Lesson 11

The purpose of this warm-up is to elicit student ideas for how a tape diagram could be used to represent a Take From problem involving lengths. This will be useful when students solve story problems in the context of length in a later activity. While students may notice and wonder many things about these images, the connections students make between the image, the tape diagram, and the equation are the important discussion points.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan? // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿Qué piensan que pueden tener en común el diagrama y la cinta?” // “What do you think the diagram and the ribbon could have in common?” (Maybe the 54 is cm or in, so 16 is how much of the ribbon is being cut off.)
• “¿Qué puede representar el signo de interrogación?” // “What could the question mark represent?” (The longer part of the ribbon after it is cut. It represents the value of \(54-16\).)

The purpose of this activity is for students to solve Take From problems and make sense of tape diagrams that represent this problem type. Students use the diagram to make sense of the context and help guide their calculations as they solve the problem (MP2).

• Groups of 2
• Give students access to base-ten blocks.
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Estas niñas de la India tienen puestos vestidos sari. Normalmente las mujeres y las niñas usan saris. Estos se hacen envolviendo entre 5 y 7 metros de tela de una forma especial” // “These girls from India are wearing saree dresses. Sarees are usually worn by women and girls and are made by wrapping 5–7 meters of fabric in a special way.”
• “Muchos saris están hechos de seda de colores brillantes. La seda es una tela suave” // “Many sarees are made from brightly colored silk, which is a soft fabric.”
• “A veces, cuando los saris se quedan pequeños o están desgastados, se cortan en tiras para hacer cintas de sari” // “Sometimes when sarees get too small or are worn out, they are cut into strips to make saree ribbon.”

• “Priya y sus amigas planean hacer collares de cinta de seda para sari. Ellas quieren estar seguras de que tienen las medidas correctas” // “Priya and her friends are planning to make saree silk ribbon necklaces. They want to make sure they get their measurements correct.”
• “Lean el problema. Luego, observen el diagrama de Andre y discutan las primeras dos preguntas con un compañero” // “Read the problem. Then look at Andre’s diagram and discuss the first two questions with a partner.”
• 1 minute: independent work time
• 3–4 minutes partner discussion
• “Trabajen individualmente para encontrar el valor desconocido. Luego comparen sus respuestas con su compañero. No olviden incluir las unidades” // “Work independently to find the unknown value and compare your answer with your partner. Don’t forget to include the units.”
• 4–5 minutes: independent work time
• 2 minutes: partner discussion

If students add the known values instead of subtract, consider asking:

• “¿Qué ocurre en esta historia?” // “What is happening in this story?”
• “¿Tu respuesta debe ser una longitud mayor o menor que 44 pulgadas?” // “Should your answer be a length that is longer or shorter than 44 inches?”

• “¿Cómo les ayudó el diagrama de cinta a pensar en lo que necesitaban hacer para encontrar el valor desconocido?” // “How did the tape diagram help you think about what you needed to do to find the unknown value?” (The diagram shows that 18 was being taken away, so I decided to subtract 18 from 44.)

The purpose of this activity is for students to solve Take From problems within 100 with the unknown in all positions. Students label tape diagrams and use them to make sense of the story problems before solving them (MP2). In Difference Unknown and Change Unknown problems, students may not be able to anticipate whether the unknown length will be longer or shorter than the length of the part they know. It is okay if they do not accurately label the smaller part of the tape diagram with the smaller length as long as they are accurately making sense of the problem.

Students are encouraged to use the Three Reads routine as a strategy for making sense of and persevering in solving problems (MP1).

• Groups of 2
• Give each group access to base-ten blocks.
• “Todos los niños de la clase de Priya están haciendo collares de cinta con seda para sari, así que están cortando cintas para compartir entre todos” // “The kids in Priya’s class are all making saree silk ribbon necklaces, so they are cutting ribbons to share with each other.”

• “Van a leer cada historia 3 veces con su compañero. La primera vez, lean para comprender lo que ocurre en la historia. La segunda vez, lean para entender las matemáticas. Piensen sobre lo conocido y lo desconocido. Y la tercera vez, lean para hacer un plan completando el diagrama” // “With your partner, you are going to read each story 3 times. First, read to understand what is happening in the story. Second, read to understand the math. Think about what is known and unknown. And third, read to make a plan by completing the diagram.”
• “Juntos, marquen cada diagrama. Luego, solos, encuentren los valores desconocidos. Usen cualquier estrategia que tenga sentido para ustedes” // “Work together to label each diagram, and then find the unknown values on your own using any strategy that makes sense to you.”
• “Después de hacer cada problema, comparen con su compañero para ver si están de acuerdo” // “After each problem, compare with your partner to see if you agree.”
• 10 minutes: partner work time
• Monitor for students who recognize they need to add to find the answer for the third problem.

If students subtract to find the solution for the Start Unknown problem, consider asking:

• “¿Qué tan larga es la cinta que le quedó a Priya? ¿Piensas que, antes de que la cortara, su cinta tenía una longitud mayor o menor que 38 pulgadas?” // “How long is the ribbon that Priya has left? Do you think her ribbon should have been longer or shorter than 38 inches before she cut it?”
• “¿Tu solución muestra que la cinta de Priya era más larga o más corta antes de que ella la cortara?” // “Does your solution show that Priya’s ribbon was longer or shorter before she cut it?”
• “¿Cómo puedes descubrir cuánto medía la cinta antes de cortarle cualquier longitud?” // “How could you find out how long the ribbon was before any length was cut off?”

• Invite selected students to share how they solved the last problem.
• “¿Qué fue distinto en el último problema?” // “What was different about the last problem?” (Even though it was about cutting ribbon, I found the answer by adding.)