What activity would best informally assess students' knowledge of composing and decomposing fractions?

The choice to provide a warm-up question that asks students to write one way to decompose 3/4 is particularly effective for an informal assessment of their understanding of composing and decomposing fractions. This activity engages students directly with the concept, requiring them to think critically about how fractions can be expressed in different ways.

By asking students to demonstrate their understanding of decomposition, they are actively showing not just rote memorization but a deeper comprehension of how fractions can be broken down into smaller parts. This method allows the teacher to quickly gauge individual student progress and misconceptions in a low-pressure setting, thus making it an excellent informal assessment tool.

While other options may provide some level of insight into student understanding, they do not focus as directly on the specific skills of composing and decomposing fractions. For example, leading a discussion on fractions might foster understanding but does not specifically assess individual student knowledge. Similarly, a pop quiz is more formal and might not allow for the same level of engagement or creativity in demonstrating knowledge. Including these concepts in homework, while beneficial for practice, doesn't provide immediate feedback or insight into student thought processes.

In contrast, the warm-up question encourages students to articulate their understanding in their own terms and allows the teacher to assess comprehension in real-time.