Anno's Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno

Mathematical Strand:

Number and Operations

Topic:

Students will work with large numbers & recognizing mathematical symbols and the factorial symbol and its meaning.

Grade Level:

6-8

Lesson Created by:

Joe Gelroth, Eugene Field Elementary, Manhattan, KS

LESSON Description

Materials

• Book (Anno's Mysterious Multiplying Jar, by Masaichiro and Mitsumasa Anno), pencils & paper for students, 6 or 24 unifix cubes in 3 or 4 colors (18 or 96 total).
  

1. Launching the lesson (engage):

1. Read the story and have the students listen to it - stop after reading the question: "But how many jars were in all the boxes together?"
   
2. Have the students guess the answer to the question and write is down.
   
3. Re-read the story, but this time have the students take notes. They should list one island, two countries, three mountains, four walled kingdoms, etc. By asking how many total mountains (1 x 2 x 3 = 6), and how many total walled kingdoms (1 x 2 x 3 x 4 = 24), they should recognize the pattern.
   

2. Developing the lesson:

1. Have the students solve for the total number of jars in all the boxes. Calculator use should be discouraged - the math is not that difficult and the exercise is a good use of multiplication skills.
   
2. After the students have reached their solution, have them compare their answer (3,628,800) with the guess they made. The students will probably be amazed at how many jars are in all the boxes and how different their guess was.
   
3. Continue to read the story and introduce the mathematical symbol for factorial. The book gives a graphical representation of the numbers through 8! and explains that to show 9! and 10! would take up 180 more pages in the book.
   

3. Closure/Discussion/Elaboration:

1. Use the "Afterward: A little more about Factorials" section to develop an extension activity. This section of the book explains how factorials can be used in another situation. The authors use an example of how students can arrange their desks in a schoolroom. (A note of caution - it is assumed, but not stated in the example, that the desks are not moveable.)
   
2. Use the unifix cubes to demonstrate how 1, 2, 3, or 4 students can arrange themselves in the desks. Or, if you have enough unifix cubes and time, have the students use the cubes as a more concrete representation of the problem.
   
3. Have the students solve the desk arrangement problem based on the number of students in your classroom. You can decide whether to allow the use of calculators. The solution to 25! is a bit tedious to work just using a pencil and paper. Be aware that most elementary calculators are unable to display very large numbers (usually only to 11!). Some calculator programs on a personal computer can display 15! or even 32!