Lesson 17

The purpose of this True or False is to elicit strategies and understandings students have for multiplying one-digit whole numbers by multiples of 10. The reasoning students do here helps to deepen their understanding of the associative property as they decompose multiples of ten to make multiplying easier.

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

• Share and record answers and strategy.
• Repeat with each statement.

• “¿Cómo pueden justificar su respuesta sin encontrar el valor de ambos lados?” // “How can you justify your answer without finding the value of both sides?”
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien quiere agregar algo al razonamiento de _____?” // “Does anyone want to add on to _____’s reasoning?”
  • “¿Podemos hacer alguna generalización basándonos en las afirmaciones?” // “Can we make any generalizations based on the statements?”

The purpose of this activity is for students to consider a situation and think about all the mathematical questions they could ask about it. This gives students a chance to make sense of the situation before they are asked to solve problems. Students might choose to write a multiplication equation like \((g \times 6) + 94 = 142\). Acknowledge that this represents this situation, but focus the discussion in the synthesis on division to connect to the work in the next section.

• Groups of 2
• “Esta situación se trata de planear una fiesta. ¿En qué cosas deben pensar cuando planean una fiesta?” // “This situation is about planning for a party. What are some things that you have to think of when you plan for a party?” (Making enough food. Places for people to sit or hang out. Activities for people to do.)
• 1 minute: quiet think time
• Share responses.

• “Ahora, con su compañero, invéntense tantas preguntas como puedan sobre esta situación” // “Now, work with your partner to come up with as many questions as you can about this situation.”
• 3–5 minutes: partner work time
• Share and record responses.
• Display: “¿Cuántos invitados caben en cada mesa de la sala B?” // “How many guests fit at each table in Room B?” or circle the question if mentioned by a student.
• “Ahora respondan esta pregunta con su compañero” // “Now work with your partner to answer this question.” (I found \(142 - 94\) to find out how many guests were in Room B. There were 48 guests and 6 tables, I put the same amount of guests at each table and there were 8 guests at each table.)
• 3–5 minutes: partner work time

• “¿Qué información del problema usamos?” // “What information did we use in the problem?” (The number of guests at the party. The number of guests in Room A. The number of tables in Room B.)
• “¿Cómo podemos escribir una ecuación que represente el problema y que tenga una letra para representar la cantidad desconocida? Expliquen su razonamiento” // “How could we record an equation with a letter for the unknown quantity that would represent the problem? Explain your reasoning.” (\((142 - 94) \div 6 = g\). We had to find \(142 - 94\) to find out how many people were in Room B. We had to divide the number of people in room B by 6 to find out how many guests were at each table. The g represents how many guests fit at each table in Room B.)
• Display: \((142 - 94) \div 6 = g\)
• If students don’t use parentheses, say: “En esta ecuación, podemos usar paréntesis para mostrar que restamos primero” // “In this equation, we can use parentheses to show that we subtracted first.”
• “Los paréntesis nos muestran que la resta se hace primero en la ecuación que representa el problema. Tengan esto en mente cuando trabajen en la siguiente actividad” // “The parentheses show us that the subtraction is done first in the equation to represent the problem. Keep this in mind as you work on the next activity.”

The purpose of this activity is for students to solve two-step word problems using all four operations. Students should be encouraged to solve the problem first or write the equation first, depending on their preference. Encourage students to use parentheses if needed to show what is being done first in their equations.

When students make sense of situations to solve two-step problems they reason abstractly and quantitatively (MP2).

• Groups of 2
• Give students access to grid paper and base-ten blocks.

• “Resuelvan estos problemas individualmente. En cada caso, escriban una ecuación que represente la situación. Usen una letra para representar la cantidad desconocida. Pueden escoger si primero resuelven el problema o si primero escriben la ecuación” // “Work independently to solve these problems and write an equation with a letter for the unknown quantity to represent each situation. You can choose to solve the problem first or write the equation first.”
• 5–7 minutes: independent work time
• “Compartan sus soluciones y sus ecuaciones con su compañero. También, díganle a su compañero si creen que sus soluciones y sus ecuaciones tienen sentido o por qué no lo tienen” // “Share your solutions and your equations with your partner. Also, tell your partner if you think their solutions and equations make sense or why not.”
• 5–7 minutes: partner discussion

If students don't write a single equation to represent both steps of the problem, consider asking:

• “¿Qué ecuaciones escribiste para cada parte del problema?” // “What equations did you write for each part of the problem?”
• “¿Cómo podrías combinar tus ecuaciones para escribir una ecuación que represente el problema?” // “How could you combine your equations into one equation that would represent the problem?”

• For each problem have a student share their equation and discuss how it represents the problem.
• Consider asking:
  • “¿En qué parte de la ecuación vemos ______ del problema?” // “Where do we see ______ from the problem in the equation?”
  • “¿Qué información de la situación necesitamos para escribir y resolver nuestra ecuación?” // “What information from the situation did we need to solve and write our equation?”
  • “¿Cómo se usan los paréntesis en la ecuación?” // “How are parentheses used in the equation?”