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Activity Synthesis

“La imagen muestra un tipo de juego que se llama mancala. Es uno de los juegos más antiguos del mundo” // “The picture shows a type of a game called mancala. It is one of the world’s oldest games.”
“Muchos expertos creen que mancala se inventó en Africa. Tiene cientos de nombres diferentes y se puede jugar de muchas formas diferentes. En la mayoría de juegos hay un tablero que tiene varios agujeros o huecos. Cada jugador usa una cierta cantidad de semillas que ubica en su lado del tablero. Los jugadores pueden usar semillas reales o conchas marinas, piedras o chaquiras” // “Many experts believe mancala was created in Africa. The game has hundreds of different names and can be played in many different ways. Most games are played with a board that has different pits or holes in it. Each player uses a certain amount of seeds that they place on their side of the board. Players might use real seeds or they may use shells, rocks, or beads.”
“Por turnos, cada jugador pone sus semillas en el tablero. En la mayoría de los juegos, cada jugador trata de 'capturar' más semillas que el otro” // “Each player takes turns placing their seeds on the board. In most games, you try to ‘capture’ more seeds than the other player.”
“En Ghana y el Caribe, un juego popular de mancala se llama Oware. El tablero tiene 12 agujeros, 6 para cada jugador, y en el juego se usan 32 semillas” // “In Ghana and the Caribbean, one popular mancala game is called Oware (oh-WAH-reh). The board has 12 pits, 6 for each player, and the game uses 32 seeds.”
“En Sudán, un juego popular de mancala se llama Bao. El tablero para Bao tiene 28 agujeros, 14 para cada jugador, y en el juego se usan 64 semillas” // “In Sudan, one popular mancala game is called Bao (baOW-woo). The board for Bao has 28 pits, 14 pits for each player, and the game uses 64 seeds.”
“Uno de los juegos de mancala más grande se llama En Gehé y se juega en Tanzania. ¡El tablero puede tener hasta 50 agujeros y los jugadores usan 400 semillas!” // “One of the largest mancala games is called En Gehé (ehn geh-HEY) and is played in Tanzania. The board can have up to 50 pits and the players use 400 seeds!”
“Mancala se juega en todo el mundo. Este tablero muestra un juego que se juega en India que se llama Pallanguzhi (pah-LAHN-guhr-ee). El tablero tiene 14 agujeros y se usan 70 semillas” // “Mancala is played all over the world. This board shows a game played in India called Pallanguzhi (pah-LAHN-guhr-ee). The board has 14 pits and uses 70 seeds.”
“¿Qué preguntas matemáticas podríamos hacer sobre esta imagen?” // “What math questions could we ask about this image?” (How many seeds are there in all? How many seeds are in the holes? How many seeds are not in holes? How many more seeds are on the top than on the bottom?)

Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR6 Three Reads

Materials

To Gather

Base-ten blocks

Activity Narrative

The purpose of this activity is for students to make sense of tape diagrams, and how they can be used to show part-part-whole relationships. Students have previously used tape diagrams to show comparisons. In this activity, they connect tape diagrams to Compare problems and Put Together/Take Apart problems (MP2).

Students begin the activity by looking at the first problem displayed, rather than in their books. At the end of the Launch, students open their books and work to find the diagram that matches the story problem. They do not solve the problems in this activity. The Activity and Synthesis are focused on developing student strategies for making sense of problems before solving them (MP1).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

Launch

Groups of 2
Give students access to base-ten blocks.
“Clare y Han juegan un juego de tipo mancala con semillas” // “Clare and Han are playing a game like mancala with seeds.”

Activity

MLR6 Three Reads

Display only the problem stem for the first problem, without revealing the question.
“Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
1st Read: “Clare captura 54 semillas. Han captura 16 semillas menos que ella” // “Clare captured 54 seeds. Han captured 16 fewer seeds than her. ”
“¿De qué se trata esta historia?” // “What is this story about?”
1 minute: partner discussion.
Listen for and clarify any questions about the context.
2nd Read: “Clare captura 54 semillas. Han captura 16 semillas menos que ella” // “Clare captured 54 seeds. Han captured 16 fewer seeds than her.”
“¿Cuáles son todas las cosas de esta historia que podemos contar?” // “What are all the things we can count in this story?” (Clare’s seeds. Han’s seeds. The difference between their seeds. The total of their seeds.)
30 seconds: quiet think time
1 minute: partner discussion
Share and record all quantities.
Reveal the question.
3rd Read: Read the entire problem, including the question aloud.
Ask students to open their books.
“¿Cuál de los diagramas muestra una forma en la que podemos representar este problema?” // "Which of the diagrams shows a way we could represent this problem?" (See Student Responses, first problem).
30 seconds: quiet think time
1–2 minutes: partner discussion
Share responses.
“Lean cada historia con su pareja. Después, individualmente, escojan un diagrama que corresponda” // “Read each story with your partner. Then choose a diagram that matches on your own.”
“Cuando los dos hayan escogido un diagrama, comparen sus elecciones y expliquen por qué el diagrama corresponde a la historia o por qué otros diagramas no corresponden a la historia” // “When you have both selected a match, compare your choices and explain why the diagram matches the story or why other diagrams do not match the story.”
5 minutes: partner work time

Marca el diagrama que le corresponde a cada historia. Después, explícale a tu compañero por qué le corresponde.

