Lesson 7

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. The images in the warm up are built for students to further explore the commutative property, to which they were introduced in a prior lesson. When students see that addends can be added in any order, they discern number patterns or structure (MP7).

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?” 
• Flash the image.
• 30 seconds: quiet think time

• Display the image. 
• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• If needed, “¿Qué ecuación representa esta imagen?” // “What equation represents this image?”
• Repeat for each image.

• “¿En qué se parecen las dos últimas imágenes? ¿En qué son diferentes?” // "How are the last two images the same? How are they different?" (Both images could be represented with \(8 + 2 = 10\) and \(2 + 8 =10\). They both show 8 and 2. One has 8 yellow and 2 red and one has 8 red and 2 yellow.)

Consider asking:

• “¿Alguien puede expresar con otras palabras la forma en la que _____ vio los puntos?” // “Who can restate the way _____ saw the dots in different words?”
• “¿Alguien vio los puntos de la misma forma, pero lo explicaría de otra manera?” // “Did anyone see the dots the same way but would explain it differently?”

The purpose of this activity is for students to revisit stage 3 of the Shake and Spill center, introduced in kindergarten. In this stage, students see a quantity broken into two parts in different ways. Student write equations to represent each decomposition. Students may write an equation in any way they choose, but the number of counters is presented first to encourage students to write the total before the equal sign. This activity builds toward a future lesson in which students solve Put Together/Take Apart, Addend Unknown story problems and write equations to match them. 

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 \(9 = 7 + 2\). 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).

• Each group of 2 needs 10 two-color counters and a cup (at least 8 oz).

• Groups of 2
• Give each group a cup, 10 two-color counters, and recording sheets.
• “Hoy vamos a retomar un juego que jugábamos en kínder, que se llama ‘Revuelve y saca’. Juguemos una ronda juntos para asegurarnos de que todos recuerdan cómo jugar” // "Today we will revisit a game you played in kindergarten called Shake and Spill. Let's play one round together to make sure everyone remembers how to play."
• 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 counters in the cup as you count aloud.
• “Voy a escribir 6 debajo de ‘número total de fichas’” // “I’m going to write 6 under Total Number of Counters."
• 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
• Record responses in the table.
• “¿Qué ecuación podemos escribir que corresponda 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.

• “Jueguen con su pareja. Para la primera ronda usen 9 fichas y escriban en su libro. Después de la primera ronda, escojan el número de fichas que quieren usar y escriban en la hoja de registro” // “Play the game with your partner. For the first game, you will use 9 counters and record in your book. After the first game, you may choose the number of counters that you want to use, and record on the separate recording sheet.”
• 10 minutes: partner work time
• If needed, ask “¿Hay otra ecuación que pueden escribir para mostrar esta ronda?” // “Is there another equation you can write to show this round?”
• Monitor for and collect 5–6 combinations and equations from round 1.

• Display collected combinations and equations.
• “¿Qué observan acerca de las ecuaciones que escribí 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 nine. Sometimes the total is before the equation and sometimes it is after.)
• “¿Qué significa la ecuación \(9 = 7 + 2\) ?” // “What does the equation \(9 = 7 + 2\) mean?” (The nine counter total is the same amount as seven red counters and two yellow counters or seven yellow and two red.)

The purpose of this activity is for students to solve Put Together/Take Apart, Both Addends Unknown story problems in the context of the game they played in the previous activity. Students find different ways the red and yellow counters could look, and write equations to match each way.

During the activity synthesis, record equations in which the total is before the equal sign as well as after. 

• Groups of 2
• Give students access to 10-frames and two-color counters.

• “Resolvamos problemas-historia sobre el juego que acabamos de jugar” // “Let’s solve some story problems about the game we just played.”
• 6 minutes: independent work time
• “Compartan sus ecuaciones con su compañero. Si su compañero tiene ecuaciones que ustedes no escribieron, agréguenlas a su lista” // “Share your equations with your partner. If your partner has equations you did not write, add them to your list.”
• 4 minutes: partner discussion
• Monitor for students who showed different combinations for the problem with 10 counters.

• Display 4–5 equations.
• “¿Cómo corresponde cada ecuación al problema?” // “How does each equation match the problem?”
• “¿Qué números de la ecuación deben tener un cuadro alrededor de ellos? ¿Por qué?” // “What numbers in the equation should have boxes around them? Why?“ (The number of red counters and the number of yellow counters. We already know the total, and have to find the combinations.)
• “Trabajen con su pareja para dibujar un cuadro alrededor de las respuestas de la pregunta del problema 1” // “Work with your partner to put a box around the answers to the question for problem 1.”