The more I dig into my students’ math work this year, the more I am realizing that many of them lack a solid understanding of place value and its role in mathematical problem solving. This is particularly evident in my Tier 2 and 3 math students- those students who are not working on grade level and yet are being expected to master grade level standards.
The Shocking Realization
At the beginning of the year, I was able to give my students a diagnostic assessment to pinpoint where they were individually and where I should begin their instruction in small groups. The thing that was most apparent: a lack of place value understanding in 3 digit numbers. During a counting question, I observed students counting “107, 108, 109, 200…207, 208, 209, 300..” I was shocked that so many third grade students were not able to correctly count through 3 digit numbers. Suddenly, my frustrations from trying to teach rounding and operations with 3 digit numbers made sense. I realized I could not expect students to understand rounding with 3 digit numbers if they did not understand the values of the digits in a number.
After identifying the pattern of lacking understanding in place value, I looked back through prerequisite standards in K-2. Kindergarten is the only grade that has Counting and Cardinality as a standard domain. Within that domain, there is the standard K.CC.A.1: Count to 100 by tens and ones. I thought back on my four years as a Kindergarten teacher and remembered assessing this standard. I simply asked my students to count. I stopped them when they got to 100. I placed a check mark by that standard and moved on. They could count to 100- great! That’s as far as I needed to assess them. Fast forward to third grade, and we assume students come to us with a knowledge of counting, and that, if they can count to 100, they can count to 1000. If I want my students to develop a deeper understanding of mathematical processes, this is not an assumption I can afford to make.
This year I have been fortunate enough to observe some amazing math teachers in grades above me. I saw some incredible teaching and learning happening in these classrooms. As a result, I learned some great ideas to take back to my third graders. The one thing that stood out to me above all else: teachers are constantly teaching and reinforcing place value, year after year. As the mathematical processes get more difficult in the upper grades, we can’t forget that some of our students may not have a concrete understanding of place value. Without solidifying that, they are going to continue to struggle more and more each year as the math gets “harder”. We have to keep that in the front of our minds as we teach math, and make a conscious effort to bridge the place value gap for our struggling students.
How can we help our students develop a deeper understanding of place value?
This year I have used traditional base ten blocks and mats, as well as resources from the National Library of Virtual Manipulatives. I let my students manipulate these virtual base ten blocks so they can see the break-apart as they decompose numbers. Students need practice decomposing 3 digit numbers by tens, not only traditional expanded form. They need to see that 486 is 48 groups of 10 with 6 ones remaining. In addition, they need to see the number as 4 hundreds, 8 tens, and 6 ones.
These practices can also be used to strengthen addition and subtraction skills. Prompt students to represent numbers in various forms to show their understanding of place value and its role in mathematical problem solving. This is a skill students will need to develop math reasoning skills beyond the surface-level memorization and recall.