Congruence
5 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to orient themselves to an image of ovals on a grid. This image will be used in an upcoming activity as students study congruence of curved shapes. Creating mathematical questions about an image gives students an opportunity to make sense of problems (MP1).
This is the first time Math Language Routine 5: Co-Craft Questions is suggested in this course. In this routine, students are given a context or situation, often in the form of a problem stem (for example, a story, image, video, or graph) with or without numerical values. Students develop mathematical questions that can be asked about the situation. A typical prompt is: “What mathematical questions could you ask about this situation?" The purpose of this routine is to allow students to make sense of a context before feeling pressure to produce answers, and to develop students’ awareness of the language used in mathematics problems.
Launch
Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Use Co-Craft Questions to give students an opportunity to familiarize themselves with the image, and to practice producing the language of mathematical questions.
-
Display the image for all to see.
Ask students, “What mathematical questions could you ask about this image?” -
Give students 1–2 minutes to write a list of mathematical questions that could be asked about the image before comparing questions with a partner.
As partners discuss, support students in using conversation and collaboration skills to generate and refine their questions, for instance, by revoicing a question, seeking clarity, or referring to their written notes. Listen for how students use language about congruence and corresponding parts.
Student Task
Sample Response
- Which ovals are congruent to each other?
- What rigid transformation will take one congruent oval to another?
- Which ovals have the same area?
- What are the dimensions of each oval?
Activity Synthesis (Teacher Notes)
Invite several partners to share one question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as testing the congruence of the shapes.
Math Community
At the end of the Warm-up, display the Math Community Chart. Tell students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Using the Math Community Chart, offer an example of how the “Doing Math” actions can be used to create norms. For example, “In the last exercise, many of you said that our math community sounds like ‘sharing ideas.’ A norm that supports that is ‘We listen as others share their ideas.’ For a teacher norm, ‘questioning vs telling’ is very important to me, so a norm to support that is ‘Ask questions first to make sure I understand how someone is thinking.’”
Invite students to reflect on both individual and group actions. Ask, “As we work together in our mathematical community, what norms, or expectations, should we keep in mind?” Give 1–2 minutes of quiet think time and then invite as many students as time allows to share either their own norm suggestion or to “+1” another student’s suggestion. Record student thinking in the student and teacher “Norms” sections on the Math Community Chart.
Conclude the discussion by telling students that what they made today is only a first draft of math community norms and that they can suggest other additions during the Cool-down. Throughout the year, students will revise, add, or remove norms based on those that are and are not supporting the community.
Standards
- 8.G.2·Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
- 8.G.A.2·Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Congruence
5 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to orient themselves to an image of ovals on a grid. This image will be used in an upcoming activity as students study congruence of curved shapes. Creating mathematical questions about an image gives students an opportunity to make sense of problems (MP1).
This is the first time Math Language Routine 5: Co-Craft Questions is suggested in this course. In this routine, students are given a context or situation, often in the form of a problem stem (for example, a story, image, video, or graph) with or without numerical values. Students develop mathematical questions that can be asked about the situation. A typical prompt is: “What mathematical questions could you ask about this situation?" The purpose of this routine is to allow students to make sense of a context before feeling pressure to produce answers, and to develop students’ awareness of the language used in mathematics problems.
Launch
Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Use Co-Craft Questions to give students an opportunity to familiarize themselves with the image, and to practice producing the language of mathematical questions.
-
Display the image for all to see.
Ask students, “What mathematical questions could you ask about this image?” -
Give students 1–2 minutes to write a list of mathematical questions that could be asked about the image before comparing questions with a partner.
As partners discuss, support students in using conversation and collaboration skills to generate and refine their questions, for instance, by revoicing a question, seeking clarity, or referring to their written notes. Listen for how students use language about congruence and corresponding parts.
Student Task
Sample Response
- Which ovals are congruent to each other?
- What rigid transformation will take one congruent oval to another?
- Which ovals have the same area?
- What are the dimensions of each oval?
Activity Synthesis (Teacher Notes)
Invite several partners to share one question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as testing the congruence of the shapes.
Math Community
At the end of the Warm-up, display the Math Community Chart. Tell students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Using the Math Community Chart, offer an example of how the “Doing Math” actions can be used to create norms. For example, “In the last exercise, many of you said that our math community sounds like ‘sharing ideas.’ A norm that supports that is ‘We listen as others share their ideas.’ For a teacher norm, ‘questioning vs telling’ is very important to me, so a norm to support that is ‘Ask questions first to make sure I understand how someone is thinking.’”
Invite students to reflect on both individual and group actions. Ask, “As we work together in our mathematical community, what norms, or expectations, should we keep in mind?” Give 1–2 minutes of quiet think time and then invite as many students as time allows to share either their own norm suggestion or to “+1” another student’s suggestion. Record student thinking in the student and teacher “Norms” sections on the Math Community Chart.
Conclude the discussion by telling students that what they made today is only a first draft of math community norms and that they can suggest other additions during the Cool-down. Throughout the year, students will revise, add, or remove norms based on those that are and are not supporting the community.
Standards
- 8.G.2·Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
- 8.G.A.2·Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.