The Decimal Dilemma: 8 Common Misconceptions and How to Avoid Them
Decimals can be a tricky concept for students. Without a solid foundation in 4th and 5th grade, students may struggle with algebra, science, and even life! I used decimals this morning when I paid for my latte and last night when I cooked dinner. Decimals are everywhere!
But decimals don’t have to trip up your students. By understanding the misconceptions your students are likely to develop, you can help your students avoid them! This blog post will explain 8 concepts that students might struggle with, and give you strategies and resources for making sure YOUR students master these key math concepts.
Read to the end to download a FREE resource to help you combat these misconceptions in YOUR classroom!
Click the links to jump to a specific section.
Misconception #1: Adding more zeros changes the value of a decimal.
When they learned about whole numbers, students were taught that 10 < 100. Putting another zero to the right shifts the value, and so it makes sense that students will try that trick with decimals as well. But, the decimal point communicates the value of the digit, so this “rule” does not hold true for decimals.
Strategy 1 – Math Talk
I like to use this Math Talk to help students understand that trailing zeros don’t change the value of the decimal number. It is the conversation and the struggle to explain that makes this powerful. You might follow up by having students write about this in their math journals.
Write this on the board, or download the free resource at the end of the post and project it.
This problem is deceptively simple. Students likely have background knowledge that tells them the two coins are not the same value. But, can students explain why the values are different? As you question students, push them to explain their thinking and tie their understanding of money to decimals. As they find the words to explain the difference in values, I like to look for a moment to pop the numbers into a place value chart and compare them. That really brings the concept home for students. It can be helpful to follow up with more comparisons to reinforce the concept.
Misconception #2: Decimal numbers can’t be between whole numbers.
This misconception probably has its roots in kindergarten math. When students learned to count, they learned the standard counting sequence: 1, 2, 3, 4…. and so on. No one mentioned all the numbers they were skipping over. So it can be difficult to go back to something that has been rock solid for half of their life, and change it now.
Strategy 2 – Number Lines
Number lines are your best friend for helping students learn that there are all kinds of decimal numbers between whole numbers. I like to start by giving students an 18-inch strip of paper to make a number line. We fold it in half 4 times, which makes 16 sections. Then, open the strip and ask students to make a mark on the fold in the exact center. Label this .5. Tell students that each fold is a tenth, and ask them to find and label 0, and then find and label 1. Then, fill in the correct tenth for each fold. This exercise helps reinforce the concept that decimals fall between whole numbers.
Note: This is an amazing time to label the negative decimals that come just before 0 and the decimals that fall just after 1. I find that briefly introducing these concepts now avoids misconceptions later!
Misconception #3: A longer decimal is always greater.
This misconception also dates back to early instruction on place value. Somewhere along a student’s education, someone told them, “423 is greater than 42 because it has more digits.”
While that rule works for whole numbers, it does not work for decimals. In my classroom, I call that a “Rule that Expires”. The rule only works for awhile, but it does not hold true for decimal numbers.
It is vital for students to understand that the decimal point determines the value, not how many digits a number has. That rule does NOT expire, and it works for decimal numbers AND whole numbers!
Strategy 3 – Place Value Blocks
To help students understand that a longer decimal might have a smaller value, I like to grab place value blocks. Early in their math career, students learned that these blocks represent 1, 10 and 100. Now, I tell them we are going to name the flat as our whole. That means the rod is 1 tenth and a unit is 1 hundredth. Set up a problem where students compare 7 rods and 25 units. Ask students to lay the blocks out on their desks and label each decimal. It will look like this. (This image is included in the FREE download!)
Using a concrete example with manipulatives clearly shows students that the larger decimal has one digit while the smaller decimal has two digits. Lead a discussion and give students additional examples to bring the concept home.
Misconception #4: The decimal point is not an important part of the number.
I think this misconception comes from students thinking that the comma that separates hundreds from thousands is optional, and so they assume the decimal point is too. 1524 = 1,524. That leads students to reason that 2.7 = 27. But of course, the decimal point has much more meaning than the comma.
Strategy 4 – Place Value Chart
Shifting decimal numbers on the place value chart helps students understand the meaning of the decimal point. Start by writing an easy number in the place value chart. This example uses 24. Then, shift the numbers one place to the right and lead students through a discussion of the change in value. Shifting to the right decreases the value by 10x. In other words, 2.4 is one tenth of the value of 24. It might look something like this (this image is also in the FREE download).
