way to build geometric intuition!
Pattern #197, from Stephanie Bowyer, Symbols

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ADVENTURES IN BASIC ALGEBRA & GEOMETRY

Pattern #28, Surface area

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ADVANCED MATHEMATICAL ENDEAVORS

Pattern #98, Centers are collinear, Fraction of the original circle shaded

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PUZZLING RECREATIONS

Pattern #52, Cubes

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TEACHING TIPS

  • My daughter is struggling with online homework in her calculus class — not because the math is too hard, but because the interface is anti-intuitive. So David’s (@davidwees) post resonates with me: Online Practice is Terrible Practice. And I love his challenge to find and teach to the Big Ideas of math.
  • I’d like to wrap up the carnival with an article you may have seen before. If you haven’t read it, you’re in for a treat. And if you have, well, it’s very much worth re-reading. Annually. As we wrap up the old year and prepare for the new … Francis’s (@mathyawp) Mathematics for Human Flourishing.

“Shalom and salaam, my friends. Grace and peace to you. May you and all your students flourish.”

— Francis Su

Pattern #174, from Katie Gates, Squares

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LOOKING AHEAD

And that rounds up this edition of the Math Teachers at Play carnival.

I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of January 22–26, 2018, at … well, we don’t know!

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up.

To share your favorite blog post with the carnival, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Older-but-still-relevant posts are welcome, as long as they haven’t been published in past editions of this carnival (at least, not in recent memory).

Past posts and future hosts can be found on our blog carnival information page.

Pattern #30, from John Golden, Squares

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Advent Math Activity Calendars

Once again, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the run-up to Christmas.

Including an especially-tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar home pages.

For Primary Students

Easier activities for elementary and middle school.

Math puzzle fun, plus a printable coloring page.

2017 Primary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Secondary Students

Activities for middle and high school.

Each day features a challenge from the Short Problems Collection.

2017 Secondary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Teens and Adults

“This year we’ve decided to bring you some of our favourite Plus videos. There’s nothing more soothing that a bit of fascinating maths, explained by a fascinating mathematician, that doesn’t even require you to read stuff. Happy watching!”

When you get to the +Plus Magazine website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

Plus Advent Calendar 2017

One link becomes live each day — so come back tomorrow and discover something new!

Christmas Meta-Puzzle

Or try your hand at the biggest mathematical mystery of them all — and save Christmas for Alex, Ben, and Carol!

Santa’s lost his memory, and the elves are cursed to alternate between lying and truth-telling. It’s up to you to piece together the clues and figure out which presents go where.

Christmas Logic Puzzle

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.


“Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Check Out These Cool Math Sales

I’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math.

You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

Sale price is $30 from December 2-15.

Cuisenaire Rod Activities Blowout Bundle

But Wait, There’s More

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

Their newest book is just off the presses — Funville Adventures, a math adventure chapter book.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

Natural Math Book Sale

Stock Up on My Playful Math Books

Finally, if you’ve been wanting to pick up a paperback copy of Let’s Play Math or some of my game books, or maybe a set of dot-grid math journals, I’m currently offering a discount on bulk orders.

Bundle ANY assortment of titles. Stock up on books for your family, friends, or homeschool group.

  • 2–4 books: 15% discount off retail prices
  • 5–9 books: 25% discount
  • 10–19 books: 35% discount
  • 20+ books: 35% discount, and free Continental U.S. standard shipping or the equivalent discount off other shipping options

Bulk Order Playful Math Paperbacks

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

Do You Know of Any Math Deals?

Apollonian greetings from my homeschool co-op kids, and best wishes for a grace-filled holiday season.

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


10 Ways to Play Math with Play-Doh

Today we have a guest post from Lucy Ravitch, author of the new Kickstarter picture book Trouble with Monkeys: A math concept story of place value. She’s sharing a few ideas from her Math Activity Thursday (M.a.Th.) video series. Enjoy!


Hello, math fans and enthusiasts! Each week I try to give you and your family a fun math activity to try. Two months ago I posted this video with ten ways to turn play dough into an engaging activity for lower and upper elementary math.

If you want to make your own dough from scratch here are a few simple recipes. I encourage you to let your children play freely at first, before trying these activities.

Below I have identified some of the math concepts that your kids will experience as they play.

