By IM Certified Facilitators, Cheryl Fricchione and Rachel Rundstrom Consider this:A child whose primary language isn’t English does not participate in the classroom to the degree that their Englishspeaking peers do....
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FASTalk: Activating the Power of Families to Support Mathematics
Sep 28, 2021
By Elisabeth O’Bryon, cofounder and Chief Impact Officer at Family Engagement Lab and Megan Lorio, Managing Editor at Family Engagement Lab Engaging families in meaningful and equitable ways is a cornerstone of student...
Choosing Math Tools and Representations that Work:
“100 chartless in Grade 2”
Sep 20, 2021
By Maureen D. O’Connell, Math Specialist Some math tools and representations help students solve inthemoment problems. Other math tools and representations help students solve problems and grow their conceptual...
Multigrade Classrooms and
IM K–5 Math™
Sep 8, 2021
By Jen Hawkins, IM Facilitator and IM K5 Product Specialist Illustrative Mathematics believes that students can achieve success as mathematical thinkers by working through problems and consolidating their learning through...
Introducing the IM Implementation Reflection Tool
Aug 30, 2021
by Liz Ramirez, Director of Implementation “This makes the expectations for what I need to change visible.” “It’s not about the tool. It’s about the conversation using the tool.” Quotes from leaders who participated in IM’s...
A Love for Math Reignited
Jul 26, 2021
By Michael Ramirez, Senior Coordinator of School Transformation, Elementary Math When I began school as a kindergartener, I absolutely adored math. As a lower elementary school student, I remember relatives asking me what...
IM K–5 Math: An End and a Beginning
Jul 13, 2021
By William McCallum On March 20, 2015, I received the following email: Thank you for submitting your proposals to the K–12 OER Collaborative. We are pleased to advise you that Illustrative Mathematics has been selected as a...
Culturally Responsive Teaching and Math
Jun 30, 2021
By Asya Howlette, Director of Mathematics and Science at Thurgood Marshall Raise your hand if you have been perplexed by professional learning that told you your class needs to be culturally responsive, but left you...
Fluency Development Within and Across the Grades in IM K–5 Math™, part 4: Multiplication and Division
Jun 7, 2021
By Dionne Aminata, Grade 2–5 Lead Writer and Sarah Caban, Grade 5 Lead Writer“Some students are never given the opportunity to engage with mathematics in rich and meaningful ways that emphasize critical thinking and problem...
Fluency Development Within and Across the Grades in IM K–5 Math™, part 3: Multiplication and Division
Jun 1, 2021
By Dionne Aminata, Grade 2–5 Lead Writer and Sarah Caban, Grade 5 Lead Writer “The idea of being a ‘math person’ is based on two pervasive world views; first, the socalled ‘fixed’ mindset, that what one knows about math...
What does it mean to enjoy mathematics?
May 17, 2021
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...
Fluency Development Within and Across the Grades in IM K5 Math™, part 2: Addition and Subtraction
Apr 27, 2021
By Sarah Caban, Grade 5 Lead Writer and Dionne Aminata, Grade 2–5 Lead Writer"We have to break from the notion that learning mathematics must be a linear and procedural endeavor mastered through rote practice and...
Fluency Development Within and Across the Grades in IM K–5 Math™, part 1: Addition and Subtraction
Apr 20, 2021
By Sarah Caban, Grade 5 Lead Writer and Dionne Aminata, Grade 2–5 Lead WriterWhen do students practice their math facts? How is math fluency assessed?”—current and prospective IM K5 Math™ teachers everywhere We...
Building Equitable Learning Environments for Each Student
Mar 22, 2021
By Danielle Seabold All students can be successful in mathematics. For most mathematics educators, we lean into this. We believe that all students can learn mathematics, that they can be successful. However, as we focus our...
Explorations in IM K–5 Math: Challenges for Curious Students
Mar 2, 2021
By Jen Hawkins and Mike Nakamaye What do we do with curious students who are ready, willing, and able to go further with math ideas? Some students cannot wait to dig deeper into the mathematics they are studying in class....
What Does It Mean to Use Mathematics?
Feb 22, 2021
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...
Supporting Culturally Responsive Pedagogy with IM K–5 Math™
Feb 17, 2021
By Dionne Aminata “We are striving to . . . compose a country committed to all cultures, colors, characters, and conditions of man. And so we lift our gazes not to what stands between us, but what stands before us.” Poet...
By the End of Grade 3: Developing Fluency with Multiplication
Jan 25, 2021
By Zack Hill The major work of grade 3 includes representing and solving problems that involve multiplication and division. Then, by the end of grade 3, students are expected to know from memory all products of two...
What does it mean to know mathematics?
Jan 4, 2021
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...
The Nuances of Understanding a Fraction as a Number
Dec 7, 2020
By Kristin Gray This was originally posted on Kristin Gray’s personal blog, Math Minds, on November 15, 2020. Student work is just the best. It is the one thing that will always motivate me to write! So, let’s kick this...