One thing to consider is your own language around decimal points. When you read a number, do you say, “two point four” or do you say the number correctly, “two and four-tenths”? I think using the correct language helps stress the value of the decimal numbers, and reinforces that they are NOT the same as whole numbers. Language matters! We know that the brain needs language to process concepts, so hold yourself accountable to using the correct terminology. Your students will learn it from you.
This FREE resource helps students solidify key decimal concepts, and is perfect for preventing misconceptions 4 and 5. Click here to get it today, along with other FREE resources, tips and insights to grow your teaching.
Misconception #5: Tenths and hundredths are the same.
Misconceptions 4 and 5 are related. If students understand that the decimal point is an important marker that separates the whole numbers from the decimal numbers, they will more easily understand that the value of a decimal is determined by its distance from the decimal point.
Strategy 5 – Math Journal
Because this misconception connects to misconception 4, I suggest that students use a place value chart to address this one too. I like to connect this to what students already know about whole number place value with a journal prompt. The concept is the same for decimal numbers as it is for whole numbers. Using this prompt for their Math Journal helps students explore the relationship between whole number digits and decimal number digits.
How does a whole number’s place in the place value chart affect its value? Do decimals change value in the same way? Use examples like 10, 1, .1, and .01 to explore this concept and explain your thinking. A place value chart might be a helpful visual in your explanation.
Misconception #6: A decimal with a large face value is larger than a whole number with a smaller face value.
This misconception is also rooted in students’ understanding of counting whole numbers. When you count, 6 comes after 5, so 6 is bigger. But what happens when you compare .6 with 5? Is .6 greater than 5?
Of course, the answer is no because the decimal means that the 6 is no longer in the ones column. It has shifted to the tenths column. And tenths are smaller than whole numbers. So, .6 < 5, even though the face value of the digits suggests otherwise.
Strategy 6 – Shopping Scenario
Because students have background knowledge about money, setting up a shopping scenario helps students easily understand this concept. Try this word problem.
Serena has $4.00. She would like to buy a glitter pencil that costs $0.80. Does she have enough money? How do you know?
Again, this problem is deceptively simple. Students will immediately say something like, “Yeah, $0.80 is less than $4.00!” Don’t let them stand on that statement. Push them to explain their thinking. Point out that 8 is larger than 4 to really make students confront the misconception and work through it. Explicitly pointing out the face value of a digit and discussing the importance of the place of that digit is really helpful in combating this misconception. Encourage students to use a place value chart or other visual to thoroughly explain their thinking.
Misconception #7: Fractions and decimals are unrelated.
Fractions and decimals are both representations of partial numbers. Understanding this, and developing the ability to choose between the two representations helps students navigate authentic situations.
Strategy 7 – Pizza Math
Pizza is a perfect way to connect decimals and fractions. Show a picture of a pizza (or better yet, buy a pizza) cut into ten pieces. Ask students to label the pizza with decimals and with fractions. The visual does the heavy lifting to help students connect fractions and decimals. You can grab this image for FREE in the download at the bottom of the post!
For students who are ready, this video helps cement the connection between fractions and decimals.
Misconception #8: Align decimals to the right when adding and subtracting.
If you have ever taught upper elementary students, you know that students often add or subtract numbers without lining up the decimal points. Instead of telling students to line up the decimal points, help students understand why you line up the decimal points. Building that conceptual understanding will cement the concept. Remind your that they need to add or subtract decimals from the same place, just as they do for whole numbers, and that the decimal point determines the place.
Strategy 8 – Problem Sequence
I like to explore this concept by starting with an equation the students can add easily, for example 3 + 4. Write that on the board, and ask students to solve the equation. Then, rewrite the equation with the same numbers, but include tenths with one of the addends. Keep going, using the same digits but including decimals. At this point, I choose numbers that do not require regrouping. Your sequence might look something like this.
FREE Decimal Misconceptions pdf
I hope that exploring these misconceptions has helped you feel ready to tackle them with your class. If you would like to project the images from this blog post, I’ve put them into this handy FREE download. Grab it today, and set your students up for decimal success!
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