Atomistic-to-continuum(a/c) coupling methods, also termed as quasicontinuum(QC) methods, are a class of concurrent multiscale methods for the simulation of crystal defects. Such methods couple the atomistic description of a solid to its corresponding continuum approximation usually obtained by the Cauchy-Born rule. In this talk, we present the modeling and analysis for the blended type of coupling schemes of the atomistic model to a higher order continuum (HOC) elasticity based on a higher order Cauchy-Born approximation. We first briefly review the classic and higher order Cauchy-Born approximation to demonstrate the advantage of the later in (large) elastic deformation. We then concentrate on two blended atomistic-to-higher order continuum coupling (BQHOC) methods that are based on energy minimization and force balance respectively. We show that the higher order convergence of the solution is only obtained by the force-based method but not the energy-based one. We give an explanation of the intrinsic reason for this phenomenon and numerically demonstrate our analytical results.