In this activity, students develop questions about a diagram. In the diagram a whole length, , is split into two parts. By creating questions about the diagram, students make sense of problems and persevere in solving them (MP1).

The purpose of this discussion is to explore the relationship between a part and 1 minus that part: that they create one whole.

Invite several partners to share one question with the class, and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as “equivalent,” “fractions,” and “parts.”

If students do not see the relationship that a part and 1 minus that part create one whole, mention this connection before moving to the next activity.

This activity is an opportunity to talk about subtracting fractions from 1, multiplying by fractions, and the distributive property, using the number line as a representation for sense-making. In the last question, students are asked to express regularity in repeated reasoning (MP8).

Monitor for students who write different equivalent expressions to help them reason. In the synthesis, draw connections between these different expressions.

This activity is an opportunity to use the properties that come into play in the associated Algebra 1 lesson to practice creating and identifying equivalent expressions. The expressions with exponents allow for review of performing operations in the conventional order (exponent before multiplication), as well as the convention for raising a number to the 0 power. Identifying moments to use these conventions are opportunities to look for and make use of structure (MP7).