Lesson 10

Reading: MLR6 Three Reads. This is the first time Math Language Routine 6 is suggested as a support in this course. In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. During the first read, students focus on comprehending the situation; during the second read, students identify quantities; during the third read, students brainstorm possible strategies to answer the question. The question to be answered does not become a focus until the third read so that students can make sense of the whole context before rushing to a solution. The purpose of this routine is to support students’ reading comprehension as they make sense of mathematical situations and information through conversation.
Design Principle(s): Support sense-making

How It Happens:

1. In the first read, students read the problem with the goal of comprehending the situation.

   Invite a student to read the problem aloud while everyone else reads with them and then ask, “What is this situation about?”

   Allow one minute to discuss with a partner, and then share with the whole class. A clear response would be: “Diego and Andre both bought tickets to a concert.”

2. In the second read, students analyze the mathematical structure of the story by naming quantities.

   Invite students to read the problem aloud with their partner or select a different student to read to the class and then prompt students by asking, “What can be counted or measured in this situation? For now we don’t need to focus on how many or how much of anything, but what can we count in this situation?” Give students one minute of quiet think time followed by another minute to share with their partner. Quantities may include: the number of tickets Diego bought, the number of tickets Andre bought, the amount Diego paid, the amount Andre paid, the rate of dollars per ticket that Diego paid, the rate of dollars per ticket that Andre paid.

   Call attention to the fact that whether we are talking about Andre or Diego, the two important quantities in this situation are: number of tickets, and amount paid in dollars.

3. In the third read, students brainstorm possible strategies to answer the question, “Did they pay at the same rate?”

   Invite students to read the problem aloud with their partner or select a different student to read to the class. Instruct students to think of ways to approach the question without actually solving the problem.

   Consider using these questions to prompt students: “How would you approach this question?,” “What strategy or method would you try first?,” and “Can you think of a different way to solve it?”

   Give students one minute of quiet think time followed by another minute to discuss with their partner. Provide these sentence frames as partners discuss: “To compare the rates, I would use a double number line by….”, “One way to approach the question would be to….”
   
   Sample responses include: “I would figure out how much each person paid for one ticket”, “I know that if I multiply 3 tickets by 3, I get 9, so I would see what happens when I multiply $47 by 3”, “I would draw a diagram to figure out how much 3 groups of three tickets would cost at Diego’s rate”, and “I would use a double number line to scale up the rate for Diego’s tickets (or scale down the rate for Andre’s tickets) to see if they are the same rate.” This will help students concentrate on making sense of the situation before rushing to a solution or method.

4. As partners are discussing their strategies, select 1–2 students to share their ideas with the whole class. As students are presenting ideas to the whole class, create a display that summarizes ideas about the question.

   Listen for quantities that were mentioned during the second read, and take note of strategies for relating number of tickets to cost (amount paid).

5. Post the summary where all students can use it as a reference, and suggest that students consider using the Three Reads routine for the next activity as well.

Reading: MLR6 Three Reads. This is the first time Math Language Routine 6 is suggested as a support in this course. In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. During the first read, students focus on comprehending the situation; during the second read, students identify quantities; during the third read, students brainstorm possible strategies to answer the question. The question to be answered does not become a focus until the third read so that students can make sense of the whole context before rushing to a solution. The purpose of this routine is to support students’ reading comprehension as they make sense of mathematical situations and information through conversation.
Design Principle(s): Support sense-making

How It Happens:

1. In the first read, students read the problem with the goal of comprehending the situation.

   Invite a student to read the problem aloud while everyone else reads with them and then ask, “What is this situation about?”

   Allow one minute to discuss with a partner, and then share with the whole class. A clear response would be: “Diego and Andre both bought tickets to a concert.”

2. In the second read, students analyze the mathematical structure of the story by naming quantities.

   Invite students to read the problem aloud with their partner or select a different student to read to the class and then prompt students by asking, “What can be counted or measured in this situation? For now we don’t need to focus on how many or how much of anything, but what can we count in this situation?” Give students one minute of quiet think time followed by another minute to share with their partner. Quantities may include: the number of tickets Diego bought, the number of tickets Andre bought, the amount Diego paid, the amount Andre paid, the rate of dollars per ticket that Diego paid, the rate of dollars per ticket that Andre paid.

   Call attention to the fact that whether we are talking about Andre or Diego, the two important quantities in this situation are: number of tickets, and amount paid in dollars.

3. In the third read, students brainstorm possible strategies to answer the question, “Did they pay at the same rate?”

   Invite students to read the problem aloud with their partner or select a different student to read to the class. Instruct students to think of ways to approach the question without actually solving the problem.

   Consider using these questions to prompt students: “How would you approach this question?,” “What strategy or method would you try first?,” and “Can you think of a different way to solve it?”

   Give students one minute of quiet think time followed by another minute to discuss with their partner. Provide these sentence frames as partners discuss: “To compare the rates, I would use a double number line by….”, “One way to approach the question would be to….”
   
   Sample responses include: “I would figure out how much each person paid for one ticket”, “I know that if I multiply 3 tickets by 3, I get 9, so I would see what happens when I multiply $47 by 3”, “I would draw a diagram to figure out how much 3 groups of three tickets would cost at Diego’s rate”, and “I would use a double number line to scale up the rate for Diego’s tickets (or scale down the rate for Andre’s tickets) to see if they are the same rate.” This will help students concentrate on making sense of the situation before rushing to a solution or method.

4. As partners are discussing their strategies, select 1–2 students to share their ideas with the whole class. As students are presenting ideas to the whole class, create a display that summarizes ideas about the question.

   Listen for quantities that were mentioned during the second read, and take note of strategies for relating number of tickets to cost (amount paid).

5. Post the summary where all students can use it as a reference, and suggest that students consider using the Three Reads routine for the next activity as well.

Writing, Conversing: MLR1 Stronger and Clearer Each Time. Use this routine to help students improve their writing, by providing them with multiple opportunities to clarify their explanations through conversation. At the appropriate time, give students time to meet with 2–3 partners, to share their response to the question, “How do the two mixtures compare in taste?” Students should first check to see if they agree with each other about how Lin and Noah's mixtures compare. Provide listeners with prompts for feedback that will help their partner add detail to strengthen and clarify their ideas. For example, “How did you use double number lines to solve this problem?” or “Can you say more about what each ratio means?” Give students with 3–4 minutes to revise their initial draft based on feedback from their peers. This will help strengthen students' understanding of how to determine whether two situations involve equivalent ratios.
Design Principle(s): Support sense-making; Optimize output (for explanation)

Writing, Conversing: MLR1 Stronger and Clearer Each Time. Use this routine to help students improve their writing, by providing them with multiple opportunities to clarify their explanations through conversation. At the appropriate time, give students time to meet with 2–3 partners, to share their response to the question, “How do the two mixtures compare in taste?” Students should first check to see if they agree with each other about how Lin and Noah's mixtures compare. Provide listeners with prompts for feedback that will help their partner add detail to strengthen and clarify their ideas. For example, “How did you use double number lines to solve this problem?” or “Can you say more about what each ratio means?” Give students 3–4 minutes to revise their initial draft based on feedback from their peers. This will help strengthen students' understanding of how to determine whether two situations involve equivalent ratios.
Design Principle(s): Support sense-making; Optimize output (for explanation)