1. Toss It

Practice counting. With older children, record your results and make a graph of the data.

  • How many times can you catch it in a row? What’s your average number of tosses?
  • Talk about attributes. Does the size or color of the play dough balls make a difference?
  • How high are you tossing it? Talk about measuring systems. Do you use feet and inches, or meters and centimeters?
  • If you know how to juggle, time how long you can keep the balls going.

2. Smash It

Make several small balls or pieces. Then play as you smash them.

  • Play a NIM game: Make 10-15 small play dough balls. Take turns. On your turn, you can smash one ball or two. Whoever smashes the last ball wins the game.
  • Or smash your math facts: Choose several equations for your children to practice. Write each answer on a 3×5 card. Lay out each card next to a play dough piece. As you call out the equations, kids smash the play dough next to the correct card.

3. Shape It

Have fun molding your play dough. Roll it out to cut shapes.

  • Try making 3D shapes while practicing your math vocabulary. MathisFun.com has a great section about solid geometry. Can you find three math terms that are new for you?
  • Roll out the dough and cut 2D shapes. Discuss their attributes. Can you cut your shape in half to be symmetrical?

4. Hide Things in It

Find small objects around the house and enclose them inside play dough.

  • Take turns hiding small objects in play dough. Optional: Give a one-minute time limit to guess before opening it. This gives you and your kids a chance to talk about size, shape, or other attributes.
  • Have challenges to use the least amount of dough to hide identical objects. Two players have two minutes to hide an object in as little play dough as possible. The object must be completely concealed within the dough. What methods will you use?

5. Make Imprints on It

Show off your design skills and observe textures.

  • You can practice counting as you poke and press your fingers or objects into the dough. Older children can discuss the distance between impressions and/or the pressure applied.
  • As you and your kids make designs, talk about what you notice: Is your design symmetrical? What tools did you use (toothpicks, pencils, marbles, fingers, toy cars)? Which objects make interesting textures?

6. Cut It

Use a butter knife or the edge of a ruler to cut your play dough. Discuss findings as you play and explore.

  • In the video, I posed the question: how many sections do you get if you make only three cuts? Try it and see.
  • Does the number of pieces change if you use a shape other than a flat circle?
  • Discuss making straight cuts that will intersect or be parallel. Bring in more geometry terms.
  • Experiment with a different number of cuts.

7. Weigh It

Pull out a kitchen scale or balancing scales to use with dough.

  • Older children can make conversions between ounces to grams. They can make calculations about doubling or multiplying the measured weight. With younger kids, try using balancing scales. Compare the weights between pieces.
  • Try making two pieces that weigh exactly the same. This is harder than it sounds! For small children, this gives them the opportunity to see that the mass (weight) of an object can come in different shapes.

8. Measure It

Use a ruler or measuring tape while you play. There are several ways you can measure your dough — height, width, and length.

  • How long can you extend one ounce of dough? Pick your own size/weight of play dough and see who can get the longest. What fraction of a yard or meter is it?
  • Discuss height and what it takes to make dough stand vertically. How tall can you get three ounces to stand? Can anything help make it taller?

9. Roll It

Make sure you have plenty of room for this activity. Playing outside or on smooth floors works best.

  • With one push how far does your play dough roll? Is there an ideal size for a piece? Is there an ideal weight for rolling?
  • Is the ground sloped? What effects does the rolling surface have?
  • Why do some shapes roll easily while others don’t? Can you create a not-round shape that will roll?

10. Compare It

Compare similarities and differences between dough colors and types. Consider comparing the previously listed activities

  • If you made your own dough, compare consistency between batches. Is homemade dough denser or lighter than store-bought dough?
  • What are differences between the dough you played with and the dough that has not been touched?
  • Which of these activities do you think will take the shortest amount of time? The longest? Or put the activities in order based on how much dough you will need — least to greatest.

May you and your students have fun as you play with dough!


About the Author

Lucy blogs at kidsmathteacher.com and is the author/creator of Kids Menu Books. The first book in that series is The Pancake Menu, an interactive book that lets kids practice math as they play restaurant.

And be sure to visit Lucy’s Kickstarter project! She’s teamed up with artist Trav Hanson to create the delightful picture book Trouble with Monkeys: A math concept story of place value.

