The purpose of this activity is for students to make sense of and solve a new type of story problem—Add To, Change Unknown. Students may solve in any way that makes sense to them (MP1). In addition to the methods listed below, look for the different ways students plan their strategy. For example, look for students who may use two different colors of objects or intentionally keep the objects or drawings they start with physically separated from those they add on.

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

• Show 6 objects, add and remove objects until they count a total of 8 (guess-and-check).
• Show 6 objects, add 2 more objects as they count on to 8.
• Draw 6 objects, draw 2 more objects as they count on to 8.

The approaches are sequenced from more concrete to more abstract to help students make sense of the ways in which each approach represents the actions and the answer to the question in an Add to, Change 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:     
  • “How are these approaches the same? How are they different?”
• Connect students’ approaches to the learning goal by asking:
  • “How do you see how many books Kiran had at first in each representation?”
  • “How do you see how many books Kiran had in all?”
  • “How do you see how many books Kiran got from his friend?”
• As needed, highlight different ways students showed the answer to the question.

The purpose of this activity is for students to represent and solve an Add To, Result Unknown or an Add To, Change Unknown story problem. Students then compare each problem, including the structure of the problems and the strategies used to represent and solve them. Students attend to precision and use clear and precise language to explain how they solved and represented the problems (MP6). The Activity Synthesis draws out differences in the story problems as well as differences in how they are solved.

Students will be working on 1 of the 2 problems with a partner. Consider different ways you may read the problems to students to ensure they all have access to mathematics. For example, you may read both problems to students before they work or you may consider reading the first problem, inviting students assigned to that problem to start on their work, and then read the next problem to the remaining students. You may also consider assigning roles to students who may be able to support rereading the story or clarifying the task directions.

• Display both problems and student posters of how each problem was solved.
• As needed, reread each problem.
• “What differences do you see between the two story problems?” (In Problem 1, we know how many books Mai checked out, but in Problem 2 we don’t. In Problem 1 we don’t know how many books she has total, but in Problem 2 we do.)
• “How do these differences change what you had to do to solve the problem?” (In Problem 1, we just drew 5 books and 4 more books. Then we had to count how many there were altogether. In Problem 2, we had to start with 5 books, and draw more until we had 9. Then count how many more we drew.)
• Keep the problems and student work samples displayed for the Lesson Synthesis.