Lesson 3

The purpose of this Number Talk is to encourage students to think about using known sums to create easier calculations and to rely on the properties of operations or the relationship between addition and subtraction to mentally solve problems. The methods elicited here will be helpful as students add and subtract within 20.

• 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

• Record answers and strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “Algunos de nosotros usamos \(7 + 8\) como ayuda para encontrar el valor de \(15 -7\). ¿Con qué otra expresión de resta nos ayuda \(7 + 8\)?” // “Some of us used \(7 + 8\) to help with \(15 -7\). What other subtraction expression does \(7 + 8\) help with?” (\(15 -8\). It’s like the other subtraction equation, you just have to find a different unknown addend.)

The purpose of this activity is for students to add and subtract within 20. Students are encouraged to find sums and differences in as many different ways as they can. They record their thinking and then do a gallery walk to look at their classmates’ work. Set-up for the gallery walk by putting all the posters for a specific expression together. The synthesis focuses on how decomposing a number to lead to a ten can be a helpful method when subtracting within 20 (MP7).
This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• Groups of 2
• Give each group tools for creating a visual display and access to connecting cubes in towers of 10 and singles.

MLR7 Compare and Connect

• Read the task statement.
• “Creen una presentación visual que muestre cómo pensaron en cada una de las expresiones. Incluyan detalles, como dibujos, números, palabras o ecuaciones, para ayudar a los demás a entender sus ideas” // “Create a visual display that shows your thinking about each expression. You may want to include details such as drawings, numbers, words, or equations to help others understand your thinking.”
• 7 minutes: partner work time
• “Ahora vamos a hacer un recorrido por el salón para que puedan ver el trabajo de sus compañeros. Busquen algunas formas en las que el trabajo de sus compañeros se parece y en las que es diferente al de ustedes” // “Now we will do a gallery walk so you can look at your classmates' work. Look for ways that their work is the same and different.”
• 7 minutes: gallery walk

• “¿En qué se parecen y en qué son diferentes las formas en las que ustedes y sus compañeros sumaron o restaron?” // “What is the same and what is different about how you and your classmates added or subtracted?” (Some of us wrote equations. Some of us made 10 for the addition and subtraction expressions.)
• Display \(13 - 6 = \boxed{\phantom{7}}\), \(13 - 3 - 3\), \(10 - 3 = 7\).
• “¿Cómo encontró este estudiante la diferencia entre 13 y 6?” // “How did this student find the difference between 13 and 6?” (They broke 6 into 3 and 3. They took 3 from 13 to get to 10 and then took the other 3 away.)
• “¿Por qué es útil buscar formas de obtener un 10 cuando hacemos restas?” // “Why is it helpful to look for ways to get to a 10 when subtracting?” (Once you are at 10 it is easy to subtract another number because we know our ten facts.)

The purpose of this activity is for students to practice adding and subtracting within 20. Students add to find the sum of two numbers, and either add or subtract to find the unknown addend when one addend and the sum are given.

• Groups of 3
• Give students number cards and access to connecting cubes in towers of 10 and singles.
• “Vamos a jugar un juego que se llama ‘Frente a frente’. Este juego se juega con tres estudiantes” // “We are going to play a game called Heads Up. This game is played with three students.”
• Demonstrate with two students. Ask each student to choose a card without looking at it and hold it up to their foreheads.
• “Cada uno de mis compañeros escogió una tarjeta. Mi tarea es encontrar la suma y decírsela a mi grupo. Después, cada uno de mis compañeros va a usar el número del otro jugador y la suma para encontrar el número que tiene en su frente. Luego, todos escribimos la ecuación que representa lo que hicimos” // “My partners have each chosen a card. My job is to find the sum and tell my group. Then, each of my partners use the other player’s number and the sum to determine what number is on their head. Then we all write the equation that represents what we did.”
• Demonstrate writing an equation to show how you found the sum of the two numbers.
• Ask students how they would find the number on each player's head and record the equations.
• “Después de cada ronda, intercambien roles y jueguen otra vez” // “After each round switch roles and play again.”

• 15 minutes: small-group work time

If students only write equations using one operation when it is their turn to find an unknown addend, (for example, they only write subtraction equations), consider asking:

• “¿Qué otra ecuación podrías usar para averiguar qué número está en tu frente?” // “What is another equation you could use to figure out what number is on your head?”
• “¿De qué forma podrías usar la resta (o la suma) para encontrar el número que está en tu frente?” // “What is a way you could use subtraction (or addition) to find the number that is on your head?”
• “¿De qué forma es más fácil descifrar el número que está en tu frente? ¿Por qué?” // “Which way is easier for you to think about figuring out the number on your head? Why?”

• “En una ronda de ‘Frente a frente’, la pareja de Diego tenía un 3 en su tarjeta. A Diego le dijeron que la suma de sus números era 12. ¿Qué ecuaciones puede usar Diego para descifrar qué número está en su tarjeta?” // “During one round of Heads Up, Diego’s partner had a 3 on their card. Diego was told that the sum of their numbers was 12. What equations can Diego use to figure out what number is on his card?” (\(12 - 3 = \underline{\hspace{1 cm}}\) or \(3 + \underline{\hspace{1 cm}} = 12\))
• “Expliquen cuál de estas ecuaciones usarían para encontrar el número desconocido” // “Explain which of these equations you would use to find the unknown number.” (I would use \(12 - 3\) because it is really easy to count back 3. I would choose \(3 + \underline{\hspace{1 cm}} = 12\) because I prefer adding. I would add 7 to get to 10 and then 2 more.)