Geometry Hs Mathematics Unit 11 Lesson 01 Answers

Tell students they will continue to study transformations, only now without a grid.

This is the first time 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 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 an image of the task statement (the collection of points, along with the steps for the person with the problem card and data card) along with the question:

Triangle\(TDG\) has been reflected so that the vertices of the image are labeled points. What is the image of triangle \(TDG\)?

Ask students, "What specific information do you need to find out what the image of the triangle is?" Select students to ask their questions. Respond to each question with, "Why do you need that information?" Once students justify their question, only answer questions if they can be answered using these data.

Data Card

The image of \(A\) is \(G\) and the image of \(G\) is \(A\)

The image of \(D\) is \(D\)

The image of \(N\) is \(N\)

The image of\(V\) is\(I\) and the image of\(I\) is\(V\)

The image of\(L\) is\(Q\) and the image of\(Q\) is\(L\)

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. (Since \(D\) and \(N\) are taken to themselves by the reflection, the line \(ND\) must be the line of reflection. Since the image of \(T\) is a labeled point, the point \(J\) is the only point that makes sense as its image when reflected across \(ND\). The image of triangle \(TDG\) when reflected across line \(ND\) is triangle \(JDA\).)

The fact that the image and original figure overlap might be confusing for students. If not mentioned by students, ask them to reflect each point individually and then look at the final result.

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. Encourage students to annotate their diagram.

Conversing: This activity uses MLR4 Information Gap to give students a purpose for discussing information necessary to solve problems involving ________. 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

Engagement: Develop Effort and Persistence. Display or provide students with a physical copy of the written directions. Check for understanding by inviting students to rephrase directions in their own words. Keep the display of directions visible throughout the activity.
Supports accessibility for: Memory; Organization