The purpose of this Number Talk is to elicit strategies and understandings students have about the relationship between addition and subtraction and combinations of numbers that make 10. The activity also provides an opportunity to informally assess how students make sense of the equal sign and what it means for an equation to be true. These understandings help students develop fluency and will be helpful later in this lesson when students represent solutions to Put Together/Take Apart, Both Addends unknown problems with equations.
Launch
Display one expression.
“Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Encuentra mentalmente el valor desconocido.
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿En qué se parecen estas ecuaciones? ¿En qué son diferentes?” // “How are these equations the same? How are they different?” (They all have 10 or expressions that are the same as 10. The box, or the unknown, is in different places. Sometimes 10 or the total is after the equal sign and sometimes it’s before.)
“¿De que otras maneras pueden completar la última ecuación para hacer que sea verdadera?” // “What are other ways you could complete the last equation to make it true?” (0 and 10, 10 and 0, 1 and 9, 9 and 1, 2 and 8, 8 and 2, 3 and 7, 7 and 3, 6 and 4, 5 and 5)
Activity 1
Standards Alignment
Building On
Addressing
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 ).
The purpose of this activity is for students to revisit Stage 3 of the Shake and Spill center, introduced in IM Kindergarten. In this stage, students see a quantity broken into two parts in different ways. Earlier in the unit, students used expressions to represent their solution. This time, all students are encouraged to write equations to represent each decomposition. In addition to opportunities to look for the ways student strategies have changed over time, the Activity Synthesis provides an opportunity for students to continue to make sense of the meaning of the equal sign.
During this activity, the teacher collects and displays different equations that students write for the first round. This includes equations where the total is before the equal sign, such as . During the Synthesis, students are encouraged to think about how an equation with the total before the equal sign relates back to the context of playing the game (MP2).
MLR2 Collect and Display. Collect the language students use to describe the equations they create during the Activity and Synthesis with a focus on how they describe the equal sign and the total. Display words and phrases such as: “signo igual”, “primero”, “último”, “izquierda”, “derecha”, “lo mismo que”, “sumando”, “total” y “ecuación” // “equal sign,” “first,” “last,” “left,” “right,” “same as,” “addend,” “total,” and “equation.” During the Synthesis, invite students to suggest ways to update the display by asking, “¿Qué otras palabras o frases deberíamos incluir?” // “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed. Advances: Conversing, Reading.
Launch
Groups of 2
Give each group a cup, 10 two-color counters, 2 recording sheets, and access to red and yellow crayons.
“Hoy vamos a retomar un juego llamado ‘Revuelve y saca’ que jugaron en una lección anterior. Juguemos una ronda juntos” // "Today we will revisit a game you played in an earlier lesson called Shake and Spill. Let's play one round together."
Display two-color counters and the cup.
“Tengo algunas fichas de dos colores. Contémoslas juntos” // “I have some two-color counters. Let’s count them together.”
Place 6 counters in the cup as you count aloud.
“Ahora sabemos cuántas fichas tenemos. Revolvámoslas” // “Now we know how many counters we have. Let's shake them up."
Demonstrate shaking and spilling the counters.
“¿Cuántas fichas rojas hay? ¿Cuántas fichas amarillas hay?” // "How many red counters are there? How many yellow counters are there?”
30 seconds: quiet think time
Demonstrate drawing a quick picture on the recording sheet to match the counters.
“La última vez que jugamos usamos expresiones para representar nuestras fichas. Ahora vamos a usar ecuaciones” // “The last time we played we used expressions to represent our counters. Today we will use equations.”
“¿Qué ecuación podemos escribir que correspondan a las fichas?” // “What equation can we write to match the counters?” (4 + 2 = 6, 6 = 4 + 2, 2 + 4 = 6, 6 = 2 + 4)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
If needed, play another round.
Activity
“Jueguen con su compañero. Usen 10 fichas en las primeras tres rondas. En las demás rondas, pueden escoger el número de fichas” // “Play the game with your partner. For the first three rounds, use 10 counters. For the rest of the rounds, you may choose the number of counters.”
6 minutes: partner work time
If needed, ask, “¿Pueden escribir otra ecuación que muestre esta ronda?” // “Is there another equation you can write to show this round?”
Monitor for and collect 5–6 combinations and equations for the rounds with 10 counters.
Activity Synthesis
Display collected combinations and equations.
“¿Qué observan sobre las ecuaciones que recopilé durante la primera ronda?” // “What do you notice about the equations I collected during the first round?” (There are different numbers in the equations. They all equal ten. Sometimes the total is before the equation and sometimes it is after.)
“¿Qué significa la ecuación ?” // “What does the equation mean?” (The 10 counter total is the same amount as 7 red counters and 3 yellow counters or 7 yellow and 3 red.)
Highlight student responses to emphasize:
The equal sign means “la misma cantidad que” // “the same amount as” or “igual a” // “equals.”
The addition expression or the total could be on either side or the equal sign.
Activity 2
Standards Alignment
Building On
Addressing
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 ).
The purpose of this activity is for students to revisit Stage 4 of the Shake and Spill center. Students know the total number of counters and the number of red counters and have to determine the number of yellow counters. Earlier in the unit, students recorded an expression for each round. Now students should complete an equation by adding the equal sign and the total. They may do this before or after the lines given on the recording sheet. Students may also record their equation before finding the unknown using a box to represent the unknown, or they may record the equation after they find the unknown.
During the activity, the teacher collects 4–5 student combinations of 10 to display during the Synthesis. It is important to display some equations with the total before the equal sign. In the Synthesis, students have the opportunity to share strategies they used that are related to using known combinations of 10. They also relate the equations to the Shake and Spill game by boxing the part of the equation that says how many yellow counters are under the cup (MP2).
Launch
Groups of 2
Give each group a cup, 10 two-color counters, recording sheets, and access to 10-frames.
“Hoy vamos a jugar de nuevo ‘Revuelve y saca: Cubre’. Esta vez vamos a escribir ecuaciones. Juguemos una ronda juntos. Necesito 10 fichas. Contemos juntos mientras pongo las fichas en el vaso” // "We are going to play Shake and Spill—Cover Up again today. This time, we will write equations. Let's play one round together. I need 10 counters. Let's count together as I put the counters in the cup."
Count out 10 counters.
“Voy a revolver y sacar las fichas. Luego, voy a cubrir las fichas amarillas con mi vaso antes de que mi compañero las vea. Cierren los ojos. Déjenlos cerrados hasta que yo les diga” // “I’m going to shake and spill the counters. Then I am going to cover up the yellow counters with my cup before my partner sees them. Close your eyes. Keep them closed until I tell you."
Shake the counters in the cup, spill the counters, and cover the yellow counters with the cup.
“Abran los ojos. ¿Cuántas fichas amarillas hay debajo del vaso? ¿Cómo lo saben?” // "Open your eyes. How many yellow counters are under the cup? How do you know?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“Pueden escribir una ecuación antes de decir cuántas hay debajo del vaso” // “You can write an equation before you say how many are under the cup.”
Write an equation that represents the total (10) and the red counters with a box for the unknown. For example, if there were 6 red visible, display:
“O pueden escribir una ecuación después de decir cuántas hay debajo del vaso” // “Or you could write an equation after you say how many are under the cup.”
Write another addition equation to match the round. For example, .
Activity
“Jueguen con su compañero. Usen 10 fichas en las primeras tres rondas. En las demás rondas, pueden escoger el número de fichas” // “Play the game with your partner. For the first three rounds, use 10 counters. For the rest of the rounds, you may choose the number of counters.”
6 minutes: partner work time
If needed, ask, “¿Pueden escribir otra ecuación que muestre esta ronda?” // “Is there another equation you can write to show this round?”
Monitor for and collect 5–6 equations that include a symbol for the unknown for the rounds with 10 counters.
None
Student Response
None
Advancing Student Thinking
Activity Synthesis
“¿En qué es diferente este juego del que jugamos primero?” // “How is this game different from the first game we played?” (In the first game, we knew the total, but the number of yellow and red counters changed each time. We could see all the counters and count them to find how many. In this game, we could only see the red counters and had to figure out the yellow.)
Display 4–5 equations.
Invite students to share how they determined the unknown addend.
Consider asking: “¿Cómo usaron las ecuaciones que escribieron en el primer juego como ayuda para encontrar el sumando desconocido en este juego?” // "How did you use the equations you wrote in the first game to help you find the unknown addend in this game?"
Activity 3
Standards Alignment
Building On
Addressing
1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations , , .
Number Puzzles Addition and Subtraction Stage 1 Gameboard, Spanish
Number Puzzles Digit Cards
Activity Narrative
The purpose of this activity is for students to learn a new center called Number Puzzles. Students build fluency for addition and subtraction within 10. They use number cards to fill in addition and subtraction equations up to 10 on a gameboard. The unknown values are in different places in the equations and each digit (0–9) may only be used once in a puzzle. Puzzles with fewer than 10 spaces will have leftover cards.
