# Small Changes to Questions About Integers

Last week, one of my classes began reviewing for a test focused on integer operations and word problems.   We discussed some homework questions, then I used a series of questions to guide students through a brain dump.  In this activity, I ask students to write down everything they know about a concept (usually the major idea of a unit).  This review activity works well with students, but I needed to prompt students more this time since it was their first experience of the year with the activity.   As we wrote down everything we knew about integers, I found myself using the question, “What is the rule for…?” many times.   I don’t like this terminology because it usually implies memorization for students over understanding.  Next time, I will use a phrase like, “What is the process for…?” or “What do we need to consider before computing…” to give integers a better flavor and emphasize thinking about problems before solving.   The rules are logical and become second nature with time, but using a term like rules when students are learning about integers for the first time can taint the subject.   Beyond identifying questions for improvement, I also noticed some questions that worked well during the activity.  Some questions that generated good thought and responses included:

• What is the relationship between adding and subtracting integers?
• Why do we rewrite subtraction of integers using addition statements?
• How is absolute value useful besides telling me the distance of an integer from 0?
• What is the relationship between multiplying and dividing integers? How does this relationship help us solve problems?
• How do I know which operation is most powerful when solving an order of operations problem without using PEMDAS or GEMA?

These questions allowed students to explain the relationship between concepts in their words, as well as giving me further insight into their strengths and weaknesses in understanding integers.   By the end of the activity, students had a tangled web of information on their papers that included concepts, definitions, and arrows connecting related topics.  My whiteboard was filled, too.   While we still have some work to do in wrapping up our integer unit, I liked how the questions I used in this activity pushed students to communicate mathematics and connect ideas.