Standards-based assessment and Instruction

Math 3-5

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?

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

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.

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

15 Callers

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.

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.

Click on a level for student example.
Novice The Novice will not have an approach that will work.
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.

Our teacher-friendly tasks are designed to support both the Common Core and Citywide instructional expectations. GO Math! alignments are also available.
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I was amazed to see the differentiation and the student examples. So many times we see the problems, but not actual student work. Thank you so much for allowing me to see student work and the DIFFERENT ideas so that it's not me creating "mini mes" but showing students how to arrive at the answer in many different ways!

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