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Activity 1

15 mins

Un nuevo tipo de diagrama

Standards Alignment

Building On

Addressing

Instructional Routines

None

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

None

Activity Narrative

The purpose of this activity is for students to interpret and solve multiplicative comparison problems. Students interpret tape diagrams that label each box with a value, which is different from the discrete diagrams from previous lessons. They also write equations to represent the situations and explain how the equations connect to the tape diagrams (MP2). The problems in this activity have unknown lesser quantities, greater quantities, or multipliers. Questions are provided to support students in representing the unknown in tape diagrams and in identifying the unknown in given situations.

Action and Expression: Develop Expression and Communication. Provide alternative options for expression. Encourage students to examine each diagram first and write down or talk about what they know with a partner before answering each set of questions.
Supports accessibility for: Visual-Spatial Processing, Language

Launch

Groups of 2
Display and read the first problem.
30 seconds: quiet think time
1 minute: partner discussion
“¿15 páginas es una estimación muy alta o muy baja de lo que Andre leyó?” // “Is 15 pages too high or too low of an estimate for Andre?” (Too low, because the diagram shows he should have read more than Mai.)
“Si Andre leyó 9 veces el número de páginas que Mai leyó, ¿con qué número se debería reemplazar el signo de interrogación en el diagrama? ¿Por qué?” // “If Andre read 9 times as many pages as Mai, what number should replace the question mark in the diagram? Why?” (135, because the 9 rectangles represent 9 times as many as 15. There should be 9 fifteens.)
30 seconds: quiet think time
1 minute: partner discussion

Activity

3 minutes: independent work time
8 minutes: partner work time
Monitor for students who:
- Explain the connection between their equations and the diagram.
- Show understanding that each rectangle represents the same amount.

Student Task Statement

Mai y Andre comparan el número de páginas que leyeron el primer día del concurso de lectura.

diagram. two rectangles. bottom rectangle, Andre's pages. partitioned into 9 equal parts, total length question mark. Top rectangle, Mai's pages. Same size as one of 9 parts of bottom rectangle, labeled 15.

¿Cuál sería una buena estimación del número de páginas que leyó Andre?
El diagrama muestra las páginas que Lin y Kiran leyeron, cada uno, un día durante el concurso de lectura.

diagram. two rectangles. bottom rectangle, Kiran's pages. partitioned into 6 equal parts each labeled 9, total length question mark. Top rectangle, Lin's pages. Same size as one of 6 parts of bottom rectangle, labeled 9.
1. Completa la afirmación y explica cómo lo sabes.
  
  Kiran leyó _____ veces el número de páginas que Lin leyó.
2. Escribe una ecuación de multiplicación para comparar el número de páginas que leyó Lin y el número de páginas que leyó Kiran.
3. ¿Cuántas páginas leyó Kiran en total ese día?
Jada leyó algunas páginas. Han leyó 60 páginas en total.

diagram. two rectangles. bottom rectangle, Han's pages. partitioned into 3 equal parts each labeled question mark, total length 60. Top rectangle, Jada's pages. Same size as one of the 3 parts of bottom rectangle, labeled question mark.
1. ¿Han leyó cuántas veces el número de páginas que Jada leyó? Explica cómo lo sabes.
2. Escribe una ecuación de multiplicación para comparar el número de páginas que leyó Han y el número de páginas que leyó Jada. Usa un símbolo para representar el número desconocido.
3. ¿Cuántas páginas leyó Jada? Explica cómo lo sabes.
Elena leyó 72 páginas. Clare leyó 9 páginas.

diagram. two rectangles. bottom rectangle, Elena's pages. partitioned into 2 parts. One part labeled 9. Other part unknown. total length, 42. Top rectangle, Clare's pages, same length as left part of bottom rectangle, also labeled 9.
1. ¿En qué se diferencia este diagrama de los anteriores?
2. Escribe una ecuación de multiplicación para comparar el número de páginas que leyó Elena y el número de páginas que leyó Clare. Usa un símbolo para representar el número desconocido.
3. ¿Elena leyó cuántas veces el número de páginas que Clare leyó?

