Lesson 6

The purpose of this warm-up is to elicit the strategies and understanding students have for composing a ten when adding within 100. This Number Talk focuses on adding fives to compose a ten mentally. Each successive expression is ten more than the previous. When students notice and express the regularity in this pattern, they use the structure of base-ten numbers and the properties of operations (MP7, MP8). These understandings help students develop fluency with addition within 100.

• 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.

• “Comparen \(15 + 5\) con \(5 + 5\). ¿Qué pueden decir?” // “How does \(15 + 5\) compare to \(5 + 5\)?” (It’s 10 more)
• “Comparen \(15 + 15\) con \(15 + 5\). ¿Qué pueden decir?” // “How does \(15 + 15\) compare to \(15 + 5\)?” (It’s 10 more)
• “Comparen \(15 + 25\) con \(15 + 15\). ¿Qué pueden decir?” // “How does \(15 + 25\) compare to \(15 + 15\)?” (I see \(10 + 20 = 30\) and the \(5 + 5\) is 10 more.)
• Highlight how to see the 10 more structure in these sums: the tens place of one number grows by one each time.

The purpose of this activity is for students to interpret and solve Compare problems involving length where the language suggests an incorrect operation. For example, the first problem uses the word “shorter” which usually suggests subtraction. However, in this problem students are looking for an unknown that is the greater length and must add the two known values.

The Three Reads routine is used to help student practice making sense of the problem before solving. Students begin the activity by looking at the first problem displayed, rather than in their books. At the end of the launch, students open their books and work to find the diagram that matches the story problem. This further helps them to visualize the quantities in the problem before they work to find a solution (MP1).

After reading the other story problems, students consider which pet is longer or shorter and choose tape diagrams to match the lengths in the problem (MP2). Students solve each story problem independently and compare their solutions.

This activity uses MLR6 Three Reads. Advances: Reading, Listening, Representing

• Groups of 2
• Give students access to base-ten blocks.
• “Ambas, Lina y Jada, tienen lagartijas como mascotas. Ellas comparan las longitudes de sus mascotas” // “Lin and Jada both have pet lizards. They are comparing the lengths of their pets.”

• Display only the problem stem for the first problem, without revealing the question. 
• “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
• 1st Read: “La lagartija mascota de Lin mide 62 cm de largo. Es 19 cm más corta que la de Jada” // “Lin's pet lizard is 62 cm long. It is 19 cm shorter than Jada's.”
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion.
• Listen for and clarify any questions about the context.
• 2nd Read: “La lagartija mascota de Lin mide 62 cm de largo. Es 19 cm más corta que la de Jada” // “Lin's pet lizard is 62 cm long. It is 19 cm shorter than Jada's.”
• “¿A qué medidas de la historia es importante prestar atención?” // “Which measurements are important to pay attention to in the story?” (the length of Lin’s lizard, the length of Jada’s lizard, the difference between the lengths of the two lizards).
• 30 seconds: quiet think time
• 2 minutes: partner discussion 
• Share and record responses.
• Reveal the question.
• 3rd Read: Read the entire problem, including the question aloud.
• “La lagartija mascota de Lin mide 62 cm de largo. Es 19 cm más corta que la de Jada. ¿Cuál es la longitud de la lagartija mascota de Jada?” // “Lin's pet lizard is 62 cm long. It is 19 cm shorter than Jada's. How long is Jada's pet lizard?”
• “¿De qué formas podríamos representar este problema?” // “What are different ways we could represent this problem?” (tape diagram, equations, base ten blocks)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

• “Lean cada historia con su compañero. Luego, individualmente, marquen el diagrama que corresponde” // “Read each story with your partner. Then circle the diagram that matches on your own.”
• “Cuando ambos hayan seleccionado un diagrama, comparen sus elecciones y expliquen por qué el diagrama corresponde a la historia” // “When you have both selected a match, compare your choices and explain why the diagram matches the story.”
• “Luego, resuelvan el problema individualmente” // “Then solve on your own.”
• 10 minutes: partner work time

• Invite students to share the correct diagram for the second problem.
• Display the diagram.
• Consider asking:
  • “¿De qué manera el diagrama corresponde al problema-historia?” // “How does the diagram match the story problem?” (You can see that Mai’s rectangle is longer and there is a question mark for Diego’s pet.)
  • “¿Cómo supieron cuál mascota era más corta?” // “How did you know which pet was shorter?” (It said that Mai’s snake was 17 cm longer, so Diego’s is shorter.)

The purpose of this activity is for students to make sense of and solve Compare story problems involving length. Students use measurements provided for reptiles and create their own Compare problems to solve with a partner. Students must solve a Compare, Difference Unknown problem when creating their mystery problem. When they solve their partner's mystery problem, they must solve a Compare, Bigger Unknown or Compare, Smaller Unknown problem. Encourage students to use diagrams or other drawings to show how they know which reptiles their partner picked. Some students may choose to use equations to represent the lengths.

• Groups of 2
• Give students access to base-ten blocks.
• Assign students as Partner A and Partner B.

• “Vamos a jugar un juego de adivinanzas. Van a escoger un reptil de su lista y un reptil de la lista de su compañero. Mantengan ambos reptiles en secreto” // “We are going to play a guessing game. You will choose one reptile from your list and one reptile from your partner’s list. Keep both reptiles a secret.”
• “De manera independiente, escojan sus reptiles y completen las frases” // “Work independently to pick your reptiles and complete the sentences.”
• As needed, demonstrate as if you were Partner A with the class.
• 4 minutes: independent work time
• “Ahora compartan sus frases con su compañero. Luego, descubran cuáles reptiles escogió su compañero. Hagan un diagrama o usen ecuaciones para mostrar que ustedes tienen razón” // “Now, share your sentences with your partner. Then find which reptiles they picked. Draw a diagram or use equations to prove you are correct.”
• 6 minutes: partner work time
• Monitor for students who use tape diagrams to represent their partner’s reptiles.

If students find the correct difference between the reptiles they pick, but create a word problem that cannot be solved, consider asking:

• “¿Cómo podrías dibujar un diagrama para representar los reptiles que escogiste?” // “How could you draw a diagram to represent the reptiles you picked?”
• “¿Tu diagrama corresponde al problema-historia que creaste? ¿Por qué sí o por qué no?” // “Does your diagram match the story problem you created? Why or why not?”
• “¿Qué palabra o qué números podrías cambiar para que tu diagrama correspondiera a los reptiles que escogiste?” // “What word or numbers could you change to match the reptiles you chose?”

• Invite previously identified students to share how they determined their partner’s reptiles.
• Consider asking:
  • “¿Cuál reptil era más corto? ¿Cómo se muestra esto en su diagrama?” // “Which reptile was shorter? How does your diagram show this?”
  • “¿Sumaron o restaron para encontrar el otro reptil? ¿Cómo les ayudó su diagrama?” // “Did you add or subtract to find the other reptile? How did your diagram help you?”