Clip 22/41: Standard 3: Construct Arguments & Critiques Using Rates Part 1

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others.

Joe Condon works with his 6th grade students to identify strategies for comparing unit rates. In these clips, the students actively engage with the concepts individually, in small groups, and in large group discussions. His students are asked to write a rate for each student and justify who is fastest at counting beans. Students use different approaches to calculate the rate, and one student observes that if the rate is seconds per bean it needs to be the smallest rate to win, but if it is beans per second it needs to be the largest rate.

Students first think on their own, then share in groups before class discussion. Another student shares a conjecture with the class: If the rate is seconds per step Alex wins, but if the rate is steps per second Joe wins. Students talk in groups to try to figure out how she got this conjecture and whether it makes sense. A final student concludes that the goals are different for each rate. During whole class discussion, one group interprets a simpler strategy for simplifying unit ratio and shares with the class.

See this video in the context of an entire lesson.

(Parts 1-6)