Lesson 19

This Number Talk encourages students to think about decomposing and composing numbers leading to a ten in order to add numbers more easily. The first addend in each expression is 2 away from a ten, so students consider decomposing the second addend to make the numbers more friendly for mental calculations (MP7).

• 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 strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Qué patrón observaron en estas expresiones?” // “What pattern did you notice with these expressions?”
• “Al resolver mentalmente, ¿cómo les ayudó pensar en componer una decena?” // “How did thinking about composing a ten help you solve mentally?” (Each time the first number was only 2 away from a ten. Then it was a more friendly number.)

The purpose of this activity is for students to match story problems in the context of money to tape diagrams. Students make sense of stories and determine which diagram represents the situations. One pair of stories are one-step story problems while the other pair are two-step stories. The numbers in the stories are the same so students will have to focus on relationships between the quantities in the stories to math them to tapes (MP2). 

Students may choose and justify different matches than those given in the student responses (MP3). For example, diagram B could match Jada's story. Since this story is naturally interpreted as a comparison, it naturally matches diagram C. For the two-step problems as well, either could be represented by diagram A or diagram D.  For the basketball story, we know that the basketball costs \$39 less than the football and soccer ball while for the clothes we know that the pair of pants costs \$39 and want to know how much more the shirt and shoes cost. Diagram A matches the clothes story because the 39 is known but the difference is not known. Diagram D matches the basketball story because the difference 39 is known.

• Groups of 2
• “Hoy van a resolver problemas-historia con cantidades de dinero que son más que 1 dólar” // “Today you will solve story problems with amounts of money that are more than 1 dollar.”
• “A veces gastamos grandes cantidades de dólares cuando compramos cosas que necesitamos o cuando compramos regalos para otros en ocasiones especiales” // “Sometimes we spend large dollar amounts when shopping for items we need or to buy gifts for others on special occasions.”
• “Compartan con un compañero una historia sobre una vez que hayan ido de compras” // “Share about a time you went shopping with a partner.”
• 2 minutes: partner discussion

• “Ahora van a examinar problemas-historia sobre compras. Cada historia está representada con un diagrama” // “Now you will look at story problems about shopping. Each story is represented with a diagram.”
• “Empareja cada historia con un diagrama y escribe la letra al lado de la historia” // “Match each story to a diagram and write the letter next to the story.”
• “Traten de emparejar individualmente y después comparen con su pareja” // “Try matching on your own, and then compare with your partner.”
• “Expliquen cómo saben que cada diagrama corresponde a la historia” // “Explain how you know each diagram matches.”
• 5 minutes: independent work time
• 3 minutes: partner discussion

If students mismatch stories and diagrams, consider asking:

• “¿De qué se trata el problema-historia?” // “What is the story problem about?”
• “¿Cómo representa el problema una suma o una resta?” // “How does the story problem represent addition or subtraction?”
• “¿Cómo muestra el diagrama una suma o una resta?” // “How does the diagram show addition or subtraction?”

• “¿En qué se parecen y en qué son diferentes los diagramas?” // “How were the diagrams the same or different?” (
  • Every diagram has 39 and a 68 and some of them have a 29.
  • The numbers are in different places. 
  • Some of the diagrams look like they are comparing quantities while one of them puts two quantities together.)
• “¿Cómo decidieron cuál diagrama iba con cada historia?” // “How did you decide which diagram went with each story?” (
  • In two of the stories there was something that cost \$29 and something that cost \$68 so I could look at tapes A and D and figure out how the stories match.
  • In some stories the larger amount had the prices of two things added together, so I looked for that in the diagrams.
  • The story about Diego I just need to find out how much Diego needed and that was the simplest tape.
  • For Jada's story, the diagram compares what she had to how much more she needed.)
• Share and record responses.
• As needed, invite students to share how some stories could be represented by more than one diagram by explaining how they match the quantities and the context.
• “En la siguiente actividad, van a tener la oportunidad de resolver algunos de estos problemas-historia y otros más” // “In the next activity, you will have a chance to solve some of these story problems and a few others.”

The purpose of this activity is for students to solve two-step problems without the scaffold of having the first step explicitly stated. Students solve in a way that makes sense to them and might use diagrams to help them make sense of the story. In the synthesis, the tape diagram is highlighted.

• Groups of 2
• “Con un compañero, escojan un problema de la primera actividad que quieran resolver. Discutan cómo el diagrama les puede ayudar a pensar en el problema” // “With a partner, choose a problem from the first activity to solve. Discuss how the diagram can help you think about the problem.”
• 4 minutes: partner work time

• “Ahora, individualmente, van a resolver algunos problemas sobre dinero” // “Now you will be solving a few money problems on your own.”
• “Si les ayuda, usen un diagrama para darle sentido a la historia” // “Use a diagram if it helps you make sense of the story.”
• 10 minutes: independent work time
• Monitor for students who use a diagram to represent and solve the problem about Tyler, Andre, and Noah.

If students want to represent the story with a diagram or equation but need support to start, consider asking:

• “¿De qué se trata la historia? ¿Cómo podrías partir el problema en partes más pequeñas?” // “What is the story about? How could you break the problem into smaller parts?”
• “¿Cómo podrías usar un diagrama o una ecuación para representar las partes más pequeñas?” // “How could you use a diagram or equation to represent the smaller parts?”

• Invite previously identified students to share the diagram for comparing Tyler's money to Andre's and Noah's money.
• “¿De qué manera este diagrama representa la historia?” // “How does this diagram represent the story?” (It shows Tyler's amount and then the combined amount of Andre and Noah. I can see that Tyler has less than Andre and Noah and that I need to add Andre's amount and Noah's amount and then subtract Tyler's amount from that.)