The Millennium Project, an international participatory think tank that uses futures research to systematically explore, create and test both possible and desirable futures in order to improve decisions in the present, presents unprecedented challenges for Australian education. Their publication, 2015-16 State of the Future, outlines 15 global challenges that represent an unparalleled invitation for educators to think creatively and imaginatively to design experiences whereby students successfully engage in ‘border crossing’ (Giroux, 1992). The act of border crossing provides unprecedented opportunities for children, young people and adults to develop intercultural competencies and skills that better enable them to live together mindfully. We present a new border pedagogy based on the concept of hybridity that works to build students’ and citizens’ intercultural competence by encouraging them to embrace potential miscommunication and intercultural conflict. By learning how to embracing hybridity, students can work productively to put what is known into crisis by constantly blurring and problematising boundaries, binaries and identities. Our new border pedagogy promotes living ‘together-in-difference’ (Ang, 2001) by encouraging students to critically interrogate issues of difference they face as they border cross. The border pedagogy for living together-in-difference encourages students to embrace intercultural conflict and potential miscommunication because of the questions and wonderings it kindles and inspires. Importantly, it presents a pedagogy that assists educators in building on the educational goals of the Melbourne Declaration and engaging effectively with the Australian Curriculum’s cross-curriculum priorities so students can prosper individually, collectively and communally in a globalised world.