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This study, which was supported by a quantitative research paradigm with two experiment and two control groups of 4x4 quasi-experimental design, aimed to find out the impact of a sustainable progressive STEAM (SP-STEAM Model) application model on 5th grade primary school students critical thinking dispositions and mathematic achievements in Northern Cyprus. The treatment model was applied to experimental groups for 14 weeks of time. Split-plot multiple group analysis of variance (Split-plot ANOVA) statistical technique was used to calculate between and within group significances regarding exogenous variable. SPSS24 software package was used for the analysis. Pre-test and post-test results derived from experiment and control groups revealed significant effect of SP-STEAM Model on 5th grade primary school students’ critical thinking dispositions as measured with CCTDI and mathematic achievements as measured with a dedicated ex-am. The results were discussed in detail under the light of related literature and suggestions for further studies were proposed.