Lesson 4

The purpose of this Number Talk is to highlight the calculations that students will make when they use the standard algorithm. The first three calculations are partial products. The fourth calculation is the sum of the first three and this is the number that is recorded when performing the standard multiplication algorithm to which students will be introduced in this lesson.

• Display one problem.
• “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 problems and work displayed.
• Repeat with each problem.

• “¿Cómo se relaciona el último producto con los tres primeros?” // “How is the last product related to the first three?” (It is the sum of the first three.)
• “¿Los tres primeros cálculos los ayudaron a encontrar el último producto?” // “Did the first three calculations help you find the last product?” (Yes, I was able to add them together to find \(3 \times 623\).)

The goal of this activity is for students to understand how to record newly composed units when using the standard algorithm for multiplication. Students compare the familiar partial products algorithm to the standard algorithm. Students may draw on their experience with the standard algorithm for addition to make sense of the new units being composed. 

When students discuss their interpretation of Elena's calculation and improve their explanations they construct viable arguments and critique the reasoning of others (MP3).

• Groups of 2
• Display the problems.
• “Tómense un momento para revisar cómo Elena y Han calcularon \(318 \times 3\). Explíquenle a su compañero lo que hizo cada estudiante” // “Take a moment to look at how Elena and Han calculated \(318 \times 3\). Explain to your partner what each student did.”
• 2 minutes: quiet think time 
• 2 minutes: partner discussion

• 5–6 minutes: independent work time
• Monitor for students who:
  • explain that the 2 represents the 20 in 24, which is the product of \(3 \times 8\).
  • explain that the 5 represents 5 tens because 3 times 1 ten is 3 tens, plus 2 more tens is 5 tens.

• “Compartan sus respuestas con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion 
• Repeat with 2–3 different partners.
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft based on the feedback you got from your partners.”
• 2–3 minutes: independent work time

If students do not explain what the 2 or 5 represents, ask, “¿Cómo podemos usar productos parciales para averiguar qué representa el 2 o el 5?” // “How can we use partial products to figure out what the 2 or 5 represents?”

• Invite previously selected students to share their revised explanations.
• “Elena usó el algoritmo estándar de multiplicación para encontrar el producto. En el algoritmo estándar, cuando componemos nuevas unidades en base diez, registramos el nuevo número de estas encima del valor posicional que está a la izquierda del dígito que estamos multiplicando” // “Elena used the standard algorithm for multiplication to find the product. When we compose a new unit in the standard algorithm, we record the new number of new units over the place value to the left of the digit we are multiplying.”

The purpose of this activity is for students to use the standard algorithm to multiply a multi-digit number by a one-digit number. Students find products that involve one or more compositions of a new unit.

• Groups of 2
• “Van a practicar la estrategia de multiplicación de Elena, es decir, el algoritmo estándar” // “You are going to practice Elena’s multiplication strategy, the standard algorithm.”

• 5-6 minutes: independent work time
• 2-3 minutes: partner discussion time

• Invite students to share their solutions and reasoning for the first and second problems.
• “¿Cuáles fueron las nuevas unidades en base diez que compusieron en el primer problema?” // “Which new units did you compose in the first problem?” (New tens because \(4 \times 5 = 20\) and ten-thousands because \(3,\!000 \times 4 = 12,\!000\)).
• “¿Cuáles fueron las nuevas unidades en base diez que compusieron en el segundo problema?” // “Which new units did you compose in the second problem?” (New ten-thousands because \(3 \times 6,\!000 = 18,\!000\).)
• Invite students to share their solutions for the third and fourth problems.