Activity Synthesis

Select 2–3 students to share their responses and their reasoning.
“¿Cómo nos ayudan los diagramas a comprender lo que sabemos sobre la situación y lo que necesitamos encontrar?” // “How do the diagrams help us figure out what we know about the situation and what we need to find out?” (Each diagram shows two quantities being compared, and the ‘times as many’ amount that compares them. The quantity that is missing is the part we need to find out.)
“¿Cómo muestran los diagramas el ‘número de veces’?” // “How do the diagrams show ‘times as many’?” (‘Times as many’ is represented by the number of times each rectangle in the diagram is repeated.)
Display:
“¿Cómo nos ayuda esta ecuación a encontrar el número de páginas que leyó Jada?” // “How does this equation help us find the number of pages Jada read?” (We know that Han read 60 pages, which is 3 times as many as Jada, because the diagram shows 3 equal-size rectangles for Han and one rectangle for Jada. We just need to know the amount that each rectangle represents, which will be the amount of pages that Jada read.)

Activity 2

20 mins

¿Quién leyó más?

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

None

Activity Narrative

The purpose of this activity is for students to represent multiplicative comparison situations and solve for an unknown factor or unknown product.

In the Activity Synthesis, students make connections between the description, their diagram, and multiplication equations that represent the situation (MP2).

MLR8 Discussion Supports. Synthesis: At the appropriate time, give students 2–3 minutes to make sure everyone in their group can explain “estrategia” // “strategy,” “ecuación” // “equation,” and “diagrama” // “diagram.” Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing

Launch

Groups of 2
Read directions for the activity aloud.
“¿Qué vamos a hacer en cada problema de esta actividad?” // “What will we do with each problem in this task?” (Write an equation, with the unknown represented by a symbol, draw a diagram to show comparison, and answer the question.)

Activity

4 minutes: independent work time
2 minutes: partner discussion about the first problem
“Compartan con su compañero cómo representaron el valor desconocido en su diagrama y en su ecuación” // “Share with your partner how you represented the unknown value in your diagram and in your equation.”
“Resuelvan el resto de los problemas con su compañero” // “Work with your partner on the rest of the problems.”
8 minutes: partner work time
Monitor for students who:
- Draw and label each comparison.
- Identify and represent the unknown in their equation and in their diagram.
- Use “times as many” language to describe each comparison.
If students finish early, they can create their own situation and question, and then trade with their partner. The partner will write the equation, draw a diagram, and answer the question.

Student Task Statement

En cada situación:

Escribe una ecuación que represente la situación. Usa un símbolo para representar el número desconocido.
Dibuja un diagrama que muestre la comparación.
Responde la pregunta sobre la situación.

Lin leyó 7 libros. Diego leyó 8 veces el número de libros que Lin leyó.
1. Ecuación:
2. Diagrama:
3. ¿Cuántos libros leyó Diego?
Tyler tiene algunos libros. Clare tiene 72 libros, que es 12 veces el número de libros que Tyler tiene.
1. Ecuación:
2. Diagrama:
3. ¿Cuántos libros tiene Tyler?
Noah leyó 13 libros. Elena leyó 130 libros.
1. Ecuación:
2. Diagrama:
3. Completa la afirmación:
  
  _______________ leyó _____ veces el número de libros que _______________ leyó.

Activity Synthesis

“¿Qué información usaron en cada situación para saber cómo dibujar cada diagrama?” // “What information did you use in each situation to know how to draw each diagram?”
- The number of repeating rectangles in the greater quantity represents “times as many.”
- The row with one rectangle is the amount being multiplied.
- The row with multiple rectangles represents the greater quantity in the comparison.
“¿En qué se diferencia el último problema de los dos primeros?” // “How is the last problem different from the first two?” (The unknown value is how many “times as many.”)

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Lesson 4

Resolvamos problemas de comparación multiplicativa con números grandes

Warm-up

Observa y pregúntate: ¿Demasiadas veces más?

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Activity Synthesis

Activity 1

Un nuevo tipo de diagrama

Standards Alignment

4.OA.A.1

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Activity 2

¿Quién leyó más?

Standards Alignment

4.OA.A.2

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Lesson Synthesis

Have a correction or suggestion?

Standards Alignment

4.OA.A.2

Student Response

Advancing Student Thinking

Are You Ready for More?

Student Response

Advancing Student Thinking

Are You Ready for More?

4.OA.A.2