Clare captura 54 semillas. Han captura 16 semillas menos que ella. ¿Cuántas semillas captura Han?

A

B

C
Clare tiene 54 semillas en su lado del tablero. Han tiene 16 semillas en el suyo. ¿Cuántas semillas hay en el tablero?

A

B
Clare tiene 54 semillas. Ella tiene 16 semillas en sus manos. El resto están en el tablero. ¿Cuántas de sus semillas están en el tablero?

A

B

C
Hay 54 semillas en el tablero. Algunas semillas están en el lado de Han. 16 semillas están en el lado de Clare. ¿Cuántas semillas están en el lado de Han?

Escoge los 2 diagramas que corresponden.

A

B

C

D

Student Response

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Advancing Student Thinking

If students may say Diagram A matches the second story problem because the diagram shows the amount of seeds both players have in the story, consider asking:

“¿Qué representa el signo de interrogación en cada diagrama?” // “What does the question mark in each diagram represent?”
“¿Cuál diagrama muestra mejor las semillas de Han y Clare, y la pregunta de la historia?” // “Which diagram best matches Han and Clare’s seeds and the question the story asks?”

Activity Synthesis

Invite students to share correct diagrams for the last three problems.
Display each correct choice. Consider asking:
- “¿Cómo corresponde el diagrama al problema-historia?” // “How does the diagram match the story problem?”
- “¿Cómo muestra el diagrama lo que se conoce y lo desconocido?” // “How does the diagram show what is known and what is unknown?”
- “¿Dónde ven sumas o restas?” // “How do you see addition or subtraction?”

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

Card Sort Story Problems and Diagrams Cards, Spanish

To Gather

Base-ten blocks

Activity Narrative

The purpose of this activity is for students to connect different types of story problems to tape diagrams and to solve the problems. Students identify representations that match a story problem and justify their decisions by describing how the diagrams represent the relationships between the quantities or the actions in the story problem (MP4). When students analyze and connect the quantities and structures in the story problems and tape diagrams, they think abstractly and quantitatively (MP2) and make use of structure (MP7). Students will use the story problems from this Card sort again in a future lesson.

Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, make sure students are discussing amongst themselves and highlight groups that are following the protocol, so that students know what is being expected of them.
Supports accessibility for: Social-Emotional Functioning, Organization

Launch

Groups of 2
Give each group a set of cards.
Give each group access to base-ten blocks.

Activity

“Estas tarjetas tienen problemas-historia y diagramas” // “This set of cards includes story problems and diagrams.”
“Por turnos, van a leer un problema-historia. Después de que una persona lee, busquen un diagrama que corresponda al problema-historia. Cuando crean que encontraron una correspondencia, explíquenle a su pareja por qué las tarjetas corresponden. Luego, escojan otro problema-historia” //“You are going to take turns reading a story problem. After one person reads, match the story problem to a diagram. Work with your partner to explain your reasoning. Then pick a new story problem and find a diagram that matches.”
“Si les ayuda, pueden escribir en las tarjetas de diagrama para explicar sus correspondencias” // “If it helps, you may label the diagrams to explain your matches.”
As needed, demonstrate the activity with a student volunteer.
“Cuando su grupo termine, escojan 2 problemas-historia de las tarjetas A, B, C o D y resuélvanlos” // “When your group finishes, choose 2 story problems from Story Problems A, B, C, or D and solve them.”
8 minutes: small-group work time
Monitor for students who explain how each diagram matches the quantities in the context of the story problem.
4 minutes: independent work time
Monitor for students who solve Story Problem B or C using methods based on place value.

Tu profesor te va a dar varias tarjetas que muestran problemas-historia y diagramas.

Empareja cada problema-historia con un diagrama. Prepárate para explicar tu razonamiento.
Escoge 2 problemas-historia. Resuélvelos. Muestra cómo pensaste. Usa dibujos, números o palabras.

Activity Synthesis

Invite students to share how they decided which diagrams go with Cards A, B, and C.
Consider asking:
- “¿Cómo saben que el diagrama corresponde al problema-historia?” // “How do you know the diagram matches the story problem?”
- “¿Qué hicieron para resolver el problema?” // “What did you do to solve the problem?”
If time, select previously identified student(s) to share their method for solving Cards B or C.