The purpose of this Warm-up is to elicit different strategies for counting objects arranged in groups of 2, which will be useful when students multiply by 2 in a later activity. While students may notice and wonder many things about these images, flexible ways of seeing the groups and strategies for finding the total number of objects are the important discussion points.
When students see the socks are grouped by 2 and use that to find the total, they are looking for and making use of structure (MP7).
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
¿Qué observas? ¿Qué te preguntas?
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Cómo se relaciona este problema con lo que sabemos sobre la multiplicación?” // “How does this problem relate to what we know about multiplication?” (There are equal groups of socks, we can say there are 6 groups of 2.)
Activity 1
Standards Alignment
Building On
Addressing
3.OA.A
Represent and solve problems involving multiplication and division.
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
The purpose of this activity is for students to build on the work they have done with scaled picture graphs to use the tape diagram as a new representation of multiplication. The scale of the picture graph will be used to help students think about a category of the graph as a situation involving equal groups.
To add movement to this activity, students could find someone in the class who represented a different category than they did or represented the same category in a different way. When they find a person, they can describe what is the same and what is different about their representations.
MLR8 Discussion Supports. Synthesis: When students compare the diagram and the scaled picture graph, display sentence frames to support whole-class discussion: “_____ y _____ se parecen porque . . .” // “_____ and _____ are the same because . . ..” “_____ y _____ son diferentes porque . . .” // “_____ and _____ are different because . . . .” Advances: Speaking, Representing
Launch
Groups of 2
Display the picture graph and tape diagram.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (The picture graph key says each square represents 2 signs. The diagram shows 3 groups of 2. I wonder whether they represent the same thing.)
1 minute: quiet think time
1 minute: partner discussion time
“¿Cómo muestra el diagrama las señales de límite de velocidad que Elena vio camino a casa?” // “How does the diagram show the speed limit signs that Elena saw on the way home?”
Share responses.
Activity
“Ahora, individualmente, representen los datos de otra categoría de la gráfica con su propio dibujo o diagrama” // “Now independently represent the data from another category in the graph with your own drawing or diagram.”
1–2 minutes: independent work time
“Compartan con su compañero la forma en la que representaron los datos en su dibujo o diagrama” // “Share how you represented the data in your drawing or diagram with your partner.”
2–3 minutes: partner discussion
Monitor for students who create a tape diagram to represent one of the other categories to use during the Activity Synthesis.
La gráfica muestra el número de señales que Elena vio durante su regreso a casa.
¿Cómo representa el diagrama las señales de límite de velocidad que Elena vio?
Representa los datos de otra categoría de la gráfica con tu propio dibujo o diagrama.
Student Response
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Advancing Student Thinking
Activity Synthesis
Have students share different ways they represented a category in the graph.
Display a student created tape diagram or make a quick sketch of one to represent the street signs Elena saw on the way home.
“¿Cuál categoría está representada por este diagrama de cinta? ¿Cómo lo saben?” // “Which category does this tape diagram represent? How do you know?”
“¿En qué se parece el diagrama a la gráfica de dibujos con escala?” // “How is the diagram the same as the scaled picture graph?” (Each picture and each part of the tape diagram represents 2 signs.)
“¿En qué se diferencian el diagrama y la gráfica de dibujos con escala?” // “How is the diagram different than the scaled picture graph?” (In the graph, you have to read the key to know that each picture shows two signs. In the diagram, each part is labeled with a 2.)
Activity 2
Standards Alignment
Building On
Addressing
3.OA.A
Represent and solve problems involving multiplication and division.
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
The purpose of this activity is for students to connect situations involving equal groups to drawings and tape diagrams. This sorting task gives students opportunities to analyze situations and diagrams closely and make connections (MP2, MP7). Students explain why two cards match and have opportunities to critique and question their peers' reasoning (MP3). When explaining, students have opportunities to revise their language to make their explanations more precise and clear (MP6). After sorting and describing their sort, students notice that all of the representations reinforce the meaning of multiplication as a way to express equal groups.
Students will spend all of the next lesson working with multiplication expressions. Keep the equal groups cards for the next lesson.
