IPhone will only send messages over data plan, even when connected to Wi-Fi?

So all messages I send are automatically charged to my data plan, even though I'm connected to a strong Wi-Fi connection. I only have limited texting, so you can see my problem. The iPhone is 4th gen, not sure what iOS version.

Text messages are not sent using Wi-Fi though so that would be the problem, The only thing iphone would send over Wi-Fi would be a iMessage but everyone you text would also have to have a iphone for this to work.
You could also download a messaging app like wahtsapp messenger this also uses the Wi-Fi on the phone to send a message but you would also need the people you want to send sms to to have the app on there phone.

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