Which math curriculum is best?

Dec 3, 2020

That is the question that I am asked most often when going to schools. There are so many different options out there, but is there a perfect math series?

As I always say, the book isn’t your curriculum; the standards are your curriculum. The book, whether it’s Math Expressions, GoMath, My Math, Everyday Math, Ready Common Core, Eureka Math, etc., that was purchased for you is a really great resource that helps you build a common language for math instruction. Each of the series has great components that can help as you develop a curriculum for your school. 

I also say that curriculum shouldn’t be stagnant. It should change from year to year. But when you open your book from last year, it looks the same as it did last year, doesn’t it? Does it have some of the guiding principles that you’re looking for with student engagement? Does it integrate the 8 Mathematical Practices? Does it help students to be able to construct viable arguments and critique the reasoning of others? Is it less about just getting into the direct teaching of the lesson?

At SIS4Teachers, we’ve done lots of curriculum development to help teachers have some kind of roadmap for their math curriculum as they apply the 8 Mathematical Practices and help students access the curriculum in various ways. Without a plan of some kind, we end up with a “binder series” kind of school, where one teacher has something from TPT, one teacher found something cute on Pinterest, another teacher stole an idea from someone else…although they’re all following the same standards, the glue of a common language to hold it all together is missing. Don’t get me wrong, I’m a huge fan of things being free. I’ve done tons of work with Eureka Math and Engage New York, and I love having an online platform that you can mold to meet your district’s needs.

For all these reasons, I’m so excited about IM K–5 Math™, an openly-licensed curriculum authored by Illustrative Mathematics. You might have heard that Illustrative Math is for the grades 6-8 and grades 9-12, and they are known for that, but they’re releasing a K-5 series in 2021

Each grade level contains 8 or 9 units that contain anywhere from 8 to 25 lesson plans each. Each lesson plan is designed to fit into a 60-minute math period. I know what you’re thinking – yeah right, those “60 minute” lesson plans are totally unrealistic with actual 2nd graders! But these lesson plans from Illustrative Math are the real deal! They give you flexibility because they offer optional activities that you can include for additional student practice or centers, or just on certain days when you have more time. 

Some of the grade levels have a pre-unit practice within each section, which I think is really important. Sometimes, we get eager to dive right into the content of the lesson, but our students aren’t ready because it might have been a while since they used that skill. This pre-unit helps make sure we’re all ready at the same time.

Each of the lessons and assessments are aligned to center activities that support unit content and ongoing procedural fluency. Many of the activities they have require Blackline Masters and include recording sheets. There are some game boards and cards that might require some teacher prep (printing, cutting, plastic baggies), but a lot of the materials you need are already done there for you. 

One of the most important parts of this Illustrative Math series is the design principles used to create a problem-based curriculum that really fosters the development of math learning with the community in a classroom. The five principles really align with what SIS4Teachers is all about, and the result is a resource that gives access to mathematics through a really cohesive progression, that provides an opportunity for students to get that deep understanding in mathematics, and helps promote student thinking.

Five Guiding Principles

The first guiding principle is that students are capable as learners of mathematics. This principle is really important in a world where the teacher is viewed as the giver of all the information in math. We know that students are capable of learning math, that they can make use of learning communities to make math meaningful and meet their own unique needs. Students can practice through equitable structures that provide experiences that are accessible to their particular grade level. The resource includes classroom structures that support students taking risks. It is really important for kids to take risks because, so many times, they don’t even want to raise their hand and engage for fear that they’re going to not be correct. The ideas of math discourse and productive struggle come into play in this “students as capable learners” idea, which are two of the main underlying concepts that we talk about at SIS, come into play in this particular design principle.

Another guiding principle is learning mathematics by doing mathematics. Within their learning communities, this looks like students learning mathematical concepts and procedures while engaging in the 8 Mathematical Practices. Can kids make sense of problems and persevere in solving them? Reason abstractly and quantitatively? Create viable arguments and critique the reasoning of others? Can they model with mathematics? Can they use the appropriate tools? Can they attend to precision and using the language that they’re supposed to? And can they look and make sense of structure and express regularity in repeated reasoning? 

Remember, it’s not about you doing it as the teacher. We go through the math practices every day! But it’s about allowing the students to really engage with the practices with peers or others, which really helps them have the opportunity to see themselves, that their thinking is really worthwhile and their ideas have perspective. 

The fact that this principle is incorporated into a program, instead of you having to integrate these practices yourself, is amazing! 

The third one principle is problem-based lesson structure. Students learn mathematics as a result of solving problems. To support our students in productive struggle, giving them problem-based instructional frameworks to help them understand their mathematics is really important. At SIS, we talk a lot about performance tasks and three acts tasks – getting kids to have a higher level of thinking. The teacher’s role in this kind of framework is that of a listener, a facilitator, a questioner, a synthesizer. As we’ve talked about in so many past blogs, it’s about taking a back seat and becoming a co-learner with your students. Illustrative Math includes these tasks as part of their guides, which I think is awesome!

I also think that teachers can guide students in understanding problems by asking questions. We can help students think in a more productive way as they approach problems. Using question stems like What did you notice? What do you wonder? Is a pivotal piece of what we talk about at SIS.


