Quick review: A tessellation is a repetitive patterns of shapes that fit perfectly together across a 2-dimensional plane of space. The tessellated shape can be regular, as are these Christmas tessellations, or irregular, as are the shapes in our original tessellations activity post and video.

We made Christmas tessellations using simple triangles, as well as traditional fir or pine tree shapes. The concept of how to tessellate each pattern is the same, so once kids understand how it works they will want to experiment!

Materials

• Graph paper
• Plain white paper, such as art or construction paper
• Scissors
• Pencil
• Ruler
• Markers, colored pencils, crayons, for coloring and decorating the trees

Simple Triangle Tessellations

Making Christmas tree tessellations with an isosceles triangle is the easiest way, so we will start with that.

On the graph paper, draw an isosceles triangle. An isosceles triangle has two equal sides. In our photos you can see examples of two different isosceles triangles we used as our pattern.

To form an isosceles triangle, draw a rectangle or square on the graph paper. Any size will do; it can be tall or squat, your choice. The top point of the triangle starts in the midpoint in the top side of the rectangle. Draw two lines, one each from the top point to each of the bottom corners of the rectangle. Ta da!

Now, cut out the triangle. This will be the template for the tessellation. If you wish, glue it to a piece of heavy paper or card stock and cut on the outline to have a sturdier template.

Place the triangle template on your white paper and draw the outline of the triangle. Then, move the template over and line up the bottom edge with the triangle you just drew. Continue in this manner until you have a line of triangles.

At this point, savvy kids will realize that the space between the triangles is exactly the same shape as their template, only upside down. They will be quick to understand how to fill the paper with this new, groovy tessellation pattern.

Christmas Tree Shape Tessellations

This slightly fancier tree shape based on fir or pine tree shapes takes a bit more skill to draw, but it's still easy!

Begin by counting out a rectangle on graph paper with an x-axis of 10 squares and a y-axis of 12 squares. Make a dot at the mid point of the top line (5,12). That is the tippy top of the tree.

Draw lines from:

• (0,0) to (2,3)
• (2,3) to (1,3)
• (1,3) to (3,6)
• (3,6) to (2,6)
• (2,6) to (4,9)
• (4,9) to (3,9)
• (3,9) to (5,12)

Materials

Both Halloween tessellation projects use the same basic materials. You probably have all these common household items.

• Paper
• Pencil and pen
• Square sticky notes or other small square of paper
• Tape
• Scissors
• Colored pencils, crayons or markers

Ghost Tessellation Instructions

If you've ever made tessellations with your kids before, you'll recognize how easy it is to make these repeating ghosts. They are even easier than the cat tessellations we made, but the concept is the same!

Step 1. Decide how wide you want your ghosts to be. We cut our square sticky note in half to make long thin ghosts, but you can skip that step to make short, squat ghosts. After all, ghosts come in all body types!

Step 2. Draw a half circle at the top of your sticky note without touching the top of the paper. This steps allows for some creativity. Do you want your ghost to have a round head? A pointy or lopsided head? The pattern will still tesselate, so give your ghost some personality. (For reference: at the bottom of this post, you can see the specter in our ghost tessellation bookmark has a pointy head.)

Step 3. Cut the paper on the line you just drew.

Step 4. Move the cut portion of the paper to the bottom to form your ghost template and secure with tape. TIP: You can make your ghost shorter or longer depending on where you align the two pieces.

Step 5. Place ghost template on a sheet of paper and trace. Repeat this step, lining up the template on the paper so it forms a tessellated pattern. You can stager your columns of ghosts, or keep them aligned.

Step 6. The all important finish is to give your ghosts cute faces and color them however you wish!

Alternative Ghost Tessellation

Creating this alternative ghost template for a tessellation pattern is not as basic as our first ghost template, but it's not hard, either!

Use the instructions in our original how to draw abstract tessellations instructions (or watch the how-to video below) to create an abstract shape. Rotate this shape until you can imagine it as a ghostly apparition and then tessellate!

