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A New Necklace

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					                                              Exemplars

                                          A New Necklace
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
ninth bead be?




Exemplars             TM

                                              A New Necklace   - Page 1-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                            Exemplars

Grade Level K–2

A New Necklace

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 ninth bead be?

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

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 manufacture 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!



Exemplars                                 A New Necklace (cont.)                  - Page 2-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                           Exemplars

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 and then a circular.

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

Unifix cubes or other manipulatives, beads, string, paper, crayons.

Possible Solutions

blue–red–green–blue–red–green–blue–red–green

Benchmark Descriptors

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


Exemplars                                 A New Necklace (cont.)                  - Page 3-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                          Exemplars

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.

Author

This task was written by Deb Armitage, K–8 Mathematics Assessment Consultant at the
Vermont Department of Education, and piloted by her in collaboration with Vermont
teachers.




Exemplars                                 A New Necklace (cont.)               - Page 4-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                                  Exemplars

                                                    Novice




                          The student demonstrates little           The student uses no
                          or no understanding of the task.            math language.




Exemplars                                          A New Necklace (cont.)                 - Page 5-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                             Exemplars

                                           Apprentice




        The student uses                  The student does not give   Some parts of the
       no math language.                    an answer to the task.     task are correct.




Exemplars                                   A New Necklace (cont.)            - Page 6-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                             Exemplars

                                           Practitioner




                                          The student achieves a
          The student labels               correct answer with        The student uses
            his/her work.                   supporting work.        some math language.


Exemplars                                  A New Necklace (cont.)               - Page 7-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
                                             Exemplars

                                               Expert




  The student achieves
    a correct answer.




                                                                     The student extends the
             Correct math                      The student             solution and makes
           language is used               summarizes results in      mathematically relevant
             throughout.                   an organized chart.            observations.


Exemplars                                   A New Necklace (cont.)                 - Page 8-
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050

				
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