Smartphones can be great, but they only give you a few options to handle incoming calls: ring, vibrate or silent. You can eliminate distractions by using a silent ringtone as the default and changing it for just the important contacts.
On many phones, you can do something similar with the Do Not Disturb setting, but I've found this works well. By combining a silent ringtone as the default and assigning an audible ringtone to your child, spouse and other important contacts, you can greatly reduce the amount of distractions and get back to work.
Incoming calls will still display on the screen, but if they have not been individually assigned a ringtone other than the default, you will have no audible cue that a phone call happened until you check your phone later, and they will simply go to your voicemail.
Making a silent ringtone is the same as turning any song into a ringtone — only you use a silent MP3, like one of these. Then, just make it the default ringtone for your device in its settings. Don't forget to assign a different ringtone to your desired contacts!