Lesson 11

The purpose of this warm-up is to elicit the idea that quantities can be compared, which will be useful when students compare connecting cube towers in order to make them have the same number of cubes, in a later activity. While students may notice and wonder many things about this image, comparing the quantity of cubes in each tower is the important discussion point. When English speaking students use the language “Jada has less cubes than Diego,” the teacher should revoice using the grammatically correct language “fewer” to support students with developing precise language (MP6). For Spanish speaking students, the single word “menos” is used for both “fewer” and “less” so the previous clarification does not apply.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.
• Revoice and emphasize “más que” // “more than” and “menos que” // “fewer than.”

• “Vamos a usar torres de cubos encajables y a pensar en cómo lograr que tengan el mismo número de cubos” // “We will use connecting cube towers and think about how to make them have the same number of cubes.”

The purpose of this activity is for students to find ways to make two quantities the same. Students may use connecting cubes to represent and solve the problems, if they choose. Students are more likely to add cubes to make the towers have an equal number of cubes, but some students may take cubes away. Students record how they solved each problem in a way that makes sense to them. During the synthesis, the teacher records equations that match the way students solved the problem to build on work in previous sections.

• Create a tower of 9 blue connecting cubes and a tower of 5 red connecting cubes.
• Each group of 2 needs 4 towers of 10 connecting cubes.

• Groups of 2
• Give each group four towers of ten connecting cubes.
• Display a tower of nine blue connecting cubes and a tower of five red connecting cubes, or the image in the student book.
• “Diego y Jada construyen torres de cubos. ¿Cómo pueden Diego y Jada hacer que sus torres tengan el mismo número de cubos? Recuerden: no compartan la respuesta con su pareja; compartan su método para resolver el problema” // “Diego and Jada are building connecting cube towers. How can Diego and Jada make their towers have the same number of cubes? Remember, you are not sharing the answer with your partner; you are sharing your method for solving the problem.” (They can add some cubes to the red tower or take some off the blue tower.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

• “Van a anotar cómo pensaron este problema y van a resolver dos problemas más sobre cómo hacer que las torres de Diego y Jada tengan el mismo número de cubos. Si quieren, pueden usar los cubos encajables como ayuda” // “You are going to record your thinking for this problem and solve two more problems about making Diego and Jada’s connecting cube towers have the same number of cubes. You may use the connecting cubes to help if you choose.”
• 5 minutes: independent work time
• Monitor for students who have clear representations for problem 3 showing: 
  • adding cubes to Diego’s tower
  • counting up the difference between Diego’s tower to Jada’s tower
  • taking cubes from Jada’s tower
  • counting back the difference between Jada’s tower to Diego’s tower

• Invite previously identified students to share.
• “¿Qué observan sobre todos estos métodos?” // “What do you notice about all these methods?” (They all got the same answer, even if they added cubes or took cubes off.)
• “¿Qué ecuación escribirían que corresponda a este problema-historia? ¿Cómo muestra su ecuación la forma en la que resolvieron el problema-historia?” // “What equation would you write to match the story problem? How does your equation show how you solved the story problem?” (\(3 + 7 = 10\), because I added 7 cubes onto Diego’s tower to make them the same. \(10 - 3 = 7\), because I broke off from Jada’s tower and counted what I broke off.)

The purpose of this activity is for students to solve Compare, Difference Unknown story problems in the context of connecting cube towers. Students solve comparison problems with given constraints that encourage students to add or break apart cubes to make towers with the same number of cubes. As students explain their thinking during the synthesis, record both addition and subtraction equations. When students answer the question, "How do you know?" they are beginning to explain their reasoning and construct viable arguments (MP3).

• Gather 1 red tower of 8 connecting cubes, 1 yellow tower of 3 connecting cubes, and a handful of yellow cubes.
• Each group of 2 needs 4 towers of 10 connecting cubes.

• Groups of 2 
• Give each group four towers of ten connecting cubes.
• Display one red tower of eight connecting cubes, one yellow tower of three connecting cubes, and the handful of yellow connecting cubes.
• “Tengo dos torres y debo hacer que tengan el mismo número de cubos, pero solo tengo estos cubos amarillos. ¿Cómo puedo hacerlo?” // “I have two towers and I need to make them the same number of cubes. But I only have these yellow cubes. How can I make them the same?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Lin trabaja para lograr que el número de cubos de cada torre sea el mismo. Cada problema les dirá con qué cubos cuenta Lin para trabajar. Anoten cómo pensaron con cada torre" // “Lin is working to make the number of cubes in each of her towers the same. Each problem will tell you what cubes she has to work with. Record your thinking for each tower.”
• 8 minutes: independent work time
• “Compartan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 4 minutes: partner discussion
• Monitor for a student who solved the problem with 7 yellow cubes and 3 red cubes by adding 4 red cubes or drawing 4 more red cubes.

• Display selected student work.
• “¿Cómo resolvieron ellos el problema?” // “How did they solve the problem?” (She added 4 red cubes.)
• “¿Cuál ecuación corresponde a la forma como resolvieron el problema? ¿Cómo lo saben?” // “What equation matches how they solved? How do you know?” (\(3 + 4 = 7\) because Lin started with 3 red cubes and she added 4 cubes to make it the same.)
• “¿Cuál número de la ecuación representa la respuesta al problema?” // “Which number in the equation represents the answer to the problem?” (4 because that is how many cubes Lin added.)
• Put a box around the 4.