Describing Transformations
10 min
Teacher Prep
Setup
Required Preparation
Narrative
The purpose of this Warm-up is to prepare students for the Info Gap activity that follows. First, students are given a problem with incomplete information. They are prompted to brainstorm what they need to know to solve a problem that involves transformations. Next, they practice asking for information, explaining the rationale for their request, and persevering if their initial questions are unproductive (MP1). Once students have enough information, they solve the problem.
Launch
Display the image and the first sentence of the Task Statement for all to see. Ask students what the location of P′ is. When they recognize that not enough information is given, display the second sentence and ask students what they need to know to be able to solve the problem. Display the sentence frame “Can you tell me .” for all to see, and invite students to use it to frame their information requests. Give students 2 minutes of quiet think time.
Student Task
P′ is the image of P after some transformations.
What specific information do you need to be able to solve the problem?
Sample Response
Sample responses:
- Can you tell me the order of the sequence of transformations?
- Can you tell me how much and which direction P is translated?
- Can you tell me how much and which direction P is rotated?
- Can you tell me the line of reflection?
Activity Synthesis (Teacher Notes)
Tell students that the problem is a part of an Info Gap routine. In the routine, one person has a problem with incomplete information, and another person has data that can help with solving it. Explain that it is the job of the person with the problem to think about what is needed to answer the question, and then request it from the person with information.
Tell students they will try to solve the problem this way as a class to learn the routine. In this round, the students have the problem, and the teacher has the information needed to solve the problem.
- Ask students, “What specific information do you need to find out where P’ is?”
- Select students to ask their questions. Encourage students to use the format of “Can you tell me . . . ?” Respond to each question with, “Why do you need to know ?”
- Once students justify their question, only answer questions if they can be answered using these data:
- P is translated and then rotated to get P’.
- P is not reflected.
- P is translated up 2 units and left 2 units.
- P is rotated 90 degrees counterclockwise.
- The center of rotation is the vertex that is 90 degrees.
- If students ask for information that is not on the data card, respond with, “I don’t have that information.”
When students think they have enough information, give them 2 minutes to solve the problem.
Tell students they will work in small groups and use the routine to solve problems in the next activity.
Math Community
After the Warm-up, display the Math Community Chart with the “doing math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example,
- If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.
-
If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.
After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Describing Transformations
10 min
Teacher Prep
Setup
Required Preparation
Narrative
The purpose of this Warm-up is to prepare students for the Info Gap activity that follows. First, students are given a problem with incomplete information. They are prompted to brainstorm what they need to know to solve a problem that involves transformations. Next, they practice asking for information, explaining the rationale for their request, and persevering if their initial questions are unproductive (MP1). Once students have enough information, they solve the problem.
Launch
Display the image and the first sentence of the Task Statement for all to see. Ask students what the location of P′ is. When they recognize that not enough information is given, display the second sentence and ask students what they need to know to be able to solve the problem. Display the sentence frame “Can you tell me .” for all to see, and invite students to use it to frame their information requests. Give students 2 minutes of quiet think time.
Student Task
P′ is the image of P after some transformations.
What specific information do you need to be able to solve the problem?
Sample Response
Sample responses:
- Can you tell me the order of the sequence of transformations?
- Can you tell me how much and which direction P is translated?
- Can you tell me how much and which direction P is rotated?
- Can you tell me the line of reflection?
Activity Synthesis (Teacher Notes)
Tell students that the problem is a part of an Info Gap routine. In the routine, one person has a problem with incomplete information, and another person has data that can help with solving it. Explain that it is the job of the person with the problem to think about what is needed to answer the question, and then request it from the person with information.
Tell students they will try to solve the problem this way as a class to learn the routine. In this round, the students have the problem, and the teacher has the information needed to solve the problem.
- Ask students, “What specific information do you need to find out where P’ is?”
- Select students to ask their questions. Encourage students to use the format of “Can you tell me . . . ?” Respond to each question with, “Why do you need to know ?”
- Once students justify their question, only answer questions if they can be answered using these data:
- P is translated and then rotated to get P’.
- P is not reflected.
- P is translated up 2 units and left 2 units.
- P is rotated 90 degrees counterclockwise.
- The center of rotation is the vertex that is 90 degrees.
- If students ask for information that is not on the data card, respond with, “I don’t have that information.”
When students think they have enough information, give them 2 minutes to solve the problem.
Tell students they will work in small groups and use the routine to solve problems in the next activity.
Math Community
After the Warm-up, display the Math Community Chart with the “doing math” actions added to the teacher section for all to see. Give students 1 minute to review. Then share 2–3 key points from the teacher section and your reasoning for adding them. For example,
- If “questioning vs. telling,” a shared reason could focus on your belief that students are capable mathematical thinkers and your desire to understand how students are making meaning of the mathematics.
-
If “listening,” a shared reason could be that sometimes you want to sit quietly with a group just to listen and hear student thinking and not because you think the group needs help or is off-track.
After sharing, tell students that they will have the opportunity to suggest additions to the teacher section during the Cool-down.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations: