Joy to the World!

If the embedded video doesn’t work on your computer, you can find the original here: Mannheim Steamroller – ‘Joy To The World’ Live.

My heart is steadfast, O God,
my heart is steadfast;
I will sing and make music.

Awake, my soul!
Awake, harp and lyre!
I will awaken the dawn.

I will praise you, O Lord, among the nations;
I will sing of you among the peoples.

For great is your love, reaching to the heavens;
your faithfulness reaches to the skies.

Be exalted, O God, above the heavens;
let your glory be over all the earth.

— Psalm 57:7-11

[Taken from the Holy Bible, New International Version, (c)1973, 1978, 1984 by the International Bible Society, used by permission of Zondervan Bible Publishers.]


In the Beginning Was the Word …

John 1:1-5; 8:12 recited in English, Cantonese, Japanese, Spanish, Croatian, Turkish, and French.

In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made. In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it.
… Again Jesus spoke to them, saying, “I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life.”

Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.


Holiday Math Puzzles and Activities for Christmas, Winter Break

Hapollonian Holidays from my Math Circle kids, and best wishes for a grace-filled holiday season.
Hapollonian Holiday Greetings from my co-op class kids, and best wishes for a grace-filled holiday season.

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

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. 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.

ADVENT MATH ACTIVITY CALENDARS

Every year, 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.

Pattern #9, Snowflakes

LET IT SNOW! LET IT SNOW! LET IT SNOW!

  • 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…
Pattern #20, Helmets

HAPPY CHANUKAH

Pattern #30, from John Golden, Squares

HANDS-ON HOLIDAYS

Pattern #197, from Stephanie Bowyer, Symbols

FOLLOWING YONDER STAR

Pattern #132, from Math Curmudgeon, Diagonals

MATHY CHRISTMAS CARDS

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

SANTA CLAUS IS COMING

Pattern #8, Penguins

ROCKIN’ AROUND THE CHRISTMAS TREE

Pattern #152, from John Golden, Circles

PUZZLES UNDER THE TREE

  • Unfortunately, the holidays come smack in the middle of flu season. Did you come down with The Grinch Bug?
Pattern #52, Cubes
  • Speaking of Christmas carols, the Christmas Price Index shows the current cost for one set of each of the gifts given in the song “The Twelve Days of Christmas.” I wonder what’s the cumulative cost of all the gifts, when you count each repetition in the song?

CHRISTMAS ADVENTURES WITH ALEXANDRIA JONES

Alexandria Jones and her family are fictional characters from my old Mathematical Adventures newsletter. Their stories appear sporadically as I find time to transcribe them from the back-issues. You can find them all on this blog page.

Here are all the Alexandria Jones stories Christmas stories, with activity and craft ideas…

Pattern #174, from Katie Gates, Squares

WHAT ABOUT WORKSHEETS?

Do you need to keep your kids busy and work in a bit of math practice? Try these Christmas word problems:

Or visit the sites below for worksheets to cover all ages:

Pattern #28, Surface area

CREDITS: “Circle Packing” feature graphic (top) by fdecomite via Flickr (CC BY 2.0). Picture pattern puzzles from Visual Patterns website.

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 pages.

For Primary Students

Easier activities for elementary and middle school.

A problem or game that uses dice for each day in the run up to Christmas.

2018 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.

Most of the tasks require dotty paper or circles which you can find on the Nrich Printable Resources page.

2018 Secondary Advent Calendar

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

For Teens and Adults

“Because sometimes, in the midst of all the family fun, it’s good to put your headphones in and retreat into a word of your own, this year’s advent calendar brings you some of our favourite Plus podcasts. From the secrets of the Universe to the maths of football stadiums, there should be something there for everyone. Happy listening and happy Christmas from the Plus team!”

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 2018

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!

“It’s nearly Christmas and something terrible has happened: one of Santa’s five helpers — Jo Ranger, Fred Metcalfe, Kip Urples, Meg Reeny, and Bob Luey — has stolen all the presents during the North Pole’s annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.”

Christmas Logic Puzzle

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

Still More Mathy Fun

Colleen Young has collected several more holiday math calendars — enough to keep your kids playing and learning well into the New Year. Take a look!

Mathematical Advent Calendars

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

Holiday Math and More: Playful Math Education Carnival 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!

Continue reading Holiday Math and More: Playful Math Education Carnival 114

The Mysterious Block Puzzle

3-way-block-puzzleFor toddler Renée’s Christmas gift, Alex and Leon crafted a puzzle set of wooden blocks.

First, they made a sturdy box with circle, square, and triangle shapes cut in the lid.

To make the blocks large and baby-safe, Alex and Leon bought a 4-foot 2×2 board. Then they asked Uncle Will to help them create a set of special blocks to fit through the holes.

