The COVID-19 pandemic has forced school closure thus shifting teaching and learning towards full home-based learning (HBL). Technology plays a key role but the considerations to design online learning environments that meaningfully engage students are complex. This exploratory, qualitative study attempted to elicit eight mathematics teachers' considerations and perspectives in designing online home-based learning lessons for the engagement of elementary and secondary students. Data were gathered through interviews. Ground-up thematic analyses were conducted. The following implications are derived--(1) student engagement in online learning context is paramount to their learning, (2) there is no one software application for all the learning activities, (3) teacher professional development is necessary to keep them up-to-date, (4) online social networking platforms may be necessary for students' discussion beyond official online lesson time, and (5) students need to be inculcated with more self-directed skills and habits for learning in online and face-to-face contexts. This study gathers evidence-informed considerations for teachers to design lessons and engage students meaningfully in a unique, online HBL environment. While this is an exploratory study, future studies can inform this area of work by including more teachers across subjects, grades, schools, and geographical contexts. Studies involving students and parents would also be meaningful.