Scoring rubric

3 points
The response accurately states the pattern of beads on the portion of the necklace inside the box with a clear, detailed explanation of how this determination was made. The box should contain 4 colored beads, 1 white bead, 5 colored beads, 1 white bead and 4 colored beads, in that order. White and colored beads alternate. Beginning with 1 of each bead, the number of colored beads increases by 1 for each repetition. i.e. 1 white, 1 colored, 1 white, 2 colored, 1 white, 3 colored, 1 white, 4 colored, 1 white, 5 colored, and so on. By examining the pattern it can be determined that 4 colored beads, 1 white bead, 5 colored beads, 1 white bead, and 4 of the next 6 colored beads are in the box.

2 points
The response shows nearly complete understanding of the problem's essential mathematical concepts by correctly listing the pattern of beads inside the box. Any errors are minor. The explanation may be somewhat unclear, causing the reader to make inferences, but will be essentially accurate.

1 point
The response show limited understanding of the problem by recognizing that a pattern exists, but incorrectly identifying the
pattern. There will be an incomplete explanation that will cause the reader to make inferences.

0 point
The response shows insufficient understanding of the problem's essential mathematical concepts. The procedures, if any, will contain major errors. An explanation, if offered, will be unclear, illogical, or not relevant.