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 

By Kristin Gray

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: Factors and Multiples

In this unit, students build on their grade 3 understandings of multiplication and division to explore factors and multiples. At the beginning of the unit, students use the concept of area as a context for understanding factors and multiples. They use tiles to build different rectangles and learn that the different side lengths of the rectangles represent factor pairs for the whole-number area, and that the area represents a multiple of each of the side lengths.  As the unit progresses, students apply what they have learned about factors and multiples conceptually to other contexts.

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.)

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?