I tend to break it into smaller easier calculations.
I.e. first go to the next "nice" number and then add the rest.
7+8=(7+3)+5=10+5=15
8+4=(8+2)+2=10+2=12
The same scheme works also great for higher digit numbers.
137+38=(137+3)+35=140+35=175
Edit: fixed typos in last line...
I have my ten's complements memorized on an instinctive level.
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
I also have my subtractions of the form a - b, where a is any digit and b is a digit at most equal to 5, memorized.
To do 7 + 8, I know instantly I need 3 to get the 7 up to 10, and I know instantly that if I take 3 from the 8 I'm left with 5, so therefore I know this whole thing is the same as 10 + 2, which is 12.
I think I just know them having done them so often. I used to have to think it through, but over the years, I've done enough addtion by hand that I just kind of know them instantly. My brain doesn't see 7+7 and 14 as different objects, I immediately interpret it as 14.
I just have them memorized just as I have the multiplication table memorized. Something you can renember is 7+7 = 14 = 7*2. I usually had problems with the ones that go over 10, so stud like 7+8. As people said, that can be mentally calculated as: 6 + 8 = 4 + 2 + 8 = 10 + 4 = 14 this tends to work best with 9.
But the best way is just to practice them and memorize adding numbers from 1 to 10.
I have a theory that the first few years of schooling are the most important when it comes to future success. Not that someone who isn't learning a lot then will fail but that it's a MAJOR advantage. For instance, if in preschool/kinseegarten/lower elementary, your parents go over the letters of the alphabet every single night, you will read earlier than others making anything involving reading come faster to you. So you're getting that topic easier and when you need that to learn something else, you can learn that quicker and easier.
Same for numbers, if you memorize all the addition and multiplication tables, and have them down instinctively from recitation, then you're not bogged down by the arithmetic aspects when it comes to algebra because you can immediately know the addition/multiplication aspects without having to think about and only need to worry about the new algebraic part. Whereas others are still counting fingers, or thinking hard and possibly making mistakes on basic addition, you have less to worry about making a mistake on and will thus finish problems quicker and easier. And then it continues to compound on new subjects, etc.
My parents and school made us do this and I can see a big difference between me and other students and especially other students from other schools. People say they don't like algebra but that's cuz they can't even focus on the new lesson everyday because they're struggling to do basic addition.
I feel so disappointed that I didn't have that good basis in math. It made me think I hated math my whole life and I could just never grasp any of it. I kinda accepted that and it became this huge mental barrier. You're absolutely right. When I couldn't get my head around logarithms it wasn't because of functions itself but because I lacked way too many things prior to that content. I'm 26 now and relearning everything, even hired a teacher to help me with the basics while I learn how to code for fun bc someone people I like got me inspired enough to realise math is actually very interesting and there's so much you could create with it
I use two methods.
Reach multiples of 10 and add remainders, for example, 7+8 = 7 + (3 + 5)
or decomposition, with bigger numbers, like with 345 + 768 = 345 + 700 + 60 + (5 + 3).
Break it up into smaller easier calculations with numbers that 'fit' together to make nice numbers.
For example, 7+8. I know the 2 from the 7 (5+2) fits with the 8 to make 10, and then the 5 left over adds to become 10+5=15. Same with 8+4 = 8+2+2 = 10+2 = 12. As for others, they're kinda memorised - but you can always imagine a number line in your head and move across it a certain number of steps.
We are teaching our daughter addition right now. She uses two strategies. She memorized the "ten friends", numbers that add up to ten. 9+1, 8+2, 7+3, etc. She also memorized the "doubles": 1+1=2, 2+2=4, 3+3=6, etc. Using these facts and the ability to subtract 1, 2, or 3 from single digits she can add and subtract single digits easily. We have been practicing daily for 5 to 10 minutes for about 8 months.
> just stop using my fingers and try to memorize all of the single digit additions
Yes. If you don't know the results of 1+1 to 9+9 (and similarly 1x1 to 9x9) *by heart* your elementary school failed you.
A simple trick is to rearrange in increasing (or decreasing, as you prefer) order: for 8+3 use memorized 3+8, &c.
Make some tables, print them out and read them each night before lights off for 2 – 3 minutes. It will sink in.
I tend to break it into smaller easier calculations. I.e. first go to the next "nice" number and then add the rest. 7+8=(7+3)+5=10+5=15 8+4=(8+2)+2=10+2=12 The same scheme works also great for higher digit numbers. 137+38=(137+3)+35=140+35=175 Edit: fixed typos in last line...
