Goal
It is the goal of this inquiry to introduce students to many instances within the disciplines (besides math, alone), in which the concept of "infinite" appears. Students begin to connect the notion of "infinite" as foundational to other concepts to which they may have been exposed in previous years, including ideas such as Divisibility, the Law of Big Numbers, Repeating Decimals, Statistical Samples, The Endless Expanding Universe and Generations.

Objectives

• Understand in a developmentally appropriate way, the concept of "infinite"
• Practice listening, speaking and asking questions in a jigsaw "home group," and "expert group"
• Gain experience in discussing philosophical questions and thinking logically
• Write or draw a representation to show the relationship between their topic (see activities, below) and the notion of "infinite"
• Develop curiosity and/or questions about the "infinite"

Materials

• Thirty Cards (or however many students are in your class), each with one of five stamped symbols (used to determine home group)
• Five drawings by M.C. Escher cut into 30 puzzle pieces (used to determine expert group): Mobius Strip, Reptiles, and Waterfall.
• Handouts with the questions listed under "Activities," below

Activities
Students are told they will be thinking about the concept of the infinite. They are reminded of experiences during which they've already encountered the infinite, such as in reading fiction about space exploration, counting numbers and multiples, thinking about African Ancestors and legacies, looking at patterns which go on forever, and dividing fractions on and on.

Students are given a card stamped with a symbol to organize them into groups of five for their "home groups." Each group discusses and draws a semantic web around the word "infinite." Each student uses a distinctly colored marker (which will help the teacher assess participation) and its responsible for writing down his or her own idea(s) within the web. Semantic webs are posted throughout the room, followed by a brief discussion during which a class semantic web is drawn on the board. Here is an example of a simple semantic web or idea map created using the Inspiration software.

Each student is given one puzzle piece of an M.C. Escher drawing and asked to find the people who have the pieces needed to complete the pictures. As students assemble complete pictures, they discover the people in their expert group.

One of the following questions is written on a handout for each group (each person receives a copy). Students are told they should use their own piece of paper to take notes that will help them explain their discussion of the question to their home group.

1. Take a look at the following drawings by M.C. Escher, Mobius Strip, Reptiles, and Waterfall. What do you notice about these drawings? What makes them unique? [students use Visual-Spatial, Interpersonal intelligences (see Howard Gardner's work)]
2. What are some patterns you've seen in math, which could go on forever? [students use Logical-Mathematic, Interpersonal intelligences]
3. Has anyone invented a machine that moves or works forever? Does your group think this is possible? [students use Logical, Interpersonal intelligences]
Students re-group into their home groups and share their findings. Each home group writes or draws a definition of "infinite," on a second poster/piece of butcher paper.

Closure
Students next re-group as a class and share their findings, as individuals. During the debriefing, the teacher asks, "Were there any obstacles that came up for you in talking about the 'infinite?' What have we learned about the 'infinite?' What have we learned about working together?

Assessment
Since students each use a corresponding color to their name, the teacher can see by looking at the semantic webs and posters, if each child contributed. The structure of the home groups and expert groups provides a venue in which each student is accountable to bring back new information to their home group. By comparing the semantic webs each home group made to their second poster representing their definition of infinity, the teacher may determine whether or not the group developed new ideas about the concept.

Extensions
Students discuss or write about why companies may choose to name their products, "Infinity."

Plan B
If too much confusion arises as a result of having two jigsaw groups and six questions, the class can meet in "simple" jigsaw groups to discuss the same questions, debriefing with a semantic web as a class.

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