Math can be really intimidating for learners at all levels. Intimidation often leads to mental roadblocks, and those mental roadblocks lead to math amnesia and our students seemingly forgetting what they have learned. Our job as math teachers is to help our students hurdle over those mental roadblocks so they can continue learning. One example that I see again and again is multiplying decimals.
All prior multiplication knowledge seems to go out the window (aka it’s stuck behind the mind block) when I tell students we are going to multiply decimals. This is where the fun begins. I love helping my students build a bridge right over that mental roadblock and see just how similar multiplying decimals is to regular multiplication! In this blog post, we’ll explore 3 different ways you can teach your students how to multiply with decimals.
Start With What Students Already Know!
Before diving into multiplying decimals, my class and I review what we already know about multiplication. This helps with building confidence and reassuring my learners that, yes, in fact, you DO know what is going on. The small smiles to themselves make this teacher’s heart so happy!
When teaching my students about multiplying decimals (or any new concept) I don’t totally focus on one way or one strategy. Instead, I’ve found that giving my students guidance with different strategies, along with teaching them how to think through and reason their answers gives them a much stronger math foundation. Want to find out what led to this change in my approach? Check out this blog post on why I don’t teach decimal operation rules.
Doodle Notes to the Rescue!
My students love their math doodle notes. That’s why we always start with them. Not only does it keep them engaged as we learn a new topic, but it also creates a reference tool they can refer to again and again.
When I introduce multiplying decimals, we take doodle notes on our Multiplying Decimals Doodle Math Wheel Notes. Students have the five steps written out at the top of each of the sections. We talk through all the steps to multiplying decimals using the example on the doodle wheel. Once done, their math notes include a quick explanation of the step and a concrete example to refer to throughout the unit.
Each section focuses on a different step to help with multiplying decimals.
- Estimate – I always teach my students the importance of estimating to help them determine if their answer is reasonable. I have my students round to the nearest whole number to determine what the estimated product could be. For example, 3.9 x 7.43 would be rounded to 4 x 7 = 28. Hold on to that – we will use it again at the end.
- Set-Up Like Whole Number Multiplication – Next, my students learn how to align the numbers vertically. On the top is the number with more digits. Both numbers in the math equation are aligned to the right because the decimals do NOT need to be lined up.
- Multiply Like Whole Numbers – Now that we have our numbers aligned, we work on solving for our answer. Students multiply the numbers just like they would for whole numbers. There is no need to add decimals in this step. I remind students that the 0 is used as a placeholder in the second row. These two rows will be added together to find the answer.
- Place the Decimal – We need to return to the original decimal numbers we multiplied together in order to put the decimal point in the correct place. Before we think about the ‘rule’ for placing the decimal point, we think about where it would make sense to put the decimal point in the digits 28877. Our estimate was 28, so the most reasonable place to put the decimal point is between the 8s. This gives us 28.877, which we can double-check with the rule.
- We count how many digits are to the right of the decimal points in the problem. There are 3 digits to the right of the decimal points. So we’ll count three digits from the right in the number 28877. Once the decimal point is in place, you have your answer of 28.877!
- Compare to Estimate – To see if our answer is logical (or double-check if we only used the rule), we need to take our answer from Step 4 and compare it to our estimate from Step 1. By comparing, we’ll see if the answer is accurate or if we need to move the decimal point to a different spot. In our case, 28.877 is quite close to our estimated answer of 28. However, if we had gotten an answer like 2.8877 or 288.77, we would have needed to go back and check over our work since it did not match up with our estimate.
Let’s Get Started!
Now that my students understand the basic steps behind multiplying decimals, we dive into 2 different strategies they can use when solving these types of problems. No matter which strategy they choose, they will continue to use the 5 steps from our doodle notes.
An emphasis is placed on the first step of estimation because I want my students to be able to determine the logical placement of their decimals in the answers based on their estimated answers. Estimation can be a useful tool in real-world situations where exact calculations may not be necessary or possible. It can also help your students to build confidence in their math abilities making them comfortable working with larger numbers.
1. Multiplying Decimals with the Standard Algorithm
As a teacher, it can be nerve-wracking to teach a concept that you do not feel 100% about. When you feel this way, go back to the basics. I love a tried and true “oldie but a goodie” strategy!
As we practice the standard algorithm, we do a lot of estimating, modeling, and working through problems together.
