Lesson 10

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying within 100. These understandings help students develop fluency and will be helpful later in this lesson when students are to multiply side lengths to find area. While recording students’ thinking, consider using equal groups or arrays as in the images in the warm-up of the previous lesson.

• 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.

• “¿Qué pasa cuando aumentamos uno de los factores en 1?” // “What happens when we increase one of the factors by 1?” (The product goes up by 1 of the other factor.)
• “¿Qué hace que esto pase?” // “What makes this happen?” (The amount increases by 1 group. Each group gets 1 more.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de ________ de otra forma?” // “Who can restate _______ 's reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de ________?” // “Does anyone want to add on to____’s strategy?”

The purpose of this activity is for students to solve a real-world problem involving area. The activity includes a rectangle where the side lengths are labeled. When students solve problems with multiple solutions and have to choose and justify a solution, they make sense of problems and persevere in solving them (MP1). In their small groups and in the class discussion students have an opportunity to explain and defend their choices (MP3).

• Groups of 3–4
• “Una huerta comunitaria es un espacio de siembra compartido por miembros de la comunidad. Cada miembro recibe su propio espacio para crear su parte de la huerta comunitaria” // “A community garden is a garden space that is shared by members of the community. Each member gets their own space to create their part of the community garden.”
• “Este es un problema sobre pintar una pared de la huerta comunitaria. ¿Qué materiales necesitan para pintar?” // “This is a problem about painting a wall in a community garden. What materials do you need when you paint?” (Paint. Brushes. Paint rollers. Drop cloth. Painter’s tape.)
• 1 minute: quiet think time
• Share responses.

• “Resuelvan el problema en grupo” // “Work with your group to solve the problem.”
• 5 minutes: small-group work time
• Monitor for different solutions mentioned in the sample responses.

If students don’t find a solution to the problem, consider asking:

• “Dime qué has hecho hasta ahora para resolver el problema” // “Tell me about what you’ve done so far to solve the problem.”
• “¿Cómo podrías representar el problema?” // “How could you represent the problem?”

• “¿Cómo encontraron el área de la pared que Noah está pintando?” // “How did you find the area of the wall that Noah is painting?” (I counted by 3 six times since I pictured 3 squares in each column and 6 columns. I multiplied 3 by 6 and got 18.)
• Discuss several different responses and their accompanying reasoning.
• Consider asking:
  • “¿Cómo saben que eso sería suficiente para cubrir toda la pared?” // “How do you know that would be enough to cover the whole wall?”
  • “¿Sobraría pintura? ¿Para cuántas yardas cuadradas alcanzaría?” // “Would there be paint left over? Enough to paint how many square yards?”

The purpose of this activity is for students to solve an area problem that involves missing side lengths. The problem has multiple solutions, as the area of the garden could be between 20 square feet to 30 square feet. The launch serves to familiarize students with the ideas involved in designing a garden before they solve the problem.

When students share with other groups and describe what others did that was different they are making and understanding mathematical arguments (MP3).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

• Groups of 3–4
• Display the image.

MLR6 Three Reads

• Display only the problem stem, without revealing the question(s).
• “Vamos a leer este problema 3 veces” // “We are going to read this problem 3 times.”
• 1st Read: “Elena está planeando cómo usar su espacio rectangular de la huerta comunitaria. Necesita un espacio que tenga por lo menos 20 pies cuadrados para que quepan sus plantas. Tiene suficiente tierra para un jardín de 30 pies cuadrados. El espacio que tiene disponible debe tener 3 pies en un lado” // “Elena is planning how to use her rectangular space in the community garden. She needs a space that is at least 20 square feet to fit her plants. She has enough soil for a garden that is 30 square feet. The space she has available has to be 3 feet on one side.”
• “¿De qué se trata esta situación?” // “What is this situation about?”
• 1 minute: small-group discussion
• Listen for and clarify any questions about the context.
• 2nd Read: “Elena está planeando cómo usar su espacio rectangular de la huerta comunitaria. Necesita un espacio que tenga por lo menos 20 pies cuadrados para que quepan sus plantas. Tiene suficiente tierra para un jardín de 30 pies cuadrados. El espacio que tiene disponible debe tener 3 pies en un lado” // “Elena is planning how to use her rectangular space in the community garden. She needs a space that is at least 20 square feet to fit her plants. She has enough soil for a garden that is 30 square feet. The space she has available has to be 3 feet on one side.”
• “Nombren las cantidades. ¿Qué podemos contar o medir en esta situación?” // “Name the quantities. What can we count or measure in this situation?”
• 30 seconds: quiet think time
• 1–2 minutes: group discussion
• Share and record all quantities.
• Reveal the question(s).
• 3rd Read: Read the entire problem, including the question aloud.
• “¿Qué estrategias podemos usar para resolver este problema?” // “What are some strategies we can use to solve this problem?”
• 30 seconds: quiet think time
• 1–2 minutes: group discussion
• Give each group tools for creating a visual display and access to square tiles and grid paper.

• “Resuelvan el problema en grupo. Hagan un póster para mostrar cómo resolvieron el problema” // “Work with your group to solve the problem. Create a poster to show how you solved the problem.”
• 10 minutes: group work time
• Monitor for students who:
  • recognize that they are missing a side length of the garden.
  • create an expression or equation that reflects the missing side length with a missing factor.
  • come up with multiple gardens that could be built.

• Display students' posters around the room.
• “Ahora, la mitad de la clase se va a quedar junto a sus pósteres mientras la otra mitad visita los pósteres de los demás estudiantes. Si se quedan junto a su póster, expliquen cómo resolvieron el problema. Cuando visiten otros pósteres, hagan las preguntas que tengan sobre la solución del problema” // “Now, half of the class is going to stand with their posters while the other half visits other students’ posters. If you’re standing with your poster, explain how you solved the problem. As you visit other posters, ask any questions you have about the solution to the problem.”
• Ask half of the groups to stand with their poster and share their ideas or answer questions as the other half visit their posters.
• 5 minutes: gallery walk
• Remind students to switch posters at 2 minutes if they haven’t already so they see a few posters.
• Switch group roles and repeat.