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Colonial forces led by Colonel William Prescott and General Israel. had fortified hills near Boston, the British which were led by General William Howe invaded these hills and fought the colonists. The British were victorious, making the colonists retreat because they were low on ammunition but the British suffered great casualties.
The battle of bunker hill was important because it made the colonial forces confident that they could defeat the British and win the war. -
During the winter of 1777-1778 the continental army led by George Washington settled at Valley forge in Pennsylvania but suffered from hunger, cold and lack of supplies which lead to disease and thousands of deaths. At the end of winter, the army emerged as a more disciplined army capable of defeating the British
This even was important because it was when the continental army turned from a poor trained army to a more disciplined, professional and highly trained army.