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It depends on what insulin regimen he/she is on. If they are taking a basal insulin eg lantus and fast acting insulin with each meal then I would advise that they continue with their basal insulin (even if they take this in the morning) and omit the fast acting insulin when they do not want to eat (or reduce the dose if they don't want to eat as much). It's a pity they don't want a pump as this would be a good answer. Teens are probably one of the most challenging age groups of people to treat (for all sorts of reasons) but it sounds like they have had some severe hypoglycaemic attacks and need to understand the seriousness of this.  Your diabetes team will be able to give some advice on carbohydrate counting and insulin dose adjustment according to what you eat. Good luck!