Lesson 12

The purpose of this True or False is to elicit strategies and understandings students have for using place value to compare numbers and determine if an equation is true. When students share how they know an equation is true or false based on looking at the total number of tens or total number of ones on each side, they look for and make use of the base-ten structure of numbers and the properties of operations (MP7).

•  Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time.

• Share and record answers and strategy.
• Repeat with each statement.

• “¿Cómo pueden usar lo que saben sobre decenas y unidades para explicar su respuesta a la última pregunta?” // “How can you explain your answer for the last equation using what you know about tens and ones?” (There are only 4 tens on the right.)

The purpose of this activity is for students to interpret and solve two-step problems involving length. After reading each story problem, students consider what questions could be asked and what information will be needed in the second part of the problem. Students read each story with a partner, and then solve each story problem independently and compare their solutions.

Students begin the activity by looking at the first problem displayed, rather than in their books. Students represent the problem in a way that makes sense to them and share different representations during the synthesis, explaining how these representations helped solve the problem (MP1, MP2, MP3).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Groups of 2
• Give each group access to base-ten blocks.
• “Los estudiantes de la clase de Priya están compartiendo cintas para hacer collares y pulseras para sus amigos y familiares” // “The students in Priya’s class are sharing ribbons to make necklaces and bracelets for their friends and family members.”

MLR6 Three Reads

• Display both parts of the story, but only the problem stems, without revealing the questions.
• “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
• 1st Read: “Lin encontró un pedazo de cinta que medía 92 cm de largo. Ella le dio a Noah un pedazo que medía 35 cm. Luego, Lin cortó 28 cm de cinta para Jada” // “Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin cut off 28 cm of ribbon for Jada.”
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Lin encontró un pedazo de cinta que medía 92 cm de largo. Ella le dio a Noah un pedazo que medía 35 cm. Luego, Lin cortó 28 cm de cinta para Jada” // “Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin cut off 28 cm of ribbon for Jada.”
• “En esta historia, ¿a cuáles longitudes de cinta es importante prestarles atención?” // “Which lengths of ribbon are important to pay attention to in the story?” (length of ribbon Lin started with, length of ribbon given to Noah, length of ribbon given to Jada, length of ribbon Lin has in the end)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion
• Share and record all quantities.
• Reveal the questions.
• 3rd Read: Read the entire problem, including the questions, aloud.
• “¿De qué formas diferentes podemos representar este problema?” // “What are different ways we could represent this problem?” (tape diagram, equations)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

• “Con su compañero, lean la historia nuevamente. Luego, decidan cómo representarla y resuélvanla solos” // “Read the story again with your partner. Then decide how to represent and solve it on your own.”
• “Cuando ambos hayan respondido las preguntas, comparen para ver si están de acuerdo” // “When you have both answered the questions, compare to see if you agree.”
• 10 minutes: partner work time
• Monitor for students who represent each part of the story with:
  • tape diagrams
  • base-ten diagrams
  • other clearly-labeled drawings or diagrams
  • equations

• Invite 2–3 previously identified students to display their work side-by-side for all to see.
• “¿Cómo les ayuda cada representación a entender el problema?” // “How does each representation help you understand the problem?” (In the diagrams, they used labels to show what each part means. I can see how they used Lin's length of ribbon in both parts. In the equations, I can see the same numbers, but it's a little harder to tell what each part means. I can make sense of them by looking at the other diagrams people made.)

The purpose of this activity is for students to represent and solve two-step story problems. The story problems are presented in parts, and students are encouraged to represent each part in a way that makes sense to them. In the synthesis, students compare different ways they represent and solve the problem.

• Groups of 2
• Give students access to base-ten blocks.

• “Lean cada problema con su compañero, pero resuélvanlo solos. Muestren cómo pensaron. Usen diagramas, ecuaciones o palabras” // “Read each problem with your partner and solve it on your own. Show your thinking using diagrams, equations, or words.”
• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who use tape diagrams, base-ten diagrams, and equations to represent each part of the last problem.

Students may represent and solve the first part of each problem accurately, but see the second part as a problem with two unknowns. Consider asking:

• “¿Qué información nueva te da la segunda parte del problema? ¿Qué necesitas averiguar? ¿Qué sabes ya?” // “What new information does the second part of the problem give you? What do you need to figure out? What do you already know?”
• “¿Qué ocurrió en la primera parte de la historia? ¿Qué descubriste? ¿Cómo puedes usarlo en la segunda parte del problema?” // “What happened in the first part of the story? What did you figure out? How could you use that in the second part of the problem?”

• Invite previously identified students to share their diagrams and equations for each part of the problem.
• “¿Cómo representó _____ el problema? ¿De qué manera cada representación muestra el problema-historia?” // “How did _____ represent the problem? How does each representation show the story problem?”