Rabbit Trails and Fibonacci Poetry

Homeschooling Memories…

Well, I hadn’t planned on spending my day that way. But one of the great things about homeschooling is the freedom to follow rabbit trails.

While browsing the Carnival of Homeschooling, I found a link to Farm School blog’s article Fib Foolery, which sent me to Gotta Book for his articles The Fib and More Fibbery (read the comments on both threads, but be warned that some are crude) and several other posts, all of which set me off on a morning of poetic fun.

A “Fib” is a Fibonacci poem. It’s based on syllable count, like a haiku, but the lines follow the Fibonacci counting series: 1, 1, 2, 3, 5, 8… Each number is the sum of the previous two numbers.

I knew what I was going to share at our Tuesday Teatime and Poetry Reading that afternoon.

Here’s the best one I’ve come up with so far:

Math:
Word
Problem,
Mental play.
Archimedes shouts,
“Eureka! I figured it out.”

The Kids Join the Fun

While we always enjoyed our tea and poetry times, that day was the only one that inspired the kids to actually write poetry themselves.

My 7yo dd was so proud to be able to count syllables and write:

Cat.
Soft.
Pretty,
But sleeping.

While my 12yo ds really took off, creating more than a dozen Fibs. His first two are still his favorites:

Ducks
Have
No luck,
But they do
Have many feathers.
Hunters like to shoot ducks a lot.

and

Paul
Is
Revered
A lot by
Paul Revere’s Fan Club.
What is Paul’s last name, anyway?

Wouldn’t you like to try it, too? Please share your Fib in the comments below!


Feature photo: “Rabbit” by Save the Bay via Flickr (CC BY 2.0).

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


How You Can Play with Math #106

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

  • How many times would you have to slice the pizza to get 106 pieces?

Click here for all the mathy goodness!

Dot Grid Doodling

What can you DO with a page full of dots?

Yesterday, I mentioned my new series of paperback dot grid notebooks, and I promised to share a few ideas for mathematical doodling.

Doodling gives our minds a chance to relax, wander, and come back to our work refreshed. And though it goes against intuition, doodling can help us remember more of what we learn.

Math doodles let us experiment with geometric shapes and symmetries. We can feel our way into math ideas gradually, through informal play. Through doodles, our students will explore a wide range of mathematical structures and relationships.

Our own school experiences can make it hard for us to teach. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

—Julie Brennan

I like to doodle on dotty grid paper, like the pages in my math journals, but there’s No Purchase Necessary! You can design your own printable dot page at Incompetech’s PDF generator, or download my free coloring book (which includes several pages of printable dot and graph paper).

Patterns in Shape and Angle

To make a faceted mathematical gemstone, start with any shape you like. Then build other shapes around it. What do you notice? Does your pattern grow outward from its center? Or flow around the corner of your page? How is each layer similar, and how is it different?

Arbitrary constraints can lead to mathematically interesting doodles. For instance, create a design out of 45-45-90 triangles by coloring exactly half of every grid square. How many variations can you find?

Symmetry Challenge

Play a symmetry puzzle game. Draw a line of symmetry and fill in part of the design. Then trade with a partner to finish each other’s doodles.

Make more complex symmetry puzzles with additional reflection lines.

Math Doodle Links

  • Who can talk about mathematical doodling without mentioning Vi Hart? If you’ve never seen her “Doodling in Math Class” video series, you’re in for a treat!
  • See if you can draw a rotational-symmetry design, like Don’s “Order 4” graphs.
  • Or experiment with the more flexible rules in John’s “Knot Fun” lesson.
  • And my latest obsession: the “ultimate” tutorial series on Celtic Knotwork, which explores the link between knots and their underlying graphs.
My favorite knot doodle so far.

Inspirations: A Recreational Mathematics Journal
Reflections: A Math Teacher’s Journal
Explorations: A Math Student’s Journal
Contemplations: A Homeschooler’s Journal

Also available through: Barnes-Noble-logo the_book_depository_logo CreateSpace-logo

Before you start doodling: How to Break In Your New Math Journal.


Feature photo (top): Sommermorgen (Alte Holzbrücke in Pretzfeld) by Curt Herrmann, via Wikimedia Commons. [Public domain]

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.