This Warm-up prompts students to carefully analyze and compare features of equations. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of different equations.
During the Synthesis, students build on their work in the unit with addend-unknown problems to describe the relationship between a subtraction equation and an addition equation with an unknown addend. Students will continue to make sense of and begin to produce equations in the next section.
Launch
Groups of 2
Display the 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 cómo 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
Display Equations A and D.
“¿En qué se parecen estas ecuaciones? ¿En qué son diferentes?” // “What is the same about these equations? What is different?” (They both have 3 and 5. 5 is the total in both, and 3 is one of the parts. The unknown is 2 in both equations. One equation is addition and has an unknown addend, and the other is a subtraction equation with an unknown difference.)
Activity 1
Standards Alignment
Building On
Addressing
1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1.
The purpose of this activity is for students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (MP1). Students are asked to tell a story about an image in order to generate observations that lead them to ask mathematical questions about the context. This prepares students to solve story problems about the given context in the second activity.
MLR8 Discussion Supports. Display the following sentence frames to support partner discussion:
“La imagen muestra...” // "The picture shows. . . ." and “Puedo contar...” // “I can count. . . .”, and “Puedo preguntar...” // “I can ask. . . .” Advances: Speaking, Conversing
Launch
Groups of 2
“Usen números para describir la imagen” // “Use numbers to describe the image.”
1 minute: quiet think time
2 minutes: partner discussion
Share responses.
Activity
“Piensen en las matemáticas que hay en esta imagen. ¿Qué preguntas matemáticas se pueden hacer acerca de esta imagen?” // “Think about the math in this image. What math questions could be asked about this picture?”
3 minutes: independent work time
2 minutes: partner discussion
Monitor for students who ask questions about how many altogether or how many more or fewer.
¿Qué preguntas matemáticas puedes hacer acerca de esta imagen?
Student Response
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Advancing Student Thinking
Activity Synthesis
Invite several students to share one question with the class.
Record responses.
If needed, ask, “¿Se puede responder esta pregunta con la imagen? ¿Cómo lo saben?” // “Can this question be answered by the image? How do you know?”
“¿En qué se parecen estas preguntas? ¿En qué son diferentes?” // “What do these questions have in common? How are they different?” (Some of them use the same numbers. Some ask to find the total and others ask to find the difference.)
Activity 2
Standards Alignment
Building On
Addressing
1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1.
The purpose of this activity is for students to solve a variety of story problems that could be represented as an equation with an unknown addend. Students solve Put Together/Take Apart, Addend Unknown; Compare, Difference Unknown; and Add To, Change Unknown problems. Students may solve in any way they want and should be encouraged to explain how their representations and solution methods match the actions or quantities in each story (MP2). Listen for the ways students explain how their representations, including any expressions or equations they may use, represent the story.
Look for ways students' understanding of story problems and the types of representations they use have developed over the course of the unit. In particular, look for students who show they may be thinking flexibly about addition or subtraction when solving problems that involve an unknown addend, including Add To, Change Unknown problems. This idea is explored in the Lesson Synthesis, although all students are not expected to use this strategy at this point in the course.
Action and Expression: Internalize Executive Functions. Invite students to plan a method, including the tools they will use, for representing and solving the story problems. If time allows, invite students to share their plan with a partner before they begin. Supports accessibility for: Organization, Conceptual Processing
Launch
Groups of 2
Give students access to connecting cubes, two-color counters, or 2 types of pattern blocks.
Activity
“Van a resolver problemas relacionados con los del calentamiento. Las preguntas pueden ser parecidas a algunas que ya hicieron. Muestren cómo pensaron. Usen dibujos, números o palabras. Prepárense para compartir con su compañero cómo pensaron” // “You will solve problems about the setting from the Warm-up. The questions may be like some of the questions you asked. Show your thinking using drawings, numbers, or words. Be ready to share your thinking with your partner.”
As needed, read each problem to students before giving independent work time and time for partner discussion.
6 minutes: independent work time
4 minutes: partner discussion
Monitor for students who use counting on or other addition strategies and others who count back or use other subtraction strategies for the first two problems.
Priya tiene 10 fichas geométricas.
7 son triángulos.
El resto son cuadrados.
¿Cuántas fichas geométricas son cuadrados?
Muestra cómo pensaste. Usa dibujos, números o palabras.
Elena tiene 4 fichas geométricas.
Tyler tiene 6 fichas geométricas.
¿Cuántas fichas geométricas menos tiene Elena que Tyler?
Muestra cómo pensaste. Usa dibujos, números o palabras.