Creating Time and Space for Students to Develop Foundational Mathematical Ideas
Nov 16, 2020
By Maureen D. O'Connell “Slow down, you’re moving too fast, you got to make the morning last...” When we consider early childhood mathematics this familiar song comes to mind. In our hurried society where more is more,...
Reading Graphs is a Complex Skill
Nov 4, 2020
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...
Making Sense of Story Problems
Oct 27, 2020
by Deborah Peart, Grade 2 Lead Many people have an aversion to word problems. They cringe at the mention of them. In elementary classrooms, teachers often report that this is what their students struggle with most. When...
The Story of Grade 5
Oct 15, 2020
by Sarah Caban From the start of the year, we want students to know they are capable of engaging in gradelevel mathematics. In the Opportunity Myth (2018), data shows that there is an opportunity gap for historically...
Planning for the Student Experience
Sep 4, 2020
by Sarah Caban and Kristin Gray Teachers are so amazing and resilient. Amid all of the many thoughts and feelings about the challenges this school year brings, conversation continually revolves around their students. When...
Facilitating the “Choral Counting” Routine Online
Aug 25, 2020
by Janaki Nagarajan How can we best do mathematics together in an online environment? When school suddenly shifted online last spring, I found myself overwhelmed by the learning curve for new technologies—for both myself...
Helping Elementary Students Cultivate a Strong Math Community
Aug 18, 2020
by LaToya Byrd and Jenna Laib School looks different this year. It’s easy to focus on the changes that will need to be made—the new practices, the new routines, the new technologies—but we must first focus on our central...
Coming Together Around Distance Learning
Jul 7, 2020
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 facetoface interaction with...
English Learners and Distance Learning: CoCraft Questions
Jun 15, 2020
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...
Looking to the Fall, Part 2: Creating a Supportive Resource for K–5 Teachers
May 20, 2020
By Kristin Gray, Director K–5 Curriculum and Professional Learningand Kevin Liner, IM K–5 Professional Learning Lead In our previous post, we highlighted important considerations in planning to support students in the fall....
Looking to the Fall, Part 1: Welcoming and Supporting K–5 Students
May 7, 2020
By Kristin Gray, Director K–5 Curriculum and Professional Learningand Kevin Liner, IM K–5 Professional Learning Lead It is overwhelming to think about how teaching and learning will look in the fall. The uncertainty of the...
Thoughts on the BacktoSchool Problem
Apr 27, 2020
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...
IM Talking Math
Mar 26, 2020
By Kristin Gray Most importantly, I hope everyone is taking care of themselves, their families, and others as much as they are able to during this time. With schools and districts pushing instruction online with a quick...
Links to Resources for Shifting Instruction Online
Mar 14, 2020
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
Mar 14, 2020
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...
Shifting Practices: Helping Everyone—from Students to Administration—Find their Voice in the Math Classroom
Feb 29, 2020
It was easy to say yes! By Crystal Magers Last spring, I was approached by our Math Coordinator and asked about piloting a new math program. I knew my staff was ready for buildingwide consistency and we were ready to try...
K–5 Curriculum Design Features that Support Equity and Inclusion
Feb 29, 2020
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...
The Art of Reflection
Feb 3, 2020
“In times of stress, the best thing we can do for each other is to listen with our ears and our hearts and to be assured that our questions are just as important as our answers.” —Mr. (Fred) Rogers By Kaneka Turner We are...
Ratio Tables are not Elementary
Jan 12, 2020
By William McCallum In grade 3, as students start to learn about multiplication, they think about products like 6 x 7 in terms of equal groups. 6 x 7 is the number of things when you have 6 groups with 7 things in each...
Using Diagrams to Build and Extend Student Understanding
Nov 25, 2019
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...
Building a Math Community with IM K–5 Math
Nov 2, 2019
“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...
Creating an Accessible Mathematical Community with IM K–5: the power of “yet” for students and adults
Oct 22, 2019
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...
Using Instructional Routines to Inspire Deep Thinking
Oct 13, 2019
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,...
Which Vertex is the Center of a Triangle?
Sep 23, 2019
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...
First Impressions: The First Units in IM K–5 Math
Jul 23, 2019
“I've learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.” ? Maya Angelou By Kristin Gray When I think back to my 8th grade math class, I...
Realizing the promise of open resources, part II
Jun 17, 2019
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...
Storytelling in the IM K5 Math Curriculum
Jun 4, 2019
By Kristin Gray, Director of K–5 Curriculum & Professional Learning Curriculum "An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and...
The Power of Small Ideas
May 21, 2019
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...
Designing Coherent Learning Experiences K12
May 7, 2019
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...
NCSM NCTM Recap
Apr 15, 2019
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 roundup below. We enjoyed the conversations we had with...
What is a Measurable Attribute?
