I get students of all ages who are struggling to memorize their times tables, or who didn’t memorize them by the time they finished primary school. I understand it can be a pain to get them memorized, but unfortunately it’s a necessary pain. If you don’t have them well memorized by high school, your math work will be a lot slower and much more tedious, which means homework will take longer, and tests will take longer (possibly to the point of not having enough time to finish). You may start to feel left behind or lost because you’re stuck on recalling a multiplication or division fact, or wondering where a particular number came from, as your teacher quickly moves on in a problem. With one-on-one tutoring, we can take things a bit slower, but our progress may be hampered by spending too much time on the multiplication and division involved in more complex problems. As such, I emphasize to all of my students the importance of memorizing their times tables, as it will help them not only with multiplication, but with division, fractions, algebra, and more. I’ve written this short article on the importance of memorizing times tables, and a guide to go with it, to give to my students who currently need to memorize them. I’m posting the article and guide here in the hopes that it may help other students, as well!
Why We Need to Memorize Our Times Tables
Mathematics requires almost no memorization, and is much more about concepts and the behavior of numbers. I’d argue that one could get through calculus without memorizing almost anything, and you can find professors teaching advanced mathematics who don’t remember some of their times tables. That being said, a small amount of memorization helps us to perform tasks quickly and more efficiently, and allows a student to focus more on the concepts behind what he or she may be doing than the number crunching or guessing. You could get through calculus without memorizing your times tables, but you’re not going to have a fun time if you must skip-count, look at a multiplication table, test several guesses, or grab your calculator every time you need to multiply, divide, simplify a fraction, factorize a polynomial, derive a function, etc. As a teacher, I put much more emphasis on understanding of concepts than on memorization of facts, formulae, or identities, but one of the few things I highly recommend my students memorize is their times tables. Knowing your times tables well will help a student be faster at multiplication, division, working with fractions, and algebra, to name a few, and will make getting through homework and tests much faster and easier.
It is best for a student to memorize their times tables by the end of year 5, not only because the efficiency of tasks in the following years will depend on it, but also because this will ensure memorization before “bad habits” for getting a product tend to form. Although the earlier the better, it’s never too late to get your times tables memorized. I won’t pretend that it won’t be tedious, boring, and even difficult to get them properly memorized, but if you are determined and put your mind to it, you can accomplish this feat and you will be grateful for the ease and speed it affords you in tackling your math problems.
My recommendation for memorizing times tables doesn’t simply involve being able to recite them in order. I want my students to know their times tables forwards, backwards (inversely), and out of order. This is my guide that any student who is working on memorizing their times tables should follow:
How to Thoroughly Memorize Your Times Tables
Focus on only one or two numbers’ table(s) at a time as you follow this guide, as you don’t want to spread your brain’s memorizing power out too wide. After you’ve mastered the one or two you’re focusing on, add on another one or two, but don’t completely leave out the previous ones you’ve memorized. Periodically review the previously memorized numbers and make sure you still have all previously numbers memorized before adding on the next ones. Keep it up until you’ve memorized all your times tables from 1 to 12!
Step 1 – Writing in Order
Begin the memorization process by writing the times table out, in order, several times. You should be writing each multiplication fact in full (ie 2 x 3 = 6). Your goal is to be able to write it out, in order, without looking for the answers. Once you can do that you have that times table mostly memorized in order.
Step 2 – Reciting in Order
Exercise your brain by recalling the table you just memorized in a different way – say them out loud (or, if you must, say them in your head) in order. You should be reciting the multiplication fact in full (ie “two times three equals six”). Once you can do this you have the times table pretty well memorized in order.
Step 3 – Recall Out of Order
Now that you know them in order, it’s time to start being able to recall them out of order. This is most similar to how you’ll encounter a multiplication problem naturally. You may find this step surprisingly difficult, but if you’ve done steps 1 & 2, you should pick it up pretty quickly. There are a few ways to practice this, and I’d recommend using more than one as they will exercise your brain’s recall in slightly different ways. Whichever method you are practicing with, your goal is to be able to recall them quickly without having to skip-count up to the fact or look for the answer. If you encounter one that you can’t recall, then make it a point to pause, repeat the fact, and resolve to remember it the next time it comes up. Once you can smoothly get through a times table in random order (without skip-counting or taking a long time to recall an answer) then you’ve done well to fully memorize the times table in a forwards direction.
