Mental math is one of those areas that you either love or hate. You either grew up doing mental math and feel confident doing it or you are learning it as a grown up. I have always been a paper-pencil kinda gal. I write EVERYTHING down. (I say it's because my brain is going at 100 miles an hour, and it helps me focus. Truly, I think it's because I can't remember anything as I continue to age.)
It has been very eye-opening learning mental math through a Singapore education. There's so much emphasis on playing with numbers and manipulating numbers. When I was growing up, I liked math because it followed rules. As an adult, I'm learning those rules can change and numbers can truly be flexible.
Watching young children grow with this mindset has been incredible. When they begin seeing numbers as flexible objects that can be manipulated to solve different problems, they have an understanding I didn't quite grasp until an adult. That's why it's so important to focus on mental math beginning in Kindergarten and encourage it as students continue in their mathematical understanding.
There are lots of mental math strategies that students learn through their developing sense of operations. Beginning in first grade, students take their understanding of the composition of numbers and begin using it to manipulative numbers by making a ten or using doubles to add. These strategies help students to quickly add and subtract within 20.
These strategies teach so many concepts within one set of facts. They teach place value and an understanding of ones and tens. They teach students how numbers can be manipulated and described in different ways. I did an entire mental math unit in our Facebook group where we looked at each strategy and how it helps students develop fluency. (You can access it in the Facebook group or as part of the video library membership with over 200 videos.) You can also grab this quick and easy download with all these strategies listed by clicking below.
Another strategy that can be challenging for students, but changes the way students do math, is the ability to use compensation for addition and subtraction. Students learn they can substitute a number for another number to perform the operation. This shows true flexibility of numbers and an understanding of how operations work together.
This was NOT the way I did math, and in fact, it still makes me uncomfortable. This is not the standard paper and pencil method. This is not adding tens and ones. This is changing numbers, and I grew up thinking you could not do that. Learning how to be flexible with numbers using compensation has been such a game changer when performing operations mentally.
Here's a great example: when adding 97 and 28, we know there's going to be renaming in the ones place. So, instead, we can add 100 and 28 to get 128, but we added 3 extra ones. If we subtract those 3 extra ones, we get the answer of 125. The beauty of this strategy is that it can be performed in other ways. For example, some students may add 97 and 30 and then subtract 2. Compensation allows students to use strategies they know and to manipulate numbers in a way that makes sense to them.
If you haven't tried compensation, it is definitely a great strategy to use for addition and subtraction of 2 and 3-digit numbers. You can check out the videos I have available as part of the video library to see the best way to teach these strategies or you can grab the free download below to practice these skills with a FREE matching game.
Using mental math strategies can definitely improve the confidence and understanding of your young math learners. It may even change the way you think about math as a grown up.
How are you using mental math? How do you see it in your every day life? How are you using it with your students? Leave me a comment and share some of your favorite strategies.