This race game uses pattern blocks (yellow hexagons, red trapezoids, blue rhombuses—or rhombi—and green equilateral triangles) as concrete representations of units and fractions of units, specifically halves, thirds, and sixths, per the 3rd grade standards. (We declare that our unit will be the area of the top of a yellow hexagon. So
- 1 = the area of a yellow hexagon (our unit).
- 1/2 = the area of a red trapezoid since 2 red trapezoids exactly cover (tile, pave) the top of a yellow hexagon (our unit).
- 1/3 = the area of a blue rhombus since 3 blue rhombuses exactly cover (tile, pave) the top of a yellow hexagon (our unit).
- 1/6 = the area of a green equilateral triangle since 6 green equilateral triangles exactly cover (tile, pave) the top of a yellow hexagon (our unit).
We use a cube (6-sided) die with faces equal to first 6 members of the sixths family (after 0/6): 1/6, 1/3, 1/2, 2/3, 5/6, and 1.