K–5 Curriculum Design Features that Support Equity and Inclusion

By Dionne Aminata

Before I joined the K–5 curriculum writing team at IM, I was a K–8 regional math content specialist for a public charter organization that largely consisted of Title I schools, or schools receiving federal funding to support a large concentration of students in poverty. Prior to that I had experienced the joys and challenges of serving communities like these as a teacher and math coach in South Central Los Angeles and Crown Heights Brooklyn. 

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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 \frac{2}{3}

What do you notice? How would you explain the things you notice?

If you are like us, or the students in Ms. Stark’s grade 5 classroom, you may have noticed many things. Things such as each expression has the same denominator, or the way in which the values increased as the problems progressed. When students notice these things, we often ask, ‘Why is that happening?” but it can be challenging to explain why beyond the procedure one followed. 

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The 5 Practices: Looking at Differentiation Through a New Lens

By Catherine Castillo

Our district had seen a downhill trend in standardized test scores in mathematics. This forced us, as educators, to take an intentional look at our teaching practices.

The past few years have been an exciting time in math instruction. Research on brain plasticity and mindset have caused a shift in the idea of what it means to know and do mathematics. 

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Building a Math Community with IM K–5 Math

“I’m not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me.”

By Tabitha Eutsler

This was my conversation with our math coordinator after my first few days of teaching IM K–5 MathTM with my third graders. Those five students were having great conversations. However, my other students just sat there wide-eyed, silent, and staring blankly at their papers. I felt lost. Was this the best for my students? Could we survive a whole year of math like this? I wanted my students to love math and have a deeper understanding of mathematical concepts. How would this get them there? 

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Creating an Accessible Mathematical Community with IM K–5: the power of “yet” for students and adults

Does the perfect elementary math curriculum exist? Armed with a growth mindset and the Alpha IM K–5 curriculum, teachers in Ipswich Public Schools push their thinking to reach all mathematicians. 

By Maureen D. O’Connell

I preach growth mindset daily. When my students say they can’t do something, they almost always add their own “…yet.” However, walking this walk as an elementary school teacher is another story. Creating, mastering, and modifying curricula to reach each and every student—in every content area—is a daunting expectation. We hold ourselves to near impossible standards. 

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Using Instructional Routines to Inspire Deep Thinking

We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So what can we do to support this other kind of thinking in class—the slow, deep kind?

By Jenna Laib

One way is through instructional routines like “Which One Doesn’t Belong” and “Notice and Wonder.” These routines give structure to time and interactions. Within the structure, there are opportunities to have time to think deeply and a predictable way to share and deepen thinking with partners and the whole class. 

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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 floating a question like:

  • I wonder if graduates of more expensive universities tend to earn more in their careers?
  • Do you think the time it takes a pendulum to swing back and forth depends on how heavy it is?
  • What do you think is the most efficient way to get 2,000 calories a day?

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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 post, “Which vertex is the center of a triangle?” It doesn’t have an answer. None of the vertices is the center of a triangle; all three are equally necessary for it to exist. Similarly, all three vertices of the instructional triangle—students, teachers, and content—need equal attention in the work of teaching mathematics. And not only the vertices but the arrows between them, which “represent the dynamic process of interpretation and mutual adjustment that shapes student learning [and] instructional practice.”1 If there is something special about what we do in writing curriculum it is to pay equal attention to all parts of the instructional triangle. 

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Updates to Supports for Students with Disabilities and English Language Learners in IM 6–8 Math

At Illustrative Mathematics we are committed to creating a world where learners know, use, and enjoy mathematics. We believe that every student can learn grade-level mathematics with the right opportunities and support. Our approach is to remove unnecessary barriers and provide teachers with options for additional support so that every student can engage in rigorous mathematical content. We’ve been busy this year working on some exciting enhancements to the teacher tools and supports to empower teachers to deliver instruction that meets the specialized needs of English learners and students with disabilities.

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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, we’ve gathered some posts from IM’s blog with different purposes to help get your year off to a good start.

By Kate Nowak

Before we dive into the links, if you are new to the IM curriculum, here are some tips to help you stay on pace

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