Grade Level
6th-8th grade
Objective
This lesson will teach students what a network is and how to construct a network to solve a problem situation. They will also be able describe and defend the solution to a network problem.
Activity #1
(This activity will be used as a “warm-up.”)
Ø Find enough space for the class to stand in a circle, shoulder to shoulder. You might want to do this in two groups if you have a large number of students.
Ø Ask students to grab hold of somebody’s right hand with their right hand.
Ø Then have them do the same thing with their left hand.
Ø Now, ask them to untangle the circle without letting go.
The students started off in a tangled network. As they untangled themselves, they straightened out their network and made it easier to see. This activity would be used while introducing the concept of a network.
Activity #2
(This is used as a learning activity)
The “Don’t Lift That Pencil” activity (Activity Sheet 1) will allow students to explore different networks. They will discover how paths are put together to create a working network.
Ø Pass out Activity Sheet #1 and ask students to try to trace each figure without lifting their pencil or going over a line segment twice.
Ø Ask the students if they can do this on all the shapes. If not, why?
Ø If the students don’t figure it out, tell them that only the networks with no more than two odd-numbered intersections will work. Each figure has exactly two odd-numbered intersections except the third one. So, it is impossible to trace without lifting or tracing over a line twice.
Activity #3
(This activity requires critical thinking and problem solving)
Have students do the “Ice Cream Stands Problem.” This problem is easy to understand, but there is no simple way to solve it. Students will experiment with a variety of approaches.
Ø Pass out copies of the map of Iceberg (Activity Sheet 2) and present the following directions to the class by using the blackboard, overhead projector, or handout:
What I have given you is a map of the town of Iceberg. It is an unusual map where the lines represent streets and the dots are street corners. The map does not have any houses, but we do know that there is at least one house at each corner. Iceberg would be a great place to live, except for one problem: you can’t get ice cream anywhere in town. So, Jack and Jill Icicle have founded the “Icicle and Iceberg Ice Cream Company” in order to fix the ice cream problem. They are going to build ice cream stands all over the town where people can go to buy ice cream and so Jack and Jill can make a little extra money. At first, they wanted to put a stand on every corner, but that was too expensive. So, they figured that people would still eat lots of ice cream if they only had to walk down the street to get it. Their solution was to build the ice cream stands so that people could get ice cream either right there on the corner where they live, or at the very most, have to walk down only one street to find an ice cream stand. Now they need your help figuring our where to put them stands. Where should they put them? How many do they have to build?
Ø Have the students experiment with their maps to decide where they think the ice cream stands should go. As they experiment, remind them Jack and Jill want to build the least amount possible and still help everyone. Ask if there is any way to rearrange their configuration of ice cream stands so that one or more can be eliminated.
Ø After the students have had a chance to work on the activity, show them how it was made by displaying a transparency of the secret solution (Activity Sheet 3)
Ø Explain to the students that first drawing the solution, then disguising it with several other lines, made the puzzle. You can show them this point by laying a transparency of the map of Iceberg over the transparency of the solution and like magic, the solution “vanishes.”
Discussion
Ø What strategies did you use to figure out where to put the ice cream stands?
Ø How did you make sure that no house was too far away from an ice cream stand?
Ø Ask students to think of other situations in real life that might present themselves as a puzzle like this.
Homework
Have each student make a similar puzzle of their own using place that interests them (shopping malls, toy stores, candy stores, etc…). Remind them to make the solution first, and then disguise it. Questions for the homework include:
Ø How did you make your own puzzle?
Ø If you didn’t use ice cream stands, how did you decide what to use instead?
Ø What happened when you showed your puzzle to other people?
Ø Were they able to solve it?
Last Updated: April 15, 2004
Background courtesy of: http://www.ou.edu/special/owp/yummy/backgrounds/background.html