*Illustrative Mathematics*

It was great to see so many of you at NCSM and NCTM in San Diego. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below.

*Illustrative Mathematics*

It was great to see so many of you at NCSM and NCTM in San Diego. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below.

*Kristin Umland,VP Content Development*

A great conversation I had with the IM elementary school curriculum writing team got me thinking: What *is* a measurable attribute? That is, when given an object, what can we measure about it? Before you jump in with your own answer, consider these questions:

Is “redness” a measurable attribute? Why or why not? Does this picture help you decide?

Continue reading “What is a Measurable Attribute?”*Tina Cardone, Geometry Lead, & Gabriel Rosenberg, Curriculum Writer*

There is no doubt that proof plays a central role in the human endeavor of mathematics, but there remains much debate on what role it should play in high school mathematics. At least two standards for mathematical practice in the common core focus on this concept. Certainly MP3, “Construct viable arguments and critique the reasoning of others”, is about the need for students to be able to write their own proofs and to analyze the proofs of others. MP6, “attend to precision” goes deeper, though, by noting the need for precision, including the use of clear definitions, when communicating their reasoning. This is what we mean by rigor in mathematical proof.

Continue reading “Rigor in Proofs”*Kate Nowak, Director of 6-12 Curriculum*

When I was teaching high school mathematics, my local colleagues and I spent a whole lot of time creating problem-based lessons. We were convinced that this style of instruction was a good way to learn, but the textbooks in use at our school simply contained definitions and theorems, worked examples, and practice problems. One day I was talking to my dad about how much time I had been spending lesson planning. His response was, “People have been teaching geometry for, what, 3,000 years? Shouldn’t the lessons be, like, *already planned*?”

*By Greta Anderson & Patti Drawdy, IM Certified Facilitator*

I read the lesson three times through, but was still unsure why the number line below shows $3 – 7$. My aha moment arrived courtesy of the grade 1 standards.

Continue reading “Representing Subtraction of Signed Numbers: Can You Spot the Difference?”*By Anna Polsgrove*

When I first started the Math Methods course at University of California, Irvine, all of my ideas on how to learn math took a complete 180.

During the first two months, a million questions swirled in my head as I worked through problems with my classmates: *We don’t just teach the algorithm anymore? What do you mean “use representations to build conceptual understanding”? What is an area diagram? What are all of the multiple strategies to solve a problem? How am I supposed to anticipate misconceptions when I have never taught the curriculum?*, just to name a few. Continue reading “The IM 6–8 Math Curriculum Changed My Math Methods Experience”

*By Allison Van Voy*

When I started teaching four years ago, I had no idea how important number sense was to a student’s math understanding. I was fresh out of college, brand new to teaching, and number sense was not a concept I had learned in my math courses.

Continue reading “Using Math Routines to Build Number Sense in First Grade”

*By Kristin Gray*

As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have great, accessible problems but also create opportunities for students to openly share their ideas with others. It only makes sense that when I learned about routines that encouraged students to share the many ways they were thinking about math such as Number Talks, Notice and Wonder, and Which One Doesn’t Belong?, I was quick to go back to the classroom and try them with my students. It didn’t matter which unit we were in or lesson I had planned for that day, I plopped them in whenever and wherever I could because I was so curious to hear what students would say. Continue reading “Warm-up Routines With a Purpose”

*By Jody Guarino*

As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical understandings for the class.

First, I need a task that will make student thinking visible. Here’s a task from Illustrative Mathematics, Peyton’s Books.

Peyton had 16 books to take on his trip. He lost some. Now he has 7 books. How many books did Peyton lose?

Continue reading “Adapting Problems to Elicit Student Thinking”