Grades 6–8 Math
What does it mean to know mathematics?
By William McCallum A world where all learners know, use, and enjoy mathematics. Perhaps the most mysterious verb in the IM vision—a world where all learners know, use, and enjoy mathematics—is the first one: know. Knowing...
Reading Graphs is a Complex Skill
Newspapers are full of graphs, far more than 10 or 20 years ago. Indeed, I have a graph to show that! (Source, Priceonomics) And yet I wonder how often readers see graphs as pictures illustrating a point, rather than as...
Equitable Teaching Practices in IM K–12 Math
by Tina Cardone The vision of Illustrative Mathematics is to create a world where learners know, use, and enjoy mathematics. This raises the question: Which learners? And what role do the authors of a curriculum play in...
English Learners and Distance Learning: Math Language Routines
by Vanessa Cerrahoglu, Jennifer Wilson, and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful...
New IM 6–12 Resources for Addressing Unfinished Learning and Engaging Students in Distance Learning
by David Petersen and Kate Nowak In our previous post, we described how we are thinking about planning for next fall. We are also creating some new resources to support users of IM K–12 Math in the fall. Some of this is to...
Coming Together Around Distance Learning
By William McCallum I can't imagine what it must feel like right now to be a teacher facing the uncharted territory that is the coming school year. Will I be teaching 100% online, or have some face-to-face interaction with...
English Learners and Distance Learning: Compare and Connect
By Vanessa Cerrahoglu, Jennifer Wilson, and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful...
English Learners and Distance Learning: Co-Craft Questions
By Jennifer Wilson and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful opportunities for students...
English Learners and Distance Learning: Clarify, Critique, Correct
By Jennifer Wilson and Liz Ramirez We want to acknowledge that we are all in different situations that shape how we respond to the call to adapt our teaching to fit a model for distance learning. This impacts the access we...
Looking Ahead to 2020–21 in IM 6–8 Math and IM Algebra 1, Geometry, and Algebra 2
By David Petersen, Lead Curriculum Writer and Kate Nowak, Director of K–12 Curriculum Strategy This school year has been strange and stressful, and there is uncertainty about what next year will look like. Due to school...
English Learners and Distance Learning: Enhancing Access
By Liz Ramirez Which students are experiencing success in today’s “distance learning”? What barriers do other students face? While virtual learning platforms have made it possible for some live instruction to continue...
Thoughts on the Back-to-School Problem
By William McCallum One of the consolations in these difficult times has been tweets and Youtube videos of parents discovering just what it takes to be a teacher. Maybe it takes a crisis like this to restore the respect...
Planning for Learning in Spring of 2020
Some schools are sending home printed packets and establishing teacher office hours by phone. Some are conducting their regular class schedule, but online. And lots are doing something in between. We understand that it is...
Aggregated Support for the IM Math Community in Spring 2020
We want to share our deepest gratitude for the work each of you has been doing to protect yourselves, your families, your students, and your school communities, as you face hard decisions about how to support students while...
Links to Resources for Shifting Instruction Online
First and most importantly, take care of yourself, your family, and your students. That might not look like doing math, or it might. To the extent that it’s useful, we have curated this list of resources recommended by our...
Links to Math Resources for Caregivers
Here is a collection of links the content team here at IM has used with our own students and kids to start mathematical conversations, play math games together, explore new topics, come up with projects, and have fun. There...
Using Diagrams to Build and Extend Student Understanding
By Jenna Laib and Kristin Gray Take a moment to think about the value of each expression below. $\frac{1}{4}\times \frac{1}{3}$ $\frac{1}{4}\times \frac{2}{3}$ $\frac{2}{4}\times \frac{2}{3}$ $\frac{3}{4}\times...
Making Authentic Modeling Possible
The first thing you have to understand is that asking people to model with mathematics makes them mad. Not in all contexts, though! At a social gathering with a generally amiable and curious group of people, you might try...
Which Vertex is the Center of a Triangle?
By William McCallum I am sometimes asked what is the secret to the success of our curriculum, what is the special property that sets it apart from other curricula. That question is like the one in the title of this blog...
