## neXtu Directions

Object:
To place your pieces on the game board and capture your opponents pieces so that you finish the game with more points.

Set-Up:
The game board is a tessellation consisting of hexagons, squares, and triangles. Each player has a collection of shapes–3 hexagons, 14 squares, and 11 triangles–to be played, but only one of each shape is available on a given turn. Both players collections consist of shapes with the same point values.

Play:
On each turn, a player is able to play a hexagon, square, or triangle. (The point values of the available pieces on a given turn are randomly determined.) The piece must be played on a region with the same shape.

When a piece is played on the game board, the player receives points in the following ways:

• The player captures the region where the piece was placed, and gets that many points for it.
• In addition, the player captures the adjacent regions occupied by the opponent that have a lesser value. An adjacent region is only captured if it shares a side with the dropped piece; it is not captured if it only shares a vertex.
• Any adjacent regions occupied by the same player have their values increased by 1.

As an example, assume that the red player places a Red 13 hexagon so that it touches four adjacent squares with values of Blue 8, Blue 14, Red 9, Red 15. The Blue 8 becomes a Red 8, because the Red 13 has a greater value. Nothing happens to the Blue 14, because the Red 13 has a lesser value. Finally, Red 9 increases to Red 10 and Red 15 increases to Red 16, because they were reinforced by placing an adjacent hexagon of the same color.

The game ends when both players have placed all of the shapes in their collection.

Winning the Game:
At the end of the game, the player with more points wins.

Math Concepts: Greater than, less than, tessellations, and symmetry

What You Can Do: For very young students, the concepts of more and less are critical in their development of number sense. Curriculum Focal Points recommends that pre-kindergarten students should be able to “compare quantities (using language such as ‘more than’ and ‘less than’)” and “order sets by the number of objects in them.”

Students have an inherent understanding of the concept from real-world experiences, especially from those arising out of fairness (“she has more raisins than I have”). However, this concept needs to be formalized through the use of counting and understanding the order of numbers. Students may be able to compare two quantities when the difference is obvious, but they may have more difficulty when the difference is small (“I have 6, you have 7”). Using various representations with students is one way to develop the concept. Using a number line to show the order of the integers is one strategy; students should understand that numbers to the right (on a horizontal scale) or above (on a vertical scale) represent greater values.

In real-world contexts, parents can foster an understanding of “more” and “less” by asking simple questions. At the grocery store, for instance, parents could ask their child, “Would you rather have this bag or that bag of cookies?” and “Which of these baskets has more strawberries?”

The game board of Nextu uses a symmetrical pattern of regular polygons. Describing and analyzing shapes, as well as understanding congruence and symmetry, are important aspects of a child’s geometric education. With geometry surrounding us, parents and teachers can foster understanding by discussing geometric shapes with children. Looking for patterns in tile floors, identifying congruent and similar shapes in a building design, and talking about the shape of musical instruments are all ways to ensure that elementary students master the basic skills necessary to succeed with more abstract geometric concepts that they’ll encounter in middle school and high school.

Math in the Game: On every turn, students match shapes to place pieces, and they also compare point values to determine if an opponent’s piece can be captured. In addition, the tessellation arrangement of the game board has an effect on strategy, because a given shape may be adjacent to 2, 3, 4, or 6 different pieces.

Related Resources:
Island Inequality Mat
Students use a context with fish swimming toward food to think about the concepts of more and less.
Tessellation Creator
The game board for Nextu consists of hexagons, squares, and triangles. The shapes form a semiregular tessellation, which is a complete covering of the plane that uses two or more regular polygons. With the Tessellation Creator, students are able to use polygons to create their own tiling patterns.
Nim Games
Students use math strategy to play variations of the classic math game, Nim.