Сложение и вычитание обыкновенных дробей

(Приложение 1)

1. Актуализация знаний, постановка задач урока.

1) Устная работа найдите лишнюю дробь и поясните почему.

а)
б)
в)
г)
д)  .

2) Игра «Верю – не верю»

Ребята самостоятельно отвечают на вопросы

3) Историческая справка (рассказывает учитель или подготовленный ученик ).

В русском языке это слово появилось лишь в 8 веке. Происходит слово “дробь” от слова “дробить, разбивать, ломать на части”. В первых учебниках дроби назывались “ломаные числа”. Современное обозначение дробей берёт своё начало в древней Индии; дробная черта появилась в записи дроби лишь около 300 лет назад. Названия “числитель” и “знаменатель” ввёл в употребление греческий монах учёный-математик Максим Пеануд. Долгое время дроби считались самым трудным разделом математики. У немцев даже сложилась поговорка “попасть в дроби”, что означает попасть в трудное положение.

Давайте обсудим три первых вопроса из нашей таблицы.

4) Задача урока: Доказать, что  мы с честью выйдем из трудного положения.

2. А теперь рассмотрим цветные квадраты на ваших столах. Разрежьте квадрат по линиям.
– На сколько частей вы разрезали квадрат?
– Данное число мы запишем виде числителя или знаменателя?
– Возьмите 4 части зеленого цвета. Какая дробь у нас получилась?
– Возьмите 2 части желтого цвета.
– Какая дробь у вас сейчас получилась?
– Теперь  4 зеленых и 2 желтых части поместим на белый квадрат.
– Сколько цветных частей у вас получилось? Запишите эту дробь.
– Какое действие мы с вами выполнили?
– Ребята сформулируйте тему нашего урока.

Тема: «Сложение обыкновенных дробей»

– Теперь, ребята, давайте вместе запишем правило сложения обыкновенных дробей. Вставьте слова.

Чтобы сложить дроби с ____________ знаменателем, нужно _________ их __________, а __________ оставить прежним.

Как бы вы записали правило сложения дробей с помощью кластера?

1) Графическая модель сложения дробей с одинаковыми  знаменателями:

2) Символьная модель сложения дробей с одинаковыми  знаменателями:

3) Чтобы сложить дроби с одинаковыми знаменателями, надо сложить  их числители, а знаменатель оставить без изменения.

4) Найдите сумму следующих дробей:

1)                   2)             3)                4)                          5)

– Чем отличаются решения примеров 1 и 2?
– Чем отличаются решения примеров 1 и 3?
– Чем отличаются решения примеров 4 и 5 от решения примера 1?
– Как вы теперь сформулируете правило сложения дробей с одинаковыми знаменателями?
– Чтобы сложить дроби с одинаковыми знаменателями, надо сложить  их числители, а знаменатель оставить без изменения и упростить полученную дробь (сократить, выделить целую часть).
– Теперь посмотрим на табличку верю/не верю. Какой вариант решения теперь вы считаете правильным?

Физкультминутка: все учащиеся делятся на две группы:мальчики – числители, девочки – знаменатели. Встают. Если дробь правильная, то ученики-числители руки поднимают вверх, а ученики-знаменатели – руки в стороны; если дробь не правильная, тонаоборот; если числитель равен знаменателю, то все стоя хлопают один раз в ладоши над головой.

5) Найдите разность следующих дробей:

1)                   2)                      3)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

– Какой пример вызвал затруднение?
– Обратимся теперь к нашим цветным моделям.
– Заполним цветными квадратиками весь белый квадрат- это целая часть.
– Как мы ее можем записать? 1 или 
– Отнимем  (4 квадратика). Сколько осталось?
– Давайте сформулируем правила вычитания дробей с одинаковыми знаменателями с помощью кластера.

1) Графическая модель вычитания дробей с одинаковыми  знаменателями:

2) Символьная модель вычитания дробей с одинаковыми  знаменателями:

3) Чтобы выполнить вычитание  дробей с одинаковыми знаменателями, надо из числителя уменьшаемого вычесть числитель вычитаемого, а знаменатель оставить без изменения и упростить полученную дробь.
Запишите правило вычитания правильной дроби из 1.
Чтобы вычесть правильную дробь из 1 , надо 1 представить виде неправильной дроби .

3.  Закрепление: № 423, 425, 426.

4. Итог урока:

Составьте синквейн:

1. Дроби
2. Правильные, неправильные.
3. Складывали, сокращали, выделяли.
4. Сложение и вычитание обыкновенных дробей.
5. Числитель, знаменатель.
5. Домашнее задание:

– §24
– Выучить правила
– № 424, 427.