The present invention relates to modular construction panels, floor panel and construction assemblies that can be made therewith. The construction panels comprise an insulation layer, a plurality of studs and a sheathing layer positioned adjacent the insulation layer. The sheathing layer is attached to plurality of studs through the insulation layer in order to reduce thermal bridging between the two. The floor panels comprise a plurality of floor joists extending between a first end of the floor panel and a second end of the floor panel, a floor sheet connected to each of the plurality of floor joists and a first end piece that comprises a first stud-aligning abutment, a second stud-aligning abutment and a stud-receiving slot positioned therebetween for receiving studs of the construction panels.