In this activity, students find the number that makes addition and subtraction equations with mixed numbers true, without a context. The equations are designed to encourage students to decompose or to write equivalent fractions for one or more numbers to find the unknown value, but students may choose to reason without doing either. When students share their strategies with their group, they construct viable arguments (MP3).

• Invite students to share how they went about finding the unknown numbers. Display or record their reasoning for all to see.
• To invite others into a discussion, consider asking:
  • “Did anyone find the missing number in this equation the same way?”
  • “Who used the same or a similar strategy but would explain it differently?”

In this activity, students analyze a set of addition and subtraction expressions and consider whether it is helpful or necessary to decompose a number in order to find the value of each expression. In doing so, they practice looking for structure in expressions, which they can in turn use to find sums or differences more effectively (MP7). Note that there is more than one way to sort the expressions, as students may have different ways of reasoning about these expressions.

• Select groups to share the expressions they put in each category and invite others to agree or disagree.
• Ask other students to choose 1–2 expressions that they evaluated from each category and show that it is or is not helpful or necessary to decompose a number. (For example, if they put Expression A in the 'not necessary to decompose' category, their work should show that the difference can be found without decomposing.)