Lesson 22

The purpose of this warm-up is for students to look for and make use of structure in a set of related equations each having less information specified (MP7). The specific structure they might notice is that each expression on the left is equivalent to 9. Students may notice that the first two equations will result in the same thing, but there is flexibility with the end result of the last equation. The synthesis gives students an opportunity to make a story to represent the equation which they will continue to explore in the upcoming activities.

• 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 debe ir en los cuadros para que estas ecuaciones sean verdaderas?” // “What goes in the boxes to make these equations true?”
• “¿A qué historia podrían corresponder estas ecuaciones?” // “What story might these equations match?”

The purpose of this activity is for students to write equations to represent the data they collected in Unit 1. Students can write any equation that makes sense to them.

This activity is intended to follow the last lesson of Unit 1. If that lesson was not completed, students can use sample data from the blackline master to complete this task.

When students use real-world data that they collect and determine ways of fitting their data into an existing mathematical model—put-together problems with unknowns in various positions—they model with mathematics (MP4).

To make this activity more challenging, students can share only their equation. Then their partner looks at the data and determines what story the writer intended to represent.

• Gather survey data from the last lesson in the previous unit, Animals in the Jungle.

• Groups of 2
• Give each group the data or posters from the previous unit or the sample data from the blackline master.
• “Miren el trabajo que hicieron hace unas semanas. Revisen lo que investigaron y lo que descubrieron” // “Take a look at the work you did a few weeks ago. Review what you investigated and what you discovered.”
• 1 minute: quiet think time
• “Discutan con un compañero” // “Discuss with a partner.”
• 2 minutes: partner discussion 

• Read the task statement.
• 5 minutes: independent work time
• “Por turnos, díganle a su compañero un problema-historia que corresponda a las ecuaciones que escribieron” // “Take turns telling your partner a story problem that matches the equations you wrote.”
• 5 minutes: partner discussion 

• “¿Qué observaron sobre inventar un problema-historia para su ecuación? ¿Algunas fueron más fáciles que otras? ¿Por qué fueron más fáciles?” // “What did you notice about making up a story problem for your equation? Were some easier than others? Why were they easier?”

The purpose of this activity is for students to use their data to generate questions and represent the answer using an equation. Then students take turns asking and answering each other’s questions.

Students need access to the survey data used in the previous activity.

• Groups of 2
• “Vamos a usar nuestros datos de nuevo. Esta vez usaremos sus datos para crear preguntas de ‘cuántos más’ y ‘cuántos menos’. Ustedes les pedirán a sus compañeros que las respondan” // “We’re going to use our data again. This time we will create how many more and how many fewer questions about your data that you will ask your classmates to answer.”
• Read the task statement.
• “Usen las categorías de los datos de su encuesta para completar las preguntas. No es necesario que ustedes respondan las preguntas” // “Use the categories in your survey data to complete the questions. You do not need to answer the questions."
• 3 minutes: independent work time

• “Tomen turnos con su compañero para hacer y responder las preguntas. Después de hacer su pregunta, dejen que su compañero les muestre el trabajo que hizo en su libro” // "Take turns asking and answering questions with your partner. After asking your question, let your partner show their work in your book."
• 10 minutes: partner work time 

• “Clare preguntó: ‘¿Cuántos estudiantes más prefieren comer pizza que hamburguesas?’. Su compañero dijo que seis personas más prefieren la pizza que las hamburguesas y escribió \(10 - 4 = 6\)” // "Clare asked, 'How many more students like pizza than burgers?' Her partner said six more people like pizza than burgers and wrote \(10 - 4 = 6\)."
• “¿Cómo podríamos convertir esta pregunta de tipo ‘cuántos más’ en una pregunta de tipo ‘cuántos menos’? ¿Cambiaría esto la ecuación que escribirían? ¿Por qué sí o por qué no?” // “How could we turn this ‘more than’ question into a ‘fewer than’ question? Does this change the equation you would write? Why or why not?"