There was a time when learning math involved memorization. Today we tend to shy away from memorization or never get around to it. I’m here to tell you that, even with calculators and computers, we still need to memorize certain facts in math.
This is always the number one thing math teachers tell students to memorize. It is also the number one thing that math students claim they can use their calculator for instead of memorizing them. Here’s the truth. Calculators are slower than your brain. On any given day it will take longer to enter 7x6= into a calculator than it will for you to remember that the answer is 42. This may seem like a sacrifice your students are willing to make but let’s put it into perspective. Most good math programs have students doing 30 or more problems per day. If every problem takes longer because of typing into a calculator math class can get extended much longer than it needs to be. Further, when students take college entrance exams, they are timed. Test takers need every single second they can get.
Human error is another problem with calculators. I call it “fat fingers”. It’s amazing how easy it is to hit the wrong key on your calculator. If you are not carefully watching every digit entered, you won’t even know you made the mistake. If you are watching every digit, you’re taking a lot more time.
Being able to quickly do your multiplication portion of math problems will improve retention of concepts. If students are fumbling through punching multiplication factors into a calculator, they are being distracted from the concept they are learning. This distraction makes it more difficult to learn and remember.
There are many different methods for memorizing multiplication facts. The simplest way to do it is to just start writing them. Flashcards and memorization charts are also very useful. I took an idea from my mother’s school days, back in the 1940’s and created a great little mini-book called Multiplication Memorization Circles. If you get our newsletter, this is the March newsletter Freebie. (You can sign up for our newsletter here)
Memorizing multiplication facts can be started as early as second to third grade. If your students are older and haven’t done it yet, do it now. It’s never too late.
It is not necessary to memorize all addition facts, but it is helpful to memorize how to make ten. For all the same reasons you should memorize multiplication facts, you should memorize how to make ten.
If you are adding up a column of numbers, it’s extremely helpful to be able to find all the tens first, carry that number, then you only need to add a couple of numbers. Don’t forget that not only does two plus eight equal ten but so does eight plus two.
This can be memorized as early as first or second grade. If your students are older and haven’t done it yet, now is a great time.
This is technically a vocabulary thing, but it’s important to memorize it. Because learning how to add with carrying and subtract with borrowing moves students from one column to another, they need to be able to talk about what they’re doing and understand their teachers when they talk. As they move along in science classes the need to know these will become more apparent as well. I cannot over emphasize the importance of knowing the difference between a ten and a tenth.
Learning place values begins as early as first grade for some, but needs to be a focus throughout the elementary years. If your students are older and are shaky with their understanding of place values, take some time to learn, grasp, and memorize place values.
Order of Operation
Please memorize PEMDAS which stands for Parentheses, Exponentials, Multiplication, Division, Addition, Subtraction. This is the order in which equations are evaluated. It means you take care of whatever is inside parentheses first. Then you raise things to their powers. Only after these things are done, you multiply, then divide, then add, and finally subtract.
Most math program teach these things in the reverse order. Students learn addition before subtraction, then multiplication, then division, and so on. This should make it easy to teach students as you go. Each time a new concept is taught tell them that this gets done first when evaluating an equation that uses multiple operations.
The real value of memorizing PEMDAS (Order of Operation) become clear when students take algebra. In algebra students are often asked to isolate a variable, in other words, get “x” alone on one side of the equation. This is done in the exact opposite order as proper order of operation. If anything is “connected” to the “x” through subtraction add it to both sides of the equation to remove it from the side with the “x”. Only after all the things added to or subtracted from the “x” are moved to the other side of the equation can you multiply or divide to remove things “connected” to the “x” with division or multiplication. Please note that this is not a math lesson and is an over simplification of the concept. There are always exceptions to this straight forward description of solving equations. The point is that if you have PEMDAS memorized, you will have the beginnings of knowing how to solve equations. If you do not memorize PEMDAS, you will struggle to solve equations easily and correctly.
Difference Between a Unit & a Ten
This lesson should be taught as they learn about numbers. In the early years of schooling, children can already handle being taught about the difference between a unit and a ten. If your students are older and have never learned this, take time to teach it so they understand and can memorize the difference between a unit and a ten.
Anything Times One Stays the Same
This is kind of an odd thing to memorize because it seems so simple. Some of the most powerful statements are the simplest. The application and implementation of this concept is most valuable with fractions. You may not realize this, but a fraction is a tiny division problem. If you have ten parts of a thing that was divided into ten parts, you have the whole thing. You have one whole of it, or one of it. This is powerful!
Students are usually very quick to jump on shortcuts in math. They often forget why they started doing the thing to begin with. “Crossing Out” with fractions is one of those areas. They learn early on that they can cross out things and make the fraction easier to work with. Then somehow in their minds they forget that they are not erasing those numbers or variables. They are not making them just disappear. There is a reason they can cross them out. The reason is that the two numbers are a single fraction of one number over itself, or one. Please follow this example.
That was a simple example using small numbers. I use this example with students new to fractions, all the way up to Algebra II students. If they don’t have this down by then they will never pass Algebra II, so remember it, it’s important.
This lesson starts as soon as children begin learning to multiply. It’s important to remind them of it when learning fractions. Students should have this memorized and be using it with fractions by the time they start fifth grade. If your students are older and haven’t memorized this, have them memorize it now.
There are a lot of things to memorize in math, but these are the things that tend to get skipped and shouldn’t. The vocabulary is important. All the skills are important. The most important thing is that students do it every day. They cannot do well doing math only one or two days a week. It doesn’t matter how many problems they do on those days. They need daily reinforcement of the new concepts. Do not skip that to memorize these things. Memorize on top of learning the lessons. If you students didn’t memorize these lessons “on time” don’t worry. They will greatly benefit from memorizing them now.
Our company Powerline Productions offers a great how-to-homeschool book, Joyful and Successful Homeschooling, by my friend Meredith Curtis. There is an entire chapter on how to teach math, as well as a chapter on how to teach every other subject (Reading, Writing, History, Science, P.E., etc.).
This books goes way beyond on to teach! You will discover how to choose curriculum, discover your children's learning style, set up learning areas in your home, and manage your home and family. Explore philosophies of learning, family ministry, and teaching out of the box. There are also organization tips, different ways to teach subjects you never thought of, and lessons on keeping Christ in the center of homeschooling. If you're just getting starting, there's an entire section on beginning the homeschool adventure.
Learn more about Joyful and Successful Homeschooling here.
Let me know how your family's adventure with math memorization goes. I'd love to hear from you in the comments below.
Until next time, Happy Homeschooling!
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