Preparing for the School Year, Updated with Tips for Staying on Pace
Last year, we put together some reading to help people get started planning their year with IM 6–8. Now, we have another year’s worth of blog posts to choose from, plus a shiny, new high school curriculum! So once again,...
Building a Supportive Home/School Partnership
While families arrive with different school experiences and perspectives on what “doing math” means, they often share common questions: What do I need to know to set my child up for success in math this year? and How can I...
Co-Creating Classroom Norms with Students
Establishing norms is critical to creating an environment where all students see themselves as knowers and doers of mathematics. Reflecting on the Illustrative Mathematics mission statement, Creating a world where learners...
Explicit Classroom Norms to Teach Kids How to Learn From Solving Problems
This blog post is the fourth in a series of four blog posts exploring the student experience of problem-based learning. The first three posts are available here: (1) “How Do Students Perceive Problem-Based Learning?” (2)...
Concrete Representations that Give Students a Way to Get Started
This blog post is the third in a series of four blog posts exploring the student experience of problem-based learning. The first two posts are available here: “How Do Students Perceive Problem-Based Learning?” and “Inviting...
Introducing IM Certified 9–12 Math
IM Algebra 1, Geometry, and Algebra 2 courses are now available to all. Alright, folks, this is not a drill: IM 9–12 Math is now available to all. By Ashli Black So now what? To help folks dive into the curriculum, we’ve...
Making Peace with the Basics of Trigonometry
Six months ago, I hated trigonometry. By Becca Phillips In fact, when my daughter missed a week of school, she announced on her first day back, “Someone has to teach me trig because I missed the whole thing.” Her father...
Realizing the promise of open resources, part II
By William McCallum In my first post on the topic of realizing the promise of open educational resources, I described the IM Certified program. Our partners offer multiple versions, including a free online version and...
The Power of Small Ideas
By William McCallum, IM President Big ideas are popular in mathematics education, and you can find many lists of big ideas on the web. Some are more thoughtful than others, and I can see how some might be useful for...
Making Sense of Distance in the Coordinate Plane
By Linda Richard, Curriculum Writer I used to teach my high school 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...
Designing Coherent Learning Experiences K-12
By 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...
Developing Conceptual Understanding and Procedural Fluency
By 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? Some argue that procedure has to...
NCSM NCTM Recap
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. We enjoyed the conversations we had with...
What is a Measurable Attribute?
By 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...
Rigor in Proofs
By 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...
Presenting IM Algebra 1, Geometry, Algebra 2
By Kate Nowak 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...
How do you start the year?
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,...
What is problem-based instruction?
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...
Extra Supports for Algebra 1: The Gateway Resources
By Sadie Estrella Illustrative Mathematics’ high school curriculum is scheduled to be released this summer. This is an exciting time for Algebra 1, Geometry, and Algebra 2 teachers. I honestly am ready to take a job at a...
Realizing the promise of open resources
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...
Truth and Consequences Revisited
By William McCallum What are extraneous solutions? A while ago I wrote a blog post about solving equations where I talked about seeing the steps in solving equations as logical deductions. Thus the steps \begin{align*}3x +...
The Power of Noticing and Wondering
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...
Catalyzing Change through the IM Algebra 1, Geometry, Algebra 2 Math
NCTM has called for structural and curricular changes in high school mathematics. Learn about how IM's high school curriculum is aligned with the vision put forth by NCTM to end tracking, implement effective targeted...
Proof in IM’s High School Geometry (A Sneak Preview)
Supporting high-school students to write detailed, precise proofs is challenging. Learn about some of the design elements that IM used to invite students to a deep exploration of proof. In IM’s high school Geometry...
Planning for Meaningful Practice
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...
IM Preparing for the School Year
There are always so many things to do in preparation for a new school year. At this point of the summer, to-do lists start getting made, materials get purchased, rooms are organized, and math class planning begins....
The IM 6–8 Math Curriculum Changed My Math Methods Experience
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...
NCSM and NCTM 2018 Roundup
It was great to see so many of you at NCSM and NCTM. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below. We enjoyed the conversations we had with those of you that are using the IM 6–8...
Warm-up Routines With a Purpose
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...