Lining Up
Pat decided to line up everyone in her class. She put a boy first, a girl second, a boy third, and a girl fourth. Who will be tenth?
Grade Level KÐ2
Lining Up
Pat decided to line up everyone in her class. She put a boy first, a girl second, a boy third, and a girl fourth. Who will be tenth?
Context
This task was given to kindergarten students who had been working with ordinal numbers. The teacher had also been working on the use of a key and hoped students might use one. A few did!
What This Task Accomplishes
This task allows the teacher to assess students' understanding of ordinal numbers up to ten. It also assesses students' skills in communicating solutions.
Time Required for Task
One 45 minute class period.
Interdisciplinary Links
This task can lead to instruction on even and odd numbers. Students could count a variety of objects in your classroom and determine whether there are even or odd numbers. You could have a discussion about whether there are an equal number of boys and girls in your class or in most classes. Students could survey other classes to see. Another discussion could be about why we line up and places in our world where we must get in line.
Teaching Tips
Students who have difficulty with writing numbers could have an assortment of cards available stating ordinal numbers that they could then glue on to their papers. The task could be made more complicated by changing the pattern to boyÐboyÐgirl, etc.
Another way to document student solutions is to have a "Scribing Table." This is a designated place students in the classroom can go to have someone write their thoughts about their solution. An example of this can be seen below. This student's work shows three situations in which she solicited the assistance of a scribe. After each of her attempts she went to the scribe table to have recorded the reasons behind her changes in approach. Please note that when scribing, it is important for the scribe to act as a human tape recorder, writing exactly what the student says without paraphrasing. This preserves the integrity of the assessment.
Many students will begin by drawing figures of boys and girls. Some will use letters or symbols to represent boys and girls rather than drawing them all out. Other students will use manipulatives to represent boys and girls and then line them up to arrive at the solution. Since we had been practicing using keys, some students will make a key showing what their different symbols mean.
Suggested Materials
Paper, pencils, stickers, cards with ordinal numbers written on them randomly displayed; other manipulatives that could represent boys and girls.
Possible Solutions
boyÐgirlÐboyÐgirlÐboyÐgirlÐboyÐgirlÐboyÐgirl
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. Little or no math language will be evident, 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, or may solve the task in more than one way to verify the solution.
Author
This task was written by Deb Armitage, KÐ8 Mathematics Assessment Consultant at the Vermont Department of Education, and piloted by her in collaboration with Vermont teachers.