Lesson 1

The purpose of this warm-up is for students to discuss the location of digits in the products, which will be useful when students try to find the greatest product in a later activity. While students may notice and wonder many things, the location of the digits 6, 4, 1, and 8 is the important discussion point.

• Groups of 2
• Display the image.

• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Sin encontrar los valores, ¿cuál producto creen que va a ser mayor? Expliquen cómo razonaron” // “Without finding the values, which product do you think will be greater? Explain your reasoning.” (I think \(841 \times 6\) will be greater because 841 is a lot more than 641. I think \(641 \times 8\) will be larger because there is 4,800 in each and the second product has more 41s.)
• “Vamos a retomar estos problemas en la síntesis de la lección” // “We are going to revisit these problems in the lesson synthesis.”

The purpose of this activity is for students to practice using the standard algorithm and explain how the placement of the digits in factors impacts the value of the product when multiplying a two-digit number by a one-digit number. Students multiply different factors which use the same 3 digits and determine which combination yields the greatest product. While the problems were intentionally structured to encourage students to use an efficient strategy, such as the algorithm, students should use whatever strategy makes sense to them when solving these problems.

Students critically analyze a claim about the largest product that can be made with 3 digits and discuss their reasoning with several partners (MP3). 

• Groups of 2
• “Van a discutir una afirmación durante 2 rondas. En la primera ronda, lean la afirmación y expliquen por turnos si están de acuerdo, en desacuerdo o no están seguros. Después, cambien de grupo y completen la ronda 2” // “You will discuss a talking point in 2 rounds. In the first round, read the statement and take turns explaining whether you agree, disagree, or are unsure. Then we will switch groups and complete Round 2.”
• Partner work time: 2–3 minutes

• After partner work time, rearrange students into groups of 4. New groups of 4 should be formed where partners are not in the same group.
• “Ahora van a completar la ronda 2 con su nuevo grupo. Cada persona del grupo tendrá tiempo para expresar nuevamente su razonamiento” // “Now, you will complete Round 2 in your new group. Each person in the group will be given time to restate their reasoning.”
• 1–2 minutes: group discussion
• “Decidan si quieren reconsiderar lo que pensaron y prepárense para explicar por qué cambiaron de idea. Cada persona del grupo va a decir si cambió su respuesta o no, y va a explicar por qué sí o por qué no” // “Decide if you want to revise your thinking and be prepared to explain why you changed your thinking. Each person in the group will say whether or not they changed their answer and explain why or why not.”
• 1–2 minutes: small-group discussion
• “Piensen en algo nuevo que hayan aprendido al discutir con su grupo o algo que todavía se pregunten” // “Think about something new that you learned from your group or something that you are still wondering about.”
• 1–2 minutes: independent work time
• 1-2 minutes: partner discussion
• “Ahora usen lo que aprendieron para completar el segundo problema” // “Now, use what you learned to complete the second problem.”
• 1-2 minutes: independent work time

• Display:

  \(72\times 5 =(70\times 5)+(2\times5)\)

  \(52\times 7 =(50\times 7)+(2\times 7)\)

• “¿Por qué \(52\times 7\) es mayor que \(72\times5\)?” // “Why is \(52\times 7\) greater than \(72\times5\)?” (The product of ones and tens is the same in these products but \(52 \times 7\) has a larger product of ones and ones.)
• “¿Qué aprendieron sobre la posición de los dígitos cuando se multiplica un número de dos dígitos por un número de un dígito?” // “What did you learn about placement of digits when multiplying a two-digit number by a one-digit number?”

The purpose of this activity is for students to practice using the standard algorithm and to use place value reasoning to explain how the placement of the digits in factors impacts the value of the product when multiplying (MP7). 

• Groups of 2

• Display:

  7, 3, 2, 5

• “Si usamos solo estos dígitos, ¿qué expresiones de multiplicación podemos escribir?” // “Using only these digits, what multiplication expressions could we write?” (\(723 \times 5\), \(32 \times 57\), \(7 \times 3 \times2 \times 5\), \(73 \times 5 \times 2\).)
• 1 minute: quiet think time
• Record answers for all to see.
• “¿Cuál de estas expresiones creen que va a tener el mayor producto? Prepárense para explicar cómo razonaron” // “Which of these expressions do you think would make the greatest product? Be prepared to explain your reasoning.” (I think the three-digit by one-digit expression would make the greatest product because you can put the 7 in the hundreds place.)
• “Usen los dígitos 7, 3, 2 y 5 para formar el mayor producto” // “Use the digits 7, 3, 2, and 5 to make the greatest product.”

• 5–7 minutes: partner work time

If students need help getting started, refer to the products generated during the launch and ask students to evaluate them. Ask them to order the products from least to greatest and explain what they notice. Next, ask them to generate other products using the same digits. Continue to check in with them and ask them to explain any patterns they notice.

• “¿Cuál expresión de multiplicación va a tener el mayor producto?” // “Which multiplication expression will have the greatest product?”
• Poll the class.
• Record responses for all to see.
• Display or write these expressions for all to see:

  

  

  

  

• “¿Por qué al intercambiar las posiciones del 5 y del 7 aumenta el valor del producto?” // “Why does switching the placement of the 5 and the 7 increase the value of the product?” (Both products have 35 hundreds, but when 7 is the second factor, the product has 7  groups of 32 instead of 5 groups.)
• Display or write these expressions for all to see:

  

  

  

  

• “¿Por qué al intercambiar las posiciones de los dígitos 2 y 3 aumenta el valor del producto?” // “Why does switching the placement of the digits 2 and 3 increase the value of the product?” (Both products have partial products \(50 \times 70\) and \(2 \times 3\), but when we switch the digits 2 and 3, the partial products in \(72 \times 53\) are greater.)