# Tag Info

46

https://www.theguardian.com/news/datablog/2013/may/31/times-tables-hardest-easiest-children There are links to a dataset in the article. As far as I can tell, this isn't a formal study: But some new data generated by pupils at Caddington Village School in Bedford sheds light on which multiplications are actually the hardest – and how kids do overall. The ...

33

Anything that is just a trick leads to students having wrong ideas about what math is. But methods that help students see the patterns can help them learn the multiplication facts, along with getting a better feel for what's going on. I'd call this a way to think about 9s. (There are many.) This method shows that you add 10 for each new nine, and then take ...

26

As an example of one curriculum, the Common Core standards say that students, "By the end of Grade 3, know from memory all products of two one-digit numbers." (http://www.corestandards.org/Math/Content/3/OA/C/7/) This matches my personal experience, too, for what it's worth, in the 1970's. In the U.S., this would be around age 8 or 9 years old. Now, as ...

20

Yes. This is also a trick that you can do on your fingers, too. For instance, let's say you wanted to calculate $9\times3$. Hold out your hands and bend your third finger down as shown. So nine fingers are "up" (fingers up, $9$, finger #3 down. (9x3). You have two fingers to the left of the bent finger and seven to the right, indicating the product of $27$...

19

Reasons for having automaticity with single-digit times tables (from the perspective of a community college lecturer with many remedial courses): Long multiplication algorithm Long division algorithm, and thus: Convert fractions to decimals Understand why rational numbers have repeating decimal expansions Understand the proof why $\sqrt{2}$ is irrational ...

18

I realize that your question is about the $100 \times 100$ table: But since you ask about approaching the multiplication table in ways other than by rote learning alone, I thought I would leave you with a list of problems I generated based on the $10 \times 10$ table. [Edit 5/9/14: You can find some of the problems below in an informal paper of mine; the ...

16

Someone already mentioned this but I don't think people understand the importance: The purpose to know things off by heart in Maths is to recognize the inverse applications. I explain to my students that recognizing 121 as the square of 11 is like spotting a friend in a crowd. If you did not know his face he will just be another number. This is true for ...

15

There is some relevant research (and bibliography) in this paper: "Improving basic multiplication fact recall for primary school students" (Wong and Evans, 2007) http://link.springer.com/article/10.1007/BF03217451 For me the most striking thing is how low the scores reported in their Figure 2 are (36.89/60 at best), even after interventions that they ...

15

I'm teaching a course of math for future primary school teachers and discussed with them a little bit this point. In my opinion teaching multiplication table is necessary up to 10 and completely useless afterwards. The point is that the usual multiplication algorithm is devised exactly with this purpose in mind: you cam multiply every pair of numbers as ...

14

Let me add my 2 cents in. As someone who grew up in Latin America (where the tables were drilled into us, or else) and who now tutors mathematics, more than once I've had the experience of students were AMAZED that I could recall simple multiplication faster than they could type it in their calculator. I personally like to think we memorize the tables for ...

11

I hope I can contribute an answer with a story. I failed one grading period in 3rd grade math because I stubbornly refused to memorize the multiplication tables. At that age I understood that multiplication was explained as repetitive addition. My reasoning was "why memorize that which I can derive?" I failed because quizzes were timed, and I couldn't ...

