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3-6, 13+

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## Multiplication as Combinations

Students learn to systematically identify all possible combinations, first among 2 objects with 3 possibilities each and then among 3 objects with 2, 2 and 4 possibilities each.

### Overview

Students learn to systematically identify all possible combinations, first among 2 objects with 3 possibilities each and then among 3 objects with 2, 2 and 4 possibilities each. This Cyberchase activity is motivated by an episode in which the CyberSquad searches to recover and return the Black Crystal. To recover it, they must break through different types of security systems.

3-6

1 hour

### Media Resources

Lock Combinations of Knobs and Keys QuickTime Video
Force Field Combinations of Switches, Levers and Buttons QuickTime Video

### Part I: Learning Activity

1. Distribute the How Many Combinations? handout in which students are asked to list the combinations of knobs and keys. There are three different colors choices for each.

2. Ask students to work the problems of the How Many Combinations? handout.

3. Collect and discuss their results and methods.

4. Tell the students that they will watch a video segment in which the CyberSquad attempts to solve the problem in the handout.

5. Show the Lock Combinations of Knobs and Keys QuickTime Video .

6. Discuss with the students the approaches in the video segment and the students' approaches to the combination/multiplication problem, paying close attention to the variety of representations used.

7. Distribute the Triple Threat Force Field handout . Ask the students to work the problems on the handout.

8. Collect and discuss their results and methods for the handout.

9. Tell the students that they will watch a video in which the CyberSquad tries to solve the problem from the Triple Threat Force Field handout.

10. Show the Force Field Combinations of Switches, Levers and Buttons QuickTime Video .

11. Discuss with the students the relationship of combinations and multiplication. Ask them to think about how multiplication can be used to find the answer efficiently. Compare the grid solution with the tree or path diagram.

(Note to Teacher: the method for finding the answer (using multiplication) for the How Many Combinations? handout is 3x3 and for the Triple Threat Force Field handout is 2x2x3. They could have extended the grid approach to a cube to allow for the 3-dimension problem: switches, levers and buttons.)

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to figure out the number of combinations of 1 key and 1 knob from a selection of 6 different keys and 4 different knobs.

Assessment: Level B (above proficiency): In a variant of a traditional question from the Chinese menu selection students are asked to choose 1 item from column A, 1 from column B, and 1 from column C. A has 3 items, B has 4 items, and C has 3 items. Students are asked to figure out the number of combination meals one could select from the menu.

## Educational Standards

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