The purpose of this activity is for students to solve a new type of story problem—Add To, Start Unknown. Students represent and solve the problem in any way that makes sense to them. 

Monitor for and select students with the following approaches to share in the Synthesis:

• Show 10 objects, remove or move 3 to show the counters that were added, count the remaining objects.
• Start with 3 objects and count up to 10 (commutative property).
• Represent or think of the problem as   and use a known fact.

The approaches are sequenced from more concrete to more abstract to help students make sense of and connect different approaches that can be used to represent and solve an Add to, Start Unknown story problem. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “¿En qué se parecen las formas en que ellos resolvieron el problema?” // “What is the same about how they each solved the problem?” (They all showed the 3 counters that Han put in the cup. They all showed that there were 10 counters all together. They all show that there were 7 counters in Han’s cup to start.)
• Connect students’ approaches to the learning goal by asking:
  • ”En lo que hizo cada estudiante, ¿dónde ven el número de fichas que estaban en el vaso de Han al comienzo?” // “In each students’ work, where do you see the number of counters that were in Han’s cup to start?” (The 7 that were not moved away show the counters that were already in the cup. The 7 that he counted up to get to 10. The 7 that she added to 3 to get a total of 10.)

The purpose of this activity is for students to solve various Add To and Take From problems with the unknown in all positions. Problems are presented through the familiar Shake and Spill context, and all sums are within 10 so students can attend to making sense of each problem. Students may count on, take away or they may use the commutative property or known sums.

When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2). During the Activity Synthesis, students share equations and compare the Start and Change Unknown problems, as well as how the commutative property can help them solve story problems with an unknown start. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

• Invite previously identified students to share.
• “¿En qué se parecen el problema sobre Kiran y el problema sobre Clare? ¿En qué son diferentes?” // “How are the problems about Kiran and Clare the same? How are they different?” (They are alike because they both have a number of counters missing, not the total number. You can use addition or subtraction to find the answer to both. They are different because I know how many Kiran starts with, but I don’t know how many counters Clare starts with.)
• If needed ask, “¿Qué ecuaciones representan estos problemas-historia?” // “What equations represent these story problems?”
• “¿Qué ecuaciones representan el problema de Noah? ¿Y el problema de Priya?” // “What equations represent Noah’s problem? Priya’s problem?”