What is mental math?
Simply put, mental math is manipulating numbers and thinking flexibly about math in order to make calculations more manageable. It’s the kind of everyday-math that is useful at the grocery store to help you estimate the sales tax, or a discount. Instead of resorting to an inefficient algorithm, mental math skills allow you to efficiently do calculations in your head. Some people may refer to mental math as “math tricks” but I don’t see it that way at all. These “tricks” are really just creative displays of number sense.
Here’s an example:
Question: 3.3 – 1.9
You may be tempted to grab your pencil and paper and stack these numbers. However, a solid understanding of what subtraction really means can help you find the answer in seconds.
Number Sense: Subtraction means “find the difference”. This can be illustrated as the space between numbers
Knowing the true meaning of subtraction, I can use this to my advantage and manipulate the numbers.
Mental Math Strategy: shift both numbers slightly (while keeping the same space, or difference between them) so that you’re subtracting a whole number, instead of a decimal number.
Adjust both the minuend and the subtrahend by +0.1. This keeps the same difference between them, but allows for a more simple mental calculation.
Now that I have reframed my question as 3.4 – 2.0 it seems much less daunting! It’s 1.4 🙂
Try these:
3.4 – 2.9
7.1 – 3.7
5.3 – 2.4
4.15-1.88
Check out this video to review the strategy and check your answers to the question above:
Why should I teach mental math strategies?
A July 2020 issue of The Athens Journal of Education states: “[Mental Math] is an important thinking process because it enables children to: learn more in depth about how numbers relate to each other, make decisions about procedures, and create strategies for calculating” (Tsao, 2011; Everett,Harsy, Hupp, & Jewell, 2014). I very much agree with this! As a math teacher for over 15 years, I have seen a direct correlation between the mental math skills of my 6th, 7th & 8th graders and their overall skills in the general math curriculum.
Interestingly, mental math IS explicitly taught to younger students. There tends to be a heavy focus on it in the early years which is so great. But, it trickles away as students get older. Mental math is not explicitly written into the middle school math curriculum (standards). But, as I learned first hand, setting a small amount of time aside every day to work on mental math skills will positively affect students’ performance in all other areas of the math curriculum in the long run.
The positive effects will spill into high school as well. I have spoken with many high school math and science teachers, as well as tutored many struggling middle and high school students. Basic number and operational sense is lacking for so many. Imagine staring down a quadratic equation, without having a good understanding of integers, order of operations or even your multiplication facts. Without a solid foundation in the fundamental skills, many kids will give up and unfortunately end up labelling themselves as “bad at math”.
Everyone can be good at math. I believe in student-centered learning, giving kids time to master skills before moving on, and intentionally focusing on mental math at all levels will build math confidence as well as skill.
How can I fit mental math into my day?
You’re going to need a plan!
My very first teaching assignment was in a grade 7 math class. It was eye-opening in so many ways. I went in assuming these kids had mastered the content of previous years. I was so ready to dive into the grade 7 curriculum (standards), but I soon realized that they had quite a few learning gaps that needed tending to. As most new teachers do, I stumbled my way through and spent my evenings and weekends working overtime in an attempt to help my students gain some ground in their number sense. Over the next few years I developed and refined what I found to be a very efficient and effective mental math system. It looked something like this:
- Choose 12 essential mental math skills for each grade level.
- For the first 12 weeks of the year, focus on 1 skill per week.
- For the remainder of the year, practice all 12 skills every week and assess at the end of each week. Students use a graph to track their own performance each week.
This is the skeleton plan. Of course it needed to be presented in a way that was engaging, efficient and offered variety so that students weren’t dreading it or getting bored quickly. Here is how I broke the week up:
Monday: present a prompt or problem that would involve using the target strategy to find the answer. Students then discuss it in small groups. Meanwhile, I walk around the room, listening and asking questions about their thinking and strategies. We’d then open it up to the whole class to share. Generally, a common solution and a few different methods would come out. Then, I try to strategically guide them towards the intended strategy.
Tuesday: I present another prompt with the same target strategy as Monday. Again, students discuss in small groups. This tends to go more quickly because students have more familiarity with the strategy. This time, as a class, we try to come up with the most efficient strategy (or strategies) to solve this type of question. I display the strategy in an anchor chart and/or have students create their own diagram that shows their preferred strategy.
Wednesday: Now we practice. Using a variety of game formats, students practice the target strategy for 5-10 minutes at the beginning of class. For the games, we just use numbers, no context.
Thursday: Assessment. Just a quick, very standard-looking “quiz” with 10-12 questions and space for students to show their thinking if necessary.
Friday: Small group intervention with students who were still struggling with the strategy (this involved going over the previous day’s assessment and discussing mistakes). Meanwhile, those who had mastered the strategy had another opportunity to play a game, like on Wednesday.
Mental math was given VIP status in my math class. It was a part of our routine that took 10-15 minutes at the beginning of every class. Anytime I worried about the fact that I was dedicating time to these skills instead of diving straight into the main curriculum outcomes (standards), I reminded myself that No, I AM SUPPORTING THE MAIN CURRICULUM by doing this. And I was. Time after time, the mental math strategies we did every morning found their way into the main curriculum and offered clarity for my students.
Now, as a tutor, I make sure to include mental math strategies into my sessions.
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