Elementary students can find it challenging to solve  problems with more than one solution, especially if they have never worked through this type of problem before.   Some students have the idea that every math problem has only one solution.   So working with  the Common Addition and Subtraction Situations: Put Together- Both Addends Unknown  (http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/) can help students learn more about persevering to solve unfamiliar problems. My picture book, Monkeys for the Zoo presents a model of students engaging in such a problem.

Working with this problem, Ms. Green’s students find out that some problems do have more than one possible solution. Mia sees that if you can have 3 howler monkeys and 10 spider monkeys, you could also have 10 howler monkeys and 3 spider monkeys. Then she discovers that you could change that combination to have 9 howler monkeys and 4 spider monkeys. And Jayden uses 9 + 4 to come up with 8 + 5. This problem pushes students to see the relationships between combinations and use one combination to find another.

Present your students with one of these problems. On the last page in Monkeys for the Zoo there are several suggestions, or you might make one up about another context that your students would enjoy thinking about. Students will find different entry points and enjoy working together to see how many solutions they can find. At first, some students may not accept that more than one combination of addends will work. They may be satisfied with only a few of the possible solutions. Involve them in modeling the problem and discussing solutions with their peers to help them see that there are many possibilities. Ask questions like:
“Who used one combination to help you find another? How did it help you?”
“If this combination works, how can we use it to find another?”
“What are some other ways you can use one solution to help you find another?”
For students struggling with this idea, reexamine Monkeys for the Zoo, and ask, “How do you think Rosie used the solution 3 howlers and 10 spiders to get 3 spiders and 10 howlers? How do you think Mia used 3 spiders and 10 howlers to help her find 4 spiders and 9 howlers?”

EXTENDING THE PROBLEM
When students are ready, see if they can find all of the possible solutions. Have students discuss how they know they have all the combinations, what strategies helped them find all the combinations, and which combination of addends are preferable in particular real world situations. For another challenge, you can add conditions to situations where both addends are unknown. For example, consider this problem: Juan has 8 books. He wants to put more books on his shelf than next to his bed. How many might he put next to his bed and how many might he put on his shelf? Your students may also enjoy the challenge of making up their own unknown addend problems.