There is no doubt that playing and having fun with one's child has a great effect on his correct and proper upbringing.

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This is since playing is a part of his life that he should not be deprived of.
 
So do not trivialize the act of playing with children for you will be clashing against their natures and dispositions upon which they were created. Instead, participate with them to the point that they love you, enjoy your company and heed your advice and guidance. Allaah said to His Prophet (salallaahu alayhi wa salaam): "And by the Mercy of Allaah, you dealt with them gently. And had you been severe and harsh hearted, they would have disbanded from about you" [Surah Aali Imraan:159]
 
The Prophet (salallaahu alayhi wa salaam) was the best of people towards his family as he (salallaahu alayhi wa salaam) said: The best of you is he who is best towards his family, and I am the best towards my family. [Reported by Al Haakim] 
 
The Prophet (salallaahu alayhi wa salaam) would play and have fun with children. Abu Hurayrah (Radi Allaahu anhu) said: The Messenger of Allaah (salallaahu alayhi wa salaam) would stick his tongue out to al Husayn bin Alee (Radi Allaahu anhu), so the boy would see the redness of his tongue and become ecstatic."
 
Umar (Radi Allaahu anhu) said: I saw al Hasan and Al Husayn on the shoulders of the Prophet (salallaahu alayhi wa salaam) What an excellent steed you two have below you. And the Messenger of Allaah salallaahu alayhi wa salaam) said: And what excellent riders they are! [Reported by Abu Ya'laa]
 
The Prophet (salallaahu alayhi wa salaam) would also play around with the brother of Anas bin Maalik (Radi Allaahu anhu) saying: O Abu Umair, what happened to the nughair? [Agreed Upon]
 
And once he (salallaahu alayhi wa salaam) passed by a group of people from the tribe of Aslam who were practicing archery, so he said: Shoot tribe of Ishma'eel for indeed your forefather was a marksman. Continue shooting I am with tribe so and so. Upon this one of the teams refrained from competing, so the Prophet salallaahu alayhi wa salaam) said: Why aren't you shooting your arrows? They said: How can we shoot when you are with them? So he salallaahu alayhi wa salaam) said: Continue shooting and I am with all of you. [Reported by Al Bukharee]
 
Abdullaah bun Al- Haarith (Radi Allaahu anhu) The Messenger of Allaah (salallaahu alayhi wa salaam) would line up (the children) - Abdullaah, Ubaydullaah and Katheer - of the tribe of Abbaas and say to them: Race towards me, and whosoever reaches me first will get something (I.e. As a reward). So they would race towards him and jump on his back and front and he salallaahu alayhi wa salaam) would kiss and hug them. [Reported by Ahmad].
 
Aa'ishah, may Allaah be pleased with her, would play with girls, and the Prophet(salallaahu alayhi wa salaam)would dispatch them to her so that she could play with them.[Agreed Upon].
 
Through the means of playing, you can instill good characteristics into your child - characteristics such as honesty, fidelity and so on. You can also use activities and games to make them aware of condemnable characteristics such as lying, treachery, deception, use of obscene language and so on.

From Al-Ibaanah publication: "Raising Children in Light of the Qur'aan and Sunnah"

by 'Abdus-Salaam As-Sulaymaan. The book was introduced and commended by Shaikh Saalih Al-Fawzaan