The research aimed to identify the impact of the Appleton model in the critical thinking of students in the fifth grade in mathematics, and to verify the research objective, the following hypothesis was formulated: There was no statistically significant difference at the level of (0,05) between the average grade of the students of the experimental group who study according to (Appleton model) and the average score of the students of the control group who study on (The normal way) in the test of critical thinking. The sample of the study consisted of 67 students from the fifth grade of scientific / biological in the preparatory school of Qalat Sukkar in the Directorate of Dhi Qar. A (34) students were selected as the experimental group according to the Appleton model and (B) (33) students to be the control group, which is taught according to the usual method after the exclusion of students from the two groups statistically and only one student in the Divi- sion (B) and verify their equivalence in the variables (age, time and previous sports knowledge and intelligence and the previous academic achievement of the grades of the course I tested and skilled Critical Thinking) The last four chapters of the mathematics book for the fifth grade were set to teach the students of the two research groups. The experimental and control groups studied the same subject. I rely on the research tool: (Critical Thinking Test) which consists of (30) paragraphs divided into (five) areas (knowledge of assumptions, interpreta- tion, arguments, deduction, conclusion) so that each field contains (6) Is the most appropriate choice for the test of critical thinking, and its validity was verified as well as knowledge of the cycometric characteristics in terms of difficulty and discrimination and the effectiveness of the wrong alternatives. The test of two separate independent samples, the difficulty and discrimination coefficients, the effectiveness of the alternatives, and the ETA coefficient for calculating the effect size were adopted (statistical means of research). In light of these results, the researcher recommended the adoption of Apple- ton model in the teaching of mathematics for the preparatory stage, as the results of this research showed an improvement in the level of critical thinking among the students of this stage of study.