Each block was round and square and triangular, so it could fit exactly through any of the three holes.

How can that be?

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “Christmas Tree Closeup” photo by Zechariah Judy via Flickr (CC BY 2.0).

A Polyhedra Construction Kit

To make a Christmas gift for her brother Leon, Alex asked all her friends to save empty cereal boxes. She collected about a dozen boxes.

She cut the boxes open, which gave her several big sheets of thin cardboard.

Then she carefully traced the templates for a regular triangle, square, pentagon, and hexagon, as shown below.

polyhedra-construction-kit

Click here to download the polygon templates

She drew the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs would bend easily.

She cut out shapes until her fingers felt bruised: 20 each of the pentagon and hexagon, 40 each of the triangle and square.

Alex bought a bag of small rubber bands for holding the tabs together. Each rubber band can hold two tabs, forming an edge of the polyhedron. So, for instance, it takes six squares and twelve rubber bands to make a cube.

Finally, she stuffed the whole kit in a plastic zipper bag, along with the following instructions.

Polyhedra Have “Many Faces”

Poly means many, and hedron means face, so a polyhedron is a 3-D shape with many faces.

The plural of polyhedron is polyhedra, thanks to the ancient Greeks, who didn’t know that the proper way to make a plural was to use the letter s.

Each corner of a polyhedron is called a vertex, and to make it more confusing, the plural of vertex is vertices.

Regular Polyhedra

Regular polyhedra have exactly the same faces and corners all around. If one side is a square, then all the sides will be squares. And if three squares meet to make one vertex, then all the other vertices will be made of three squares, just like that first one.

There are only five possible regular polyhedra. Can you figure out why?

Here are the five regular polyhedra, also called the Platonic solids. Try to build each of them with your construction kit.

Tetrahedron: three equilateral triangles meeting at each vertex.

Hexahedron: three squares meeting at each vertex. Do you know its common name?

Octahedron: four triangles at each vertex.

Icosahedron: five triangles at each vertex.

Dodecahedron: three pentagons per vertex.

You can find pictures of these online, but it’s more challenging to build them without peeking at the finished product. Just repeat the vertex pattern at every corner until the polygons connect together to make a complete 3-D shape.

Semi-Regular Polyhedra

Semi-regular polyhedra have each face a regular polygon, although not all the same. Each corner is still the same all around. These are often called the Archimedean polyhedra.

For example, on the cuboctahedron, every vertex consists of a square-triangle-square-triangle combination.

Here are a few semi-regular polyhedra you might try to build, described by the faces in the order they meet at each corner:

Icosidodecahedron: triangle, pentagon, triangle, pentagon.

Truncated octahedron: square, hexagon, hexagon.

Truncated icosahedron: pentagon, hexagon, hexagon. Where have you seen this?

Rhombicuboctahedron: triangle, square, square, square.

Rhombicosidodecahedron: triangle, square, pentagon, square.

Now, make up some original polyhedra of your own. What will you name them?

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “50/52 Weeks of Teddy – Merry Christmas” photo by Austin Kirk via Flickr (CC BY 2.0).

How to Make a Flexagon Christmas Card

tetra-tetraflexagonHere’s how Alex created tetra-tetraflexagon Christmas cards to send to her friends:

1. Buy a pack of heavy paper at the office supply store. Regular construction paper tears too easily.

2. Measure and divide the paper into fourths one direction and thirds the other way. Fold each line backward and forward a few times.

3. Number the front and back of the paper in pencil, lightly, as shown. Then carefully cut a center flap along the dotted lines.

4. Fold the paper along the dark lines as shown, so the center flap sticks out from underneath and the right-hand column shows all 2’s.

5. Fold the flap the rest of the way around to the front and fold the right-hand column under again. (Shown as dark lines on the diagram.) This makes the front of the flexagon show 1’s in every square.

6. Carefully, tape the flap to its neighbor on the folded column. Don’t let the tape stick to any but these two squares.

7. Gently erase your pencil marks.

Find All the Faces

A tetra-tetraflexagon has four faces: front, back, and two hidden. It is shaped like a tetragon — better known as a rectangle.

Here’s how to flex your tetra-tetraflexagon card:

  • Face 1 is easy to find. It’s on top when you make the card.
  • Turn the card over to find Face 2.
  • Face 3 is hidden behind Face 2. Fold your flexagon card in half (vertically) so that Face 1 disappears. Unfold Face 2 at the middle, like opening a book. Face 3 should appear like magic.
  • Face 4 is hidden behind Face 3. Fold the card (vertically) to hide Face 2, then open the middle of Face 3. Face 2 vanishes, and Face 4 is finally revealed.

When Faces 2 and 3 are folded to the back, you will notice that any pictures you drew on them will look scrambled. What happened?

