Did a typing test at: Typing Test · Check your Speed and Practice, WPM
got 63.56 WPM @ 97.06% accuracy.
I don’t feel as if i’ve improved at typing this week. If anything I feel a bit worse. Slowing down is not always helping with accuracy, and sometimes makes it worse. Making 100% is rare but possible. There are non-letter characters I am still bad with and numbers I have no practise with.
After you do some fraction division, you’ll want to also look at percents, ratios and decimals to make sure you’re comfortable with them too. Then you could try some unit conversions (such as converting miles to meters). Also how are you with exponents?
Some things I have noticed when doing typing practise or tests:
When typing, knowing that I am being timed makes me feel stressed and it’s harder to focus.
Once I have made a mistake while typing, it seems like I make more mistakes.
I’m sure there are things I don’t know, but I’m not unfamiliar. I’ll investigate today
Okay, so I have gone over fraction division, percents, decimals, and exponents and fractional exponents over the last two days, about ~6-7 hours total.
Exponents I am doing well with but I need more practise. I’m getting like 95% accuracy and some problems are slow.
Show some work including some you got wrong.
These notes were taken on my iPad. I hadn’t been taking them with sharing in mind so they are often formatted a bit chaotic. Some of the problems I didn’t take down and just worked on them directly so I’ve omitted those.
Some of my use of the ‘=’ is not as ‘equals’ and is more like a way to separate stages of the problem, so that might be confusing. I’ll format my note taking better in the future so that’s less of a problem.
If sharing handwritten iPad notes is a problem I can think of something else to try.
My answers are highlighted yellow.
Simplifying Fractional Powers. Exercises from Worksheet 1.8 Section 3:
Fractions/exponents w some wrong:
I’m going to do some more worksheets so will format better and share results too.
I just did another worksheet on Negative and Fractional Indicies. 86% accuracy.
~ 1hr
The apple Notes app has no convenient way to export the whole note as an image file. I’m going to look into another app. For now here are a series of screenshots:
This accuracy is too low and indicates a problem. 86% and IMO even the 95% is low enough to mean you should stop practicing what you’re doing and change your approach. Slowing down is an option but I suspect that wouldn’t be adequate to get ~100% accuracy. I think one problem relates to relying too much on formulas and memorization instead of underlying concepts. Being able to write things out the long way, and practicing doing that, would help avoid these mistakes.
So here’s a conceptual question: what is multiplication?
I’d like your answer without you looking anything up. But also, if any of the math resources you’re using answer this question, you could review what they say after you answer, and share it, and compare it with your answer, and potentially even try to evaluate if their answers are good (like do you find their answer clear or confusing).
Cool yup, that is a problem that I have been concerned about too.
Multiplication is repeated addition. 4 x 5 means: five fours added together. Or, five repetitions of the addition of 4 to 0.
What’s exponentiation?
Repeated multiplication. 4^5 means 5 fours multiplied together.
What’s addition?
Interesting. at first glance, I’m not sure how to explain addition without using addition as a concept. I’ll give it a go.
I seem to remember from Godel, Esher, Bach that numbers were thought of as having successors. So for each number there is a successor that is a unit higher than itself. This forms an infinite number line.
Addition is the the stepping up through a succession of numbers, from one number to new number, by a certain amount of steps.
So 4 + 5 could be thought of the 5th successor of 4, or the 4th successor of 5.
I’m not confident about all of this, but I think number lines concept is related.
Can you think of something similar that follows the pattern of an arithmetic operation repeating something else?
Do you still mean on the topic of addition? Do you mean can I think of a similar thing to what I said about addition, but keeping with the pattern of what I said about multiplication and exponentiation?
If so, perhaps:
Addition is repeated steps along a number line.
Yeah. Or repeated use of successor.
Do some practice problems and share work where you write out the repeated thing explicitly and solve from there.
Sure, like this, or more so? I came up with these problems myself so don’t have an answer key but they all look right.
Looks right
There’s a second concept of multiplication besides repeated addition. Any ideas? Not the geometry one which is a third.
