Have you ever thought a concept was going to be a breeze to teach, only to find yourself face-to-face with a class full of blank stares? For me, place value relationships was one of those skills that I had a hard time getting across to my students at first.
Place Value Relationships
Each state has a different way of wording this particular skill. I’ll use Texas as an example here. For Texas teachers, place value relationships falls under TEKS 3.2B: Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place.
That sounds simple enough until you get to fourth grade with TEKS 4.2A: Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left.
For the most part, my students understood the idea that every time we move up to a bigger place value, we’re increasing the value by ten times. We practiced this on our number lines, and I was confident we were ready to move on.
Then I introduced the whole “one-tenth” thing.
*Cue the blank stares*
They had a good understanding of fractions from third grade, but this threw them for a loop. Thinking of decreasing place values as “one-tenth” the value of the place before it can be a difficult concept for fourth graders to grasp. (Honestly, I think it can be a difficult concept for anyone to grasp.)
My number line approach wasn’t working. So, we pulled out the base-ten blocks, and I found some printable ones they could shade and cut.
I wanted them to see how one place could actually be a fractional part of another place on the number line. We lined the base-ten blocks up in order from the thousands down to the ones. Together, we started at the ones place and shaded each increasing base-ten block to show the value of the one before it: we shaded a one unit on the tens rod, shaded a tens rod on the hundreds flat, and shaded the hundreds flat on the thousands cube.
Then, we had a discussion about the relationships students notice between the blocks. I asked:
How many ones does the tens rod hold?
How many tens are in the hundreds flat?
How many hundreds do you see in the thousands cube?
Once we made these connections, I asked my students to stop looking at these models as base-ten blocks and imagine them as fraction models instead. We took out our scissors, and I told the class to cut out the part of the tens model that they shaded.
Now it started to click. As they carefully cut out that little ones block, I heard a student say, “Oh! It’s just the ones place now!”
We repeated the process with the hundreds flat. I asked them to cut out the one-tenth part of the model they shaded, and they were left with a tens rod. We cut out the one-tenth part of the thousands cube, and we were left with a hundreds flat.
Now that we finished with our models, we went back to the number line and filled in the bottom section. Except this time, they could actually visualize what it looked like for a place value to decrease by “one-tenth as much.”
I created an interactive notebook activity as a supplement to the lesson. It includes both place-value blocks and a number line for students to keep in their math journals as a reminder, as well as practice problems to reinforce the skill. There’s also a short quiz that goes along with the activity! Click here to check out the third grade interactive notebook activity, or if you need the version that includes the “one-tenth” as much, click here for the fourth grade interactive notebook activity.
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