Bat Tessellation Instructions

Nothing says Halloween like a colony of bats!

Step 1. Draw the outline of pointy ears and wings at the top of your sticky note. Don't forget that you want to leave space between the ears and the top of the paper.

Step 2. Cut the paper on the line you just drew.

Step 3. Move the cut portion of the paper to the bottom to form your bat template. TIP: Just like with the ghost, you can make your bat shorter or longer depending on where you align the two pieces.

We went for a bat with a short body. In this case, you want to place the cut portion near the bottom of the paper and cut on the outline. This is where a sticky note comes in handy because the top portion will stay in place while you cut!

Step 4. Now that you have a bat template, create your patterns. Place bat template on a sheet of paper and trace. Repeat this step, lining up the template on the paper so it forms a tessellated pattern. You can stager your columns of bats (as we did), or keep them aligned.

Step 5. Finish up by giving your bats sweet or fierce faces (don't forget the fangs!) and color them however you wish!

BONUS: Halloween Tessellation Bookmarks

While working on this project, we noticed that a column of tessellated bats or ghosts makes a great bookmark! Cut out a column of finished creatures and use as a bookmark. For longevity, use card stock instead of office paper, or laminate the finished product.

Combine Math and Art

Math and art intersect in lots of ways. I use math art projects as a way to get my more practically inclined son to engage his creative side. For kids more naturally inclined towards artistic projects rather than math, these are a great way to get those left brains fired up.

Tessellations

Patterning is mathematical! Teach your kids about a fun patterning technique by first showing them the basics of how to create an abstract tessellation pattern. Then, create themed tessellations. As a bonus, making tessellations can be extremely relaxing–great after a stressful school day. We have instructions for the following:

• Cat tessellations
• Heart tessellations (three ways!)
• Star tessellations (two ways!)
• Ghost and bat tessellations for Halloween

Math Tool Art

Draw with math and geometry tools like a compass, triangle and circle protractors and rulers. See how we created compass art mandelas

Use a protractor to create parabolic curves.

Möbius Strip

Math has a built in WOW! factor, which kids can demonstrate by cutting Möbius strips

• Make a Möbius strip. Cut it and see what happens. It's not what you think. After your kids have mastered the basics, cut a Möbius strip into two hearts!

Manipulate Shapes and Patterns

Make artistic designs with shapes. Start with simple triangles, move on to circles and advance to spirolaterals!

• Play around with homemade Montessori triangles. The triangles can be formed into lovely shapes and patterns, all the while teaching a bit of how geometry works.
• Explore Fibonnaci patterns with circles
• Use graph paper to draw spirolaterals and practice multiplication tables.

Explore Dot to Dots

My kids loves dot to dots, especially Extreme Dot to Dot puzzle books. They are also handy to tote along to restaurants or waiting rooms. My kindergartener gets down on the floor with a DIY giant dot to dot. Toddlers can join in the after school fun with their older siblings by completing this fun DIY toddler-friendly dot to dot puzzle!

MORE: Math Art Projects for Kids

Play a Math Game

There are loads of fun games that help kids practice their math and number skills. The following are some of our favorites:

Play Shut the Box. We have a printable version of this classic game so you don't have to run out and purchase the original wooden game.

Lu-Lu Dice Game - this is a traditional game from Hawai'i that teaches kids to recognize quantities

KenKen - this is a spin on Sudoku which requires minor calculations. Completing a puzzle gives a real sense of satisfaction.

Another spin on Sudoku is this colorku wooden puzzle. Both my kids played this for hours. It may not use numbers, but kids are learning logic, patterning, and one to one correspondence.

Card games like Tens Go Fish, Make Ten and Turn Over Ten use a standard deck of cards. (Tip: click on the name of the game to get our easy to follow instructions and start playing right now!)

Kindergarteners will enjoy the sorting element of our DIY number matching game.

Keep these 10 handy materials at home so kids can invent their own math games.

Kitchen Math

Every cook knows that cooking requires fractions, addition, and sometimes a bit of geometry. The bonus of math practice in the kitchen is that it always results in something delicious.

Here are some ideas that we tried:

• Measure and fold hand pies for a practical application of geometry.
• Twist pretzels into numbers.
• When using a timer, practice subtraction. For example, "We set the timer for 30 minutes. 20 minutes are left, how many minutes have the potatoes been in the oven?"
• Make an array of cookies on a baking sheet.
• Cook anything with this excellent children-centered cookbook from America's Test Kitchen.

Read a Math Book

You didn't think I'd let you go without a few books to pick up on your next trip to the library did you?

Use the following lists to find the perfect math-themed book for your child:

• Math chapter books are great for both independent readers and as read alouds
• Math picture books for K-2nd grade
• Advanced concept math picture books, 3rd grade and up
• Fibonnaci picture books - teach kids about patterns in nature

You can, of course, whip up your own magic square template with a few strokes of a pencil, but I've also made a snazzy magic square printable you can print out for free. Fill out the form below and the printable will magically (ha!) make its way to your inbox.

What you need:

• Fraction cards. You can make you own, or you can print out ours and cut out the pieces. (see the form below to get our printable).
• A small paper bag or a bowl
• Children ready for a rowdy fraction math game. (I may have exaggerated the "rowdy" part.)

Use the form below to get our printable fraction cards. Note: our printable contains more fractions than are necessary for the games below. Have fun coming up with your own games that use all the pieces.

Fractions Game #1

Each player needs:  one 1, one ½, three ¼'s, two ⅓'s, six ⅙'s,  six ⅛'s, and four 1/12's .

Keeping his longest fraction – the "1", or the whole – each player puts the remaining fractions in a bag or bowl.

Without looking as they draw the remaining fractions, players alternate drawing fraction pieces until all pieces are gone.

Using their pieces, players race to put together three wholes. Players use the whole for comparison to make sure they have the correct length.

Alternative: Whoever can put the most ½'s together is the winner.

MORE: Favorite math games for kids

Fractions Game #2

Each player needs:  one 1, one ½, three ¼'s, two ⅓'s, six ⅙'s,  six ⅛'s, and four 1/12's .

Keeping his longest fraction – the "1", or the whole – each player puts the remaining fractions in a bag or bowl.

Taking turns, each player draws 10 fraction pieces. (The rest are set aside.)

Players must use their fraction pieces to make wholes.

After players have used as many pieces as possible but not all of them, they can trade each other for the pieces they need.

Notes: 

• Be aware, it is not always possible to use all the pieces to make wholes. That's part of the learning process, too.
• You could turn this into a competitive game, but we found it more fun to work cooperatively, otherwise the trading got too intense.

Make Your Own Tower of Hanoi

Materials:

• At least 3 wooden or cardboard discs, all in different sizes
• One sheet of paper divided into three sections

Set up:

You'll need a stack of 3 or more discs in ascending size. The exact size and proportions are not important. I made our discs from inexpensive package of craft supply wooden circles, and some from cardboard.

Designate three separate areas for stacking. We used a piece of paper divided into three sections for guidance (I'll call these sections A, B and C.)

Stack the discs in order according to size with the smallest disc on top. and place on the far left section of your paper.

Objective and Rules

The objective is to move the stack of discs from section A to section C while observing the following rules:

• The discs can only be moved one at a time.
• A disc can only be placed on an empty space, or on a larger disc.

Solution

The solution involves a mathematical pattern. You can read about the complexities of that pattern here, but I warn you, your eyes may glaze over, as mine did.

The easiest way for kids to discover the pattern is to first play with only three discs, and then with only four discs. While the Tower of Hanoi can be played with any number of discs, the sequences of moves remains the same 1) for an even number of discs; and 2) for an odd number.

