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 with the standard algorithm. They 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).

• “Dime algo más acerca de por qué crees que el 2 representa un valor de 2” // “Can you tell me more about why you think the 2 represents a value of 2?”
• “¿Cómo puedes usar ecuaciones para representar cada uno de los productos parciales del trabajo de Han?” // “How can you use equations to represent each of the partial products in Han's work?”

• 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 número de nuevas unidades 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 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.

• Invite students to share their solutions and reasoning for the first and second expressions.
• “¿Cuáles fueron las nuevas unidades en base diez que compusieron en la primera expresión?” // “Which new units did you compose in the first expression?” (Tens because  , and ten-thousands because ).
• “¿Cuáles fueron las nuevas unidades en base diez que compusieron en la segunda expresión?” // “Which new units did you compose in the second expression?” (Ten-thousands because .)
• Invite students to share their solutions for the third and fourth expressions.