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Archive for November, 2011

Regular Polyhedra Christmas Ornament Nets

November 28th, 2011 by Math Tricks | 4 Comments | Filed in Polyhedron Nets, Regular Polyhedra




Platonic Solid Christmas Ornaments

It’s that time of the year again, and this Christmas season we have something special for you – Platonic Solid Christmas Ornaments!  These Platonic Solid nets are ready for you to print out and fold into the coolest math Christmas ornaments on the planet!  Simply cut out the pattern, and fold along the grey lines.  Fold the tabs into the solids and adhere with double-stick tape or glue.  Alternatively, you can simple tape the sides together with regular tape.  After you get the solid constructed, attach some string and add it to your tree.  Santa will be so impressed, he will surely leave extra presents for you!

These polyhedron nets make great Christmas math activities for kids!  If you are a teacher, this will be a good basis for introducing your students to polyhedra – in this case the five regular polyhedra (the Platonic Solids).  All five Platonic solids are here in their Christmas costumes: tetrahedron, hexadedron, octahedron, dodecahedron, and the icosahedron.  If you want some material for your lesson plan, here is the link to the Platonic Solids at Wikipedia.

All files are in .PNG format (Portable Network Graphic).  Simply click on the image you desire to get the full size, and then right-click on it to get the “save as” option (or print it while viewing the full sized graphic).

These are the first in this series, but more will be added later.  Check back to see when more are added, or if you are on Facebook, you can get updates there – just visit our Facebook page and “Like” us!

 

 Green Tetrahedron Polyhedron Net

green tetrahedron polyhedron net

 

 

 

 

 

Red Tetrahedron Polyhedron Net

Red Tetrahedron Polyhedron Net

 

 

 

 

 

Santa Tetrahedron Polyhedron Net

Santa Tetrahedron Polyhedron Net

 

 

 

 

 

Baby Jesus Tetrahedron Polyhedron Net

Baby Jesus Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

Poinsettias Tetrahedron Polyhedron Net

Poinsettias Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

Snowflakes Tetrahedron Polyhedron Net

Snowflakes Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

Candy Canes Tetrahedron Polyhedron Net

Candy Canes Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Motif Tetrahedron Polyhedron Net

Christmas Motif Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

Santa Shadow Tetrahedron Polyhedron Net

Santa Shadow Tetrahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 Green Hexahedron Polyhedron Net

Green Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Red Hexahedron Polyhedron Net

Red Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Hexahedron Polyhedron Net

Santa Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Baby Jesus Hexahedron Polyhedron Net

Baby Jesus Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Nativity Hexahedron Polyhedron Net

Nativity Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Merry Christmas Hexahedron Polyhedron Net

Merry Christmas Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Bear Hexahedron Polyhedron Net

Christmas Bear Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Poinsettias Hexahedron Polyhedron Net

Poinsettias Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Snowflakes Hexahedron Polyhedron Net

Snowflakes Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Candy Canes Hexahedron Polyhedron Net

Candy Canes Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Motif Hexahedron Polyhedron Net

Christmas Motif Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Shadow Hexahedron Polyhedron Net

Santa Shadow Hexahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Green Octahedron Polyhedron Net

Green Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Red Octahedron Polyhedron Net

Red Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Octahedron Polyhedron Net

Santa Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Baby Jesus Octahedron Polyhedron Net

Baby Jesus Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Poinsettias Octahedron Polyhedron Net

Poinsettias Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

 Snowflakes Octahedron Polyhedron Net

Snowflakes Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Candy Canes Octahedron Polyhedron Net

Candy Canes Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Motif Octahedron Polyhedron Net

Christmas Motif Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Shadow Octahedron Polyhedron Net

Santa Shadow Octahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

 Green Dodecahedron Polyhedron Net

Green Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Red Dodecahedron Polyhedron Net

Red Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Dodecahedron Polyhedron Net

Santa Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Baby Jesus Dodecahedron Polyhedron Net

Baby Jesus Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Nativity Dodecahedron Polyhedron Net

Nativity Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Christmas Bear Dodecahedron Polyhedron Net

Christmas Bear Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Poinsettias Dodecahedron Polyhedron Net

Poinsettias Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Snowflakes Dodecahedron Polyhedron Net

Snowflakes Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Candy Canes Dodecahedron Polyhedron Net

Candy Canes Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Motif Dodecahedron Polyhedron Net

Christmas Motif Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Shadow Dodecahedron Polyhedron Net

Santa Shadow Dodecahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Green Icosahedron Polyhedron Net

Green Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Red Icosahedron Polyhedron Net

Red Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Icosahedron Polyhedron Net

Santa Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

Baby Jesus Icosahedron Polyhedron Net

Baby Jesus Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Poinsettias Icosahedron Polyhedron Net

Poinsettias Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Snowflakes Icosahedron Polyhedron Net

Snowflakes Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Candy Canes Icosahedron Polyhedron Net

Candy Canes Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Christmas Motif Icosahedron Polyhedron Net

Christmas Motif Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

Santa Shadow Icosahedron Polyhedron Net

Santa Shadow Icosahedron Polyhedron Net

 

 

 

 

 

 

 

 

 

 

 

 Happy Holidays from Math Tricks!

 

 

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Math Tricks: Squaring Two-Digit Numbers

November 3rd, 2011 by Math Tricks | 5 Comments | Filed in Math Tricks




Squaring Two-Digit Numbers Quickly

Using this math trick, you will be able to square any two digit number very quickly.  With a little practice you can do it in your head, or you can do it on paper and still impress others with your math skills.  This method of squaring is very easy, and I will be using as an example squaring the number 23.

First, determine the closest number to your number that ends in a zero.  In this example, the number is 20.  Next, determine the difference between your number and the closest number with the zero.  In this case, it will be (23 – 20) = 3.  Add the result to your number (23 + 3 = 26).  Now, multiply the number with the zero by the sum of your number and the difference you determined:

20 x 26 = 520

Now square the difference you determined before, and add it to the result above:

(3 x 3) + 520 = 529

Presto!  There is the square of your number!

Here are some more examples:

 

The Square of 25

Closest zero number:  20 (note – 30 will also work in this example)

Difference:  25 – 20 = 5

Sum:  25 + 5 = 30

Answer:  (5 x 5) + (20 x 30) = 25 + 600 = 625

 

The Square of 37

Closest zero number:  40

Difference:  37 – 40 = -3

Sum:  37 + -3 = 34

Answer:  (-3 x -3) + (40 x 34) = 9 + 1360 = 1369

 

The Square of 81

Closest zero number:  80

Difference:  81 – 80 = 1

Sum:  81 + 1 = 82

Answer:  (1 x 1) + (80 x 82) = 1 + 6400 + 160 = 6561

Noticed how I broke down the (80 x 82) into (80 x 80) + (2 x 80)!

 

The Square of 12

Closest zero number:  10

Difference:  12 – 10 = 2

Sum:  12 + 2 = 14

Answer:  (2 x 2) + (14 x 10) = 4 + 140 = 144

 

This math trick can sometimes be very useful, and is one that I recommend that you practice on your own.  One day you just might come upon a situation where you need to square a two digit number without a calculator.  I know – you can use your smart phone… but with practice, you can solve the problem before your run your calculator app!

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