Action and Expression: Internalize Executive Functions. Invite students to plan a strategy, including the tools they will use, for placing the number cards to make each equation true. If time allows, invite students to share their plan with a partner before they begin. Supports accessibility for: Organization, Conceptual Processing, Language
Launch
Groups of 2
Give each group a set of digits (0–9) from the blackline master and a set of gameboards.
“Vamos a conocer un centro nuevo llamado ‘Acertijos numéricos’” // “We are going to learn a new center called Number Puzzles.”
Display a gameboard.
“Necesito poner mis tarjetas de números de forma que cada ecuación sea verdadera. Puedo usar cada tarjeta solo una vez” // “I need to place my number cards so that every equation is true. I can only use each number card once.”
“Intentemos unas juntos. Miren la primera ecuación. Para hacer que la ecuación sea verdadera ¿qué tarjetas de números podría poner en el tablero?” // “Let’s try some together. Look at the first equation. What number cards could I put on the board to make the equation true?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Repeat 1–2 more times, as needed.
Activity
“Con su compañero, usen sus tarjetas de números para jugar. Completen un acertijo antes de pasar al siguiente. En algunos acertijos van a tener que usar todas las tarjetas de números y en otros sobrarán algunas. Completen todos los acertijos que puedan” // “Work together to use your number cards to play the game. Complete a puzzle before moving to the next one. Some puzzles will use all of the number cards, and some puzzles will have cards leftover. Finish as many puzzles as you can.”
10 minutes: partner work time
Monitor for students who clearly explain how they know their equations are true.
None
Student Response
None
Advancing Student Thinking
Activity Synthesis
“¿Cómo pudieron asegurarse de que pusieron cada número en el lugar correcto?” // "How did you make sure you were putting each number in the right place?"
“¿Cómo saben que sus ecuaciones son verdaderas?” // “How do you know your equations are true?”
Lesson Synthesis
Display: and
“Hoy escribimos ecuaciones que correspondían a las fichas rojas y las amarillas del juego ‘Revuelve y saca’. En una ronda, un estudiante escribió estas ecuaciones. ¿Cómo pueden estas ecuaciones representar el juego? ¿En qué se parecen las ecuaciones? ¿En qué son diferentes?” // “Today we wrote equations to match the red and yellow counters in the game Shake and Spill. For one round, a student wrote these equations. How could these equations represent the game? How are they the same? How are they different?” (They are the same because they both show that equals 10. It means the same thing. There are either 3 red and 7 yellow or 7 red and 3 yellow. They are different because the total is before the equal sign in one equation and after the equal sign in the other equation.)
“Hoy también vimos que pueden usar los hechos de suma que se saben para averiguar un sumando desconocido” // “We also saw today that you can use addition facts that you know to determine an unknown addend.”
Display:
“¿Qué número hace que esta ecuación sea verdadera? ¿Cómo lo saben?” // “What number makes this equation true? How do you know?”
Student Section Summary
Aprendimos más sobre ecuaciones que muestran un total desconocido o un sumando desconocido.
Relacionamos ecuaciones con problemas-historia.
También escribimos ecuaciones que correspondían a problemas-historia.
Lin tiene 5 fichas de bingo en su cartón.
También tiene algunas fichas sobre la mesa.
En total tiene 9 fichas de bingo.
¿Cuántas fichas tiene Lin sobre la mesa?
y
Pensamos en cómo se relacionan la suma y la resta.
Usamos ambas para resolver un problema-historia.
9 estudiantes juegan bingo.
3 estudiantes usan fichas azules para cubrir sus cartones.
Los otros estudiantes usan fichas amarillas.
¿Cuántos estudiantes usan fichas amarillas?
Clare escribe .
Jada escribe .
Standards Alignment
Building On
Addressing
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 ).
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? , , , .
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations , , .
If students continue to record expressions rather than equations or only write equations with the total on the same side of the equal sign, consider asking:
“¿Qué ecuación escribiste en esta ronda?” // “What equation did you write for this round?”
“¿De qué otra manera podrías haber escrito tu ecuación? ¿El total siempre tiene que ir antes/después del signo igual?” // “What is another way you could have written your equation? Does the total always have to go before/after the equal sign?”
1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? , , , .
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? , , , .
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations , , .
