Anno's Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno
Students will learn the meaning of the word "factorial" and how to apply the factorial concept to describe a special kind of numerical relationship.
Lesson Created by:
Kathy Buyle, Susan B. Anthony Middle School, Manhattan, KS
Materials Anno's Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno (book), graph paper, pencils, paper
- Launching the lesson (engage):
- Read the story
- Stop reading on the page that poses the question, "How many jars were in all the boxes together?"
- Ask the students if they were able to keep track of the number of jars as the story was being read.
- Go back to the beginning of the story and review the numerical pattern and ask the students how they would determine the number of jars in all the boxes. Discuss their suggestions and use pencil and paper to work out a solution.
- Developing the lesson
- Continue to read the story starting with: "The answer is surprising. There were 10! jars." Show the students the way 10! is written and go on with reading until the end of the story.
- As the rest of the story is read have the students place dots on the graph paper just as shown in the book. As the story continues, the students will discover that it is impossible to keep track of the numbers of things by using dots.
- Point out the use of the factorial way of solving the problem as it is written in the book. By the end of the book, they will have gotten the point of solving the question of, "How many jars were in all the boxes together?"
- The students will apply their knowledge of using factorials by solving the desk-arranging problem in the book. First they can use graph paper and then they will describe the possible arrangements using factorials.
- Closure, Discussion, Elaboration:
- The students can extend this lesson to determining the possible number of arrangements of seats in their classroom.
- Students can determine other possibilities