The purpose of this activity is for students to represent and solve a two-step story problem involving multiplicative comparison, in ways that make the most sense to them. As they make connections between strategies for solving multi-step problems, they also compare representations that show multiplicative comparison more discretely (diagrams) and those that show the comparison more abstractly (expressions).

• “Explícame cómo organizaste la información del problema” // “Tell me more about how you organized the information from the problem.”
• “Si sabemos ______, ¿cómo nos ayuda esto a encontrar la cantidad total de ventas de ese día?” // “How can knowing ______ (quantity in step 1 of the problem) help us find the amount of total sales for that day?

• Invite previously selected students to share their representations and their reasoning for problem 1. 
• “¿Cómo se relacionan el diagrama o las expresiones de ______ con el problema?” // “How does ______’s diagram or expressions relate to the problem?” (The diagram and the expressions showed and 8 times as much.) 
• “¿En qué fue parecido resolver este problema a resolver el segundo problema? ¿En qué fue diferente?” // “How was solving this problem like the second problem? How is it different?” (The question, the numbers, and multiplicative comparison “8 times as much” were the same in both problems. The diagram from the first problem could also work with the second problem. The calculations were different because of what the problems were about.)
• “¿En qué fueron diferentes estos problemas a otros problemas que resolvimos en esta unidad?” // “How were both of these problems different from other problems we solved in this unit?” (We had to do more than one calculation to solve the problem.)
• “En ambos problemas teníamos que encontrar la cantidad de ventas totales, y en ambos teníamos que multiplicar y sumar. ¿Cómo supieron cuál operación usar y con cuáles números?” // “Both problems asked for the amount of total sales and involved multiplying and adding. How did you know which operation to use and with which numbers?” (One problem involves adding first, and then using multiplicative comparison to find the amount of total sales. In the other problem, multiplicative comparison is first, and then you add to find the amount of total sales for the day. It’s important to pay attention to the information given in the problem and the multiplicative comparisons.)

The purpose of this activity is for students to apply what they learned about interpreting and representing multiplicative comparison to solve multi-step problems. They must interpret what values are unknown and make a plan for how to represent these values.

Students reason abstractly and quantitatively when they make sense of the given information and use it to find the different numbers of books (MP2).

• Invite previously selected students to share their diagrams or equations.
• “¿Cómo los diagramas o ecuaciones de ___ se relacionan con el problema-historia?” // “How does __'s diagrams or equations match the story problem?”
• “Para este problema en particular, ¿por qué alguien preferiría mostrar lo que hizo con ecuaciones en vez de dibujar diagramas?” // “Why might someone choose to show their work with equations instead of drawing diagrams for this particular problem?”
• “¿Qué aprendieron acerca de prestar atención a lo que se está preguntando?” // “What did you learn about paying attention to what the question is asking?”
• If time, invite previously selected students to share how they revised their thinking.
  • “¿De qué se dieron cuenta cuando discutieron con su compañero? ¿Qué cambios hicieron después de darse cuenta de eso?” // “What did you notice during the partner discussion and how did you change your work after noticing it?”
  • Consider asking a different student to rephrase this revision in their own words.