How Lord Ganesh got elephant head?

We always pray to Lord Ganesh or Ganapathi or Vignaharaka to remove any obstacles from our life. He is also the God who blesses us with knowledge. So in Hindu culture any pooja starts with praying to Lord Ganapathi.
Once Goddess Parvathi was taking bath in her palace, when Lord Shiva without knocking on the door entered the garden. Goddess Parvathi was angered by such an act and told the Lord not to do so. But Lord gave a reply that it is His garden and She is his wife and He needn't take anyone's permission.  This angered the Goddess more.  So She started thinking of a solution. Next day an idea stuck her. She took the dirt from Her body and made a statue of a small boy and gave life to it. The boy looked really beautiful. He asked " Mother, you created me and gave me life. I am your son and bound to protect you. Please tell me what is my first duty?" Goddess Parvathi gave him the instructions to protect her garden gate and not allow anyone inside without her permission, as she is going to take bath. Lord Ganesh started protecting the gates with a stick in hand. Who came there?

Obviously, as usual our Lord Shiva, who didn't know his own son. Lord Ganesh who was protecting the gates, didn't allow Lord Shiva inside. Lord tried to explain. But Lord Ganesh was very adamant. Lord Shiva got angry and started fighting with our Ganesh. None of the weapons had any effect on Ganesh. It was the heights of the fight when Lord Shiva's anger knew no bounds and cut the head of Ganesh. Hearing the commotion outside, Goddess Parvathi rushed outside. Seeing the state of her son she was really angry and commanded Lord Shiva to give her son back. Lord Shiva realised his mistake and called his Shiva ganas and ordered them to bring the head of the first animal or human being who is lying down in the wrong direction. The Shiva ganas started in search of such a being, where they found a baby elephant lying in the wrong direction.  They immediately took the head of the baby elephant and handed it over to Lord Shiva and he attached the head to the body of Ganesh and gave life to it. Goddess Parvathi was not still happy to see her son like that. So Lord Shiva blessed him with a boon that Lord Ganesh will be called as Lord Ganapathi and would be prayed first anywhere and during any pooja. Other Gods and Goddesses also blessed him with several boons.