Math 3-5 Sample
View examples of student solutions by clicking on a level below:

Novice

Apprentice

Practitioner

Expert

Calling All Students

Mrs. Forest wanted to plan how to contact her students by phone in case the field trip they were going on the next day needed to be canceled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue until all students had been called. Mrs. Forest has 31 students. How many students will need to make phone calls if Mrs. Forest calls the first student?

Suggested Grade Span

Grades 3-5

Grade(s) in Which Task Was Piloted

Grade 4

Task

Mrs. Forest wanted to plan how to contact her students by phone in case the field trip they were going on the next day needed to be canceled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue until all students had been called. Mrs. Forest has 31 students. How many students will need to make phone calls if Mrs. Forest calls the first student?

Alternative Versions of Task

More Accessible Version:

Mrs. Forest wanted to plan how to contact her students by phone in case the field trip they were going on the next day needed to be canceled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue until all students had been called. Mrs. Forest has 15 students. How many students will need to make phone calls if Mrs. Forest calls the first student?

More Challenging Version:

Mrs. Forest wanted to plan how to contact her students by phone in case the field trip they were going on the next day needed to be canceled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue until all students had been called. Mrs. Forest has 31 students. How many students will need to make phone calls if Mrs. Forest calls the first student? Find a rule for determining how many phone calls will be made for any number of students.

NCTM Content Standards and Evidence

Algebra Standard for Grades 3-5

Instructional programs from Pre-Kindergarten through grade 12 should enable students to...

  • Understand patterns, relations and functions.
    • NCTM Evidence: Describe, extend, and make generalizations about geometric and numeric patterns.
    • Exemplars Task Specific Evidence: Most students will create a tree diagram to solve this task to identify and extend the growing pattern.

Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This is a short to medium length task.

Links

This task could link to a class field trip, to a unit on weather (the cause of the canceled field trip), or to a unit on the history of the telephone.

Common Strategies Used to Solve This Task

Most students will use a tree diagram to solve this task.

Possible Solutions

Original Version:

15 Callers

More Accessible Version:

7 Callers

More Challenging Version:

If an odd number of students: (N - 1) / 2 , where N = number of students that need to be called. If an even number of students: N / 2, where N = number of students that need to be called.

Task Specific Assessment Notes

General Notes: Most students will create a tree diagram to solve this task. This task does not lend itself to eliciting a lot of mathematical language.

Task Specific Rubric/Benchmark Descriptors
Click on a level for student example.
Novice The apprentice will attempt a tree diagram, but it will be incorrect or incomplete.
Apprentice The apprentice will attempt a tree diagram, but it will be incorrect or incomplete.
Practitioner The practitioner will have a correct and systematic approach to solving the task. The practitioner will have a correct solution and may make observations about patterns in the solution.
Expert The expert will analyze the situation in mathematical terms, achieving a correct solution that is well communicated.

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.