As a product manager at Duolingo, my goal would be to expand the company's offerings into math education. One way to achieve this would be to leverage the existing Duolingo platform and apply it to math learning. To begin, I would conduct extensive user research to understand the needs and pain points of students and teachers in math education. This would involve gathering data on current math education tools, identifying gaps and areas for improvement, and gathering feedback from users on what features would be most valuable to them. Once we have a clear understanding of user needs, we would begin to design and develop a math education product that leverages the strengths of the Duolingo platform, such as gamification, personalization, and adaptive learning. We would also explore partnerships with other education technology companies and institutions to ensure that our product is comprehensive and effective. In addition to product development, we would also need to develop a go-to-market strategy for our math education product. This would involve identifying target markets, developing pricing strategies, and designing marketing campaigns that effectively communicate the value and benefits of our product. Overall, my goal as a product manager at Duolingo would be to leverage the company's strengths and expertise in language learning to create a high-quality, effective, and engaging math education product that meets the needs of students and teachers alike.