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2-5

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## Multiplication as Replication

Students build tables and use patterns as an introduction to multiplication. They are encouraged to use multiplication by 10 or 100 for larger values as the beginnings of commutativity and distribution are introduced.

### Overview

Students are introduced to multiplication as repeated addition. They are encouraged to build tables and use patterns. They are also encouraged to use multiplication by 10 or 100 for larger values, as the beginnings of commutativity and distribution are introduced informally but yet not named. This activity is motivated by a Cyberchase episode in which Delete is sneezing to produce clones, and cowboy Cy-Clone is sweeping them up.

2-5

### Suggested Time

60 minutes

### Media Resources

Calculating Clones QuickTime Video
Multiplying Bigger Numbers QuickTime Video

### Part I: Learning Activity

1. Read the following: "The CyberSquad is contacted by MotherBoard. Hacker has invented a 'clonatron' and every time Delete sneezes, three newclones are made. Lucky and Inez have to work out a system to keep track of the clones, and Cy-Clone is sent to collect the clones."

2. Distribute the Clones on the Table handout .

3. Ask the students to complete the handout. Their answers will serve as their records to compare with the results on the first video segment.

4. Tell the students that they will watch a video to see how the CyberSquad keeps track of the clones Cy needs to collect.

5. Show the Calculating Clones QuickTime Video .

6. Discuss students' records from the handout and whether they agree with the CyberSquad's records.

7. Tell the students that they will watch another video segment: "Believe it or not, Delete suddenly sneezes 103 times. Can you figure out how many clones this creates?" Ask them to show how they would go about it. Some students may need additional guidance.

8. See if any students recognize that 3 x 103 = (3+3) 103 times is the same as 103 x 3 (the commutative property).

9. Show the Multiplying Bigger Numbers QuickTime Video .

10. Discuss the students' methods, Inez's method of the table and the possibility that: a) 3 x 103 = 103 x 3 using arrays and b) 103 x 3 =100 x 3 + 3 x 3 = 300 + 9. This informally introduces the commutative property and the distributive property.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to calculate the number of clones under a different condition, that is, if Delete made four copies of himself each time he sneezed.

Assessment: Level B (above proficiency): Students are asked to consider how to draw the repeated addition picture of multiplication when starting with nine clones. Then, students are asked to consider cloning in a different way. A tree (branching) diagram is presented to students, and they are asked to consider the case in which each clone makes three copies of itself at each sneeze (exponential rather than multiplicative growth).

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