Lesson 10

The purpose of this Notice and Wonder is to elicit different questions from students about a story to prepare them for writing their own questions for a math story in an upcoming activity. Although students may notice and wonder many things, the most important discussion point will be the types of mathematical questions that can be asked about the story.

• Groups of 2
• Display the questionless story problem.
• “¿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 preguntas matemáticas se pueden hacer sobre esta situación?” // “What are some mathematical questions that could be asked about this situation?”
• Record responses.
• “¿Qué tienen en común estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?”

The purpose of this activity is for students to ask a question that can be answered with the given information and then answer the question. There are many different questions students can ask including:

• Who picked the most apples?
• How many apples did they pick together?
• Did Elena or Diego pick more apples?
• How many apples did Diego pick?

These questions require all the given information to solve. Students may also ask questions which require only some of the information to solve, such as, “How many apples did Han pick?” The activity synthesis focuses on sharing different questions students asked and how they found the answer, with a focus on the multi-step problem “How many apples did they pick altogether?” Images are provided for display, however, student work should be used as much as possible in the synthesis.

• Groups of 2
• “A veces las personas compran manzanas en el mercado agrícola o en el supermercado, pero a veces van a un huerto de manzanas a recolectarlas” // “Sometimes people buy apples at the market or grocery store, but sometimes people go to an apple orchard to pick apples.”
• “Cada persona lleva una cesta para recoger las manzanas que recolectó y luego las paga” // “Each person gets a basket to collect the apples they pick, and then they pay for the apples.”
• “Recolectar manzanas es un plan divertido para hacer en familia o con amigos” // “Apple picking can be a fun outing for families and friends.”
• “Van a leer una historia y a hacer preguntas sobre unos amigos que fueron juntos a recolectar manzanas” // “You will be reading a story and asking questions about friends who went apple picking together.”

• Read the problem.
• “Piensen en las preguntas que pueden hacerle a alguien y que esta historia puede ayudarle a responder” // “Think about the questions you could ask someone that this story could help them answer.”
• 5 minutes: independent work time
• “Intercambien las preguntas con su compañero y encuentren la respuesta” // “Switch questions with your partner and find the answer.”
• “Compartan cómo pensaron y revisen si están de acuerdo en la respuesta” // “Share your thinking and check to see if you agree about the answer.”
• 5 minutes: partner work time
• Monitor for students who represent how many apples Han picked and students who represent how many apples Diego picked compared to Han to share in the synthesis as shown.

• “¿De qué se trata la historia?” // “What is the story about?”
• “¿Qué se puede contar en la historia?” // “What can be counted in the story?”
• “¿Qué cantidades conoces? ¿Qué es desconocido?” // “What quantities do you know? What is unknown?”

• Invite students to share their questions.
• Display a diagram that represents the number of apples Han picked, such as:

• “¿Qué representa el diagrama?” // “What does the diagram represent?” (The number of apples Han picked since he picked 14 more than Elena.)
• “¿Cómo encontraron cuántas manzanas recolectó Han?” // “How did you find how many apples Han picked?” (I added 30 to 14 to get 44 and then took away 1 to get 43.)
• Display a diagram that represents the number of apples Diego picked compared to Han, such as:

• “¿Qué representa el diagrama?” // “What does the diagram represent?” (How many apples Diego picked compared to Han.)
• “¿Cómo encontraron cuántas manzanas recolectó Diego?” // “How did you find how many apples Diego picked?” (I took 15 away from 43.)
• “¿Cómo encontraron cuántas manzanas recolectaron en total Elena, Han y Diego?” // “How did you find how many apples Elena, Han, and Diego picked altogether?” (I added 29, 43, and 28. I put all the tens together to get 80 and all the ones together to get 20 then added 80 and 20.)

The purpose of this activity is to interpret student work with given numbers and use a story context to determine what question was answered. The first problem shows a tape diagram which puts together the three quantities in the story. The second problem shows a compare tape diagram with the three given quantities and an unknown. In each case, students need to reason about the representations and the given given information to determine what question the work could answer (MP2). Determining the relationships between quantities and using them to ask questions and solve problems is an aspect of modeling with mathematics (MP4).

The goal of the activity synthesis is to identify questions, especially for the second problem, and discuss strategies for performing the calculations.

• Groups of 2

• “Van a examinar el trabajo de un estudiante y a descifrar cuál es la pregunta que el estudiante está tratando de responder” // “You are going to look at some student work and figure out what question the student is trying to answer.”
• Read the problem.
• 5 minutes: independent work time
• 5 minutes: partner discussion

• “¿Qué observas acerca del trabajo del estudiante?” // “What do you notice about the student work?”
• “¿Cómo crees que se relaciona el trabajo del estudiante con la historia?” // “How do you think the student work connects to the story?”

• Invite 1–2 students to share questions for the first problem.
• “¿Cómo supieron que el estudiante estaba tratando de encontrar una cantidad total?” // “How did you know the student was trying to find a total amount?” (The tape diagram and student work shows addition.)
• “¿Por qué piensan que el estudiante sumó 51 y 19 en vez de 51 y 18?” // “Why do you think the student added 51 and 19 rather than 51 and 18?” (They make 70 together. That way, there is no need to make a ten when you add the third number.)
• Invite 1–2 students to share questions for the second problem.
• “¿Cómo supieron que la pregunta podría ser sobre comparar? ¿Por qué no podía ser una pregunta sobre quitar?” // “How did you know the question might be about comparing? Why not a question about taking away?” (The operation is subtraction but Lin’s apples and Andre’s apples aren’t taken away from Clare’s apples. The diagram helps see that it is a comparison.)
• “¿Qué estrategias pueden usar para calcular \(51 - 19 - 18\)?”// “What strategies can you use to calculate \(51 - 19 - 18\)?” (Use the number line. Make a drawing. Subtract 20 and add 1, subtract 20 more and add 2.)