Representing Ratios with Tables
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four representations of situations involving ratios. In making comparisons, students have a reason to attend to quantities carefully and use language precisely (MP6). The activity also enables the teacher to hear how students use ratio language and talk about representations of ratios learned so far before working with a new representation.
Launch
Arrange students in groups of 2–4. Display the representations for all to see. 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 response with their group, and then together find as many sets of three as they can.
Student Task
Which three go together?
Sample Response
A, B, and C go together because they represent ratios with more milk than yogurt.
A, B, and D go together because:
- They represent ratios with 2 units of something to 1 unit of something else.
- For 1 unit of one quantity there is twice the other quantity.
A, C, and D go together because they all show how much of a quantity per 1 unit of the other quantity.
B, C, and D go together because they all describe the quantities in cups.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three goes 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, if students make broad or vague claims (for instance, “A and B show the same thing”), ask them to clarify the terms they used (for instance, “What do you mean by “the same thing?” or “How are they the same?”).
Also, prompt students to explain the meaning of any terminology they use, such as “equivalent ratios,” “same rate,” and “per,” 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?”
Standards
- 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Representing Ratios with Tables
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four representations of situations involving ratios. In making comparisons, students have a reason to attend to quantities carefully and use language precisely (MP6). The activity also enables the teacher to hear how students use ratio language and talk about representations of ratios learned so far before working with a new representation.
Launch
Arrange students in groups of 2–4. Display the representations for all to see. 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 response with their group, and then together find as many sets of three as they can.
Student Task
Which three go together?
Sample Response
A, B, and C go together because they represent ratios with more milk than yogurt.
A, B, and D go together because:
- They represent ratios with 2 units of something to 1 unit of something else.
- For 1 unit of one quantity there is twice the other quantity.
A, C, and D go together because they all show how much of a quantity per 1 unit of the other quantity.
B, C, and D go together because they all describe the quantities in cups.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three goes 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, if students make broad or vague claims (for instance, “A and B show the same thing”), ask them to clarify the terms they used (for instance, “What do you mean by “the same thing?” or “How are they the same?”).
Also, prompt students to explain the meaning of any terminology they use, such as “equivalent ratios,” “same rate,” and “per,” 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?”
Standards
- 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.