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3. Broken Calculator:
Strengthening number facility using a calculator
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- Understand that whole numbers can be written as a product of prime factors
- Identify prime and composite numbers
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Overview
Broken Calculator computation requires students to solve computation-based problems using calculators that have restricted number and/or operation keys. Students use actual broken calculators, calculators with designated "do-not-use" keys (Figure 1), or digital tools that simulate broken calculators to complete problems. In order to compensate for missing or restricted keys, students draw on relationships between operations and among numbers to determine valid calculation alternatives. They write "key sequences" to record and reflect on their process. In this instance, students apply their understandings of factors and multiples to generate designated numbers missing from the keypad.
Note: In the interview with Judah Schwartz, he describes the outcomes of using "What Do You Do With a Broken Calculator?" software that he has written.
The Value of This Technology
The Broken Calculator provides an authentic and engaging context within which students reflect on process and engage in high-level problem solving. The calculator allows students to conduct checks and receive instant feedback on their solutions, promoting the refinement process. As they devise key sequences to compensate for restrictions, they closely examine process, identify the critical elements to reaching accurate solutions, and synthesize understanding through recording their logical steps.
Look in the Classroom
Ms. Janack knows that mastering the concepts involved with factors and multiples prepares students for similar work in algebra, so she decides to work these concepts into a problem-solving activity a month after their formal unit on number theory.
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