This Warm-up prompts students to carefully analyze and compare features of expressions and equations. When students compare the drawing, expression, and equations, they must use language precisely to describe how the representations are alike (MP6). Listen to the language students use to describe the different characteristics of the multiplication expression and equation. After the new terms “factor” and “product” are introduced in the Synthesis, connect students’ descriptions to those terms.
This is the first time students experience the Which Three Go Together? 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
Groups of 2
Display the image, expression, and equations.
“Escojan 3 que vayan juntas. Prepárense para compartir por qué van juntas.” // “Pick 3 that go together. Be ready to share why they go together.”
1 minute: quiet think time
Activity
“Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
¿Cuáles 3 van juntas?
A
B
C
D
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿En qué se diferencia C de las otras formas en las que hemos representado grupos iguales antes?” // “How is C different from the other ways we’ve represented equal groups before?” (It has an equal sign. It’s an equation.)
“C es una ecuación de multiplicación porque tiene un signo de multiplicación y el signo igual” // “C is a multiplication equation because it contains a multiplication symbol and the equal sign.”
“Hay palabras que nos ayudan a hablar sobre las diferentes partes de una ecuación de multiplicación. Los factores son los números que se multiplican. El producto es el resultado de multiplicar esos números. En la ecuación que vimos en C, los números 2 y 5 son los factores. El producto es 10. Recuerden esas palabras hoy mientras trabajamos con otras ecuaciones de multiplicación” // “There are words that help us talk about different parts of the multiplication equation. The factors are the numbers being multiplied. The product is the result of multiplying some numbers. In the equation in C, the numbers 2 and 5 are the factors. The product is 10. Keep these words in mind today as we work with other multiplication equations.”
Activity 1
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 .
The purpose of this activity is for students to match multiplication equations to situations and representations. Students make explicit connections between the factors and the number of groups and the number of objects in each group and between the product and the total number of objects. These connections are discussed explicitly during the Activity Synthesis. When students make explicit connections between multiplication situations and equations, they are reasoning abstractly and quantitatively (MP2).
Launch
Groups of 2 and 4
“Piensen cómo pueden emparejar cada ecuación con una situación o con un diagrama” // “Think about how you might match these equations to a situation or diagram.”
1 minute: quiet think time
Activity
“Por turnos, encuentren una situación o un diagrama que corresponda a cada ecuación. Explíquenle a su compañero cómo pensaron” // “Take turns finding a situation or diagram that matches each equation. Explain your reasoning to your partner.”
5–7 minutes: partner discussion
Monitor for students who make direct connections between each factor representing the number in each group or the number of groups and the product representing the total number of objects to share during the Activity Synthesis.
“Reúnanse con otro grupo para discutir sobre las parejas que armaron” // “Get together with another group to discuss the matches you made.”
3–5 minutes: small-group discussion
Encuentra una ecuación de la lista que represente cada situación, dibujo o diagrama. Escribe la ecuación. Prepárate para explicar tu razonamiento.
Andre tiene 5 pares de calcetines.
Hay 6 manos sobre la mesa. Cada mano tiene 5 dedos.
Hay 4 cajas de marcadores. En cada caja hay 10 marcadores.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿Identificaron parejas con las que no estuvieron de acuerdo? ¿Cómo llegaron a un acuerdo?” // “Were there any matches you disagreed on? How did you come to an agreement?” (We went back and recounted the dots together.)
For the , , and matches ask, “¿De qué forma la ecuación representa la situación (o el diagrama)?” // “How does the equation represent the situation (or diagram)?” (The 2 represents the 2 parts in the diagram. The 5 represents the 5 fingers on each hand. The 50 represents how many dots were in the groups altogether.)
Activity 2
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 .
The purpose of this activity is for students to write equations that match situations and diagrams. Students use what they learned in the last activity to use multiplication equations to represent situations and diagrams. In the Lesson Synthesis, use the words “factor” and “product” to help students connect the vocabulary to the concepts.
MLR7 Compare and Connect. Synthesis: Invite groups to prepare a visual display that shows their reasoning for one of the equations using details, such as different colors, arrows, labels, diagrams or drawings. Give students time to investigate each others’ work. Ask, “¿Qué detalles o qué lenguaje les ayudó a entender las presentaciones?”, “¿Alguien escribió la misma ecuación, pero la explicaría de otra manera?” // “Which details or language helped you understand the displays?” “Did anyone create the same equation, but would explain it differently?” Advances: Representing, Conversing
Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with or decide the order to complete the task. Supports accessibility for: Social-Emotional Functioning
Launch
Groups of 2
Activity
“Con su compañero, escriban una ecuación que represente cada situación, dibujo o diagrama” // “Work with your partner to write an equation that represents each situation, drawing, and diagram.”
5–7 minutes: partner work time
Monitor for students who can justify the equations they wrote by explaining the meaning of the factors and products in their equations.
Escribe una ecuación de multiplicación que represente cada situación, dibujo o diagrama. Prepárate para explicar tu razonamiento.
Un paquete tiene 6 pares de calcetines.
El cuaderno de Diego tiene 7 secciones. Cada sección tiene 10 páginas.
Elena tiene 4 bolsas de naranjas. En cada bolsa hay 5 naranjas.
Student Response
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Advancing Student Thinking
Activity Synthesis
For each problem, invite a student to share their equation. Consider asking:
“¿Cómo saben que esta ecuación tiene sentido para esta situación, dibujo o diagrama?” // “How does this equation make sense for this situation, drawing, or diagram?”
“¿Qué partes de la situación, del dibujo o del diagrama les ayudaron más mientras escribían la ecuación?” // “What parts of the situation, drawing, or diagram were especially helpful as you wrote the equation?”
Lesson Synthesis
Display:
Expression:
Equation:
“Hoy aprendimos sobre ecuaciones y sobre cómo podemos usarlas para representar una multiplicación. En esta ecuación, los factores son 3 y 5, y el producto es 15” // “Today we learned about equations and how we can use them to represent multiplication. In this equation, 3 and 5 are the factors and 15 is the product.”
“¿En qué se parecen las expresiones de multiplicación y las ecuaciones de multiplicación?” // “How are multiplication expressions and equations alike?” (They both use the multiplication symbol. They both have factors.)
“¿En qué son diferentes las expresiones de multiplicación y las ecuaciones de multiplicación?” // “How are multiplication expressions and equations different?” (Equations have an equal sign and a product. Multiplication equations have numbers on both sides of the equal sign.)
“¿En qué casos puede servir cada una?” // “When would each be helpful?” (Expressions are helpful when you want to describe a situation with equal groups. Equations are helpful if you are trying to find the total number of objects, or the product.)
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 .
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.
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.
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.