The purpose of this Warm-up is to invite students to share what they know and how they can represent division. This is the first time students experience the What Do You Know about _____? routine in IM Grade 3. Students should be familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.
Launch
Display the word “división” // “division.”
“¿Qué saben sobre la división?” // “What do you know about division?”
1 minute: quiet think time
Activity
Record responses.
“¿Cómo podríamos representar la división?” // “How could we represent division?” (with a drawing or diagram, with connecting cubes, with an equation or expression)
¿Qué sabes sobre la división?
Student Response
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Advancing Student Thinking
Activity Synthesis
“Ya hemos aprendido bastante sobre la división. Para seguir aprendiendo sobre la división, vamos a trabajar con números mayores que los que ya hemos usado antes” // “We have already learned a lot about division. We are going to continue to learn about division by working with greater numbers than we have before.”
Consider asking: “¿Qué conexiones ven entre las diferentes respuestas?” // “What connections do you see between different answers?”
Activity 1
Standards Alignment
Building On
Addressing
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.
The purpose of this 5 Practices activity is to elicit students’ existing approaches for finding the value of quotients with greater numbers and encourage them to think about ways to multiply and divide in smaller parts. Students should be encouraged to use whatever approach makes sense to them.
Monitor for and select students with the following approaches to share in the Activity Synthesis:
Make groups of 4 with objects, drawings, arrays, or base-ten blocks. Add groups of 4 until they reach 48, and count to see how many groups they make.
Multiply up starting with .
Decompose the dividend into tens and ones and divide each part (using drawings or known facts).
The approaches are sequenced from more concrete to more abstract to help all students make sense of ways to find the quotient by multiplying or dividing in parts, especially by using what they know about place value. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently. If appropriate, discuss connections between the approaches as they are shared, rather than after all selected students have shared. It is not essential that all the listed approaches are discussed, as students will consider these ideas in upcoming lessons. The main goal here is to elicit what students currently understand, and to make connections to thinking about multiplying and dividing in parts if it comes up.
When students make sense of the contextual division problem, they reason abstractly and quantitatively (MP2). Students who use the relationship between multiplication and division make use of structure (MP7).
MLR7 Compare and Connect. Synthesis: Invite students to prepare a visual display that shows the approach they used to figure out the number of groups. Encourage students to include details that will help others interpret their thinking. For example, specific language, using different colors, shading, arrows, labels, notes, diagrams, or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students, “¿Alguien resolvió el problema de la misma manera, pero lo explicaría de otra forma? ¿Cómo se vieron los grupos de 4 en cada método? ¿Por qué al usar diferentes estrategias obtuvimos el mismo resultado?” // “Did anyone solve the problem the same way, but would explain it differently? How did the groups of 4 show up in each method? Why did the different approaches lead to the same outcome?” Advances: Representing, Conversing
Representation: Access for Perception. Synthesis: As students identify correspondences between approaches, follow along and point to the relevant parts of each approach to amplify student thinking and illustrate connections. Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Launch
Display the statement: “En una excursión al acuario, un curso de estudiantes se divide en grupos” // “On a field trip to the aquarium, a class of students is splitting into groups.”
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (They are going to the aquarium in groups. They can’t go in one big group. How many kids are in the class? How many kids are in each group? Are the groups the same size?)
1 minute: quiet think time
Share and record responses.
Give students access to connecting cubes or counters, base-ten blocks, and grid paper.
Activity
“Resuelvan este problema. Usen la estrategia o la representación que prefieran” // “Solve this problem. Use whatever strategy or representation that works best for you.”
5 minutes: independent work time
As you monitor for the approaches listed in the Activity Narrative, consider asking:
“¿En qué parte de su trabajo están los grupos de 4?” // “Where are the groups of 4 in your work?”
“¿En qué parte de su trabajo está el número de grupos?” // “Where is the number of groups in your work?”
“¿Cómo empezaron? ¿Cambiaron su estrategia en algún momento?” // “How did you start? Did you change your approach while you were working?”
“Compartan su respuesta y estrategia con su compañero. Discutan en qué se parecen y en qué son diferentes” // “Share your answer and the way you found it with your partner. Talk about how the ways are alike and how they are different.”
3 minutes: partner discussion
Hay 48 estudiantes que van de excursión al acuario. Ellos visitan las exhibiciones en grupos de 4 estudiantes. ¿Cuántos grupos hay?
Muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.
Activity Synthesis
Invite previously selected students to share in the given order. Record or display their work for all to see.
As each approach is presented, invite the class to ask questions.
Keep all the approaches displayed.
Connect students’ approaches by asking:
“¿En qué se parecen estas formas de resolver el problema?” // “How are these ways of solving the problem alike?” (All the approaches used to help break the problem into smaller parts. The approaches with division and multiplication equations both had .)
“¿En qué son diferentes?” // “How are they different?” (In some, students drew a representation. In others, students wrote multiplication or division expressions or equations.)
If some approaches show breaking the problem into smaller parts, connect students’ approaches to the learning goal by asking:
“Cómo pensó _____ en separar el problema en partes más pequeñas? ¿Por qué sirvió esa estrategia para resolver este problema?” // “How did _____ think about breaking the problem into smaller parts? Why was that approach helpful for this problem?” (They thought about multiplying by 10 first because they know , and that's close to the total. It helped because they didn't have to add or skip-count by 4 as many times or draw as many things.)
Activity 2
Standards Alignment
Building On
Addressing
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.
The purpose of this activity is for students to consider their strategies as they solve two other division problems involving equal groups with greater numbers. The divisor in the first problem is a low one-digit number. Students can see from the given situation that it is the number of groups. In the second problem, the divisor is a teen number, and the context suggests that it is the size of one group. Students are likely to adjust their strategy based on these observations. Focus the discussion on how students may have reasoned differently given a greater divisor or given what they understand about the situation.
Launch
Groups of 2
“Lean los dos problemas sobre otra excursión. Piensen en qué estrategias pueden usar para resolverlos” // “Read the two problems about another field trip. Think about what strategies you might use to solve them.”
1 minute: quiet think time
“Compartan con su compañero cómo pensaron” // “Share your thinking with your partner.”
1 minute: partner discussion
Give students access to connecting cubes or counters, base-ten blocks, and grid paper.
Activity
“Trabajen individualmente en los problemas durante unos minutos. Después compartan sus respuestas con su compañero” // “Work independently on the problems for a few minutes. Then share your responses with your partner.”
5 minutes: independent work time
3 minutes: partner discussion
Monitor for students who use different representations (drew different diagrams or wrote different types of expressions or equations) for the two problems.
En cada pregunta, muestra cómo pensaste. Usa diagramas, símbolos u otras representaciones.
En otra excursión, 72 estudiantes y profesores fueron a un museo de ciencias en 3 buses. El mismo número de personas viajó en cada bus. ¿Cuántas personas viajaron en cada bus?
Durante el almuerzo, las 72 personas se sentaron en unas mesas largas. Había 12 personas en cada mesa. ¿Cuántas mesas usaron?
Student Response
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Advancing Student Thinking
If students say they aren’t sure how to get started on the problem, consider asking:
“¿De qué se trata el problema?” // “What is the problem about?”
“¿Cómo podrías representar el problema?” // “How could you represent the problem?”
Activity Synthesis
Invite students to share their responses. Display or record their reasoning.
Poll the class on whether they used a different strategy for solving the second problem than they used for the first.
Ask those who used a different strategy. “¿Por qué cambiaron su estrategia?” // “Why did you change your strategy?” (In the first problem, the 3 represents 3 groups. In the second problem, the 12 is how many in each group. In the first, the number used to divide is smaller. In the second, the number is larger.)
Lesson Synthesis
“Hoy encontramos el valor de algunos cocientes de números mayores que los que habíamos usado antes” // “Today we found the value of quotients with greater numbers than we have worked with before.”
“Vimos problemas en los que tuvimos que dividir 48 entre 4, 72 entre 3 y 72 entre 12” // “We saw problems that involved dividing 48 by 4, 72 by 3, and 72 by 12.”
“Reflexionen sobre las estrategias que usaron. ¿El tamaño del número que estaban dividiendo —48 y 72— influyó en la forma como resolvieron el problema? De ser así, ¿cómo influyó?” // “Reflect on the strategies you used. Did the size of the number being divided—48 and 72—affect how you solved the problem? If so, how?” (When the number was larger, I broke it up into more parts. When the number was smaller, I used a drawing, but when it was larger, I used another way.)
Standards Alignment
Building On
Addressing
Building Toward
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 .
