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The purpose of this study was to design the alleged learning trajectory of HLT (Hypothetical Learning Trajectory) and problem solving-based mathematics-based local instruction theory that supports students' creative thinking skills. The research subjects were students of class VIII at SMP 1 Ternate and SMP 2 Ternate, North Maluku. The method to be used is design research, which is a form of research with a qualitative approach. Design research aims to develop Local Instruction Theory (LIT) with collaboration between researchers and teachers to improve the quality of learning. Design research consists of three stages, namely: Preliminary design, Teaching experiment and retrospective analysis. The result in this stage is HLT which consist of five activities on the Ratio concept through the context of Ternate's local cultural wisdom, namely Lapis Palaro which has gone through the stage: preparing for the experiment or preliminary design. [ABSTRACT FROM AUTHOR]

Several previous studies indicate that students have difficulty in understanding the concept of line and angles. In their worksheets, the material presented in abstract form is not used in a related context. The purpose of this study is to produce valid and practical student worksheets based on the ethnomathematics of Gending Sriwijaya dance on lines and angles material. The research method used is development research with preliminary design and formative evaluation which consists of expert review, one to one and small group. The validity is obtained at the expert review and one-to-one and the practicality is obtained at the small group. The research subjects are students of class VII Mts Patra Mandiri. The data collection techniques in this research were validation sheets, interviews and questionnaire sheets. The results of this research is producing a student worksheets based on the ethnomathematics of Gending Sriwijaya dance on Lines, and Angles material which are valid and practical, the validity based on the validation sheet as well as comments and suggestions given by validators and students at one to one. The practical based on the questionnaire sheet as well as comments and suggestions given by students at small groups. [ABSTRACT FROM AUTHOR]