Lesson 7

This warm-up prompts students to carefully analyze and compare the features of 4 images. Students consider different representations of decompositions, similar to what they worked with in a previous section. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of the images.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Qué herramientas matemáticas muestran diferentes maneras de separar el 6? ¿Qué maneras diferentes ven de separar el 6?” // “Which math tools show different ways to break apart 6? What different ways to break apart 6 do you see?”

The purpose of this activity is for students to notice that there is more than one way to solve a Put Together/Take Apart, Both Addends Unknown story problem. While there are multiple possible solutions to this story problem, students are only expected to produce one solution in this activity. The goal of the activity synthesis is to investigate different solutions and see that this type of story problem allows for multiple correct solutions.

When students attend to the mathematical features of a situation, adhere to mathematical constraints, make choices, and translate a mathematical answer back into the context, they model with mathematics (MP4).

• Groups of 2
• Give students access to connecting cubes or two-color counters.
• “Muchas familias y culturas preparan postres especiales. ¿Ustedes preparan algún postre con su familia?” // “Many families and cultures make special desserts. Are there desserts that you make with your family?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• Display the image.
• “Las paletas son populares en México. Usualmente se hacen con frutas congeladas” // “Paletas are a type of ice pop popular in Mexico. They are usually made with fruit.”
• Read and display the task statement.
• “Cuéntenle a su pareja lo que pasó en la historia” // “Tell your partner what happened in the story.”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “¿Qué estamos tratando de descifrar?” // “What are we trying to figure out?” (How many of the paletas had lime and how many had coconut.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “Muestren cómo pensaron. Usen dibujos, números, palabras u objetos” // “Show your thinking using drawings, numbers, words, or objects.”

• 2 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who show different decompositions of 6.

If students take out 6 objects or draw 6 pictures or symbols but are unsure what to do next, consider asking:

• “¿Me puedes contar lo que pasó en el problema-historia?” // “Can you tell me what happened in the story problem? What are we trying to figure out?”
• “¿Qué objetos/dibujos muestran las paletas de lima?” // “Which objects/drawings show the lime paletas? Which show the coconut paletas?”

• Invite previously identified students to share.
• “¿En qué se parecen las formas en las que _____ y _____ resolvieron el problema-historia?” // “What is the same about how _____ and _____ solved the story problem?” (They both showed 6 paletas total. They showed some lime and some coconut.)
• “¿En qué son diferentes las formas en las que _____ y _____ resolvieron el problema-historia?” // “What is different about how _____ and _____ solved the story problem?” (One showed 3 lime and 3 coconut. The other showed 5 lime and 1 coconut.
• “¿_____ y _____ resolvieron ambos el problema-historia? ¿Por qué piensan eso?” // “Did both _____ and _____ solve the story problem? Why do you think that?” (Yes. They both showed 6 paletas. They both showed some coconut paletas and some lime paletas.)
• “Hay más de 1 respuesta al problema-historia. Es lo mismo que cuando separamos las torres de cubos: había más de 1 manera de separarla en 2 partes” // “There is more than 1 answer to the story problem. Just like when we snapped our cube towers, there was more than 1 way that we could snap it into 2 pieces.”
• Record each student’s solution with an equation that begins with the total. For example:
  • Write \(6 = 3 + 3\) and say, “Había 6 paletas. 3 eran paletas de coco y 3 eran paletas de lima. Podemos escribir esto así: 6 es 3 más 3” // “There were 6 paletas. 3 of them were coconut paletas and 3 of them were lime paletas. We can write that as 6 is 3 plus 3.”

The purpose of this activity is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem. In the activity and lesson synthesis, students discuss different ways to show the 2 groups and how showing the 2 groups clearly helps you answer the questions (MP2).

• Groups of 2
• Give students access to connecting cubes or two-color counters.
• Read and display the task statement.
• “Cuéntenle a su pareja lo que pasó en la historia” // “Tell your partner what happened in the story.”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Monitor for students who accurately retell the story. Choose at least one student to share with the class.
• Reread the task statement.
• “Muestren cómo pensaron. Usen dibujos, números, palabras u objetos” // “Show your thinking using drawings, numbers, words, or objects.”

• 2 minutes: independent work time
• 2 minutes: partner discussion
• “Escriban una expresión para mostrar cuántas granadas quedaron en la repisa y cuántas quedaron en la cesta” // “Write an expression to show how many of the pomegranates were on the shelf and how many were in the basket.”
• 1 minute: independent work time
• Monitor for a student who creates a drawing that clearly shows which pomegranates are on the shelf and which are in the basket.