Add Your Designs

Alex wrote a holiday greeting on Face 1. Then she drew Christmas pictures on the other three faces of her card.

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “Happy Holidays” photo by Mike Brand via Flickr (CC BY 2.0). Video by Shaireen Selamat of DynamicEducator.com.

Alexandria Jones and the Magic Christmas Cards

The Jones family sat around the dining table performing a traditional holiday ritual: the Christmas card assembly line.

First, Dr. Fibonacci Jones (the world-famous mathematical archaeologist) signed for himself and his wife. He handed the card to Alex, who signed for herself and baby Renée. Then Alex’s younger brother Leon added his own flourish. Finally, Mrs. Jones wrote a personal note on the cards going to immediate family and close friends.

One-year-old Renée sat in her high chair, chewing the corners of an extra card.

Alex Poses a Problem

Alex dropped her pen and shook out her tired fingers.

“I’m stumped,” she said. “I’d like to send a special Christmas card to some of my friends from camp last summer. But I can’t think of anything that seems good enough.”

Leon leaned his chair back in thought.

Then he snapped his fingers. “I’ve got it! We’ll throw a handful of sand in each of their envelopes. You know, to make them remember all the fun you guys had digging up old stuff.”

Alex humphed. “How would you like to get sand in your Christmas present?” she asked. “Besides, it wasn’t stuff. It was artifacts.”

“You should not make such a display of your ignorance, young man,” Dr. Jones said. “Stuff, indeed!”

Mrs. Jones put her hand to her forehead and sighed dramatically. Then she turned to Alex. “Have you considered doing a jigsaw puzzle card? They sell them at the hobby store.”

“I’ve tried those before,” Alex said, “but the ones I had always warped. The puzzles didn’t go back together very well.”

Dad Gets an Idea

Dr. Jones got an out-of-focus, “I’m thinking” look in his eyes. He stood up, tapped his chin with his pen, and walked away. He almost ran into the wall, but he caught himself. Shaking his head, he disappeared into his study.

Mrs. Jones put down her pen and picked up Renée.

“Why don’t you two address those envelopes while we wait for your dad’s inspiration to reveal itself? I need to put a little one down to S-L-E-E-P.”

Alex laughed. “If you keep that up, Renée will learn to spell before she’s out of diapers!”

Leon thumbed the stack of envelopes and groaned. “C’mon, sis. Back to work!”

Before long, Mrs. Jones came back and chased the kids away from the table. “I’ll finish this,” she said.

Unfolding the Magic

Alex and Leon ran to the study. They found Dr. Jones at his desk, playing with a piece of paper.

“Ah, there you are,” he said. “Here, Alex. What do you think?”

“Well,” she said, “it looks like a regular piece of paper that’s been folded over on itself.”

Dr. Jones nodded. “Now you know a sheet of paper has two faces—that is, it has a front and a back.”

Leon reached for the paper and flipped it over. “Is that why you put red stripes on one side and blue stripes on the other?”

“Observe,” Dr. Jones said.

He took the piece of paper and folded it in half. Then he unfolded it and handed it to Alex.

“Hey, how’d you do that?” she asked. “Now there are blue polka-dots on this side.”

“Cool! It’s magic,” Leon said.

“It is called a tetra-tetraflexagon,” Dr. Jones said, “and it has one more hidden face. Can you find it?”

Alex folded the paper this way and that. Then she held it up in triumph.

“Look, red dots—I did it!”

She gave her dad a tremendous hug. “Thanks, Dad! I’ll make magic flexagons. They’ll be the best Christmas cards ever!”

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “Christmas Window” photo by slgckgc via Flickr (CC BY 2.0). Video by Shaireen Selamat of DynamicEducator.com.

Christmas with Alexandria Jones

Alexandria JonesAlexandria Jones and her family are fictional characters from my old Mathematical Adventures newsletter. Their stories appear sporadically as I find time to transcribe them from the back-issues. You can find them all on this blog page.

Here are all the Alexandria Jones stories Christmas stories, with activity and craft ideas…

Alexandria Jones and the Christmas Present Quandary

Alex designs tessellation wrapping paper, hunts for the perfect Christmas tree, and comes up with a lively present for her brother. We meet the rest of Alex’s family — her father was introduced in an earlier issue — along with historical figures Maria Agnesi and Leonhard Euler, and we take a brief glance at mathematics from China.

Alexandria Jones and the Christmas Gifts

Most of this issue focuses on other topics — but the Jones family has a new baby, so Alex makes two gifts.

And New This Year: Alexandria Jones and the Magic Christmas Cards

Dr. Jones suggests a way to make the “best Christmas cards ever” (according to Alex), and the Jones children create geometric gifts to celebrate the holiday.