Balanced rigor is the fourth designing principle. Those two words are really great together, right? The three aspects of rigor are really essential in math. You have conceptual understanding, procedural fluency and the ability to be able to apply the concept and skill in math problems in the real world. The NCTM talks about this in their Principles to Action where they state that interconnections support students’ understanding. Hello! This is our idea of CPA (concrete, pictorial, abstract or concrete, representational and abstract). If students don’t have the conceptual understanding, along with the procedural understanding, it’s going to be a misfit. 

The materials in Illustrative Math really offer all three aspects of the rigor by helping students access the new mathematics, really engage in rigorous routines, and connect to new representation in math language from prior learning.

I think it really requires students to apply their knowledge and really helps them to understand it. There are specific grade level expectations for procedural fluency, which come with warm ups and centers and practice problems, but there’s also continued opportunities for students to really apply their understanding in situations to give them practice of the new materials that are being presented. 

The last design principle talks about coherent progression. This is so important and I’m a huge advocate for this. At SIS, I talk about a “vertical zip,” which is the basis of the materials that support all learners through a cohesive progression of mathematics, both by the standard and research-based learning trajectories. If you don’t have this progression from grade to grade great, you’re on islands! The islands might look nice, but they don’t allow students to view mathematics as a connected set of ideas to make sense as they get older.

This kind of support helps to bring in students’ prior knowledge for the upcoming grade level work, and it’s also important for teachers to understand the progression of the materials. At SIS, we talk a lot about looking at the trajectories from grade to grade to help teachers see a flow and gain an understanding of mathematics and how it’s connected to the prior or the upcoming grade level. 

Unit Design

Each unit begins with an invitation to mathematics. The first few lessons provide an accessible entry point for all students. We do this a lot with number talks, with games like Steve Wyborney’s SPLAT!, with an engaging Math Talk picture. The invitation to come to mathematics is something that we’ve always talked about at SIS4teachers. We want to give kids an entry point where they feel like they can get going instead of just jumping into the lesson. 

Beginning with a warm up, which I often call a lesson launch, also helps students activate their prior knowledge. This part isn’t always about success, but just getting the ideas going or percolating, because they will then be followed up with the instructional activities which are an introduction to the new concepts, procedures or representations and making the connections between them. 

The lessons end with a synthesis or coming together to talk about our learning goals, so each lesson includes a cool down that helps students apply what they’ve learned, which I love. Often, with a performance task or three acts task, we’re trying to cram in so much, but Illustrative Math has done an amazing job of integrating a lot of the important components of math instruction.

So, each activity starts with a launch to help students get to their task, followed by some independent work time for students to have what I call “productive struggle” with problems individually, before they work at small groups. And the activity ends with students coming together and really talking about their work.

Building Community

Having a community in your classroom is something we talk a lot about in our SIS trainings. We want to create an environment where students feel safe, where they have a productive disposition about math, and are able to engage in mathematical practices. It’s really important us, as teachers, to start the school year by creating this safe math community that allows students to express their ideas. For most of us, that’s really hard to do because we didn’t necessarily grow up with that in our own classrooms. Additionally, kids can sometimes have an idea of how math looks and it doesn’t necessarily include conversation around mathematics. 

Each of the units in each of the grades provides a lesson structure that helps us establish this math community, establish the norms and invite students to make mathematics accessible to them. Each lesson offers opportunities for students to learn, and really go more in depth with the math language as they become familiar with the curriculum routines. Being able to create a community is what is going to help get kids feeling really tied to the different parts of what’s going on. 

Instructional Routines

As we know, instructional routines are what really creates a structure to help elicit the math conversations. They help students understand that there’s a predictable flow from day to day,.and that we have high expectations for learning. In the Illustrative Math materials, they chose a small set of instructional routines to really ensure that they’re used frequently enough to become truly routine. That small set of routines was also chosen carefully in this program so as to not overload teachers. You’re not a magician! You can’t make all of these things happen at once! So having a small set of strategies can really help teachers focus their energy on the structuring of the activities while students have thinking time and mathematical ideas play out. So each of the routines brings in a lot of the different types of parts to help build a collective understanding of the structure. These routines are aligned with the unit, the lesson, and the activity /learning goal. 

If you can’t tell by now, Illustrative Math is such a great resource!! To add a cherry on top of this resource, it also includes videos of the routines in action for teachers to watch. So many times we wonder how is it even possible to get all this done, but now you can watch it happen in a real-life scenario! There are also professional learning materials for teachers to use to practice and reflect on their craft, or maybe use as part of a PLC.

Five Practices for Orchestrating Productive Instruction.

This is a really great book (find it on Amazon) which talks about the ideas of creating task complexity, purposed representations, establishing teaching structures and practices, as well as teaching learning through curriculum materials, and then really being able to model with mathematics, K-5. And so, if you’re familiar with this book, I think that the ideas or the principles are great and they tie into this portion on what they have in Illustrative Math.

How do I get this amazing resource??

Parts of the IM K–5 Math™ are currently out right now! If you go to https://im.kendallhunt.com/, click on the K-5, and you can see the teacher and the parent resources. As of the writing of this blog, I believe unit one is all loaded, but they will be intermittently loading all the different parts, as the full launch will be in 2021. 

This program truly does mirror so many of the things we are always talking about with our schools, which is why I wanted to share the designing principles with you. I think they are so important, and it makes me so excited to share this resource with you! To be able to have all this strategically designed, standards-aligned material available in a ready-to-use format that is free…it’s amazing! 

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