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 expressions. In making comparisons, students have a reason to use language precisely. The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of algebraic expressions.
Before students begin, consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. Signals might include a thumbs-up or a certain number of fingers that tells the number of responses they have. Using such subtle signals is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.
Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three expressions 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.
Which three go together? Why do they go together?
A
5⋅2
B
4⋅?=20
C
x+5
D
5x
Sample responses:
A, B, and C go together because:
A, B, and D go together because:
A, C, and D go together because:
B, C, and D go together because:
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 “sum,” “product,” “factor,” “term,” “expression,” “equation,” “variable,” or “unknown,” and to clarify their reasoning as needed. Consider asking:
All skills for this lesson
No KCs tagged for this lesson
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 expressions. In making comparisons, students have a reason to use language precisely. The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of algebraic expressions.
Before students begin, consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. Signals might include a thumbs-up or a certain number of fingers that tells the number of responses they have. Using such subtle signals is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.
Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three expressions 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.
Which three go together? Why do they go together?
A
5⋅2
B
4⋅?=20
C
x+5
D
5x
Sample responses:
A, B, and C go together because:
A, B, and D go together because:
A, C, and D go together because:
B, C, and D go together because:
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 “sum,” “product,” “factor,” “term,” “expression,” “equation,” “variable,” or “unknown,” and to clarify their reasoning as needed. Consider asking: