Lesson 3

This Number Talk encourages students to think about the relationship between addition and subtraction to mentally solve problems. This builds on the work in the previous lesson where students used the relationship between addition and subtraction to find unknown numbers in equations. The understanding elicited here will be helpful later in the lesson when students find the value to make an equation true.

• 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 strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿De qué forma pensar sobre sumas les ayudó a restar?” // “How did thinking about addition help you subtract?” (I thought about what number I could add to the 4 to make 10. Since I know 4 + 6 = 10 then I knew 10 – 4 = 6)
• If needed, use connecting cubes to represent students’ thinking.

In this activity, students learn stage 3 of the What’s Behind My Back center. In this new stage, called 20 cubes, students work with 20 cubes, organized into two towers of 10 cubes. One partner snaps the tower and puts one part behind their back and shows the other part to their partner. The other partner figures out how many cubes are behind their partner’s back. Students record an addition equation with a blank to represent the missing cubes. Students may write equations with the blank as the first or second addend. Ask students to explain what each number and blank in the equation represents in the context of the center activity (MP2).

• Groups of 2
• Give each group 20 connecting cubes and a recording sheet.
• “Vamos a jugar ‘Que hay a mis espaldas’, esta vez con 20 cubos” // “We are going to play What’s Behind My Back, this time with 20 cubes.”
• “¿Cómo descubrieron cuántos cubos encajables había detrás de la espalda de su pareja la última vez?” // “How did you figure out how many connecting cubes were behind your partner’s back last time?” (I thought about an addition expression that would make 10. I subtracted what they showed me from 10.)
• “Juguemos una ronda con 20” // “Let’s play a round with 20.”
• Show students 2 towers of 10 cubes. Put the towers behind your back. Break off and display 8 of the cubes.
• “Esta vez, cuando jueguen, antes de descifrar cuántos cubos hay detrás de la espalda de su compañero, anoten una ecuación de suma con un espacio en blanco para representar los cubos desconocidos. ¿Qué ecuación debemos anotar?” // “This time when you play, you are going to record an addition equation with a blank to represent the missing cubes, before you figure out how many are behind your partner’s back. What equation should we record?” (\(8+\underline{\hspace{.5 cm}}=20\))
• 30 seconds: quiet think time
• Share responses.
• “¿Cuántos cubos hay a mis espaldas? ¿Cómo lo saben?” // “How many cubes are behind my back? How do you know?” (12 because 2 more makes 10 and then here’s another tower of 10.)
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• “Jueguen con su compañero. No olviden anotar una ecuación en cada ronda” // “Play with your partner. Don’t forget to record an equation each round.”

• 10 minutes: partner work time

• Display 9 cubes.
• “¿Cuál es una ecuación de suma que yo puedo escribir para representar el número de cubos que ustedes conocen y el número de cubos que tienen que descubrir?” // “What’s an addition equation I can write to represent the number of cubes you know and the number of cubes you need to figure out?” (9 + _____ = 20)
• “Cuéntenle a su compañero cómo pueden saber cuántos cubos faltan” // “Tell your partner how you can figure out how many cubes are missing.”
• Monitor for students who talk about making a 10 and knowing there is one more 10.
• Share responses.

The purpose of this activity is for students to find the value that makes an addition or subtraction equation true, with totals of 20. Students may use whatever method makes sense to them. In the launch, students work with a new partner and fill in the unknown addend in the equations on their recording sheet from Activity 1.

• Groups of 2: different than the previous activity
• Give groups access to connecting cubes.
• “Van a encontrar el número que hace que cada ecuación sea verdadera. Intercambien hojas de registro con alguien con quien no hayan jugado ‘Qué hay a mis espaldas’. Escriban el número que hace que cada ecuación sea verdadera. Prepárense para compartir con su pareja cómo encontraron cada número” // “You are going to find the number that makes each equation true. Switch recording sheets with someone who you didn’t play What’s Behind My Back with. Fill in the number that makes each equation true. Be prepared to share with your partner how you found each number.”
• 3 minutes: independent work time
• “Compartan su trabajo con su compañero. Escojan una ecuación y explíquenle cómo encontraron el número que la hace verdadera” // “Share your work with your partner. Choose 1 equation and explain to them how you found the  number that makes it true.”
• 3 minutes: partner discussion

• “Trabajen en sus libros para encontrar el número que hace que cada ecuación sea verdadera” // “Work in your book to find the number that makes each equation true.”
• 5 minutes: independent work time
• Monitor for students who look for ways to make 10.

• Invite selected students to show their thinking for \(\underline{\hspace{1 cm}}+3=20\) and \(20-\underline{\hspace{1 cm}}=18\).
• “Para encontrar la respuesta, ¿cómo les ayudó pensar sobre decenas?” // “How did thinking about a ten help them find their answer?” (They knew 20 is 2 tens so they used 1 of the tens to make the problems easier.)