Hello and welcome!You're in for another "teacher-y" episode today (sorry, not sorry... I'm on a roll and I can't stop!) By teacher-y I just mean I'll be focusing on our topic (the nature of multiplication) through the lens of the language of the standards teachers use, the grade levels we introduce things, etc...This episode is dedicated to Keith Devlin, whose articles (links below) helped me re-think both what multiplication *is* and how we should teach it:It Ain't No Repeated AdditionIt's Still Not Repeated AdditionThis episode discusses five different conceptions of multiplication, in the chronological (grade-level) order they are introduced in the Common Core State Standards. Here are some time stamps you may find helpful:13.33 - Introducing #1: Equal Groups (2nd Grade)17.08 - Introducing #2: Array/Area (2nd Grade)20.50 - Equal Groups in 3rd Grade25.57 - Array/Area in 3rd Grade26.37 - Introducing #3: Multiplicative Comparison (4th Grade)33.00 - Scaling/Multiplicative Comparison (5th Grade)42.33 - (Should we teach #3: Scaling earlier?!?!)46.21 - Introducing #4: Rates (6th Grade)49.16 - Rates cont. ("Constant of Proportionality") in 7th Grade50.48 - Rates cont. ("Slope of a line") in 8th Grade54.18 - Introducing #5: Combinations (7th Grade)Stay tuned over the next several weeks for two more episodes that continue to develop multiplicative reasoning as we discuss the nature of rational numbers as well as how multiplication and division behave when using negative numbers.