The purpose of this activity is for students to represent and solve a variety of Put Together/Take Apart problems with the unknown in different places. Two of the problems have the same addends and total, with the unknown in different places. The third problem has both addends unknown. Students should be encouraged to represent and solve the problems in any way that makes sense to them.

Look for the different ways students make sense of and represent the relationships between the quantities. Some students may be using equations to represent the problem or their answer, but they are not expected to produce equations at this point. In the Synthesis, emphasize the different ways students make sense of the unknown, with an emphasis on comparing when the total is unknown, when one addend is unknown, and when both addends are unknown.

• Invite previously selected students to share for each problem.
• Consider asking:
  • “How does ____’s representation match the story?”
  • “How did __ show the answer to the problem?”
• “How were these story problems the same? How were they different?” (They each had a total of 8 pets. In the first problem, we had to find the total. In the second problem, we had to find one of the parts. In the last problem, we didn’t know either part (addend). The last problem had different answers.)
• Highlight student comments that focus on the different unknown(s).

The purpose of this activity is for students to make sense of a strategy used to solve a Put Together/Take Apart, Addend Unknown story problem. Students are first presented with a representation of a counting on strategy similar to the one they interpreted in Section A for solving an Add To, Change Unknown problem. This is a strategy most students are familiar with at this point in the unit.

Students are then asked to interpret a representation of a strategy where a student counts back from the total to the known addend. Although the strategy is less common than counting on, some students may have used this strategy in the prior lesson as a way to make sense of Put Together/Take Apart, Addend Unknown situations. Other students may be unsure if this strategy can be used since it seems like subtraction.

This activity is used to invite all students to begin to deepen their understanding of subtraction as not only representing taking from, but also as finding an unknown addend. It is not necessary for all students to understand this concept by the end of this lesson. They will deepen their understanding during the next section of the unit and throughout the school year.

• Invite previously selected students to share how Jada’s drawing shows a way to solve the problem.
• “Do you agree with Diego that you can’t use strategies that show taking away to find an unknown addend?” (No. Jada’s way does work. Jada’s way still shows the total, one of the parts, and how to find the other part.)
• “Jada shows that you don’t just have to think about adding on to find an unknown addend. You could think about taking away the part you know from the total.”