Unit 1 Lesson 13 Focus On Mathematical Practices Answers

This is the first time in this course that students do the information gap cards instructional routine, so it is important to demonstrate the routine in a whole-class discussion before they do the routine with each other.

Explain the info gap routine: students work with a partner. One partner gets a problem card with a math question that doesn't have enough given information, and the other partner gets a data card with information relevant to the problem card. Students ask each other questions like "What information do you need?" and are expected to explain what they will do with the information.. Once the partner with the problem card has enough information to solve the problem, both partners can look at the problem card and solve the problem independently. This graphic illustrates a framework for the routine:

Diagram. information gap procedure. Problem Card Student. Data card student.

Tell students that first, a demonstration will be conducted with the whole class. As a class, they are playing the role of the person with the problem card while you play the role of the person with the data card. Explain to students that it is the job of the person with the problem card (in this case, the whole class) to think about what information they need to answer the question.

Display this problem for all to see:

100 captive Asian elephants and 100 wild Asian elephants are weighed. Is there a significant difference between the weights of the two groups of elephants? Explain your reasoning.

Explain that you will be playing the role of the person with the data card. Ask students, "What specific information do you need to find out if there is a significant difference between the weight of captive and wild Asian elephants?" Select students to ask their questions. Respond to each question with, "Why do you need that information?" Here is information from the data card. After this point, only answer the question if these data are relevant:

Data Card

The distribution of weights for each set of elephants is approximately symmetric.

Captive Asian elephants:

Mean weight of captive elephants: 3,073 kg

Standard deviation of captive elephant weights: 282 kg

Median weight of captive elephants: 3,055 kg

IQR of captive elephant weights: 399 kg

Wild Asian elephants:

Mean weight of wild elephants: 2,373 kg

Standard deviation of wild elephant weights: 121 kg

Median weight of wild elephants: 2,386 kg

IQR of wild elephant weights: 163 kg

Explain that if the problem card person asks for information that is not on the data card (including the answer!), then the data card person must respond with, "I don't have that information." Ask students to explain to their partner (you) how they used the information to solve the problem. (There is a significant difference in weights between captive and wild Asian elephants. Since the distributions are symmetric, it makes sense to use the mean and standard deviation weights for the two groups. The difference in means of 700 kilograms is very different, even in light of the standard deviations for the groups.)

Arrange students in groups of 2. In each group, distribute a problem card to one student and a data card to the other student. After you review their work on the first problem, give them the cards for a second problem and instruct them to switch roles.

Conversing: This activity uses MLR4 Information Gap to give students a purpose for discussing information necessary to solve problems involving measure of centers and variability. Display questions or question starters for students who need a starting point such as: "Can you tell me . . . (specific piece of information)", and "Why do you need to know . . . (that piece of information)?"
Design Principle(s): Cultivate Conversation

Representation: Provide Access for Perception. Display or provide students with a physical copy of the written directions and read them aloud. Check for understanding by inviting students to rephrase directions in their own words. Consider keeping the display of directions visible throughout the activity.
Supports accessibility for: Language; Memory