HomeAbout Our ProjectContact UsSite Web Map
Mathematics ProjectsSupport for StudentsSupport for TeachersSupport for MentorsSupport for ParentsHard Math Cafe

Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results

Teaching Notes for the Amida-kuji Problem

Day 1

Make sure that everyone understands the process.  Here is a way to group students in your class to work cooperatively and review amida-kuji at the same time.  This is easiest to describe if you have a composite number of students like 21, but you can adjust it to work for other numbers without much trouble.  Let's suppose that you want your 21 students to work in teams of 3 on this project.  Arrange the students in groups of twenty-one divided by three equals seven students per group.  For each group have them set up an amida-kuji like this.

network for seven students to be assigned to seven teams having no horizontal lines

Have each table fill in some horizontal lines and each students' path will determine which team to join.  Using this method, each group will assign one student to each research team and you'll have seven groups of three to continue the lesson.  

Have the teams sit together for the rest of the day to work on the warm-up problems.

Day 2

In Days 2 and 3, use the same teams as were formed in Day 1.  Review results of the warm-up problems and see if anyone has any further observations.  Challenge the teams to find ways to make the following assignments.

network  to switch 1 through 7 to 7, 1, 2, ..., 6 and a second network to order 1 through 8 to 1, 3, 5, 7, 2, 4, 6, 8

Let teams challenge other teams to solve similar problems with the fewest number of horizontal lines.

Encourage the teams to come up with a system for solving these problems.

Day 3

Allow students time to give updates on their progress toward answering the original questions.

Talk about extensions to the problem.  For example, explain the connection with sorting networks.  

Back to Top

Translations of mathematical formulas for web display were created by tex4ht.

© Copyright 2003 Education Development Center, Inc. (EDC)

EDC Logo