## Archive for March 25, 2013

### Using Dynamic Paper to Make Math Game Boards

While exploring hexagon patterns last night, Eli suggested, “Let’s play Dots and Boxes using hexagons instead of squares.” Well, now, that’s an inspired idea! So I used the Dynamic Paper tool from Illuminations to create isometric dot paper. The boys then played Dots and Triangles, actually — hexagons would work, but you’d have to remove some of the dots — and Alex narrowly edged Eli.

I am continually blown away by the power of Dynamic Paper. Suggested by a participant at the 2009 Illuminations Summer Institute and built by Math Resources, this tool does it all —

- Need the net of an icosahedron whose sides are exactly 0.58 inches? Yep, Dynamic Paper can do that. And it’ll generate a printable 8.5″ × 11″ PDF of the net that you can cut out, fold up, and tape together.
- Need graph paper with trig coordinates, going from ‑2π to 2π on the
*x*-axis, with axis tick marks starting at ‑π and appearing every 2π/3 units? Well, sure, it’ll look crazy as hell… but if that’s what you want, Dynamic Paper aims to please. - Need a tessellation of hexagons? It can do that, too, but first you have to decide if you want a Type I, Type II, or Type III tessellation. What’s that, you didn’t know there were three different types of hexagon tessellations? No worries. Dynamic Paper can make all three types, and it won’t even stick out its tongue at you while it creates them.

It also does attribute blocks, spinners, number lines, isometric dot paper, and a million other things. But I don’t have the time to list them all. Just go check it out.

The following are instructions for five different math games you can play, using game boards that you can create with Dynamic Paper.

**Dots and Triangles**. Go to Graph Paper → Isometric Dot Paper. Pick the number of rows, columns, and distance between dots, then click Add. Press Download PDF, and print it. The game is played with players connecting two dots with a straight line. If a player draws a line that forms a small equilateral triangle, that players puts her initial (or some other distinguishing mark) inside the triangle to claim it. In general, players alternate turns, but if you make a line that completes a triangle, you get another turn, which can often lead to four, five, six, or more triangles being created by a player on one turn. See the rules for Dots and Boxes for more information.

**Hex**. Go to Tessellations → Build Your Own → Hexagons (Type I, II or III). Make the tessellation as wild as you like, then click Add. Adjust the tessellation so that there are the same number of hexagons vertically and horizontally. Then play Hex, with one player trying to form an unbroken line of hexagons **from top to bottom**, and the other trying to form an unbroken line of hexagons **from one side to the other**. (Decide who’s trying for a vertical or horizontal line before play begins.) Players then alternately choose one of the hexagons and claim it by placing an initial in the hexagon. First one to form an unbroken line wins.

- Sample Hex Game Board (PDF)

Note: This board is 8 hexagons tall but only 7 hexagons wide, so the player trying to connect top to bottom should go first.

**Make 12**. Go to Graph Paper → Grid Paper, choose the number of rows and columns, and then enter the same value for the row height and column width. Players then alternately create rectangles with an area of 12 square units. The last player to place a rectangle wins. For variations, use a different size rectangle, or play that the last player to place a rectangle loses.

**Secret Number**. Okay, you don’t really need a board game for this one, but a board can be useful to keep track of numbers that have been eliminated. With Dynamic Paper, go to Number Grids, and you can make a grid of numbers from *m* to *n*, where *m* and *n* can have any values you like. For young kids, I use a hundreds board, but why not try a grid with numbers from 38 to 73 with six numbers in each column? To play, one player secretly chooses a number, then the other player(s) ask questions such as, “Is the number odd or even?”, “Is the units digit a 5?” or any other yes-no question. The only yes-no question not allowed is, “Is __ your number?”

**Polar Coordinate Battleship**. Just like regular battleship, but for older kids. Go to Graph Paper → Polar Coordinates, then set your parameters. Have each player place one ship each of length 2, 3, 4, and 5 units. (Some people allow ships to be placed on a curve. I think that’s unacceptable except for the 2‑unit ship, but you can play however you like.)

**What math games do you play? Can Dynamic Paper be used to create the game boards for any of your favorite math games?**