Lesson 9

The purpose of this Number Talk is to elicit strategies and understandings students have for finding the value of differences when they may need to decompose a ten. When students consider how they can use known differences, like \(10 - 6\) or \(14 - 6\), to find the value of the other expressions, they look for and make use of structure and express regularity in repeated reasoning (MP7, MP8).

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Cómo pueden usar el resultado de \(14 - 6\) para encontrar el valor de \(54 - 6\)?” // “How can you use the result of \(14 - 6\) to find the value of \(54 - 6\)?” (54 has 4 more tens than 14 so add 4 tens or 40 to the result of \(14 - 6\).)
• “¿Cómo pueden usar el resultado de \(54 - 6\) para encontrar el valor de \(54 - 26\)?” // “How can you use the result of \(54 - 6\) to find the value of \(54 - 26\)?” (26 has 2 more tens than 6 so that means 2 tens need to be taken away from the answer to \(54 - 6\).)

The purpose of this activity is to sort story problems into categories students choose. Monitor for students who identify these types of story problems:

• one-step problems
• two-step problems
• problems that compare quantities

Students may also use addition, subtraction, or both addition and subtraction as their categories. This may create some ambiguity since students might sort based on the operation suggested by the overall story structure or by the operation they would use to solve the problem. Some of the two-step stories may require both operations to solve. If students use the operations to sort and sort in different ways, this provides a good opportunity for discussion.

The goal of the activity synthesis is to share the different characteristics students used to sort the problems.

• Create a set of cards from the blackline master for each student.

• Groups of 2
• “Al final de cada año escolar, en algunas escuelas donan libros a las familias u organizaciones benéficas para fomentar la lectura durante el verano. Los estudiantes y los profesores clasifican los libros para decidir cuáles regalan y con cuáles se quedan” // “At the end of each school year, some schools donate books to families or charities to encourage summer reading. The students and teachers sort books, so they can decide which ones to keep and which ones to give away.”
• “Algunos estudiantes reflexionan sobre los libros que han leído y escogen sus favoritos. Muchos estudiantes piensan en los libros que quieren leer durante el verano” // “Some students reflect on the books they have read and choose their favorites. Many students think about the books they hope to read over the summer.”
• “Ustedes van a clasificar y a resolver problemas-historia sobre libros y lectura” // “You will be sorting and solving story problems about books and reading.”
• As needed, consider asking:
  • “De los libros que leyeron este año, ¿con cuáles se quieren quedar y cuáles estarían dispuestos a regalar?” // “Which of the books that you read this year would you want to keep and which would you be fine giving away?”
  • “¿Cómo podrían clasificar los libros de nuestra biblioteca (nuestro salón)?” // “What ways could you sort the books in our (classroom) library?”
  • “¿Cuántos libros quieren leer este verano?” // “How many books are you hoping to read this summer?”

• “En esta actividad, van a clasificar los problemas-historia de una manera que tengan sentido para ustedes” // “In this activity, you are going to sort the story problems in a way that makes sense to you.”
• “Pueden pensar en las categorías que quieran usar, teniendo en cuenta en qué se parecen o en qué son diferentes los problemas-historia y cómo podrían resolverlos” // “You can think about the categories you would like based on what you notice is the same or different about the stories and how you might solve them.”
• 5 minutes: independent work time
• “Comparen su clasificación con la de su compañero. ¿En qué se parecen sus clasificaciones? ¿En qué son diferentes?” // “Compare your sort with your partner’s. How are your sorts the same? How are they different?”
• 5 minutes: partner discussion
• Monitor for students who sort their cards in different ways.

If students sort the story problems based on non-mathematical characteristics (for example, character names), consider asking:

• “¿Puedes explicar cómo escogiste los grupos para tu clasificación?” // “Can you explain how you decided the groups for your sort?”
• “¿Cómo puedes clasificar las tarjetas basándote en lo que sabes de la historia y lo que es desconocido?” // “How could you sort the cards based on what you know from the story and what is unknown?”

• Invite selected students to share the categories for their sorts.
• Record the various categories.
• If students do not sort in any of the ways suggested in the student responses, propose these categories and ask them to sort.

The purpose of this activity is to solve the story problems from the first activity. Monitor for the different ways students represent their thinking and solve their selected problems including:

• tape diagrams to make sense of the problems
• base-ten diagrams
• equations

The goal of the activity synthesis is to share the different methods students used to make sense of and solve story problems (MP2).

• Groups of 2

• “Escojan uno de los problemas-historia de la primera actividad y resuélvanlo. Escojan uno que sea diferente al de su compañero” // “Choose one of the story problems from the first activity to solve. Pick a different problem than your partner.”
• 5 minutes: independent work time
• “Compartan con su compañero el método que usaron y la solución de su problema” // “Share the method you used and the solution to your problem with your partner.”
• 5 minutes: partner discussion
• Monitor for students who solved the story with Jada’s stacks of books in different ways. 

• Invite selected students to share their solutions for the story with Jada’s pile of books in stacks of 10.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are their methods the same? How are they different?”