Method 1: Writing recall – Write the number of the multiplication table out 12 times with x’s next to them. Then write the numbers 1-12 in order but in random locations on your list to produce a random list of your times table. Then go in order from first to last, writing the answers. You can also find times table drill sheets online.
Method 2: Sight recall – Quiz yourself or have a friend or family member quiz you with flash cards. You can purchase flash cards (School Zone brand is quite affordable) or make your own. Put down the cards you can answer quickly, and ones that take you a long time or that you can’t recall in the back so they come up again (if you can’t remember, look at the answer, but be sure to repeat it to yourself and resolve to remember it next time). Do this until you’ve recalled all of them quickly and placed them down. Repeat this process 2-3 times each time you have a go at it.
Method 3: Auditory recall – Ask a friend or family member to quiz you verbally. Provide them with a list of the times table(s) you are practicing and a pencil to check them off. They should ask you random problems from the list, checking them off if you recall them quickly, and not if it takes you a while to get the answer or if you couldn’t remember the answer at all (if you can’t remember, have them tell you the answer, but be sure to repeat it verbally and resolve to remember it next time). Have them go back to the ones you didn’t get right away until you can recall them more quickly and can get them all checked off. Repeat this process 2-3 times each time you have a go at it.
Method 4: Provide Motivation with a Game – Use a program or app that quizzes you on random facts from a particular times table. I like to use Hit the Button with my students, which can be found at http://www.topmarks.co.uk/maths-games/hit-the-button and is available as an app. This game is great as it focuses on the table of your choosing, randomizes the questions and answer choices, is timed, and provides motivation in the form of improving your timed score. A score of 20 or more in one minute is a good goal!
Step 4 – Reverse Recall
You’ve done great so far if you’ve completed steps 1-3 for a times table. You’re not done yet, though. This last step will be easier since you already have the table memorized in a forwards direction. However, you may be surprised at the mental exertion of reverse recall at first, and you’ll definitely feel your brain exercising in a new way! Reverse recall is about seeing the answer to a multiplication problem, and recalling which number multiplies to give that answer on your times table. For example, you’re working on the 2 times table, and you need to recall 2 x ? = 6. The answer is 3. There’s a few ways to practice reverse recall, including division tables, since the inverse of multiplication is division. This is also an example of why you want to practice reverse recall, as it can help you be faster at division, among other important techniques for working with fractions and algebra. Once you can quickly recall your times table in reverse, you’ve completely memorized the times table! Time to move on to the next one until you’ve memorized the 1-12 times tables.
Method 1: Missing Factor – This method can be used with writing, sight, or auditory recall. For writing recall, you can list 12 iterations of the number of your multiplication table with ” x ___ = ” next to them (ie 2 x ___ = , 2 x ___ = , etc). Then list out the answers of the times table in order but in random locations on your list. Then go through your list, in order, filling in the missing factors. For sight recall, turn your flashcards over and go through them with the same method as before, but now you are seeing the answers and must say what number multiplies to give that answer. For auditory recall, you can have a friend or family member quiz you in a similar manner as before, but have them tell you an answer and you must provide the number that multiplies to give that answer. In addition to the above, I like to use Hit the Button (see Step 3 above) with my students, utilizing the “Hit the Question” mode.
Method 2: Division – This method involves give the answers to the division table of the times table you’re working on. Division is multiplication in reverse (ie 2 x 3 = 6, so 6 ÷ 2 = 3), so this method isn’t really much different than method 1, except it will help your brain connect related division and multiplication facts while simultaneously help you practice reverse recall. You can use writing recall in a similar way to above methods, sight recall by utilizing flash cards, or auditory recall by having someone quiz you. I recommend using Hit the Button to practice division facts.
Additional Times Tables to Explore
Once you’ve memorized the 1-12 times tables, you’ll find many tasks easier and faster to complete. There are a few times tables beyond the normal 1-12 range that you can benefit from being familiar with, or possibly memorizing if you’re up to it. A basic familiarity (being able to list the first few multiples out, in order) should be enough to be helpful when their related facts come up. I recommend looking at the 13, 14, 15, 20, 24, 25, and 50 times tables.