Tell me you're not a dart player without telling me you don't play darts.
89I think it helps to remember that 3 times 7 is 21. When I think about that it looks less wrong.
It's the stupid seven multiplication table. Whatever glitch in human software makes it look so much less intuitive than all the others messes with so many other things that should be easy. I swear I struggle every time I have to look at it. I had to double check seven times three multiple times right now.
63I don't think that actually helps, because it's all vibes. 51 looks prime, because of no reason at all, and absolutely nothing looks like it should be divisible by 17, again, because raisins.
Knowing why it's true doesn't make it look right.
38But I can wrap my head around that 51 is divisible by seventeen because of 21 and seven plus something that deals with the remaining 30 somewhere.
I know that's not how it works, but as you say it fixes my vibes when I see the 21 hiding inside the 51.
I'll say this: the other thing that makes this one a hard pill to swallow is that 17 looks way too big, and my vibes fix doesn't address that, but hey.
4
If there’s a number that’s the most oddball in the multiplication table, it’s 7.
It’s a prime number that doesn’t share any common divisors with 10, and isn’t adjacent to a divisor of 10 either.
2 and 5 are common divisors of 10, so they’re piece of cake.
3 is so small and close to 2, so it’s not too difficult to get.
9 is one off from 10, so it has a very predictable pattern.
4, 6 and 8 are even numbers, so they share common divisors with 10.
123 is easy because of the "digits sum to 3" trick, if you get stuck counting by 3s, it's easy to reset. Oh, and the proof for this is based on our 10-based number system, so your point absolutely stands.
5
There's a drinking game called 7's. Basically everyone has to count by 7 (first person: 7, second person: 14, third person: 21, etc) and you have to take a shot every time you get one wrong.
7Right now, sober, I remember my multiplication tables really well and wouldn't find it challenging.
But when I think of the mess that I left in the kitchen last night making a snack after drinks with friends, I can imagine the damage this game would cause.
2
I have to remember it in patterns.
Digits go:
7, 4, 1
8, 5, 2
9, 6, 3
0
Tens go:
0, 1, 2
2, 3, 4
4, 5, 6,
7
Then my brain recognises everything else and I can't explain it properly 😂
7
100,000,001 is also divisible by 17
34I'm really starting to think this 17 is not a good guy
18Just wait until you find out that 17 is divisible by 17
7
299,999 is divisible by 7 and 17.
31
24:3
4
So simple math problems are blowing people's minds now?
20I am more impressed that people know about divisibility. What's next, random people knowing about ideals?
1
three is the first number that starts to cause problems.
16Three is my favorite number, you take that back.
6
And 52 is divisible by 13.
14Somehow less offensive.
12
If it bothers your OCD, think of it more as (7x3)+(10x3)=17x3=51
13Or the way I do it:
- 3 * 20 = 60
- 60 - 51 = 9
- 20 - (9 / 3) = 17
So the factors are 17 and 3. I know 3 is a factor because 5+1=6, which is divisible by 3, so I just use a convenient multiple of 3 that's pretty close to the actual number to get the divisor.
I have young kids and they keep asking me to do crazy math problems while driving, so that's generally the trick I use.
1This is how I have always calculated in my head. It used to drive my mom and my teachers crazy when they asked me to verbalize my calculations. It was like I was hurting them somehow. I never understood why.
1
3 is the real culprit
13Dart players know this
10If it makes you feel any better, it's just (20 x 3) - (3 x 3).
I don't know why, but that makes me feel better.
9This must be the new math that parents are so scared of.
Back in my day, we multiplied 3 by 17 because that's how you do it. You multiply 3 times 7, you multiply 3 times 10, and you add. Simple.
Adding three to 17, to make it 20, multiplying that by 3, and then multiplying that 3 by 3 to subtract js equally valid, and easier to work out mentally IMO. It lays the framework for good estimation skills, too.
9and easier to work out mentally IMO.
And this is the key factor to why math teaching has changed. Rote memorization is actually really really awful for learning.
Teaching math used to be a case of having students fill out their times tables. I still remember having to fill out this chart in under 5 minutes:
This was a quiz that we had to do multiple times per week. It was given to us blank, and 5 minutes obviously isn’t enough time to actually calculate everything; We were expected to have it memorized. And when the students had memorized the table, the quizzes changed into a series of small calculations from the table, again under 5 minutes. So if we ever had to calculate anything out, we could just refer to our memorized times table and pull the number off of that. But the issue is that this only works up to a certain point; Nobody is going to be able to reasonably memorize their times table beyond maybe 15x15. And this means that the times table essentially becomes worthless for doing math in larger numbers.
So instead, the “new” math teaches students how to take complicated problems (like 17x3) and break it down into easier steps. 17x3 is complicated, but 20x3 is just 2x3 with an added 0, and 3x3 is easy too. So if we can convert 17x3 into (20x3)-(3x3) then it becomes much easier to do in your head. Because not everyone can calculate 17x3 accurately, but virtually anyone beyond 1st grade can calculate 60-9.
The “new” math was developed by studying how the students who were good at math actually did their calculations. And it turns out, when you actually understand the concepts, you can create mental shortcuts to break the difficult problem down into a series of smaller problems. And that’s exactly what the “new” math does.
10
4:20 pm
6C’mon Chloe! This is 3rd grade math.
5The information was there in front of Chloe and me this whole time, and still, we never realized
4
By a similar pattern, 91 is not a prime number. Really got me once.
4Is it 13? I bet it's 13. Bloody thing keeps making trouble.
7Yup, 7 and 13.
3
This bugged me but then again
30 / 3 = 10 21 / 3 = 7
7+10 = 17
So yeah that makes perfect sense.
321 being divisible by 7 was already weird, so this just seem like more of the same.
2Punctuation.
2And capitalization. Pretty much any device can do both for you, don't be lazy...
1
A bit random no?
2Good news, everyone. 314159 is not evenly divisible by 17, just as you'd expect.
2So when I turn 51 I can get into a relationship with three 17 year olds and all together they will be a perfect match for me... 🤔
Math is awesome.
1I’ve been aware of this since I was about 8. Not sure what Chloe is so upset about.
1Maybe she was 2 cents short of figuring out the answer she was looking for?
1
Product of two primes.
1Cryptographers hate this one simple trick.
1
ew
1
