A New Necklace. A New Necklace. 1 of 8. Copyright 2007, Exemplars, Inc. All rights reserved.

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1 Ted decided to make his sister a bead necklace. First, he put a blue bead on a string. Next, he put a red bead on the string. Last, he put a green bead on the string. He decided to continue this pattern. What color will the 9th bead be? 1 of 8

2 Suggested Grade Span K 2 Task Ted decided to make his sister a bead necklace. First, he put a blue bead on a string. Next, he put a red bead on the string. Last, he put a green bead on the string. He decided to continue this pattern. What color will the 9th bead be? Alternative Versions of Task More Accessible Version Ted decided to make his sister a bead necklace. First, he put a blue bead on a string. Next, he put a red bead on the string. Last, he put a green bead on the string. He repeated this same process to finish the necklace. How many beads are there in all on the necklace? More Challenging Version Ted decided to make his sister a bead necklace. First, he put a blue bead on a string. Next, he put a red bead on the string. Last, he put a green bead on the string. He decided to do this a total of 3 times. If each bead is 1/2 inch wide, at minimum, how much string will be needed for the necklace? How many of each color bead will be needed? Context This task was given to kindergarten students. These students had been working with patterning and ordinal numbers. They were beginning to work with concepts of time, such as first, next, and last. What This Task Accomplishes This task allows the teacher to assess which students have an understanding of the concepts stated above, as well as the types of problem-solving skills they possess. Also, it will show whether students are able to solve a task in an organized fashion, documenting their ideas as they go. Time Required for Task One 45-minute class period. 2 of 8

3 Interdisciplinary Links This task would link well to cultural studies. The class could discuss what types of jewelry different ethnic groups, such as Egyptians or Native Americans, wear. Discussion questions could include the types of material used to manufacture beads, the manufacturing process and the meaning of the patterns. This task could also be linked to art projects where the students design their own bead jewelry. This would be a good time to discuss how to make different types of patterns. Teaching Tips We put out manipulatives for students to use, but none chose to do so. We also had beads and string quietly on the side, but no one used those or played with them. When students completed the task, they made Fruit Loop patterns on licorice strings for snack! To further develop this task, you could discuss whether the pattern created is symmetrical or how you could change it to make it symmetrical. If students were learning shapes, you could change the task so that students first put on a square bead, then a triangular bead, then a circular bead. Most students will begin this task by drawing beads and then coloring them. Some students may prefer to use manipulatives or materials such as string and beads. A few students may use symbols in place of colors, such as G for green, R for red and B for blue. Most students will draw all nine beads, repeating the pattern until they reach the ninth bead. Suggested Materials Uni-fix cubes or other manipulatives Beads String Paper Crayons Possible Solutions blue-red-green-blue-red-green-blue-red-green More Accessible Version Solution blue-red-green-blue-red-green = 6 beads More Challenging Version Solution blue-red-green x 3 = 9 beads x.5 inches = 4.5 inches Three of each will be needed. 3 of 8

4 Task-Specific Assessment Notes Novice The Novice will demonstrate no understanding of the task. No mathematical reasoning will be present, and no math language will be used. Apprentice The Apprentice will have some parts correct, although no final answer may be present. No math language will be used, and little about the approach and reasoning used will be communicated. Practitioner The Practitioner will have all parts of the problem correct and all work will be labeled. Some math language will be used and the approach will be clearly documented. Expert The Expert will have all parts correct. Math language will be used throughout, and the approach and reasoning used will be explained. Math representations will be complete and correct. The Expert will also make mathematically relevant comments or observations. S/he may extend the task to make inferences about the color of beads beyond the ninth one. 4 of 8

5 Novice 5 of 8

6 Apprentice 6 of 8

7 Practitioner 7 of 8

8 Expert 8 of 8