Exemplars
Let’s Play
The kindergarten students were lining up to
go outside to play. The first student held a
ball. The second student held a jump rope. The
third student held a ball. The fourth student
held a jump rope. What did the seventh
student hold?
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Let’s Play
- Page 1-
Exemplars
Grade Level K–2
Let’s Play
The kindergarten students were lining up to go outside to play. The first student held a ball.
The second student held a jump rope. The third student held a ball. The fourth student held a
jump rope. What did the seventh student hold?
Context
This task was given to a group of kindergarten students who had been working on learning
patterning and ordinal numbers.
What This Task Accomplishes
This task allows the teacher the opportunity to identify which students can identify, create,
and extend patterns, as well as count to 7.
Time Required for Task
One 45 minute class period.
Interdisciplinary Links
This task could link to studies of recreation and health and fitness. Tasks that are similar to
this one include Lining Up and New Necklace featured on the Best of Math Exemplars II.
Giving students opportunities to solve the same types of problems will enhance their
confidence and build their problem–solving skills.
Teaching Tips
Some students may want to act out the task. Others may be able to use manipulatives, while
others may be able to work more abstractly. You can make the task more or less complicated
by changing the pattern.
Suggested Materials
Manipulatives that can be used as balls and jump ropes. Some students may want to use
actual balls and jump ropes.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Let’s Play (cont.)
- Page 2-
Exemplars
Possible Solutions
Student Number
1
2
3
4
5
6
7
Item
ball
jump rope
ball
jump rope
ball
jump rope
ball
Benchmark Descriptors
Novice
The novice may understand that the task involves balls, jump ropes andstudents, but
will not understand enough of the mathematics to evenbegin an approach. Little or no
math language will be used. Representations will not assist in finding a solution.
Apprentice
The apprentice will show some understanding of the task. The student may be able to
repeat the pattern and extend it to the 5th student in line but will not proceed to finding a
correct solution. Some math language will be used, and diagrams will assist in
understanding the student's solution.
Practitioner
The practitioner will achieve a correct answer showing 7 students with the pattern
repeated. Work will be labeled and easy to understand.
Expert
The expert will achieve a correct solution. Work will be labeled or supported by text.
In this case, dictation is taken of the expert student’s approach, and inthe explanation,
the student makes mathematically relevant comments, aswell as extends the problem.
Author
This task was written by Deb Armitage, K–8 Mathematics Assessment Consultant at the
Vermont Department of Education. The task was piloted by teachers and students in
Vermont.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Let’s Play (cont.)
- Page 3-
Exemplars
Novice
Little or no mathematical
reasoning or
understanding is present.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
No math language
is used.
Let’s Play (cont.)
Diagrams do not
seem to relate to
the task.
- Page 4-
Exemplars
Apprentice
Some understanding
of 7 is present.
An incorrect answer
is achieved.
Some parts
are unclear.
The student shows
some understanding
of the pattern.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Let’s Play (cont.)
- Page 5-
Exemplars
Practitioner
A correct answer
is achieved.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
An accurate numerical
notation is used, although
there are some reversals.
Let’s Play (cont.)
The diagrams
are labeled.
- Page 6-
Exemplars
Expert
The diagram is
labeled and accurate.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student achieves
a correct answer.
Let’s Play (cont.)
The student extends the
solution and recognizes
that there is a pattern.
- Page 7-