Learning Mathematics Through Representations
By Bethany Neel (third grade teacher)
In my third grade classroom, we are about to start my favorite unit of the year, fractions! I love teaching
fractions in third grade for lots of reasons, but one of my favorite parts is using the
Learning Mathematics Through Representations (LMR) unit. I have noticed that
fractions on a number line is an area where many curriculums could use a supplement
or support. The LMR fractions unit is the best way I have seen for teaching these
standards. I have used it in my classroom for a few years, and each year I love it even
more. My students are engaged, own their learning, and the scaffolding provided in the
lessons allows them to use their prior knowledge of whole-number number lines to
support their growing understanding of fractions.
I also used this curriculum when I worked in an intervention setting, specifically with fifth graders. I was able to work through the lessons, starting with positive integers to help my students build conceptual understanding of number lines, which they were then able to transfer to fractions as we progressed through the units.
What is LMR?
Learning Math Through Representations (LMR) is a free, research-based curriculum that uses number lines and Cuisenaire Rods (C-rods) to help students build their understanding of numbers.
There are three units:
- Positive integers - 8 lessons
- Fractions - 14 lessons
- Negative integers - 4 lessons
Each unit consists of several lessons that include opening problems, discussions, and partner work. This lesson structure allows students to work at their own pace for part of the lesson and provides teachers with both formative and summative assessment data. The teacher guides include extensive explanations of the mathematical concepts and background as well as common patterns of student understanding.
Caption: Third graders doing partner work in an LMR fractions lesson.
Using different-length C-rods, students explore the concepts of unit intervals, multi-unit intervals, and subunits.
What Do Students Learn in LMR?
The LMR curriculum focuses on units, multi-units, and subunits and their relationships on number lines.
Caption: Students explore relationships between c-rods.
This crosswalk shows the KY academic standards addressed in each unit. There are several lessons in the positive integers unit that could be used as students begin exploring how to build and use number lines. Then, it moves on to multi-unit number lines, which connect to skip counting and multiplication standards, where students work with units larger than 1. The fractions unit is appropriate for teaching fractions on a number line beginning in third grade. The negative integers unit (and any of the other units that build conceptual understanding) would be appropriate for middle school students.
Caption: Fractions Lesson 6 Opening Problems in a third-grade classroom
LMR is free to access and download. If you are teaching fractions in third or fourth grade, or working with older students who need support with fractions, I encourage you to give LMR a try!
Resources:
- KCM LMR Website - Download the LMR Units and learn more about using LMR
- KCM LMR Adaptions - Virtual resources
- KCM LMR/KY Academic Standards Crosswalk
- LMR Website - Download resources and learn more about the research behind LMR
