The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.
Launch
Groups of 2
Display the image.
“¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Task Statement
En este campo, cada calabaza normal pesa entre 4 y 10 kilogramos.
¿Cuántos kilogramos crees que pesa la calabaza gigante?
Escribe una estimación que sea:
muy baja
razonable
muy alta
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo usaron la imagen, o lo que saben sobre las calabazas, como ayuda para hacer su estimación?” // “How did you use the image or what you know about pumpkins or other melons to help you make estimates?”
Consider asking:
“¿Alguien hizo una estimación menor que 100 kilogramos? ¿Alguien hizo una estimación mayor que 500 kilogramos?” // “Is anyone’s estimate less than 100 kilograms? Is anyone’s estimate greater than 500 kilograms?”
“Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion, does anyone want to revise their estimate?”
Activity 1
20 mins
Falta de información: Competencia de pesos de calabazas
Standards Alignment
Building On
Addressing
3.MD.A.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).Excludes compound units such as and finding the geometric volume of a container. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.Excludes multiplicative comparison problems (problems involving notions of “times as much”); see Glossary, Table 2.
The Information Gap structure requires students to make sense of a problem by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). This process also allows students to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6). This Information Gap provides students an opportunity to solve multiplication and division problems involving weight.
Representation: Access for Perception. Begin by demonstrating one round of the Information Gap routine to support understanding of the context. Supports accessibility for: Conceptual Processing
Launch
Groups of 2
MLR4 Information Gap
Display the Task Statement, which shows a diagram of the Information Gap structure.
1–2 minutes: quiet think time
Read the steps of the routine aloud.
“Voy a darles una tarjeta de problema o una tarjeta de datos. Lean su tarjeta en silencio. No se la lean ni se la muestren a su compañero” // “I will give you either a Problem Card or a Data Card. Silently read your card. Do not read or show your card to your partner.”
Distribute cards.
1–2 minutes: quiet think time
Remind students that after the person with the Problem Card asks for a piece of information, the person with the Data Card should respond with “¿Por qué necesitas saber ______?” // “Why do you need to know _____ [that piece of information]?”
Activity
3–5 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Task Statement
Tu profesor te va a dar una tarjeta de problema o una tarjeta de datos. No se la muestres ni se la leas a tu compañero.
Image, information gap procedure. Step 1, both students silently read their cards. Step 2, problem card students says, can you tell me blank. Ask for a specific piece of information. Data card student says, why do you need to know blank. Repeat the information requested. Step 3, problem card student says, I need to know blank, because dot, dot, dot. Data card student listens to partner's reason. Answers with information from data card. Repeat steps 2 and 3 until problem card student can say, I have enough information to solve the problem. Display the problem card. Both students solve the problem independently. Continue to ask questions if more information is needed. Share data card, then compare strategies and solutions.
Haz una pausa aquí para que tu profesor pueda revisar tu trabajo.
Pídele al profesor un nuevo grupo de tarjetas. Intercambia roles con tu compañero y repite la actividad.
Activity Synthesis
“¿Qué partes del problema les ayudaron a darle sentido a la situación?” // “What parts of the problem helped you make sense of the situation?”
“¿Qué cantidades fueron importantes?” // “Which quantities were important?”
“¿Alguien resolvió el problema de una manera diferente a como lo hizo su compañero?” // “Did anyone solve the problem in a different way than their partner?”
Activity 2
20 mins
Falta de información: Competencia de pesos de cerdos
Standards Alignment
Building On
Addressing
3.MD.A.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).Excludes compound units such as and finding the geometric volume of a container. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.Excludes multiplicative comparison problems (problems involving notions of “times as much”); see Glossary, Table 2.
In this activity, students solve addition and subtraction problems involving weight.
Launch
Groups of 2
MLR4 Information Gap
“Usemos la misma rutina ‘Falta de información’ para resolver problemas nuevos sobre otra competencia de pesos” // “Let’s use the same Information Gap routine to solve new problems about another weigh-off.”
“Voy a darles una tarjeta de problema o una tarjeta de datos. Lean su tarjeta en silencio. No se la lean ni se la muestren a su compañero” // “I will give you either a Problem Card or a Data Card. Silently read your card. Do not read or show your card to your partner.”
Distribute cards.
1–2 minutes: quiet think time
Remind students that after the person with the Problem Card asks for a piece of information, the person with the Data Card should respond with “¿Por qué necesitas saber ______?” // “Why do you need to know _____ [that piece of information]?”
Activity
3–5 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Task Statement
Tu profesor te dará una tarjeta de problema o una tarjeta de datos. No se la muestres ni se la leas a tu compañero.
Usa la misma rutina “Falta de información” para resolver el problema. Luego, haz una pausa para que tu profesor pueda revisar tu trabajo.
Pídele al profesor un nuevo grupo de tarjetas. Intercambia roles con tu compañero y repite la actividad.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Qué tipos de preguntas fue más útil haber hecho?” // “What kinds of questions were the most useful to ask?”
“¿Hubo alguna pregunta que no supieran cómo responder?” // “Were there any questions you weren't sure how to answer?”
“¿Cómo representaron su razonamiento después de darse cuenta de que necesitaban sumar (o restar)?” // “How did you represent your reasoning once you realized you needed to add (or subtract)?”
Lesson Synthesis
“En las dos últimas lecciones nos hemos enfocado en resolver problemas. ¿Cómo le describirían a un amigo la forma en la que ustedes resuelven problemas matemáticos por lo general? ¿Qué ideas importantes les gustaría asegurarse de compartir?” // “We’ve been focusing on problem solving for the last two lessons. How would you describe your general approach to solving math problems to a friend? What are some important ideas you’d want to make sure to share with them?” (I start by thinking about the situation to see if I can imagine it to understand what is happening. I like to try to draw a representation like a number line or a diagram to make sense of the problem. I think about what the numbers mean and how they are related. I think about what information is given and what I want to know. I think about an equation I could write for the situation. I think about strategies I have for adding, subtracting, multiplying, or dividing depending on what is happening in the problem.)
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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).Excludes compound units such as and finding the geometric volume of a container. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.Excludes multiplicative comparison problems (problems involving notions of “times as much”); see Glossary, Table 2.