Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one solution approach over others, and enhance their perseverance toward problem solutions. Tasks are of nine types: Connect Calculation to Context, Rank Order Solutions, Identify What's Wrong If Anything, Defend an Opinion, Work Backwards, Predict and Explain, Think and Choose, Place Them Right, and Make Sense of a Situation. All tasks require application of concepts and skills from one or more domains of mathematics. As students solve these problems, they quickly identify what they know and what they are not sure about; that is, they assess their own degrees of understanding and learn at point of need. The article concludes with recommendations for implementing TALMs and an invitation for students and teachers to create their own.