11

To add on to the other answers, the reason this works is because we use the decimal system, a.k.a. the base-10 system, for our everyday maths. The multiples of the number that is one less than the base results in a phenomenon where the second digit increases at the same rate as the first digit decreases. $$9 * 1 = 09\\ 9 * 2 = 18\\ 9 * 3 = 27\\ 9 * 4 = 36\\... 10 As I tutor students and watch those with proficiency in up to 10x10, there's a clear difference in their ability to get through the problems in a timely manner. It's a distraction to use a calculator for the simple math (sometimes) required in algebra problems, say, 6 X 7. I'm not suggesting a cause/correlation of intelligence. Teachers around me are ... 8 "She knows the 10x10 multiplication table in principle, but it takes a huge amount of time till she recalls the result. Sometimes she even needs some seconds to calculate 2x3=6." This is absolutely not knowing the multiplication table. As a community college lecturer with lots of remedial courses, I see this a lot; a student will say they know the times ... 8 The point of learning multiplication tables is not to get the product of two numbers. It is to be able to quickly recognize that a larger number can be factored into smaller parts that are easier to handle. 8 Some context is missing here. But I'll go ahead and speculate scenarios for why a math teacher would (temporarily?) prohibit multiplication by stacking [and in writing? --- nothing stops the student from doing stacked multiplication in their head]. In no particular order: Sometimes, there is too much 'reflex' and not enough thinking. For example, 15 \... 7 Age is not a good marker of mathematical ability as abilities can differ so much. In addition I'd add that having a good memory obviously an advantage in the mathematical development of a child but it is not a prerequisite nor a guarantee of success. On to 'knowing' your times tables. It is tempting to say that someone that recalls 8\times 4 = 32 knows ... 7 Note 9 = 10-1 so:$$ 5 \times 9 = 5 \times (10-1) = 50 - 5 = 45, $$and the same for all the others:$$ 8 \times 9 = 8 \times (10-1) = 80 - 8 = 72. $$This works for k \times 9 where 1 \le k\le 10. Although we always have$$ k \times 9 = (k-1)\times 10 + (10-k) ,  this is the final decimal answer only when $1 \le k \le 10$. After the kids do this,...

6

I always thought that multiplication tables above 10 were used in English-speaking countries because of non-decimal units: in Italy nobody bothered with them. This said, I think tables up to 10×10 are useful in real life, even if they are no more used for long multiplication; so they should be learned by heart.

6

From A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein: Some proponents of the Activity Movement [of the early twentieth century] did not even acknowledge that reading and learning the multiplication tables were legitimate activities. As in the 1990s, there was public resistance to the [traditional] education ...

6

If he wants to memorize them, then obviously there is no other way than to memorize them. (I would let him estimate the number of entries in the bigger table compared to the usual $10\times10$-table first, though.) If he just wants to be able to quickly multiply two-digit numbers in his head, then I would start out differently: Memorize the squares, powers ...

5

Here's a quick and dirty implementation: http://nilock.github.io/MathSnips/MultQuiz/MultQuiz.html edit: This was a bit of a seat-of-pants stream-of-consciousness hack job, so the flexibility of the platform going forward is not great. Usage should be mostly self-explanatory, but I'll mention that the system is biased against questions involving 0 and 1 (...

5

In my experience, I feel this is best learned by just practicing. I understand that it may seem remedial for whatever lessons you are giving (or perhaps it isn't) and that it can take away from time you need to teach other subjects. I honestly do find that I have certain values (multiplication tables, special fractions) just "memorized", but I still know ...

5

When/where I grew up in California, ordinary second-graders (7 - 8 year-olds) were expected to learn the times tables well enough to answer randomly chosen problems without writing anything down or looking anything up; but 100 percent accuracy was more of a hope than an expectation. Flashcards, mental shortcuts, and other memorization aids were used. By ...

4

As someone who moved from computer science and programming into teaching, I always think of times tables as lookup tables. There's nothing there that you couldn't work out using repeated addition, but it's faster if you can simply recall that "6 times 7 is 42". Considering how fundamental single-digit multiplication is to other algorithms (multi-digit ...

4

Permit me to direct you to read an answer to another question by another user Benjamin Dickman first, notably the second part of the answer that begins with the line "Given the above discussion, I would like to make one additional comment" I cannot improve on the linked answer but I can connect it to your question. What you call an "intuition for numbers" ...

4

Assuming that the German "Kerncurriculum" (actually, there are 16 of them, one for each federal state. I'm referring to the one from Lower Saxony) for primary school is at least somewhat tailored for the "average person": at most two years, because at the end of second grade, pupils are supposed to state the addition table (up to 10) and confidently ...

3

Maybe instead of the "stacking" method we learned in the last century, they are supposed to use the "diagonal" method like this

3

I have 2 ideas for you. First, I have helped a student get number intuition by getting him to building factorisation lattices. For instance, 12 can be represented by a 2D, 2 node by 3 node grid/lattice: 12 6 4 3 2 1 They get really pretty when you get 3D lattices (3 unique factors, like 60). It can help to ...

3

In fourth grade, our daily math class included a three minute timed exercise. Each student had a page of approximately 50 or 100 math problems. All of the math problems were of one kind -- either adding 2-digit numbers, or subtracting 2-digit numbers, or multiplying numbers between 0 and 12, or dividing numbers between 0 and 144 by numbers between 1 and 12....

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