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches. Supports accessibility for: Attention, Organization
Launch
Groups of 2
Give each group a set of cards
Activity
“Estas tarjetas tienen situaciones, dibujos o diagramas. Formen grupos de tarjetas que correspondan entre sí. Prepárense para explicar su razonamiento” // “This set of cards includes situations, drawings, and diagrams. Find the cards that match. Work with your partner to explain your reasoning.”
5 minutes: partner work time
Monitor for students who:
Connect the ways the features of the drawings or diagrams represent the story.
Connect the ways each representation shows the same number of equal groups and the same size of each group.
Invite 1–2 previously selected students to share the matches they made and how they know those cards go together.
Listen for the language students use to describe their match. If students only reference the numbers that match, consider asking:
“¿A qué se refieren cuando dicen ______?” // “What do you mean when you say _____?”
“¿Cómo pueden usar las palabras ‘grupos iguales’ en su explicación?” // “How could you use the words ‘equal groups’ to explain?”
“Ahora van a hacer un dibujo o diagrama para representar dos situaciones diferentes” // “Now you’re going to create a drawing or diagram to represent two different situations.”
3–5 minutes: independent work time
Monitor for the students who draw equal groups and students who draw a tape diagram.
Tu profesor te dará tarjetas que muestran dibujos, situaciones o diagramas.
Forma grupos de tarjetas que correspondan entre sí. Prepárate para explicar tu razonamiento.
Haz un dibujo o diagrama para cada situación.
Hay 4 bolsas. En cada bolsa hay 2 fresas.
Hay 4 manos. En cada mano hay 5 dedos.
Activity Synthesis
For each situation in the last 2 problems, display 2–3 student representations: at least one drawing of equal groups and one tape diagram. Leave them displayed.
“¿Qué tienen en común todas estas representaciones?” // “What do all these representations have in common?” (They all show equal groups. They all have groups. Each group has the same amount.)
“¿Dónde están las 4 bolsas y las 2 fresas en cada dibujo o diagrama?” // “Where are the 4 bags and 2 strawberries in each drawing or diagram?”
“¿Dónde están las 4 manos y los 5 dedos en cada dibujo o diagrama?” // “Where are the 4 hands and 5 fingers in each drawing or diagram?”
Lesson Synthesis
Display the tape diagram.
“La lección de hoy fue sobre multiplicación. ¿Cómo se puede mostrar una multiplicación con un diagrama?” // “Today’s lesson was all about multiplication. How can a diagram show multiplication?” (The number of parts in the diagram can show the number of groups, and the same number written in each part shows how many in each group. This diagram has 4 parts, so there are 4 groups, and the 5 written in each part shows there are 5 in each group. The diagram shows 4 groups of 5.)
Display:
4 groups and 5 in each group
“Recuerden que una expresión tiene al menos 2 números y al menos una operación matemática. Una expresión de multiplicación representa el número de grupos y el número de cosas que hay en cada grupo, en cierta situación. Por ejemplo, la expresión de multiplicación representaría este diagrama porque tenemos 4 grupos y 5 en cada grupo” // “You may remember that an expression has at least 2 numbers and at least one math operation. A multiplication expression is how we represent the number of groups and the number in each group in a situation. For example, the multiplication expression would represent this diagram because we have 4 groups and 5 in each group.” Point to the 4 and 5 in the diagram and the expression as you explain.
“El símbolo que está en la mitad de la expresión es el símbolo de multiplicación. se lee: ‘4 grupos de 5’” // “The symbol in the middle of the expression is the multiplication symbol. can be read as ‘4 groups of 5.’”
Standards Alignment
Building On
Addressing
3.OA.A.1
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
If students create representations that do not match the number of groups or size of the groups in the situations, consider asking:
“¿Cómo representaste la situación?” // “How did you represent the situation?”
“¿Cómo podrías mostrar los grupos que hay en la situación? ¿Cómo podrías mostrar los objetos que hay en cada grupo?” // “How could you show the groups in the situation? How could you show the objects in each group?”