Estimating can be a little complicated for some of our learners. However, as with all math concepts, the more they are exposed to it, the easier it will become. I start off teaching standard algorithms with estimation. I do this because it’s a great way for my students to check the accuracy of their answers after solving. Through estimation, my students develop a stronger understanding of the magnitude and reasonableness of the numbers in the problem.
An example I might write on the board would be 4.5 times 2.5. The first step, according to our doodle wheel, is to estimate. I would round 4.5 to 5 and round 2.5 to 3. Our new equation is 5 x 3 = 15. Now that we have our estimated product, let’s go back to our original problem.
Decimals are strange symbols for our students to see in math, so let’s remove the decimals for now. We’ll work with 45 x 25 = 1125. Our estimated answer was 15, so we need to place the decimal in the spot where we will make a number that is close to 15. The decimal should go between 1 and 2 to make 11.25. 11.25 is much closer to 15 than 1.125 or 112.5.
I work at the board, and my students will all have a whiteboard, eraser, and dry erase marker to work on. Sometimes, I let them solve the problems ON their tables with expo markers. No whiteboard is needed. That is a real crowd-pleaser!
Throughout our practice, I’ll model what I’m thinking to help students learn the thought process behind finding a reasonable answer. I’ll also have students turn and talk with each other to explain their reasoning to each other. Not only does this help them build confidence in their own thinking, but they find errors (if any) before sharing as a whole class.
After practice, practice, and more practice, light bulbs start flashing when they learn that it’s still basic multiplication but with a “dot” to add to the fun!
2. Multiplying Decimals with an Area Model
Many students learned this strategy in a lower grade with whole numbers, so this is just a review of the strategy. Again, like with the standard algorithm, my goal is to help them see that this is just like what they already know about regular multiplication. This provides an excellent visual for your learners, allowing them to break down and see each part of the numbers they multiply! Many of my students have great success once they get the hang of this method!
First, have your students draw a box with a vertical line going down the middle and a horizontal line across the middle. Let’s use this problem for our area model example: 3.7 x 4.8. We start with estimating because that will help us determine where to put the decimal in our final answer – based on reasonableness and logic.
The first step is to round to the nearest whole number. 3.7 can be rounded to 4, and 4.8 can be rounded to 5. Our estimation is 4 x 5 = 20.
Now we will move on to multiplying our original problem using the area model. To do this, students will add the numbers to their model. The 3.7 will go across the top with one number over each square. The 4.8 will go along the side with one number next to each square. Now it is time to multiply. Students will multiply and write the answer in each of the four squares. Instead of focusing on multiple-digit numbers, this strategy allows students to focus on basic multiplication facts.
3 x 4 = 12
3 x 0.8 = 2.4
0.7 x 4 = 2.8
0.7 x 0.8 = .56
Once your students have multiplied each number against each other, they’ll add up the numbers in each square: 12 + 2.4 + 2.8 + .56 = 17.76.
The final step is to check and make sure our answer is reasonable by comparing it to the estimate. In this case, our calculated answer of 17.76 is within a reasonable range of our estimated answer of 20. To help students see this, we try moving the decimal one spot to the right and one spot to the left. I show students that the possible answers include: 1.776, 17.76, and 177.6. I then ask them which answer is reasonable based on their estimation. This makes the correct answer choice really stand out!
There’s No One Right Way…
One strategy will not fit every learner, which is why I allow my students to use the method they feel most comfortable with. Throughout our unit, you will often hear me asking students to explain why their answer is reasonable or correct. If a student isn’t sure of how to explain that, I encourage them to review the doodle notes and look at their ‘estimation’ and ‘compare to estimation’ sections. This process helps to cement the “why” behind the steps they know. And. . . it is knowing and understanding this that makes all the difference.
I hope these steps will give you and your students the boost of confidence needed to teach and learn this essential skill! Remember throughout the unit to provide real-world examples to increase student buy-in and help them see the value of this skill in everyday life.
Also, provide consistent feedback! Practice makes progress – learning how to teach decimal multiplication and learning the concept in general takes time. The more exposure and application of the skill, the more proficient your students will become!
Save these tips for teaching Multiplying Decimals
Remember to save this blog post to your favorite math Pinterest board to come back to when you are ready to teach strategies for multiplying decimals!