Apr 8, 2019
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...
Representing Subtraction of Signed Numbers: Can You Spot the Difference?
Mar 2, 2019
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....
IM K5 Math: Designing for Each Student
Feb 26, 2019
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 warmup of the...
What is problembased instruction?
Feb 19, 2019
By William McCallum When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelvecoin problem, the most difficult of all coin weighing problems. My mother and I worked on it...
Realizing the promise of open resources
Jan 25, 2019
By William McCallum All of our curriculum here at Illustrative Mathematics is released under a Creative Commons Attribution (CCBY) license, which allows anyone to "copy and redistribute the material in any medium or...
What is Multiplication?
Dec 11, 2018
Multiplication is vexation, Division is as bad; The Rule of Three doth puzzle me, And Practice drives me mad. (old nursery rhyme.) Some people might answer that multiplication is repeated addition. For example, $5 \times 7$...
The Power of Noticing and Wondering
Dec 3, 2018
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...
Professional Learning Through a Fraction Task Progression
Oct 16, 2018
Teaching mathematics is a continuous cycle of identifying where each student is in their learning trajectory and determining meaningful ways in which to build on their current understandings. While we...
Planning for Meaningful Practice
Sep 19, 2018
There is no shortage of available math resources for teachers to use in their classrooms. The difficult and timeconsuming job for teachers is weeding through all of the tools to decide which best supports students in...
Say What You Mean and Mean What You Say
Sep 11, 2018
By William McCallum In one of our professional development workshops, there is an activity in which the facilitator asks teachers to skip count by $\frac34$. The facilitator records the count, $\frac34$, $\frac64$,...
IM Preparing for the School Year
Aug 6, 2018
There are always so many things to do in preparation for a new school year. At this point of the summer, todo lists start getting made, materials get purchased, rooms are organized, and math class planning begins....
Fractions: Units and Equivalence
Jul 10, 2018
By William McCallum “I'm afraid I can't explain myself, sir. Because I am not myself, you see?” Alice in Wonderland. The idea of equivalence in mathematics is tricky for learners, because when we talk about two things being...
5th Grade: Decimal Place Value
Jun 26, 2018
By Kristin Gray There are some standards I think we do such a great job developing in early elementary, but never revisit explicitly when students learn about different numbers such as fractions and decimals. I blogged...
The IM 6–8 Math Curriculum Changed My Math Methods Experience
Jun 4, 2018
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...
Untangling fractions, ratios, and quotients
May 14, 2018
By William McCallum In everyday language, $\frac{a}{b}$, $a\div b$, and $a : b$ are all different manifestations of a single fused notion. Here, for example are the mathematical definitions of fraction, quotient, and ratio...
NCSM and NCTM 2018 Roundup
Apr 30, 2018
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 roundup below. We enjoyed the conversations we had with those of you that are using the IM 6–8...
Instructional Materials Matter: Interpreting Remainders in Division
Mar 20, 2018
By Jody Guarino We know instructional materials play a key role in student learning experiences but how do we ensure our students are learning from coherent highquality instructional materials that engage them in critical...
Adapting Curriculum For Students to Know, Use and Enjoy Fractions
Mar 13, 2018
By Melissa Greenwald You know it is time for a change when half of the students in class are lost by the third lesson of a new unit. I teach third grade in a charter school in Philadelphia. We use Go Math! and each year I...
Warmup Routines With a Purpose
Feb 27, 2018
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...
A Fraction Unit Does Not Always Begin With Lesson 1
Feb 12, 2018
By Jared Gilman As I sat down at my local coffee shop to plan my upcoming 5th grade unit on fractions, a wave of dread spread across my body. I started having flashbacks to last winter, when my students’ frustrations with...
Fraction & Decimal Number Lines
Dec 6, 2017
By Kristin Gray Recently, our 3rd, 4th, and 5th grade teachers had the opportunity to chat math for 2 hours during a Learning Lab held on a professional development day. It was the first time we had done a vertical lab and...
Ways of thinking and ways of doing
Jun 7, 2017
By William McCallum Somewhere back in days of Facebook fury about the Common Core there was a post from an outraged parent whose child had been marked wrong for something like this: $$ 6 \times 3 = 6 + 6 + 6 = 18. $$...
Misconceptions about Multiple Methods
May 24, 2017
By William McCallum You may have noticed that I am back to publishing regular blog posts! My goal for now is a blog post every second Wednesday. I am now also trying to answer forum questions promptly. I want to thank the...
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RECENT POSTS
 Gifts: A Reflection on Student Thinking October 12, 2021
 Unlocking Learners’ Thinking Using the Mathematical Language Routines October 5, 2021
 FASTalk: Activating the Power of Families to Support Mathematics September 28, 2021

Choosing Math Tools and Representations that Work:
“100 chartless in Grade 2” September 20, 2021 
Multigrade Classrooms and
IM K–5 Math™ September 8, 2021
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