The aim of the research is to build an educational-learning design according to the progressive inquiry model and to know its effectiveness in the mathematical excellence skills of second-grade intermediate students. To achieve the research objectives, the two researchers followed the experimental research method, and they adopted a quasi-experimental design with two equal groups with a pre-post test to measure the mathematical excellence skills. To achieve the goal, the following null hypothesis was formulated: there is no statistically significant difference at the significance level (0.05) between the mean scores of the experimental group students who studied the material according to the educational-learning design and the students of the control group who studied the same material according to the usual method in the pre-post test of mathematical excellence skills. The research community was identified, which represents all the students of the second intermediate grade in the governmental middle and secondary day schools of the general directorate of education in Baghdad / Rusafa I. The sample consisted of (63) students from the second intermediate grade students, (32) students for the experimental group and (31) for the control group from Al-Harith Intermediate School for Boys. As the test in its final form consisted of (30) paragraphs of the essay and objective type, and the appropriate statistical analyzes were conducted, and by adopting the appropriate statistical tools to analyze the results, the results indicated the existence of a statistically significant difference in favor of the students of the experimental group. Those who studied the prescribed subject according to the educational-learning design and among the students of the control group who studied the subject according to the usual method, and that teaching according to the educational-learning design according to the progressive inquiry model is effective in the skills of mathematical excellence.