For many years, universities have aspired to develop in students so-called 'soft skills' or graduate qualities (GQs), such as critical thinking and teamwork, that enhance both students' employability and citizen scholarship. GQs are often said to be 'embedded' in courses, but saying this does not of itself provide evidence that students have developed the qualities. Our University has recently proposed using common rubrics in all courses to measure and provide evidence of students' achievement of GQs. However, a solution to the problem of how to implement the University's rubric-based strategy has not been fully formulated. Many staff use assessment tasks that focus on measurement of discipline-specific content and procedures, rather than GQs, and the use of task rubrics and their design is variable. In this conceptual article, we advance a solution to the problem of how to implement the University's rubric-based strategy in our Health Sciences context. To formulate a solution, we adopted a design thinking approach, which is focussed on people's needs and taking iterative steps to create a design solution to meet these needs. We encountered three key design issues in our approach that led us to propose new 'bridging' concepts for assessing GQs: consistency in learning, rubric standardisation, and the audience for assessment tasks. These concepts link existing theory and research around course 'constructive alignment', rubrics, and assessment task design. Possible tests of our solution are suggested, and potential advances in course design and research are discussed. For universities planning assessment of GQs, we recommend a holistic approach, in which academics, educational and work-integrated learning professionals, students and community partners unite and are supported in the ongoing course design process.