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May. 15th, 2013 09:18 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
cbetaСашка, как оказалось, плавает в отрицательных числах. По дороге в школе рассказала ей байку, которая, кажется, помогла визуализировать задачки. На всякий случай запишу и тут, может, еще какой маме пригодится.
Imagine a country road which leads from the Day Kingdom on the right to the Night Kingdom on the left. The Day Kingdom is bright, warm, and you can see yellow Sun far away. The Night Kingdom is dark, mysterious, and the road leads towards the white Moon. All along the road we have little mile posts with numbers which say how far it is from the border, only the posts on the dark side of the road all have minuses in front of them. On the border (which is, obviously, Zero) stands a guard which asks you: where you go? How much you've covered already? How far you've still left to go? And adding is just starting from a number post and going towards the Sun (pluS), and subtracting is going towards the Moon (MiNus).
So, if we have 3-5, we start in the Day Kingdom at the post with number 3, and (minusing!) go towards the Moon, to the left. After 3 miles, we reach the guard and have to tell him how far we have left to go: 2. Then we walk for these two miles on the dark side, and reach the post with number -2. This is our answer! Similarly, if we need to do -3+5, we'd have to walk from the Night Kingdom towards the Sun, starting at -3, walking 3 miles to Zero where we answer the guard's questions, and then walk 2 last miles on the bright side.
It is useful for all sorts of manipulations with negative numbers, which Alex was completely at lost how to do. Let's say we need to find -2-3: we start on the dark side and go 3 miles into the darkness towards the Moon, away from zero, so we'll come to the post with -5 on it. And so on.
Вся эта сказочность, наверное, лишняя, но мне кажется полезным видеть ноль как границу между мирами (я и сама ее так вижу :) ). Да и вообще, по-моему, важно уметь визуализировать всякие математические манипуляции, это помогает развитию интуиции, учит сводить непонятные цифры к наглядным рассуждениям "на пальцах" (обратное тоже полезно, кстати).
Imagine a country road which leads from the Day Kingdom on the right to the Night Kingdom on the left. The Day Kingdom is bright, warm, and you can see yellow Sun far away. The Night Kingdom is dark, mysterious, and the road leads towards the white Moon. All along the road we have little mile posts with numbers which say how far it is from the border, only the posts on the dark side of the road all have minuses in front of them. On the border (which is, obviously, Zero) stands a guard which asks you: where you go? How much you've covered already? How far you've still left to go? And adding is just starting from a number post and going towards the Sun (pluS), and subtracting is going towards the Moon (MiNus).
So, if we have 3-5, we start in the Day Kingdom at the post with number 3, and (minusing!) go towards the Moon, to the left. After 3 miles, we reach the guard and have to tell him how far we have left to go: 2. Then we walk for these two miles on the dark side, and reach the post with number -2. This is our answer! Similarly, if we need to do -3+5, we'd have to walk from the Night Kingdom towards the Sun, starting at -3, walking 3 miles to Zero where we answer the guard's questions, and then walk 2 last miles on the bright side.
It is useful for all sorts of manipulations with negative numbers, which Alex was completely at lost how to do. Let's say we need to find -2-3: we start on the dark side and go 3 miles into the darkness towards the Moon, away from zero, so we'll come to the post with -5 on it. And so on.
Вся эта сказочность, наверное, лишняя, но мне кажется полезным видеть ноль как границу между мирами (я и сама ее так вижу :) ). Да и вообще, по-моему, важно уметь визуализировать всякие математические манипуляции, это помогает развитию интуиции, учит сводить непонятные цифры к наглядным рассуждениям "на пальцах" (обратное тоже полезно, кстати).
