This article notes the low rate of highly talented or gifted students formally identified in Spain compared to international benchmarks. These students are not properly identified, so a lack of specific educational responses for these highly talented students is also expected. Trying to counteract this trend, this article presents an enrichment program imparted to a group of students with high intellectual abilities during the academic year 2017/18 over three weekly sessions during school hours, where emerging technologies were an important key in how it was delivered. The experimental design included an experimental group of high ability students and two control groups, one consisting of students with high abilities who did not receive specific educational responses and another consisting of a group of regular schoolchildren in terms of abilities. The results showed that the implementation of specific educational responses improved children's levels of adaptation and in some cases, their school performance. These data are discussed in an attempt to recommend enrichment programs integrated into the classroom as an appropriate educational response to gifted or high ability students. Attention to diversity of all students in the classroom is possible, for example by resorting to ICT, increasing the educational inclusion of students with high intellectual capacity.