Lesson 1

This warm-up prompts students to compare four images. It encourages students to explain their reasoning and hold mathematical conversations. It gives you the opportunity to hear how they use terminology and talk about characteristics of the images in comparison to one another. To allow all students to access the activity, each image has one obvious reason it does not belong. Encourage students to find reasons based on mathematical properties (e.g., Figure B is the only right angle). During the discussion, listen for important ideas and terminology that will be helpful in upcoming work of the unit. The activity also gives students an opportunity to find useful tools in their geometry toolkit.

Before students begin, consider establishing a small, discreet hand signal students can display to indicate they have an answer they can support with reasoning. This signal could be a thumbs up, or students could show the number of fingers that indicate the number of responses they have for the problem. This is a quick way to see if students have had enough time to think about the problem and keeps them from being distracted or rushed by hands being raised around the class.

As students share their responses, listen for important ideas and terminology that will be helpful in upcoming work of the unit, such as reference to angles and their measures.

Arrange students in groups of 2–4, and provide access to geometry toolkits. Display the figures for all to see. Ask students to indicate when they have noticed one that does not belong and can explain why. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, tell each student to share their reasoning why a particular question does not belong. Together, find at least one reason each question doesn't belong.

Ask each group to share one reason why a particular image does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as ray, degree, or acute angle. Also, press students on unsubstantiated claims. For example, a student may make claims about the angle measures. Ask how they know the measure and demonstrate how the tracing paper or the ruler from the toolkit could be used to check.

The purpose of this activity is for students to begin to observe and describe translations and rotations. In groups of 2, they describe one of 3 possible dances, presented in cartoon form, and the partner identifies which dance is being described. Identify students who use specific and detailed language to describe the dance and select them to share during class discussion.

While students are not expected to use precise language yet, this activity both provides the intellectual need for agreeing upon common language and give students a chance to experiment with different ways of describing some moves in the plane (MP6).

Some students may interpret directions like “left” and “right” different from how their partner intended it, depending on whether they are thinking from the point of view of an observer watching the dance or putting themselves in the dance and describing things in terms of the triangle’s left, right, up, and down. Watch for miscommunications like this, point out that neither perspective is wrong, and encourage students to be more precise in their language.

Students often confuse or are unsure about the meaning of the terms clockwise and counterclockwise. Discuss with them (and demonstrate, if possible) how the hands on a clock rotate, emphasizing the direction of the rotation. Students may also be unsure of how to describe the amount of rotation. Consider asking a student who expresses angle measures in terms of degrees to explain how they see it.

Select one student to share their description for each of the pages, and display the language you observed and recorded during the activity for the different types of moves. Arrange the words in two groups, those that describe translations and those that describe rotations (but do not use these terms). Come to agreement on a word for each type, and discuss what extra words are needed to specify the transformation exactly (e.g., move right, turn clockwise 90º).

Consider asking students what they found most challenging about describing the dances: expected responses include being as precise as possible about the different motions (for example, describing whether the shape is rotating clockwise or counterclockwise). Also consider asking students if they were sometimes able to identify the dance before their partner finished describing all of the moves. All three dances begin by moving to the right, but in the second step, Dances A and B rotate 90 degrees clockwise while Dance C rotates 90 degrees counterclockwise. (So if the second move was to rotate 90 degrees counterclockwise, this must be Dance C.) Dances A and B diverge at slide 4.