Technology and the Diversity of Limits

Allow students time to answer these questions. Once they have had time to complete the questions, you may want to hold a class discussion about some or all of them.

1. Imagine that you had an unlimited number of shapes. Do you think this would lead to more or less diversity among your designs? Explain your answer.

   Students should have seen that having 14 shapes led to more diversity in the designs. From that, they should infer that having an unlimited number of shapes would allow for even more diversity. They would have more shapes to choose from, which means they would have fewer constraints on their designs. This question may serve as an opportunity for formative assessment. Although students may not have complete ideas at this point, you can assess whether they understand that the more choices they have, the more diversity the designs will have. At this phase in the 5E Instructional Model, assess students based on reasonable answers rather than on having a completely correct answer. Use the information to inform your teaching as you decide to move to the next activity or return to concepts in this activity.

2. In this activity, you were not asked to make only a 7-shape art design and a 14-shape furniture design. Why do you think you were not asked to do this?

   If students created a 7-shape art design and a 14-shape furniture design, they would have difficulty comparing the amount of diversity. This reflects the idea, if they are familiar with experimental design, of changing two variables. If they had only these two designs, they would not know whether the diversity was due to the number of shapes they were allowed to use or the type of design they were creating.

3. What new information can you add to your answer to the focus question? Your answer should be in Step 1 from the Engage activity. Add any new information using a different-colored pen or pencil.

   Students may be able to add information about constraints to their answers.

4. In this Explore activity, you worked on the teamwork skill of seeing other people’s points of view. To do that, you had to come to an agreement on your designs. What did you do to help your team come to an agreement?

   Students will have different answers to this question. They may have worked together to place the shapes or they may have each come up with ideas and voted on the best. Other answers are acceptable as well, if students show that the team worked together to come to an agreement.

5. With your team, write a paragraph that summarizes your findings in this activity. You should answer the following questions in your paragraph:

   • How do more detailed or specific criteria affect the similarity or diversity of designs?
   • How do constraints affect the similarity or diversity of designs?

   Make sure all team members have written the paragraph in their technology notebooks.

   The teams should come up with a paragraph that reflects the idea that more detailed or specific criteria cause designs to be more similar to one another. They should also see that constraints also cause designs to be more similar. The more restrictive the design goal (through either stricter criteria or more constraints), the more similar the designs will be. This question represents a crux question that pulls together the information from this activity. You may wish to use it as a formative assessment to make sure students understand the concepts of the activity. Students will revisit this question in the next activity, so you may want to have them mark it by drawing a colored star or asterisk or by placing a sticky note or paper clip near the answer.