Grades 9–12 Math

What does it mean to enjoy mathematics?

What does it mean to enjoy mathematics?

By William McCallum When I started this series of blog posts on what it means to know, use, and enjoy mathematics, I thought this one would be the easiest. Math is fun, right? How could you not enjoy mathematics? I...

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What Does It Mean to Use Mathematics?

What Does It Mean to Use Mathematics?

By William McCallum Our vision at Illustrative Mathematics is a world where all learners know, use, and enjoy mathematics. In my last post I picked up that first verb and talked about what it means to know mathematics. In...

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What does it mean to know mathematics?

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...

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Reading Graphs is a Complex Skill

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...

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Equitable Teaching Practices in IM 6–12 Math

Equitable Teaching Practices in IM 6–12 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...

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Coming Together Around Distance Learning

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...

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Thoughts on the Back-to-School Problem

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...

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Planning for Learning in Spring of 2020

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...

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Links to Resources for Shifting Instruction Online

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...

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Links to Math Resources for Caregivers

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...

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Making Authentic Modeling Possible

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...

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Which Vertex is the Center of a Triangle?

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...

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Building a Supportive Home/School Partnership

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...

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Co-Creating Classroom Norms with Students

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...

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Introducing IM Certified 9–12 Math

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...

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Making Peace with the Basics of Trigonometry

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...

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Realizing the promise of open resources, part II

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...

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The Power of Small Ideas

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...

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Making Sense of Distance in the Coordinate Plane

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...

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Designing Coherent Learning Experiences K-12

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...

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NCSM NCTM Recap

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...

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What is a Measurable Attribute?

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...

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Rigor in Proofs

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...

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Presenting IM Algebra 1, Geometry, Algebra 2

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...

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How do you start the year?

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,...

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What is problem-based instruction?

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...

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Extra Supports for Algebra 1: The Gateway Resources

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...

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Realizing the promise of open resources

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...

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Truth and Consequences Revisited

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 +...

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The Power of Noticing and Wondering

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...

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Planning for Meaningful Practice

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...

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IM Preparing for the School Year

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....

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NCSM and NCTM 2018 Roundup

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...

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Warm-up Routines With a Purpose

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...

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