This series of activities and lesson notes is part of a unit in which the purpose is, “Students will interpret visual information in order to make informed consumer decisions.” The activities begin with informal exploration.
In this blog post and the included lesson plan, Graham Fletcher and Joe Schwartz explore thinking conceptually about the standard division algorithm. In his lesson, Joe Schwartz scaffolds long division using tape diagrams.
Challenging math problems worth solving.
The name “Open Middle” might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:
* a “closed beginning” meaning that they all start with the same initial problem.
* a “closed end” meaning that they all end with the same answer.
* an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.
In this webinar, you will hear about several major concepts introduced in the book, The Problem with Math is English, further explained by the author, Concepcion "Como" Molina, EdD. The book can be purchased online at: http://www.sedl.org/pubs/catalog/item...
SEDL offers professional development for college- and career-ready mathematics at: http://highperformingschools.sedl.org.
Students often think additively rather than multiplicatively. For example, if you present the scenario, "One puppy grew from 5 pounds to 10 pound. Another puppy grew from 100 pounds to 108 pounds." and ask, "Which puppy grew more?" someone who is thinking additively will say that the one who now weighs 108 grew more because he gained 8 pounds while the other gained 5 pounds. Someone who is thinking multiplicatively will say that the one that now weighs 10 pounds grew more because he doubled his weight while the other only added a few pounds. While both are correct answers, multiplicative thinking is needed for proportional reasoning. If your students are thinking additively, you can nudge them toward multiplicative thinking with this activity.