3 estudiantes trabajan en una mesa.
Luego, algunos estudiantes más se unen.
Ahora hay 8 estudiantes en la mesa.
¿Cuántos estudiantes se unieron al grupo?
Muestra cómo pensaste. Usa dibujos, números o palabras.
Student Response
Activity Synthesis
Invite previously selected students to share for the first problem.
Record student methods and annotate their thinking with equations, as needed.
“¿En qué se parecen estas estrategias? ¿En qué son diferentes?” // “How are these strategies the same? How are they different?” (They both show thinking about the total and one of the parts. They both show a way to find the other part. One strategy shows thinking about counting on. It’s like finding an unknown addend. The other shows taking away. It’s like thinking about subtraction.)
Repeat with the second problem.
“En qué se parecen estos problemas-historia? ¿En qué son diferentes?” // “How are these story problems the same? How are they different?” (You can solve both of them by thinking about how much you need to count on or add. One is about a total and parts, the other is about comparing.)
The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 10. Students choose from previously introduced stages of these centers:
Capture Squares
Shake and Spill
What’s Behind My Back?
Launch
Groups of 2
“Ahora van a escoger un centro de los que ya conocemos” // “Now you are going to choose from centers we have already learned.”
Display the center choices in the student book.
“Piensen qué les gustaría hacer” // “Think about what you would like to do.”
30 seconds: quiet think time
Activity
Invite students to work at the center of their choice.
10 minutes: center work time
Escoge un centro.
Captura cuadrados
Revuelve y saca
¿Qué hay a mis espaldas?
Student Response
None
Advancing Student Thinking
Activity Synthesis
“Digan una cosa que hayan aprendido o en la que hayan mejorado al trabajar en las actividades que escogieron” // “What is one thing you learned or got better at by working on the activities you chose?”
Lesson Synthesis
Display and read this problem from the second activity:
3 students work at a table. Then some more students join.
Now there are 8 students at the table.
How many students join the group?
“Cuéntenle a su compañero lo que ocurrió en esta historia” // “Tell your partner what happened in this story.”
Monitor for students who emphasize the actions to share.
Display:
“¿Esta ecuación corresponde a lo que ocurre en la historia? ¿Por qué sí o por qué no?” // “Does this equation match what happens in the story? Why or why not?” (No. The story is about some students joining, we just don’t know how many. Addition would match the story better.)
Display:
“Escuché a algunas personas decir que la suma correspondería mejor a la historia porque algunos estudiantes se unieron, solo que no sabemos cuántos” // “I heard some people say that addition would better match the story because some students joined, we just didn’t know how many.”
“¿Podemos usar para averiguar qué número podría hacer que esta ecuación fuera verdadera? ¿Por qué?” // “Can we use to find what number would make this equation true? Why?” (We can because subtraction is like finding an unknown addend.)
“Al resolver diferentes tipos de problemas-historia, aprendimos que restar es como encontrar el valor de un sumando desconocido. Si tenemos que encontrar un sumando desconocido, podemos restar. Si necesitamos restar, podemos pensar en cuánto sumarle al número más pequeño” // “We’ve learned from solving different kinds of story problems that subtraction is like finding the value of an unknown addend. If we have to find an unknown addend, we can subtract. If we need to subtract, we could think about how much to add to the smaller number.”
“Incluso si no corresponde a las acciones, aún podemos usarla para resolver el problema porque podemos usar la resta para encontrar un sumando desconocido” // “Even though doesn’t match the actions, we can still use it to solve the problem because we can use subtraction to find an unknown addend.”
Student Section Summary
Resolvimos problemas tipo “¿Hay suficientes?”. Decidimos cuáles cantidades eran “más” o “menos”.
Resolvimos problemas-historia sobre “¿Cuántos más?” y “¿Cuántos menos?”.
Andre tiene 4 cubos.
Clare tiene 10 cubos.
¿Cuántos cubos menos tiene Andre que Clare?
Aprendimos que la diferencia entre una cantidad más grande y una cantidad más pequeña es la respuesta a “¿Cuántos más?” o “¿Cuántos menos?”.
Andre tiene la cantidad más pequeña.
Clare tiene la cantidad más grande.
La diferencia es 6 cubos.
Aprendimos que estos problemas se pueden resolver con una suma o una resta.
o
Standards Alignment
Building On
Addressing
Building Toward
1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., ); decomposing a number leading to a ten (e.g., ); using the relationship between addition and subtraction (e.g., knowing that , one knows ); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent ).