Watch our video to see how it's done. Near the end, I show you the Tower of Hanoi solution and basic patterns, in case you get stuck.

Tessellations

We've done this several times, and somehow it never gets boring.

• See our how to make tessellations post.
• Three ways to make heart tessellations.
• Easy cat tessellations
• Star tessellations - great for holiday art
• Ghost and bat tessellations for Halloween

Explore Symmetry

• This is great for younger kids. You're probably familiar with the ol' fold the paper in half and smoosh trick. You can make symmetry art free style, like we did.
• Create gorgeous math art with parabolic curves. My son designed his own eyeball!!
• Create gorgeous objects like these butterflies from Buggy and Buddy.
• These symmetry art aliens make me smile.

Turn number sequences into art

• We did this when we turned pi into a cityscape
• Spirolaterals will help your kids practice their multiplication tables.
• Create Fibonacci art with circles.
• This Fibonacci valentine from Math Four could be adapted for any time of the year.

Use math tools to create art

This is one of my favorite ideas. In addition to the following ideas, find time to allow your kids to explore using the math tools in their own way.

• It can be really simple, like simply giving your kids a ruler, compass and protractor and see what they come up with. If using a compass is tricky, see my tip for drawing mandalas with a compass.
• I love this protractor art project that evokes Frank Stella's artwork.
• Use a ruler to create sunburst paintings, like these at Art Bar.

Explore math art with shapes

Use shapes to make art, either by putting pen to paper or through the manipulations of objects.

• The boys love to play around with our homemade Montessori triangles. They don't even think about the fact that they are creating artistic designs!
• Explore Möbius strips, or make Möbius hearts
• Make your own peek-a-boo shape book - free printable template.
• Paint a Mondrian window.
• Build a fractal Christmas tree
• Explore triangle math with a heart geometry puzzle
• E is for Explore has a few ways kids can use Kandinsky inspired art to think about about circles and relative size.
• Use a geoboard. Crayon Box Chronicles has instructions so you can make your own.

Easy Math Game Rules

As you saw in our fun kindergarten number matching game we like to invent our own math game rules using simple materials! For this easy math game we made up our own preschool and kindergarten-friendly rules for Double Shutter.

Variation: If you don't have Double Shutter, use our printable version of Shut the Box. Instead of flipping tiles, cross of the numbers on the number lines.

With it's fun, flippable numbers and dice, Double Shutter satisfies every young child's desire to touch and manipulate everything!

Instead of playing the game by the original rules, I explained the basic concept that players role the dice and "shut" the numbers according to the combination rolled. We then modified the game by removing the strategic component and simplifying the addition.

For example, if he rolled a 5 and a 3, we counted the dots and said "5 plus 3 equals 8". Then he could shut tiles 5 and 3 or tile 8. (If this were the actual game, he could shut any combination of numbers that equaled 8). If he rolled a combination of numbers that were no longer visible on the available tiles, instead of ending the game as in the original rules, he rolled again until he got numbers that worked.

Math Skills Practiced

Even without the competitive aspect of game play, repurposing Double Shutter for a young audience helps them practice valuable skills needed for future math success. Add it to your list of playful after school math activities.

Number and quantity recognition. He matched quantity (five dots) on the die face to the numeral (5) on the tile. Suggestions: after playing this game your child will enjoy learning how quantity is related to shape with our "Oodles of Noodles" math craft.

Learning the concept of addition. A 5-year-old may not remember that 5+3=8. However, he is observing that two different quantities put together will create a new quantity. Once your child is learning their addition facts, use this addition and subtraction dice game to practice!

Fine motor skills. This one isn't really a math skill per se, but fine motor skills are necessary for manipulation. Little fingers must work delicately to shut the tiles without disturbing the tiles next to or behind them. Much future math practice will involve using manipulatives for hands-on learning and the more skillfully they can can handle them, the better. Try these lacing activities for more fine motor practice.