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Friday, March 1 • 2:25pm - 3:10pm
Two Big Diagrams for Deeper Understanding

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I present two advance organizer diagrams that I guide student thru as notes and discussion in class. I present them as I would to students, but at an advanced rate and level. One is an overview of several key concepts in 8th grade math and their interconnectedness. The other illustrates the relation between the order of operations, distributive properties and operations with exponents. Both are helpful for understanding the structure of math as opposed to merely memorized facts and procedures.
The first is presented early in the 8th grade year and illustrates relations between: Ratio and Proportion, emphasized in the 7th grade year, Dilation, Similar Figures and Indirect Measurement, Functions, Pythagorean Theorem, Slope and other related concepts. When finished, some students choose to embellish them into artwork similar to the ""student reflections"" in MidSchool Math.
This visual organizer of various but related concepts helps us understand the structure of mathematics. It is used as a touchstone now and then during the year. Also, later in the year, a very similar diagram could be presented to illustrate the transition to slope-intercept equations.
The second diagram is my presentation of the 'hierarchy of operations' as it relates to the distributive properties and operations with exponents. The understanding of this structure also extends to the topics of recursive and explicit formulas for geometric and arithmetic sequences, and logarithms in future classes.

This diagram allows one overarching concept to inform several seemingly disparate topics, deepening understand and facilitating use of algorithms and procedures. I will present as much as I do for my 8th grade students and then extend for the information of the teachers.

avatar for Sean Genovese

Sean Genovese

Math Teacher, Macomb Jr. High School
Geno's been teaching math in one way or another for 25+ years. This is mainly because a bunch of Jr. High students in study hall he was supervising told him he should. He was good at explaining their math work and that he should be a math teacher. He considers middle school to be... Read More →

Friday March 1, 2019 2:25pm - 3:10pm
  • MATH STANDARDS & PRACTICES Mainly Making Use of Structure, also Modeling. 8EE1, 8EE5, 8EE6, 8F1, 8F2, 8F4, possibly 8G4.
  • WHAT WILL ATTENDEES GAIN? Attendees will walk away with two hand made diagrams and the ability to share them and the procedure of making them with their students.
  • BEYOND "STAND & DELIVER" While this is technically Lecture / Notes, the 'construction' of the diagrams boarders on a 'hands-on' experience.
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Attendees (17)