Making Mental Math Accessible

Many of you know I launched my Mental Math Within 100 co-op course this week! I'm so excited to begin working with 10 students two times a week on creating visual strategies to add and subtract. I've mentioned before that this is not the way I learned, but I'm so thankful I'm learning it now!


When I look back at my school, I remember games like Around the World, doing flash cards and even timed tests each week to master my math facts. I was just told to memorize them. In fact, I was pretty good at memorizing. I can remember making up songs or using fun riddles to remember just about anything.


As a teacher starting out, I used to use the same tricks with my students. I could turn anything into a catchy song and still do! My students would memorize and do great...for the short term. Then, we would have a long vacation or just not sing the song for a bit and all was forgotten. It made me reflect on this practice and realize that memorization is good, but it's not the only way.


If we teach students to reason and use strategies, they are more likely to remember. When you study the way memory works through creating neural pathways, you see that it's connections that help you remember. The more connected a topic is, the more neural pathways are created, and the easier it is to recall.

It would make sense that teaching students to REASON through and use strategies would increase greater recall. It may not be as automatic as memorization, but it will be easier for students to remember long term. That's why I love all the mental math strategies students are learning using a Singapore Math education- making ten, using doubles or doubles + / - 1, using tens and ones and even using compensation.


Last week, I shared some great number bond cards to help students think about using a different number to add or subtract. When adding 98 and 24, students could look at it as 100 and 24. Then they could just subtract 2 extra. This is a great way for students to reason through numbers and use their mental math strategies.


However, this takes practice. While I was planning for my course, I started thinking about a visual way to help students see this. I began creating a work mat that would help students to draw and think about how the numbers change. In doing so, it made my visual brain work, and I'm hoping it will help you and your students too!

In this model, students can show both numbers in the middle and then trade out tens or ones to make the numbers more compatible. I've already been using it with my first graders, and they have been saying how cool it is to be able to adjust the equations. (They didn't think that was allowed!)


Subtraction models are always a bit harder, because students represent the whole and are subtracting a part. So in this model, students represent the whole and then think how the model could be adjusted to subtract with more compatible numbers. The original equation would have required regrouping. My giving each number 5 more, the difference will stay the same and it can be subtracted mentally.


Obviously these two strategies require thinking and problem solving. And using a work mat isn't really mental math. However, it's the baby step that gets them there. It's the bridge that builds visual models to help our students solve problems like this and so many more in their heads!


If you would like to snag your free adding and subtracting using compensation work mats, click below. Print them out and put them in a page protector for students to use with dry erase markers. Then, encourage students to see which problems work best for this strategy!

If you are looking for more great mental math games to help students master their math facts, check out my two resource books: Developing Addition and Subtraction Fluency and Developing Multiplication and Division Fluency. These resources include over 20 leveled games that will have your students using visualization and real problem solving to truly know their math facts!