If students take out or draw 7 objects or symbols, but it is unclear which are representing pomegranates on the shelf and which are representing pomegranates in the basket, consider asking:

• “¿Qué estamos tratando de descifrar?” // “What are we trying to figure out?” 
• “¿Puedes usar tus objetos/dibujos para contarme lo que pasó en la historia?” // “Can you use your objects/drawings to tell me what happened in the story?”

• Draw 7 circles with no labels.
• “Elena dibujó 7 círculos para mostrar las granadas de Kiran” // “Elena drew 7 circles to show Kiran’s pomegranates.”
• Invite a student who created a drawing with labels to share.
• “¿Cuál dibujo les ayuda a ver lo que pasa en la historia? ¿Por qué?” // “Which drawing helps you see what happens in the story? Why?” (In the second drawing we can just see which ones are on the shelf and which ones are in the basket, so it helps us to see the story. The circles with sh are the pomegranates on the shelf.)
• Record each student’s solution with an equation that begins with the total. For example:
  • Write \(7 = 3 + 4\) and say, “Había 7 granadas. 3 estaban en la repisa y 4 estaban en la cesta. Podemos escribir eso como 7 es 3 más 4” // “There were 7 pomegranates. 3 of them were on the shelf and 4 of them were in the basket. We can write that as 7 is 3 plus 4.”

The purpose of this activity is to introduce students to stage 3 of the Math Stories center. Students tell and represent Put Together/Take Apart, Both Addend Unknown story problems based on a picture.

After they participate in the center, students choose from any stage of previously introduced centers.

• What’s Behind My Back?
• 5-frames
• Make or Break Apart Numbers

• Gather materials from: 
  • What’s Behind My Back, Stage 1
  • 5-frames, Stages 1 and 2
  • Make or Break Apart Numbers, Stage 1

• Groups of 2
• Give each group of students a set of pictures and access to connecting cubes or two-color counters. Give each student a recording sheet.
• “Vamos a aprender una nueva forma de trabajar en el centro ‘Historias matemáticas’. Se llama ‘Historias matemáticas: ¿Cuántos de cada uno?’” // “We are going to learn a new way to do the Math Stories center. It is called Math Stories, How Many of Each?"
• Display the student book.
• “Priya recolectó todas las manzanas del árbol de manzanas. Un compañero va a contar una historia sobre cuáles manzanas puso Priya en la cesta verde y cuáles puso en la cesta roja. Piensen en una historia que le puedan contar a su pareja” // “Priya picked all the apples from the apple tree. One partner will tell a story about which apples Priya put in the green basket and which apples she put in the red basket. Think of a story you can tell your partner.”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Ahora necesito usar objetos o dibujos para mostrar lo que pasó en la historia de mi pareja. ¿Cómo puedo mostrar lo que pasó en la historia de mi pareja?” // “Now I need to use objects or drawings to show what happened in my partner’s story. How can I show what happened in my partner’s story?”
• 30 seconds: quiet think time
• Share responses.
• Demonstrate representing the story with objects or drawings based on student suggestions.
• “Cuando termine de usar objetos o dibujos para mostrar lo que pasó en la historia de mi pareja, tengo que contarle a mi pareja una historia diferente sobre las manzanas y las cestas” // “Once I finish using objects or drawings to show what happened in my partner’s story, I need to tell my partner a different story about the apples and the baskets.”
• Share a Put Together/Take Apart, Both Addends Unknown story about the apples with a different decomposition, such as: Priya collected 6 apples from the tree. She put 4 of the apples in the green basket and 2 of the apples in the red basket.
• “Por turnos y en parejas, un compañero cuenta una historia sobre la imagen y el otro compañero muestra lo que pasa en la historia usando objetos o dibujos. Después, piensen en una historia diferente acerca de la imagen” // “Take turns working with your partner. One partner tells a story about the picture and the other partner shows what happens in the story using objects or drawings. Then think of a different story about the picture.”

• 10 minutes: partner work time
• “Ahora pueden escoger otro centro. También pueden seguir jugando ‘Historias matemáticas’” // “Now you can choose another center. You can also continue playing Math Stories.”
• Display the center choices in the student book.
• Invite students to work at the center of their choice. 
• 10 minutes: center work time
• If time, invite students to choose another center.

• Invite students to share 2 different Put Together/Take Apart, Both Addends Unknown stories about the same picture.
• “¿Hay otras historias que podamos contar acerca de esta imagen?” // “Are there any other stories that we can tell about this picture?”