# Pencil-and-paper arithmetic: are kids still supposed to be able to do it? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [March 22, 2026, 6:16pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688 "2026-03-22T18:16:47Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 24, 2026, 2:47pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/41 "2026-03-24T14:47:28Z")
Keep in mind that, even in 1869, nobody is going to calcuate the cube root of 9.3 to five digits by hand, without consulting a table of logarithms. I tried it and it is… not so difficult, yet time-consuming and the chances of making a mistake begin to approach 100%. So, why is it on the test? The answer is that it is a pure exercise supposed to test that the kids know what they are doing and can come up with and apply an appropriate method. Which brings up the danger that they memorized some algorithm without really _understanding_ what is going on. [Feynman recounts a relevant anecdote.] Even today, it is up to the test writer to devise probing questions even while allowing them to bring along calculators and computers and what not. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 24, 2026, 10:18pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/42 "2026-03-24T22:18:34Z")
Some years back, I was proud of myself for developing a method for approximating square roots that requires only additions and multiplications, aside from a single division at the end. I later learned that the method goes way back, and was possibly even used by Archimedes. Key to the method is that, given two fractions \frac{a}{b} and \frac{c}{d}, the fraction \frac{a+c}{b+d} is always somewhere in between the two. ---
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [March 25, 2026, 2:21am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/43 "2026-03-25T02:21:30Z")
I kill time by doing multiplication in my head. Up to the 12’s. 11x12 is 132, 7x8 is 56 Gives me something to do at the doctor’s office or waiting in line. Funny thing. I memorized them in only one order. 6x8 is 48. I can’t tell you 8x6 unless I flip the numbers in my head. I remember struggling to learn them and flunking a couple 4th grade pop quizzes. I was living with my aunt and uncle. He turned learning the tables into a game. I had them memorized in a couple weeks. One thing that helped me. Get rid of the verbiage. My uncle had me say, 3 4’s 12. 5 5’s 25 8 8’s 64. It was a game. I could answer 30 of them in under a minute. ---
**Author:** ![echoreply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/echoreply/32/3641_2.png) [@echoreply](https://boards.straightdope.com/u/echoreply)\ **Post date:** [March 25, 2026, 9:17pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/44 "2026-03-25T21:17:20Z")
I use arithmetic to turn off my alarm in the morning. I found if I just had to tap my phone to turn off the alarm, it was too easy to fall back asleep with no memory my alarm had even gone off. Now I’m presented with a problem of the form a \times b+c where a and b are single digit numbers, and c is a two digit number. This is difficulty level 3. Often my thinking is along the lines of 7 \times 8 + 17 What’s 7 \times 8? Well 6 \times 7 = 42, so +8+8=58+17=75 Blap! Blap! Blap! Try again. 9 \times 5 +12 good, some 5s, 5-1=4, 9-4=5 so 45 then 57. Silence… I’m not exactly wide awake when I’m done, but it does engage me enough that I don’t fall back asleep and completly forget the alarm ever went off. > > > Track your sleep cycle and wake up gently with nature sounds in optimal phas... ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [March 25, 2026, 10:22pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/45 "2026-03-25T22:22:21Z")
You may have learned it under the name “cross multiplication”. This is basically the same as what AnalogSignal presented, but a little simpler: \frac{29}{67} \quad ? \quad \frac{16}{37}   Cross-multiply (numerator of each times the denomiator of the other):   29 \cdot 37 \quad ? \quad 16 \cdot 67   Do the multiplications:   1073 \gt 1072 ---
**Author:** ![GuanoLad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guanolad/32/42_2.png) [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)\ **Post date:** [March 26, 2026, 4:39am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/46 "2026-03-26T04:39:26Z")
I kind of remember cross multiplying, but not comparing results to figure out which is a larger fraction. That’s new to me. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 27, 2026, 4:50pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/47 "2026-03-27T16:50:43Z")
I teach elementary math, and the short answer is “yes, of course.” That said, there’s much more emphasis on being able to solve unfamiliar problems than there was when I was in school. And that’s a good thing. It’s much more common in life to be confronted with a weird numerical situation that must be detangled than it is to need to convert 16/37 to decimal form without a calculator. Knowing what equation will give you the answer you need is a more relevant life skill than solving long division equations. That doesn’t mean that kids shouldn’t learn facts. I’m a huge believer that by the end of third grade it’s super helpful for all kids to know their addition and multiplication facts with factors and addends up to 10, and to be fluent at deriving subtraction and division facts from those. Fourth Grade math fluency depends on knowing these skills by heart, much as fourth grade reading depends on knowing hundreds of sight words. ---
**Author:** ![Miller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/miller/32/481_2.png) [@Miller](https://boards.straightdope.com/u/Miller)\ **Post date:** [March 27, 2026, 5:42pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/48 "2026-03-27T17:42:27Z")
> [@Timz](#): > > Know the product of any pair of single digits, instantly – no thought involved. Pencil-and-paper long division takes five? ten? times as long, if you have to figure out each multiplication involved. Memorizing times tables was already a thing of the past when I graduated high school, and that was in 1994. ---
