## Conjectures and Math Arguments with Fourth Graders

My fourth grade class just started a unit on division and fractions. Students started out the unit by observing the relationship between fractions and division. This was a realization for some students as they perceived fractions as an isolated topic, separate from the division operation.  From there, students moved to adding and subtracting fractions. The class completed an Open Middle problem on Wednesday.

Last year, students were introduced to this computation skill and many were comfortable transitioning that skill to more complex fractions.  I’d say the majority of my students completed problems using a common denominator strategy.  Very few used a visual model.  For the most part, students were able to find solutions to the computation problems.

The next day, students experienced the idea of using mathematical reasoning to create conjectures.  This was brand new for the students and I recently read about how to use conjectures in class from Tracy Zager’s book.  The class discussed very simple conjectures, claims, and arguments.  After about ten minutes, a student mentioned that someone is being a “math lawyer” when they go through the conjecture, claim, and argument process.  I think the whole class laughed at that response, but agreed.  I then helped model a few different conjectures and clarified the definition.  Students then worked in table groups to role-play how to defend their claims.

Near the end of class, I was able to have students work on a page related to fractions and conjectures.  Each table group 1) looked at a specific fraction computation problem 2) each student added their own view point of whether they agreed or disagreed 3) the groups came to a consensus and wrote their argument to prove their case 4) students wrote their arguments on the whiteboard.

I was impressed with how students started to improve the clarity of their mathematical writing during this process.  This is an area of growth for all of my classes.  Writing in math class doesn’t happen as often as I’d like.  I’m hoping to complete more conjecture, claim and argument activities as the year progresses.