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Math Activities II

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Children often learn math best with concrete, real-life, physical examples that they can feel, touch, move and manipulate. Educational suppliers have long known this, and sell many different kinds of math games and manipulatives. Many of these you can make easily and inexpensively yourself. If you find you use these often, you may wish to print and laminate a set to use with crayons or dry-erase markers, both of which will wipe off the laminated surface with a cloth or tissue.

Code Breaker (like Mastermind) Black Bird Cage Labyrinth Battleship Co-ordinates Game More Math Games to Make Math Manipulatives You Can Make Everyday Math Around the House Main Math Page
Rocket Height Slime Mould Fractals Tiling Challenges Proportional Recipes Field Day-Math for Athletes My Infinity is Bigger Than Your Infinity Packing Problems Ancient Tools Lemonade Math Challenges

Code Breaker (like Mastermind)

You will need:
graph paper
a variety of different coloured pencil crayons, markers or crayons
a ruler and/or scissors
optional: plastic page protector

To make:
You will need to cut out or mark out a rectangle that is 14 squares long and 6 squares wide. Either fold or draw a line length-wise that is two squares from one of the long edges. Make two accordion-style folds at the last two rows of squares at one end (the width) to make a triangular stand like so: _______________/\ . This is where the code maker (player 1) will mark the code and hide it from the other player.

For a reusable version of this game, use a ruler to draw out a 10 x 6 rectangle on graph paper, then slide the paper inside a sheet protector. Use dry erase markers or crayons for play. Player 1 now writes the code on the back of the sheet instead of on the raised edge. An alternative is to make a cut-out version and cover it in packing tape.

To play:
Player 1 is the code maker. Before making the code, decide on what colours will be available to be used. Reserve two colours (usually red and black) to use as markers to indicate a correct colour or position and colour.
Player 1 marks their code on the back of the raised part of the paper.
Player 2, the code breaker, tries a first guess by marking colours in the first 4 squares of the first row of flat squares. The last two squres are reserved for player 1 to mark the correct guesses.
For every correct colour in the WRONG place, player 1 makes a red mark. For every correct colour in the CORRECT place, player 1 makes a black mark. You can use actual digits for this rather than dots, with no correct ones being shown with a 0.
Players continue guessing and correcting until either player 2 breaks the code, or runs out of rows for guessing. Players then switch roles and continue. You can keep a talley of how many clues each player needed, or simply count games as you go.


Black math strategy game
To play this game, start with a 6 x 6 grid. Using the patterns of the tiles at the top of the image to the right, players alternate turns by filling in lines of a roadway. The player may choose any of the patterns on his or her turn. The intersection pattern may only be used in a straight line; only the curves can make turns in the road.

The game starts in the upper left-hand corner and the object of the game is to reach the bottom right-hand square without forfeiting the game by forcing the road off of the grid. Players must not play a turn that forces the road to leave the page; if the main roadway cannot stay on the page with their turn, the player forfeits the game.

A free printable file-folder version of this game can be found at this link.

Bird Cage

Bird Cage Math Pencil GameStart by drawing (or printing) two superimposed grids of circles, one 5 x 6 and one 6 x 5 as illustrated to the left.

Players choose a colour--black or white. The players take turns drawing a line either vertically or horizontally between two of their adjacent circles. Black must try and make a continuous path that connects the right and left sides of the playing field, and white must connect the top and bottom of the field. The players must not cross lines made already. The first player to complete their path wins.

Click here for a free printable file-folder version of this game.


Labyrinth pencil game

To play this maze game, start with two 6 x 6 sections of graph paper per player. Mark out letters and numbers as shown above on each grid.

Now each player uses 20 lines to darken to create their own labyrinth on one of their grids. These lines must not create any closed "islands", nor may they seal off any squares along the edges or continue for longer than three continuous squares.

Now each player chooses a square to start and a square to finish and marks them "S" and "F". The players tell each other what the starting and ending points are, and they mark these on their blank grids.

The first player begins by choosing a square adjacent to the starting square. In the example above, that player could choose either E6 or F5. The other player must tell the first if there is a wall in the way. If not, the first player may move there and indicates this on their blank grid. If there is a wall in the way, the player may not move and must wait until their next turn.

The play continues until one player reaches their finish position. This player is the winner.

A free printable file-folder version of this game can be found at this link.

