Linda Richard, Curriculum Writer
I used to teach my students a catchy song to memorize the distance formula. We all had fun goofily singing this song. My students hummed it to themselves during tests and successfully calculated distances. I was pleased with this outcome—but what did my students actually understand about distance in the coordinate plane? In retrospect, very little.
Continue reading “Making Sense of Distance in the Coordinate Plane”
Kristin Gray, Director of K–5 Curriculum & Professional Learning
One challenge in curriculum design is considering all we know and believe to be true about math teaching and learning and translating that into realistic and actionable pieces for teachers and students. Our recent post about the K–5 curriculum focused around our belief that each and every student should be seen as a unique person with unique knowledge and needs. And while that post centered on elementary materials, to truly design around this belief we must look past K–5 to consider each student’s unique K–12 mathematical journey. A journey that, for most students, looks very different as they move from elementary to middle to high school.
Continue reading “Designing Coherent Learning Experiences K-12”
Melissa Schumacher, Curriculum Writer
Which is more important for students to have: conceptual understanding or procedural fluency? Does one have to be taught before the other can emerge?
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.
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?”
Continue reading “Presenting IM Algebra 1, Geometry, Algebra 2”
By Ashli Black, Algebra 2 Lead
Students need a chance at the beginning of the year to shake off the summer dust. Learn how IM’s curricular design builds in opportunities for review while starting the year with inviting, grade-level mathematics.
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.
By Noelle Conforti Preszler and Kristin Gray
In the following activity, think about the students in your classroom. How might each respond?
What do you notice? What do you wonder?
This activity is the drafted warm-up of the first lesson in Grade 3, Unit 1: Introducing Multiplication. While we believe the structure of this activity — “What do you notice? What do you wonder?” — implicitly supports equity, it is the word each in the question at the top that has become central to our design of the IM K-5 Math curriculum.
