Line up the decimals when you add and subtract, multiply regularly and skip the decimal over, divide regularly and bring the decimal up. That’s how we all learned about decimals, but have you ever really wondered what you were actually doing? It took me almost 6 years of teaching to get that “Aha!” moment for myself, and now I have a whole new perspective on teaching decimal operations! Let me tell you, my students are a lot more successful with decimals this year than ever before!
Students tend to groan when they hear the word decimals – and I’m not going to lie, I struggled with the conceptual understanding of decimals for a while. Growing up in a time where procedures were prioritized made it difficult for me to teach decimals conceptually. It wasn’t until I started teaching fifth grade that I really utilized base ten blocks in the classroom, and now they’re definitely my favorite manipulative. My only struggle with them is that there are never enough! By the time students get to me in fifth grade, they are working with larger numbers that require more base ten blocks. Cue the virtual manipulatives! I wrote about virtual manipulatives way back when, and you can read my post on how I use them for fractions here.
One of my favorite websites to use for virtual manipulatives is mathlearningcenter.org. The website is user friendly and the apps are free! You can access the manipulatives from a tablet app or the web app. Let me show you how I use the base ten blocks (number pieces) app they have.
First thing, what piece is what? The flat represents the ones place, the long/stick represents the tenths place, and the small cube represents the hundredths place. When I’m going over the pieces and what they mean, I also explain that if we were to take the hundredths place and break it up in to ten “teeny tiny little baby pieces,” we would have thousandths. Students laugh when I do that, but it helps them to remember the next place value!
The Value of the Decimal
Let’s get down to business. The first thing I show my students is comparing decimals with base ten blocks to understand the full value of the decimal and what it looks like. I really emphasize the number of each place value by breaking down the number to each place value. When I’m teaching the value of the digits, I also teach the amount of each place value. For example, if the number is 6.34 I teach what number is in each place value position, but then I also teach them that there are 63 tenths and 4 hundredths or 634 hundredths in the number. To extend this concept, I also have them tell me how many thousandths there are – 6,340.
I relate this concept to money to make it more meaningful to them. I say, “If this was money, how many dimes would make $6.34?” and they get that Aha! moment realizing that 10 times make $1, so 60 dimes make $6 and 3 dimes make the $0.30, so 63 dimes make $6.30, and then add the 4 pennies to make the total $6.34. Teaching the decimals this way really helps to emphasize the conceptual understanding of the value of the decimal and makes for teaching decimal operations a whole lot easier!
Another way I show this is by using the break apart tool on the website mathlearningcenter.org. This helps them to visualize how many tenths and hundredths are in the decimal. It really opens up understanding of the base ten number system as well, which is part of the fifth grade standard that is emphasized throughout most of the grade.
When comparing decimals with the base ten blocks, you show each decimals value and compare the sizes of the decimals. When students have a good understanding of the value of the decimal, this makes for an easier time comparing the value of the decimals.
Adding and Subtracting Decimals
The second skill taught in my decimals unit is adding and subtracting decimals. Again, by understanding how many of the smallest value there are, it can really help students understand the addition and subtraction of decimals. Using visuals is key when showing students these concepts because they need to see how it works to understand why it works and how it is related to the algorithms.
At mathlearningcenter.org, using the break pieces and join pieces button you can show students that you can combine some pieces to make the next larger place value or break apart pieces to make the next smaller place value. By understanding the actual value of the decimal to different place values, adding and subtracting decimals becomes a whole lot easier. This shows students why it is so important to line up the decimals when they are using the algorithm.
I have been teaching decimals this way since this year has started and I find that it is really helpful, especially when teaching multiplying and dividing decimals, which I will definitely be sharing about in a later post! The biggest misconception I find is that students will say what digit is in what place value, but not fully understand what it means. Everyday during the decimals unit, I remind students that 1 whole = 10 tenths = 100 hundredths, and so on to the point where they understand where the decimal name comes from.
I hope you find this helpful when tackling decimals with your students. My kids now get excited when we talk about decimals and I have been seeing the lightbulbs go off with every added concept taught!
If your students are still struggling with decimals, head to my TpT store to check out my decimal resources!