Materials:

• Anno’s Mysterious Multiplying Jar
• Calculators – one per student

Learning Objectives:

• N-29 read, write the symbols for, and express orally, numerals less than
  e) 1 000 000
• N-72 calculate the product by using more than two factors
• N-74 determine and use the most appropriate method(s) to find products in problem solving situations
  d) calculator

• Observation checklist: As students are calculating the amount of rice, observe their calculation usage and their concept of large numbers.

Instructional Strategies and Methods:

• Indirect Instruction: Problem solving

Procedure:

1. Begin reading the book, pausing on the page that describes the three mountains on each of the two islands.
2. Ask students to determine the total number of mountains. Facilitate a discussion of the method students employed to obtain the answer.
3. Continue reading, pausing to allow the students to calculate the total number of kingdoms.
4. Repeat this process after each new item is presented, ensuring that a discussion of the multiplication used to determine the answer is explored. Provide opportunities for students to read and record the products (IL).
   For example:
   5X4X3X2X1: Facilitate a discussion of alternate and/or easier methods to multiply the numbers.
   • Do the multiplicands have to multiplied in order?
   • Can combinations of multiplicands be multiplied to make this problem easier? Explore the associative distribution of multiplication by combining 5X2=10 and 4X3=12 to mulitply 10X12.
   • Explore the next factorial: 6X5X4X3X2X1 to determine if any multiplicands could be combined to make multiplying easier.
5. As the number sentences become increasingly complex, provide students with calculators to determine products (TL). The use of the calculator allows students to focus on understanding the problem and method in which to solve the problem rather than complex algorithms.
6. Review the pages at the end of the book in which dots are used to visually represent the number patterns the students have calculated. Facilitate a discussion of large numbers:
   • If the boxes were opened and 10 more jars were discovered, how would the total number be determined?
   • How does this problem relate to the concept of infinity?
7. It is important to note that the calculator help form students’ understanding of mathematical patterns and relationships. In this activity, calculator usage allows students to focus on the patterns and the development of the concept of factorials. The intention is not to create a multiplication drill set.

Adaptation:

• To further develop the concept of factorials, provide students with two objects and determine how many ways to order the objects
  2 objects: 2x1 = 2 different arrangements
  Distribute another object and arrange the three objects as many different ways as possible.
  3 objects: 3x2x1 = 6 different arrangements
  Continue distributing an additional object and having the students determine all the possible arrangements.
  Facilitate a discussion in which students calculate, based on the factorial pattern, how many different ways 15 objects could be arranged.
• The students determine all the possible seating arrangements for four people at a rectangular table. Students may choose to represent their strategy by listing the permutations (arrangements), recording the factorials and/or illustrating the possible arrangements.