Lesson 9

This warm-up prompts students to carefully analyze and compare features of base-ten diagrams. In making comparisons, students look for and make sue of structure as they describe representations of tens, ones, and the value of the base-ten diagrams (MP7). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of base-ten diagrams, including equivalent representations (MP6). This will be important as students compose and decompose two-digit numbers as they add and subtract within 100.

• Groups of 2
• Display the image.
• “Escojan uno que sea diferente. Prepárense para explicar por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Encontremos al menos una razón por la que cada diagrama es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

The purpose of this activity is for students to match expressions to base-ten diagrams. Students then choose 2 of the expressions to find the value of, using any method that makes sense to them. Some of the expressions do not require composing or decomposing a ten. When students match expressions with diagrams they are making use of base ten structure and the meaning of operations (MP7).

• Create a set of cards from the blackline master for each group of 2–3.

• Groups of 2–3
• Give each group a set of cards and access to base-ten blocks.

• “Cada grupo va a recibir varias tarjetas. Emparejen cada expresión con un diagrama. Cada vez que encuentren una pareja, explíquenle a su compañero por qué piensan que esas tarjetas van juntas” // “Each group will get a set of cards. Match each expression to a diagram. After you have found a match, explain to your partner why you believe they go together.”
• “Cuando hayan encontrado todas las parejas, escojan 1 expresión de suma y 1 de resta. Encuentren el valor de cada expresión de una forma que tenga sentido para ustedes” // “After you have found all of the matches, choose 1 addition and 1 subtraction expression. Find the value of each expression in a way that makes sense to you.”
• 15 minutes: partner work time
• Monitor for students who choose expressions that do not involve composing or decomposing a ten.

• “¿Qué expresiones escogieron resolver? ¿Por qué?” // “Which expressions did you choose to solve? Why?” (I chose \(35 + 42\) because it was easy for me. I knew that I could just add the ones and then add the tens.)
• “¿Cómo pueden saber si necesitan componer o descomponer una decena?” // “How could you tell if you would need to compose or decompose a ten?” (I could see that \(5 + 2 = 7\), so I knew I wouldn’t need to compose a ten.)

The purpose of this activity is for students to add and subtract within 100 using the methods that make sense to them. Throughout the activity students share their methods for adding and subtracting and compare their method with others (MP3).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Groups of 2–3
• Give each group access to base-ten blocks.

• “Encuentren el valor de cada expresión. Muestren cómo pensaron. Usen dibujos, números o palabras” // “Find the value of each expression. Show your thinking using drawings, numbers, or words.”
• “Si les ayuda, pueden usar bloques en base diez. Asegúrense de escribir cómo pensaron” // “You can use the base-ten blocks if they help. Make sure you show your thinking on paper.”
• 5 minutes: independent work time

MLR7 Compare and Connect

• “Ahora discutan en su grupo qué métodos usaron para encontrar el valor de las expresiones. ¿En qué se parecen? ¿En qué son diferentes?” // “Now, talk with your group about how you found the value of the expressions. What is the same? What is different?”
• “Hagan una presentación visual que muestre lo que pensaron sobre una de las expresiones. Muestren lo que cada miembro del grupo hizo para la misma expresión. Así, los demás podrán buscar cosas que se parezcan o sean diferentes. Incluyan detalles, como notas, diagramas, dibujos, etc., para ayudar a los demás a entender cómo pensaron” // “Create a visual display that shows your thinking about 1 of the expressions. Show the work of all of the group members for the same expression so others can look for things that are the same or different. You may want to include details such as notes, diagrams, drawings, etc. to help others understand your thinking.”
• 5 minutes: partner discussion

Students may not see the connections between their methods and other students’ methods. Consider asking:

• “¿En qué son diferentes las maneras como están representados los métodos en cada presentación?” // “How are the methods represented differently in each display?”
• “¿Cómo encontró cada grupo el mismo valor si usaron métodos tan diferentes?” // “How did each group find the same value when they used such different methods?”

• 5–7 minutes: gallery walk
• “¿En qué se parecen la manera como _____ encontró el valor y la manera como _____ lo encontró?” // “What was the same about how _____ found the value and _____ found the value?” (In the first problem, _____ and _____ both added the ones and then added the tens and combined the two sums. \(7 + 7 = 14\), \(20 + 40 = 60\), \(14 + 60 = 74\))
• “¿En qué son diferentes la manera como _____ representó cómo pensó y la manera como _____ lo representó?” // “What is different about how _____ represented their thinking and ______ represented theirs?” ( _____ used a diagram and crossed out the ones and then decomposed a ten. Then _____ crossed out the rest of the ones and the tens. _____ wrote equations to show each step.)