# Grades K-2 Math

## The Story of Grade 1

Jan 27, 2022

By Brianne Durst Grade 1 teachers have the awesome responsibility of introducing their students to, and helping them build an understanding of, the structure of our number system. This is no small task! Just think about how...

## Revisiting Distance Learning with IM K–12 Math™

Jan 18, 2022

With the surge of the Omicron variant, many schools are moving back to distance learning. Although we may not be excited to leave our classrooms again, we are better prepared for distance learning this time around. Most, if...

## In the Beginning: Unit 1 in Kindergarten

Dec 7, 2021

By Alex Clayton When was the last time you stepped into an entirely new environment? You weren’t sure exactly what was going to happen. There was no one you recognized. How did you feel: Uncertain? Anxious? Hopeful? During...

## Illustrative Mathematics Celebrates 10 Years: Letter from the CEO

Dec 1, 2021

2021 marks our 10th anniversary at Illustrative Mathematics, and we couldn’t be more proud to have impacted so many hundreds of thousands of students, teachers, and families since our humble beginnings in 2011. Our business...

## Using IM K–5 Math™ to Support Cognitively Guided Instruction (CGI)

Nov 16, 2021

By Mike Henderson “The activities require skills that students are not taught prior to doing the activity. They’re expected to just jump right in. Why isn’t there more modeling or re-teaching of basic skills so students can...

## Remembering Bob Moses

Nov 3, 2021

By William McCallum and Kristin Umland "Math literacy will be a liberation tool for people trying to get out of poverty and the best hope for people trying not to get left behind.” —Bob Moses, 1935–2021 Bob Moses, the civil...

## Together Apart: Amplifying the “Gift of Student Thinking” in Distance Learning with IM

Oct 26, 2021

By Maureen D. O’Connell, IM K–5 Math™ Pilot Teacher,IM Certified® Facilitator for IM K–5 Math “The more intensely interested a teacher is in a student’s thinking, the more interested the student becomes in his or her own...

## Unlocking Learners’ Thinking Using the Mathematical Language Routines

Oct 5, 2021

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 English-speaking peers do....

## FASTalk: Activating the Power of Families to Support Mathematics

Sep 28, 2021

By Elisabeth O’Bryon, co-founder 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 chart-less in Grade 2”

Sep 20, 2021

By Maureen D. O’Connell, Math Specialist Some math tools and representations help students solve in-the-moment problems. Other math tools and representations help students solve problems and grow their conceptual...

## Multi-grade Classrooms and

IM K–5 Math™

Sep 8, 2021

By Jen Hawkins, IM Facilitator and IM K-5 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 so-called ‘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 K-5 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 K-5 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...

## 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,...

## 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...

## 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...

## 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...

## 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 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 building-wide 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...

## When is a number line not a number line?

Feb 15, 2020

By William McCallum The number line is a seemingly simple object: a straight line with two points marked 0 and 1. Those two points are the seeds of great complexity, however. Whole numbers are located at positions marked...

## 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...

## 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 K-5 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 K-12

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...

## 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...

## IM K-5 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 warm-up of the...

## 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 (CC-BY) license, which allows anyone to "copy and redistribute the material in any medium or...

## 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...

## 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 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

Aug 6, 2018

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

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...

## 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 round-up below. We enjoyed the conversations we had with those of you that are using the IM 6–8...

## Using Math Routines to Build Number Sense in First Grade

Apr 3, 2018

By Allison Van Voy When I started teaching four years ago, I had no idea how important number sense was to a student’s math understanding. I was fresh out of college, brand new to teaching, and number sense was not a...

## Warm-up 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...

## Adapting Problems to Elicit Student Thinking

Feb 18, 2018

By Jody Guarino As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical...

## 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...

*to the IM Blog and Newsletter*

#### RECENT POSTS

- The Story of Grade 1 January 27, 2022
- A Thread Through Early Algebra 1 January 19, 2022
- Revisiting Distance Learning with IM K–12 Math™ January 18, 2022
- Taking the Long View January 11, 2022
- What Does IM Think About Unfinished Learning and Supporting Students with a Variety of Entry Points? (Grades 6–12) December 17, 2021

#### Categories

- Grades 3–5 (78)
- Grades 6–8 (84)
- Grades 9–12 (63)
- Grades K–2 (61)
- Grades K–5 (26)
- Professional Learning (49)