M challenge students to generalize this last question

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to 7 a.m. Challenge students to generalize this last question. Have them determine an algorithm that can be used to find the end time if 12 a.m. or 12 p.m. is passed. [Add the current time to the number of additional hours, divide by 12, and the remainder is the end time.] For demonstration purposes, you may want to show an analog clock during this portion of the lesson. It may help to remove the minute and hour hands, so students focus on the mathematics of the lesson and not the time. Using this discussion as a springboard, you may want to have students work in pairs to create a mod 12 addition table. Alternatively, such a table is provided as the last sheet of the Arithme-Tic-Toc Activity Sheet. Arithme-Tic-Toc Activity Sheet Students can also create mod 12 multiplication tables. Alternatively, the Arithme Tic Toc Spreadsheet can be used by students to discover how multiplication works with modular arithmetic. With this spreadsheet, students can adjust the modulus, see the resulting table, and make some discoveries about the results. Arithme-Tic-Toc Spreadsheet The spreadsheet can be used to generate class discussion on pattern relationships that exist within each table. After allowing sufficient time for group discussion, solicit responses from students and list all observations on the board. As a class, discuss the observations, and allow students to discover any incorrect observations that were made. In addition, encourage students to give reasons for some of the things they noticed. Once students understand basic computations with modular arithmetic, proceed to the handout where students will investigate relationships and discover interesting patterns. Prior to working on the handout, however, you may want to point out several properties regarding modular arithmetic and its notation: Modular arithmetic uses integers only. The notation a = b mod m implies that a and b have the same remainder when divided by m . If a = b mod m , then a b is a multiple of m . Save
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  • Spring '16
  • Jimmie Rios
  • Math

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