**Author:** ![echoreply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/echoreply/32/3641_2.png) [@echoreply](https://boards.straightdope.com/u/echoreply)\ **Post date:** [March 27, 2026, 5:42pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/49 "2026-03-27T17:42:46Z")
> [@Left\_Hand\_of\_Dorkness](#): > > all kids to know their addition and multiplication facts Just a quick (possibly unneeded) explainer. What we used to call “times tables” are now called “facts”. No idea when the change was made, or if it is just a regional or pedagogical quirk, but I learned “tables” and my kid learned “facts”. ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [March 27, 2026, 5:45pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/50 "2026-03-27T17:45:31Z")
> Nine times seven, thought Shuman with deep satisfaction, is sixty-three, and I don’t need a computer to tell me so. The computer is in my own head. > > And it was amazing the feeling of power that gave him. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 27, 2026, 5:54pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/51 "2026-03-27T17:54:39Z")
> [@echoreply](#): > > Just a quick (possibly unneeded) explainer. What we used to call “times tables” are now called “facts”. No idea when the change was made, or if it is just a regional or pedagogical quirk, but I learned “tables” and my kid learned “facts”. Thanks–almost exactly right! I prefer “facts” because it can also refer to addition, subtraction, and division, which usually aren’t taught with tables. It’s helpful to know subtraction and division facts, but less crucial than addition and multiplication, since subtraction and division are pretty easily derived from addition and multiplication. ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [March 27, 2026, 6:03pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/52 "2026-03-27T18:03:28Z")
We just finished the IAR for grades 3-8. There are 3 math tests, and two of them have scratch paper that has to be collected and destroyed after the tests. So, yes, they do. The third test is much more conceptual, and calculators are allowed for that test. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 27, 2026, 7:29pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/53 "2026-03-27T19:29:19Z")
> [@Left\_Hand\_of\_Dorkness](#): > > Thanks–almost exactly right! I prefer “facts” because it can also refer to addition, subtraction, and division, which usually aren’t taught with tables. I do not mean to nitpick or question you, but it is not tables all the way down? If you “know” that 4+8=12, is that not because you have memorized it? There are also facts that are “laws”, like a+b=b+a (works for any numbers _a_ and _b_) ---
**Author:** ![puzzlegal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/puzzlegal/32/3827_2.png) [@puzzlegal](https://boards.straightdope.com/u/puzzlegal)\ **Post date:** [March 27, 2026, 10:00pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/54 "2026-03-27T22:00:12Z")
I use math every day, and I got as far as, “hmm, they are both a little less than 1/2, so they are pretty close. And I don’t care enough about this random example that doesn’t come up in my regular life to do ny more work”. If I’d cared, I would have used the calculator on my phone. Or Excel, if I had it open. If I really needed to do it, I could have done it without electronics. But why would I really need to? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 27, 2026, 10:52pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/55 "2026-03-27T22:52:03Z")
> [@DPRK](#): > > I do not mean to nitpick or question you, but it is not tables all the way down? If you “know” that 4+8=12, is that not because you have memorized it? It is–but in my experience, a lot of kids learn multiplication via a times table, in which factors are the headers in rows and columns. That’s not a method used for learning addition facts. Such tables exist, but they’re rarely used, as far as I can tell. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 27, 2026, 11:28pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/56 "2026-03-27T23:28:46Z")
> [@Left\_Hand\_of\_Dorkness](#): > > > [@echoreply](#): > > > > Just a quick (possibly unneeded) explainer. What we used to call “times tables” are now called “facts”. No idea when the change was made, or if it is just a regional or pedagogical quirk, but I learned “tables” and my kid learned “facts”. > > Thanks–almost exactly right! I prefer “facts” because it can also refer to addition, subtraction, and division, which usually aren’t taught with tables. I wish there were a better alternative. “Tables” seems like it should refer to the way the facts are organized, rather than the facts themselves. But “facts” or (“math facts”) is too vague and general. “The derivative of sin x is cos x” and “The millionth digit of pi is 1” and “The Euler characteristic of a dodecahedron is 2” are all math facts. Which facts are we talking about? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 28, 2026, 12:11am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/57 "2026-03-28T00:11:53Z")
> [@Miller](#): > > Memorizing times tables was already a thing of the past when I graduated high school, and that was in 1994. If you’re memorizing times tables in high school, something has already gone horribly wrong. ---
**Author:** ![Miller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/miller/32/481_2.png) [@Miller](https://boards.straightdope.com/u/Miller)\ **Post date:** [March 28, 2026, 12:36am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/58 "2026-03-28T00:36:36Z")
Well, there’s a reason I was an English major… ---
**Author:** ![puzzlegal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/puzzlegal/32/3827_2.png) [@puzzlegal](https://boards.straightdope.com/u/puzzlegal)\ **Post date:** [March 28, 2026, 12:45am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/59 "2026-03-28T00:45:50Z")
My kids were expected to know their arithmetic facts. ---
**Author:** ![Miller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/miller/32/481_2.png) [@Miller](https://boards.straightdope.com/u/Miller)\ **Post date:** [March 28, 2026, 12:58am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/60 "2026-03-28T00:58:01Z")
I not saying we didn’t learn arithmetic, we just didn’t sit there memorizing a big 10x10 grid of numbers. At least, I don’t remember ever doing it. Which… might be why I’m bad at math? [Previous page](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688.md?page=2) [Next page](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688.md?page=4)