By William McCallum When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelve-coin problem, the most difficult of all coin weighing problems. My mother and I worked on it separately at the same time, and she solved it first....
By William McCallum All of our curriculum here at Illustrative Mathematics is released under a Creative Commons Attribution (CC-BY) license, which allows anyone to "copy and redistribute the material in any medium or format" and to "remix, transform, and build upon...
Q: What is the fastest way to get a heated debate going about some topic in the IM 6–-8 math curriculum? A: Show people this graph from Lesson 4 in Unit 8.5: By Kristin Umland Many of us learned that time is always the independent variable, and should therefore always...
My first years of teaching, I worried my students looked at me much like Ben Stein as the teacher in Ferris Bueller’s Day Off. I cringe to think about the series of monotonous and leading questions I strung together to a room of dazed students slowly wilting in front...
By William McCallum You will never have to subtract again. Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip representing -1. You start with the...
“At the end of the day, this wasn’t about focusing on the objective, it was about making the objective meaningful to him.” The work of teaching is both invigorating and challenging. We want to instill a love of math and learning in every student, and ensure that each...
Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind. I just began my seventh year of teaching middle school mathematics. Middle school is a limbo land filled with prepubescent pre-teens, drama, and students trying to find their...
There is no shortage of available math resources for teachers to use in their classrooms. The difficult and time-consuming job for teachers is weeding through all of the tools to decide which best supports students in learning mathematics. It is a difficult job...
When I first started teaching, at the end of each day, I would open my teacher’s guide, grab my pen, and thumb through the stack of completed worksheets. My eyes would dart quickly from the red answers in the teacher’s guide to the corresponding answers on each...
I asked my 15-year-old what she learned today at school. She paused for a moment and then answered, “What did you learn at school today?” It took me a while to think about what I had learned (which will make me more patient when I ask her again tomorrow), and then I...
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