Pattern recognition is an important skill in computational thinking. In this study, an equation puzzle game was developed by combining pattern recognition with algebraic reasoning, and scaffolding was designed to support learners' learning. Sixty participants were enrolled in this study, divided into a control group and an experimental group to compare the results and differences in game achievement, flow, anxiety, and motivation of participants with and without algebraic reasoning scaffolding. The results of the study showed that the participants in both groups had positive flow and motivation during the game, did not feel over-anxious, and there was no significant difference in the game achievement of the two groups. In addition, the game with the scaffolding may have the potential to make a positive correlation between game achievement and psychological status. The results of this study indicated that the game did not cause too much anxiety to the participants. The scaffolding-based design achieves the intended effect on the participants' assistance and facilitates the participants' engagement in pattern recognition problem solving. And as learners became more focused and engaged, they could also perform better in the game. This game mechanism can be used as a reference for designing pattern recognition games.