Moving in the Plane
10 min
Teacher Prep
Setup
Required Preparation
Make a space for students to place their sticky notes at the end of the Warm-up. For example, hang a sheet of chart paper on a wall near the door.
Narrative
This is the first Which Three Go Together routine in the course. In this routine, students are presented with four items or representations and asked: “Which three go together? Why do they go together?”
Students are given time to identify a set of three items, explain their rationale, and refine their explanation to be more precise or find additional sets. The reasoning here prompts students to notice common mathematical attributes, look for structure (MP7), and attend to precision (MP6), which deepens their awareness of connections across representations.
This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
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.
Launch
Arrange students in groups of 2–4. Display the images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three images that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A, B, and C go together because:
- The long ray points to the right of the short ray.
- They are not obtuse angles.
A, B, and D go together because:
- They are not acute angles.
- Both rays do not point downward.
A, C, and D go together because:
- They are not right angles.
- The rays do not look like a letter.
B, C, and D go together because:
- It is possible to join points on the rays to make a triangle.
- They do not make a straight line.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. 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 three go together, 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. and to clarify their reasoning as needed. Consider asking:
- "How do you know . . . ?"
- "What do you mean by . . . ?"
- "Can you say that in another way?"
Math Community
After the Warm-up, tell students that today is the start of planning the type of mathematical community they want to be a part of for this school year. The start of this work will take several weeks as the class gets to know one another, reflects on past classroom experiences, and shares their hopes for the year. Display and read aloud the question “What do you think it should look like and sound like to do math together as a mathematical community?” Give students 2 minutes of quiet think time and then 1–2 minutes to share with a partner. Ask students to record their thoughts on sticky notes and then place the notes on the sheet of chart paper. Thank students for sharing their thoughts and tell them that the sticky notes will be collected into a class chart and used at the start of the next discussion.
After the lesson is complete, review the sticky notes to identify themes. Make a Math Community Chart to display in the classroom. See the blackline master Blank Math Community Chart for one way to set up this chart. Depending on resources and wall space, this may look like a chart paper hung on the wall, a regular sheet of paper to display using a document camera, or a digital version that can be projected. Add the identified themes from the students’ sticky notes to the student section of the “Doing Math” column of the chart.
Standards
- 4.MD.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 4.MD.C.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Moving in the Plane
10 min
Teacher Prep
Setup
Required Preparation
Make a space for students to place their sticky notes at the end of the Warm-up. For example, hang a sheet of chart paper on a wall near the door.
Narrative
This is the first Which Three Go Together routine in the course. In this routine, students are presented with four items or representations and asked: “Which three go together? Why do they go together?”
Students are given time to identify a set of three items, explain their rationale, and refine their explanation to be more precise or find additional sets. The reasoning here prompts students to notice common mathematical attributes, look for structure (MP7), and attend to precision (MP6), which deepens their awareness of connections across representations.
This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
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.
Launch
Arrange students in groups of 2–4. Display the images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three images that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A, B, and C go together because:
- The long ray points to the right of the short ray.
- They are not obtuse angles.
A, B, and D go together because:
- They are not acute angles.
- Both rays do not point downward.
A, C, and D go together because:
- They are not right angles.
- The rays do not look like a letter.
B, C, and D go together because:
- It is possible to join points on the rays to make a triangle.
- They do not make a straight line.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. 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 three go together, 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. and to clarify their reasoning as needed. Consider asking:
- "How do you know . . . ?"
- "What do you mean by . . . ?"
- "Can you say that in another way?"
Math Community
After the Warm-up, tell students that today is the start of planning the type of mathematical community they want to be a part of for this school year. The start of this work will take several weeks as the class gets to know one another, reflects on past classroom experiences, and shares their hopes for the year. Display and read aloud the question “What do you think it should look like and sound like to do math together as a mathematical community?” Give students 2 minutes of quiet think time and then 1–2 minutes to share with a partner. Ask students to record their thoughts on sticky notes and then place the notes on the sheet of chart paper. Thank students for sharing their thoughts and tell them that the sticky notes will be collected into a class chart and used at the start of the next discussion.
After the lesson is complete, review the sticky notes to identify themes. Make a Math Community Chart to display in the classroom. See the blackline master Blank Math Community Chart for one way to set up this chart. Depending on resources and wall space, this may look like a chart paper hung on the wall, a regular sheet of paper to display using a document camera, or a digital version that can be projected. Add the identified themes from the students’ sticky notes to the student section of the “Doing Math” column of the chart.
Standards
- 4.MD.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 4.MD.C.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: