Сюжетные математические задачи и логика · Arithmetic Logic Models
Интерактивный аниматор сюжетных логических задач
Визуализатор классических арифметических задач: избыток и недостаток, лягушка в колодце
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Параметры эксперимента
Расчёты и показатели в реальном времени
Итоговый ответ
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Ход развёртки
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Порог выхода
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Модель рассуждения
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Вывод формул в реальном времени
Основная формула:
--Подстановка значений:
--Вывод: --
Версия для начальной школы:🎮 Мастерская вычислений столбиком ↗
Разбор типовых задач и анализ экзаменационных ошибок
Worked Problem
Условие задачи: A snail in a 12m well climbs 4m by day and slips 2m by night. How many days to climb out?
Пошаговый вывод формул:
- Target before final day = 12 - 4 = 8m. Daily net = 4 - 2 = 2m. Days to 8m = 8 / 2 = 4 days. On day 5, it climbs 4m and reaches 12m. Total = 5 days.
Worked Problem
Условие задачи: 3 empty bottles trade for 1 full beer. You buy 24 beers. What is the maximum total beers you can drink?
Пошаговый вывод формул:
- Net exchange: 3 empties = 1 full (beer + empty) means 2 empties = 1 drink. Extra drinks = 24 / (3 - 1) = 12. Total drinks = 24 + 12 = 36 beers.
Рабочий лист для урока и домашние задания
Q1. Variant 1: Ming has 18 pencils, Hua has 10. How many must Ming give Hua for equal? For Hua to have 3x Ming?
Answer Key: Equal: difference is 8; give 8/2 = 4. 3x: total is 28 (4 shares); Ming keeps 28/4 = 7; gives 18 - 7 = 11 pencils.
Q2. Variant 2: Candy sharing: 6 each lacks 12; 4 each leaves 8 surplus. How many kids and candies?
Answer Key: Kids = (Surplus + Deficit) / Rate Delta = (8 + 12) / (6 - 4) = 10 kids. Candies = 10 * 4 + 8 = 48 candies.
Q3. Variant 3: Monkey eats half + 1 peach daily. After 3 days, 1 peach remains. How many peaches originally?
Answer Key: Work backwards: Before day 3 = (1 + 1)*2 = 4. Before day 2 = (4 + 1)*2 = 10. Initial = (10 + 1)*2 = 22 peaches.
Часто задаваемые вопросы и типичные заблуждения
Why is transferring items called "Give One, Shift Difference by Two"?
Moving 1 block from A to B reduces A by 1 and increases B by 1, altering their relative difference by exactly 2!
Why does well depth divided by daily net climb fail in the frog well problem?
Because net climb factors in the night slip. On the final day, the frog tops the rim during daytime and escapes; the subsequent night slip never happens!
If the shopkeeper refuses to lend an empty bottle, do you drink fewer sodas?
Yes, exactly 1 fewer! 2 remaining empties cannot redeem without borrowing; borrowing achieves the theoretical maximum.
How to summarize all surplus-deficit formulas in a single sentence?
Denominator is always the rate delta. Numerator rule: "Opposites Add, Sames Subtract" (Surplus+Deficit adds; Surplus-Surplus subtracts).