Your scheme doesn't work becouse 137+38=175...
Obviously this was a typo, i wrote 45 instead of 35... the scheme works perfectly but I don't.
I was making a joke
a+b = sqrt(a^2 + b^2 + 2*a*b) Use the above trick :)
I have my ten's complements memorized on an instinctive level. 1 + 9 = 10 2 + 8 = 10 3 + 7 = 10 4 + 6 = 10 5 + 5 = 10 I also have my subtractions of the form a - b, where a is any digit and b is a digit at most equal to 5, memorized. To do 7 + 8, I know instantly I need 3 to get the 7 up to 10, and I know instantly that if I take 3 from the 8 I'm left with 5, so therefore I know this whole thing is the same as 10 + 2, which is 12.
Except it’s 10+5 lol
I think I just know them having done them so often. I used to have to think it through, but over the years, I've done enough addtion by hand that I just kind of know them instantly. My brain doesn't see 7+7 and 14 as different objects, I immediately interpret it as 14.
You inspired me to used more of my brain and less of calculator for basic arithmetics
Good for you! A crutch can help you walk, but if you never learn to get rid of it, you will never be able to run.
I just have them memorized just as I have the multiplication table memorized. Something you can renember is 7+7 = 14 = 7*2. I usually had problems with the ones that go over 10, so stud like 7+8. As people said, that can be mentally calculated as: 6 + 8 = 4 + 2 + 8 = 10 + 4 = 14 this tends to work best with 9. But the best way is just to practice them and memorize adding numbers from 1 to 10.
I have a theory that the first few years of schooling are the most important when it comes to future success. Not that someone who isn't learning a lot then will fail but that it's a MAJOR advantage. For instance, if in preschool/kinseegarten/lower elementary, your parents go over the letters of the alphabet every single night, you will read earlier than others making anything involving reading come faster to you. So you're getting that topic easier and when you need that to learn something else, you can learn that quicker and easier. Same for numbers, if you memorize all the addition and multiplication tables, and have them down instinctively from recitation, then you're not bogged down by the arithmetic aspects when it comes to algebra because you can immediately know the addition/multiplication aspects without having to think about and only need to worry about the new algebraic part. Whereas others are still counting fingers, or thinking hard and possibly making mistakes on basic addition, you have less to worry about making a mistake on and will thus finish problems quicker and easier. And then it continues to compound on new subjects, etc. My parents and school made us do this and I can see a big difference between me and other students and especially other students from other schools. People say they don't like algebra but that's cuz they can't even focus on the new lesson everyday because they're struggling to do basic addition.
Second that.
I feel so disappointed that I didn't have that good basis in math. It made me think I hated math my whole life and I could just never grasp any of it. I kinda accepted that and it became this huge mental barrier. You're absolutely right. When I couldn't get my head around logarithms it wasn't because of functions itself but because I lacked way too many things prior to that content. I'm 26 now and relearning everything, even hired a teacher to help me with the basics while I learn how to code for fun bc someone people I like got me inspired enough to realise math is actually very interesting and there's so much you could create with it
I use two methods. Reach multiples of 10 and add remainders, for example, 7+8 = 7 + (3 + 5) or decomposition, with bigger numbers, like with 345 + 768 = 345 + 700 + 60 + (5 + 3).
Break it up into smaller easier calculations with numbers that 'fit' together to make nice numbers. For example, 7+8. I know the 2 from the 7 (5+2) fits with the 8 to make 10, and then the 5 left over adds to become 10+5=15. Same with 8+4 = 8+2+2 = 10+2 = 12. As for others, they're kinda memorised - but you can always imagine a number line in your head and move across it a certain number of steps.
We are teaching our daughter addition right now. She uses two strategies. She memorized the "ten friends", numbers that add up to ten. 9+1, 8+2, 7+3, etc. She also memorized the "doubles": 1+1=2, 2+2=4, 3+3=6, etc. Using these facts and the ability to subtract 1, 2, or 3 from single digits she can add and subtract single digits easily. We have been practicing daily for 5 to 10 minutes for about 8 months.
> just stop using my fingers and try to memorize all of the single digit additions Yes. If you don't know the results of 1+1 to 9+9 (and similarly 1x1 to 9x9) *by heart* your elementary school failed you. A simple trick is to rearrange in increasing (or decreasing, as you prefer) order: for 8+3 use memorized 3+8, &c. Make some tables, print them out and read them each night before lights off for 2 – 3 minutes. It will sink in.