First Impressions: The First Units in IM K–5 Math

“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 

When I think back to my 8th grade math class, I cannot recall the exact problems I struggled with or exact things the teacher said or did, but I can distinctly remember how I felt each day walking into that classroom: anxious. From the very first day of school, I struggled, and my feelings of failure and self-doubt only compounded as the year progressed. I just could not keep up. While many, many years have passed, and details have faded from my memory, I have never forgotten how badly I felt about myself as a learner of mathematics each day.  

I am fortunate to have had only one of those years to remember. Imagine a student who has had years of feeling frustrated, anxious, and doubtful of their ability in mathematics as they walk into your classroom. What message does the content you teach during that first week of school send to students? What does it communicate about what math is? What feelings does it evoke for students?

As with the IM 6-12 curricula — comprised of IM Certified 6-8 Math and IM Certified 9-12 Math 2020 — the K–5 team wanted to choose content for Unit 1 that would offer students an accessible invitation to the mathematics at the very start of the school year. But we found that we couldn’t think about the content until we first considered the broader goals for Unit 1. 

At the first writer meeting in October, we jotted down all of the things we wanted to accomplish within the content we chose for the first unit.  

With all of our hopes and dreams for Unit 1 out on the table, we went back to the standards and progressions to think about the organization of content by unit. We specifically looked for mathematics that lent itself to the use of mathematical tools, offered opportunities for teachers to formatively assess students’ prior grade level understandings, and provided students with the space to work together in building their classroom community. We specifically avoided computation-heavy work like the typical place value review unit. For students who view math as only “answer getting” or “number crunching” and have struggled in previous years, we worried that type of work might evoke feelings of anxiety and frustration from the first day, which we wanted to avoid.    

Here is a list of where we landed on Unit 1 for our alpha pilot with a short excerpt from each unit overview: 

Kindergarten: Numbers 1–5

Students enter kindergarten with a range of experiences, skills, and concepts of counting. In this unit, students explore and use mathematical tools to develop counting concepts, learn routines, and connect counting to their world.

Grade 1: Collecting and Using Data

In this unit, students develop their understanding of data representations. They ask and answer questions about categorical data based on a representation of the data. This builds on the addition and subtraction work of kindergarten. 

Grade 2: Adding and Subtracting with Data   

In this unit, data provides a context for addition and subtraction problems. Students first represent data in picture graphs and bar graphs and, later in the unit, solve problems using information presented in the graphs. This builds on the addition and subtraction work of grade 1.

Grade 3: Introducing Multiplication

In this unit, students build on their grade 2 understanding of data and apply skip counting to reason about multiplication. At the beginning of the unit, students interpret and create picture graphs and bar graphs. Scaled picture graphs are then used to introduce multiplication as equal groups situations. In the remainder of the unit, students develop an understanding of multiplication through situations and representations such as drawings, expressions, equations, and arrays.

Grade 4: Fraction Equivalence and Comparison

In this unit, students build on their grade 3 understandings of fractions and fraction representations. Students generate equivalent fractions, explain equivalence, and justify fraction comparisons through a progression of representations that build from physical fraction strips to more abstract tape diagrams and number lines.

Grade 5: Introducing Volume

In this unit, students develop an understanding of volume and ways in which it can be measured. As students construct prisms with unit cubes, they reason about the structure of rectangular prisms and develop methods for computing volume. These methods build to an understanding of formulas students can then apply to find the volume of figures composed of two right rectangular prisms. (There is a quick sneak peek in this previous post.)

I can imagine that as you read, you nodded your head and thought, “this makes sense” until you hit grade 4, right? Grade 4 was the toughest content to determine, by far. In grade 4, the measurement and data standards rely on new fraction understandings and the geometry standards are vocabulary-heavy, so we worried it would not be an invitational start to the year for English learners in the classroom. The cool thing about starting with fractions, though, is the physical use of fraction strips to launch the year and the opportunity to weave fractions into routines and lessons in subsequent units. 

And while we paid a lot of attention to the way in which students would start the year in terms of content, it is naive to believe that is the sole factor in a student’s feelings about mathematics. In upcoming posts, we will take a closer look at math community structures, activity designs, and teacher reflection prompts in the materials that support both teachers and students in their positioning and beliefs around mathematics. 

Next Steps

What mathematical content typically starts your school year? How might each student feel as they engage in that content? What message does it send to students?


Kristin Gray
Kristin Gray
Elementary Curriculum Lead at | Website

Kristin Gray is a National Board Certified 21-year veteran teacher of grades 5, 7, and 8, is currently the Elementary Curriculum lead at Illustrative Mathematics and writer of IM professional learning content. She has served as a curriculum writer on the IM 6–8 Math curriculum and Teaching Channel Laureate. Kristin has developed and facilitated mathematics professional learning at district, state, and national levels and presents annually at both the NCSM and NCTM conference. As a teacher, colleague, presenter, and learner, Kristin continuously shares the value of curiosity around student thinking in her planning and instruction. To reflect on her experiences, she blogs and connects with educators on Twitter, @MathMinds. Kristin has a B.S. in elementary education with a concentration in mathematics from the University of Delaware, a M.Ed. in applied technology in education from Wilmington University and is the 2014 Presidential Awardee for Excellence in Mathematics and Science Teaching.

4 thoughts on “First Impressions: The First Units in IM K–5 Math

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  1. Oh my gosh, to be invited to see some of the early outputs of your team’s work is beyond exciting. I appreciate your thinking with respect to the 4th grade content to start the year, and the logic used in arriving at fraction equivalence. I was surprised, I admit, that 5th gr does not kick off with fractions, too, given that domain’s centrality in the upper elementary progression. But I think I can intuit the reasoning behind this: it’s fractions’ very centrality, its sheer complexity in 5th grade that disqualifies it as a welcoming mathematical idea. Going with volume feels more approachable. I just can’t wait to see how the early year unfolds in transition to other domains! Wow. This is really good stuff. Til your next post. . .Thank you!

    1. Thank you so much for the comment Scott, I so appreciate reading your insights! Yes, 5th grade fraction operations are such a huge part of the work of the grade and we did toy around with starting the year with that, but, like you mentioned, volume felt more concrete and approachable. Not to worry though, fractions pick up in units 2 and 3! The early volume work also gave us an opportunity to gradually revisit multiplication understandings and strategies through the lesson activities and Number Talk warm-ups. That led nicely into the fraction multiplication work that followed in the next unit.

    1. Thanks so much Tineille! There will be a beta pilot in 2020/2021 (more details on how to apply for that coming this fall) and then the curriculum will be available for adoption for the 2021/2022 school year!

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