Lesson 21

This warm-up prompts students to carefully analyze and compare features of expressions. In making comparisons, students practice looking for structure (MP7). The work here prepares students to reason flexibly and to use multiple strategies (including writing different expressions) to solve word problems later in the lesson.

• Groups of 2
• Display expressions.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Record responses.

• “¿Qué tienen en común todas las expresiones?” // “What do all of the expressions have in common?” (They all have a value of 450.)
• “¿Pueden escribir otra expresión que tenga el mismo valor que las demás expresiones, pero que pueda ser la que es diferente?” // “Can you write another expression that has the same value as these expressions but that doesn’t belong?”

In this activity, students encounter a multiplication problem that can be reasoned in a number of ways. After finding a solution, they analyze several other strategies. As they make sense of alternative solution paths and representations, students practice reasoning abstractly and quantitatively (MP2).

Before the lesson, display the posters with the following five strategies (as shown in the blackline master) around the classroom.

E. Mai:

• Groups of 2

• 3 minutes: independent work time
• 1 minute: partners discuss responses to the first question
• 10 minutes: gallery walk to complete the second question, 1–2 minutes per poster
• As students answer the last question, monitor for the solution paths that students identify as sensible or understandable.

Students may not see connections between their strategies and the ones shown in posters A–E. Consider offering students an option to stand at a poster labeled “una estrategia completamente diferente” // “a totally different strategy” and asking: “¿En qué se diferencia tu estrategia de las estrategias que se muestran?” // “How is your strategy different from the ones shown?” During synthesis, ask the class if they see any connections between the “totally different” strategies and a strategy they have selected.

• Poll the class on which strategy most closely resembles their own.
• Poll the class on which strategy that doesn’t resemble their own makes the most sense to them.
• Invite students to share their responses for the last question and why they found a particular strategy to make sense.

Students begin the activity by looking at the problem displayed, rather than in their books. At the end of the launch, students work on the problem. This activity prompts students to use what they know about multiplication, division, factors, and multiples to solve problems. The problem does not have a question, so students will need to make sense of the context and generate potential questions that might be answered (MP2). Students are encouraged in the task to attend to the details of the situation and to engage in genuine curiosity about the mathematics that is embedded within it.

This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing

• Groups of 2

MLR5 Co-Craft Questions

• Read only the first two paragraphs without revealing the question(s).
• “Escribe una lista de preguntas matemáticas que se podrían hacer sobre esta situación” // “Write a list of mathematical questions that could be asked about this situation.”
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses for use later in the task.
• “¿Qué información de la situación se puede usar para responder esta pregunta?” // “What information from the situation can be used to answer this question?” (The number of days tickets were purchased, the total number of money earned by the theater, the price of movie tickets)
• Reveal the task (students open books), and invite additional connections.

• “Escojan una pregunta de la lista y respóndanla” // “Choose a question from the list to answer.”
• “Completen la actividad con un compañero” // “Work with a partner to complete the activity.”
• Remind students of the list of questions generated during the launch as a reference during the activity.

Students may think of questions that cannot be answered using the information provided. Consider asking: “¿Qué necesitamos saber para poder responder esta pregunta?” // “What would we need to know to be able to answer this question?” and “¿Cómo podríamos averiguar esta información?” // “How might we find out this information?” The result of these questions may not enable the students to answer the questions, but will support them in making sense of the problem and identifying information necessary to solve the problems.

• Select 1–2 students to share their reasoning and responses.
• If not clarified in students’ explanations, discuss a possible path for finding out the number of tickets sold over the two days using the given information. (For instance: Each ticket is \$9 and we know the total amount of money earned by selling tickets in one day, \$3,132. If we divide the total amount earned by the price of each ticket, we can find out how many tickets were sold on one day. \(3,\!132\div 9 = 348\). If 348 tickets were sold on one day, then \(348 \times 2\) or 696 tickets were sold in the two days. We can also multiply \$3,132 by 2 first then divide by \$9 to get the total number of tickets.)