This Estimation Exploration prompts students to practice making a reasonable estimate based on experience and known information. In this case, it is not practical to count the paletas, but students could reason about groups of paletas by color, or estimate the complete rows and columns of paletas and extend their estimate to the whole set. Some students might also make an estimate based on their familiarity with how paletas are usually arranged in cases.
Launch
Groups of 2
Display the image.
“Estas son paletas. Se originaron en México y típicamente se hacen con muchas frutas diferentes” // “These are ice pops called paletas. They originated in Mexico and are typically made with many different fruits.”
Ask students to estimate without counting.
“¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high? Too low? About right?”
“Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
¿Cuántas paletas hay en la caja?
Escribe una estimación que sea:
muy baja
razonable
muy alta
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Alguien hizo una estimación menor que 30?, ¿mayor que 80?” // “Is anyone’s estimate less than 40? Greater than 80?”
“¿Cómo supieron que 30 era una estimación muy baja y que 80 era una estimación muy alta?” // “How did you know that 30 (or another number) would be too low and 80 (or another number) too high?”
“Teniendo en cuenta esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion does anyone want to revise their estimate?”
Activity 1
Standards Alignment
Building On
3.OA.A.2
Interpret whole-number quotients of whole numbers, e.g., interpret as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as .
In this activity, students recall what they know about division from IM Grade 3. The context allows students to connect lived experiences to the math of the activity. By inviting students to consider treats that they enjoy in their homes or neighborhoods, they share experiences and foster connections that build community.
The first question gives students an opportunity to co-craft mathematical questions based on a situation before answering a question based on a division equation. Students divide a two-digit number by a one-digit divisor, as they did in IM Grade 3, in a way that makes sense to them. The Activity Synthesis highlights different representations students made and relates them to the situation. The terms dividend and divisor are re-introduced in this lesson to describe a number being divided into equal groups and a number by which another number (the dividend) is divided, respectively. Another term familiar to students is quotient, the result of a division expression.
This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing
Action and Expression: Develop Expression and Communication. Give students access to concrete manipulatives (connecting cubes, counters, or square tiles) and grid paper. Invite students to use these to act out or draw . Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
“¿Cuáles son algunas de sus golosinas o meriendas favoritas que comen en casa?” // “What are some of your favorite treats or snacks from home?”
30 seconds: quiet think time
1 minute: partner discussion
MLR 5: Co-craft Questions
Display the opening paragraph and the first question.
“Escriban una lista de preguntas matemáticas que se puedan hacer sobre esta situación” // “Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“¿En qué se parecen estas preguntas?” // “How are these questions alike?” (The questions involve multiplying or dividing.) “¿En qué son diferentes?” // “How are they different?” (The questions can be answered using different operations.)
“Veamos la siguiente pregunta de la actividad” // “Let’s look at the next question in the activity.”
Activity
3–4 minutes: quiet work time
La tía de Diego compra paletas para una fiesta de la clase de Diego. En el mercado local hay paletas de distintos sabores. Ella compra el mismo número de paletas de cada sabor.
¿Qué preguntas matemáticas podemos hacer sobre esta situación?
Esta es una ecuación:
En la situación de la fiesta de la clase, ¿qué preguntas podría representar la ecuación?
Encuentra la respuesta a una de las preguntas que escribiste. Explica o muestra cómo razonaste.
Activity Synthesis
Display two questions that students wrote for the equation .
“¿Qué representa el 84 en ambos problemas?” // “What does the 84 represent in both problems?” (The amount being divided into equal groups.)
“En matemáticas, el número que se está dividiendo se conoce como el dividendo, y el número entre el que se divide el dividendo se conoce como el divisor. El resultado de la división se conoce como el cociente” // “In mathematics, the number being divided is known as the dividend, and the number by which the dividend is divided is known as the divisor. The result of the division is known as the quotient.”
Invite students to share their strategies for the last question. Highlight strategies that show equal-size groups and reasoning that relates multiplication and division.
Activity 2
Standards Alignment
Building On
3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2.
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
The purpose of this activity is for students to continue to use any representation or strategy to solve division problems with two- and three-digit dividends. They solve one problem that asks how many in each equal group and another that asks how many equal groups.
Launch
Groups of 2
Display images of snacks in the activity.
“Miren las imágenes. ¿Qué observan? Qué se preguntan?” // “Take a look at the images. What do you notice? What do you wonder?”
Share responses.
“Los gulab jamuns son golosinas populares en India, Pakistán y sus países vecinos de Asia del Sur” // “Gulab jamuns are sweet treats that are popular in India, Pakistan, and their neighboring countries in South Asia.”
“Los palitos de pan cubiertos con chocolate, crema de fresa u otros sabores son meriendas populares en Japón, Taiwán y otros países de Asia del Este” // “Breadsticks that are covered with chocolate, strawberry cream, or other flavors are popular snacks in Japan, Taiwan, and other East Asian countries.”
Ask a student to read the first problem aloud.
“Los problemas de esta actividad son sobre golosinas que disfrutan los estudiantes de distintos lugares de todo el mundo” // “The problems in this activity involve treats that students enjoy from different places around the world.”
Activity
6–8 minutes: independent work time
2–3 minutes: partner discussion
La mamá de Priya prepara 85 gulab jamuns para compartir con los compañeros de clase. Priya le da 5 gulab jamuns a cada estudiante de la clase.
¿Cuántos estudiantes hay en la clase de Priya? Explica o muestra cómo razonaste.
El tío de Han envía a la clase 108 palitos de pan cubiertos con chocolate para una merienda. Los estudiantes de la clase de Han están sentados en 6 mesas. Han planea repartir el mismo número de palitos en cada mesa.
¿Cuántos palitos de pan reciben en cada mesa? Explica o muestra cómo razonaste.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿En qué se parecen las preguntas de las dos situaciones (la de los gulab jamuns y la de los palitos de pan)?” // “How are the questions in the two situations—gulab jamuns and breadsticks—alike?” (They involved division into equal groups.)
“¿En qué son diferentes?” // “How are they different?” (The first looks for the number of groups. The second looks for the size of a group.)
Invite students to share their response for the second problem.
“¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “What is the same about each of these methods? What is different?”
Lesson Synthesis
“Hoy resolvimos problemas en los que se dividían números enteros. Pensamos en los tipos de problemas de división que resolvíamos: si nos interesaba encontrar el número de grupos o encontrar la cantidad que había en cada grupo” // “Today we solved problems involving division of whole numbers. We thought about the kinds of division problems we were solving—whether we were trying to find the number of groups or the amount in each group.”
Display:
“Ciento cuatro estudiantes se organizan en grupos” // One-hundred four students are put into groups.
“En esta situación, ¿qué preguntas podría representar la ecuación?” // “In this situation, what questions could the equation represent?” (How many students are in each group if 104 students are put into 8 equal groups? How many groups can be made if 104 students are put into groups of 8?)
“¿Qué significa el valor de ?” // “What does the value of mean?” (It depends on the question being answered: either the number of students or the number of groups.)
Standards Alignment
Building On
3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2.
If students are unsure how to represent with a question about the class party situation, consider asking:
“Si fueras a actuar el significado de esta ecuación, ¿qué representaría el 84? ¿Qué representaría el 7? ¿Qué representaría el signo de interrogación?” // “If you were to act out the meaning of this equation, what would the 84 represent? What would the 7 represent? What would the ? represent?”
“¿Cómo puedes usar lo que compartiste para escribir una pregunta que corresponda a la ecuación?” // “How can you use what you shared to write a question that matches the equation?”
Addressing
Building Toward
4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.