Battleship Co-ordinates Game

Create your own Battleship-style game by using graph paper and construction paper. Decide on the size of your grid then draw 4 squares, 2 for each player. Label the vertical axis alphabetically and the horizontal axis numerically, and repeat on all 4 grids. Decide on the number and size of the ships you will use, then cut out the ships for each player from construction paper. Place your ships (hidden from the other player) on one of the grids. Use a pencil to trace around them in case they slip out of place.

Player 1 chooses a set of coordinates, say, "E5". Player 2 checks to see if any of his or her ships occupy that space, and reports either "hit" or "Miss". Use a pencil to mark the hits and misses. Player 2 then takes a turn. Once all the coordinates that a ship occupies have been "hit", the ship is sunk, and the owner must report that to the other player. The object of the game is to sink the other players ships before they sink yours.

Of course, you can always play this with a more peaceful theme, such as "treasure hunt" with treasures of various sizes--use your imagination!

If you find you play often, you may wish to laminate the grids and use dry-erase markers or wipe-off crayons to mark the ships and hit/miss information. You can also use sheet protectors if you use a full sheet of graph paper inside and just outline your playing area. If you use a cut-out grid, it may slide around inside the sheet protector.

More math games, manipulatives you can make and additional math activities can be found here.

Also check my blog for more math and other educational activities:


More Math Links from Lemonade:

Around the House Sorting Laundry, Cooking & Baking Craft Stick Regrouping Jack's Beans Candy and Pasta Math Hexaflexagons Pumpkin Math Wizard Math Tricks
Make your Own Manipulatives Make a Base 10 Set Pentominoes Tangrams Fractions Pyramids, Squares & Cubes Algebra Tiles Mathematical Card Games
Math Games to Make Mancala Battleship Coordinates Game Code Breaker (like Mastermind) Black Bird Cage Labyrinth Pencil Game Corners & Dots Pencil Games

Math Links

Spatial Mathematics:

Mobius Strips and other Dimensional Wonders: the Mathematics of Topology

Mobius Bagels and Other Topological Challenges

Graphically Simulated Video on Mobius Transformations

Mandelbrot Sets in 3-D: Math and Art Meet in Chaos

Origami, Architecture and Topology Photography

Penrose Tiles

Geometrical Experiments in Art


Scratch: MIT's kid's programming language (free download)

Hilarious Videos on Mathematical Ideas from Vi Hart

Magic Squares, Fibonacci Series and other Fun Numbers to Explore

Excellent Infographic All About Pi

How Archimedes Approximated Pi

All About Quantum Mathematics

More Math and Strategy Games

Paper and Pencil Math Games

Wild About Math--More Paper and Pencil Games

Instructional, Applied Mathematics, Math Contests, Tools

The Myth of Being "Bad at Math"

Better Than PEDMAS: Why Having Students Memorize the Order of Operations Does Them a Disservice

Khan Academy: Online Instructional Math Videos

Easy Explanations for Advanced Math and Computing

Jim's Algebra Hints

Solving Equations as Proofs

The Best Way to Factor Trinomials

Engineering Megasite of Applied Math and Science Activities and Resources for Grades K-12

CEMC: Home of the UW Mathematics Competitions (loads of math resources)

Canadian Math Contests

Wolfram Alpha Computational Search Engine

All About Sliderules and How to Use One

101 Uses for a Quadratic Equation

101 Uses for a Quadratic Equation Part 2

Resources for Math Teachers

The Myth of Being "Bad at Math"

Biographies of Mathematicians

Common Math Mistakes

National Library of Virtual Manipulatives

Illusions: NCTM Virtual Manipulatives

Geometer's Sketchpad (sorry, this one is not free)

The Power of Grace in Teaching

Math Books:

Big Ideas for Small Mathematicians &
Big Ideas for Growing Mathematicians Ann Kajander

Math for Smarty Pants Marilyn Burns

Math Games for Middle School Mario George Salvadori

Mind-Sharpening Logic Games Andrea Angiolino

Mathematics Made Simple, 6th Ed. Thomas Cusick

Chaos James Gleick

Also: look for math titles by Martin Gardner--there are too many to list here

Other Resources:
Microcosms Brandon Broll (Microscopic images up to 20 million x magnification--I added this because it shows patterns, scale, Fibonacci in nature, etc.)

Online Magazines & General Math Sites

Plus Magazine
A+ Click