The goal of this paper is to present a design methodology for developing energy aware algorithms. The key idea revolves around identifying operations called kernels, which are frequently used operations in the algorithm that can be implemented in hardware. Optimising these kernels for performance or energy would then lead to a major impact in energy saving. We propose a six-step methodology for design of energy aware algorithms. The method includes: high-level algorithm analysis, identifying high frequency kernels, determining the order of computation for each kernel via asymptotic analysis, prioritising kernels in terms of energy impact, proposing alternative implementations to the kernels that cause high energy consumption and investigating further opportunities for energy optimisation specific to the studied algorithm. We further propose a simple and efficient method for estimating a kernel's energy cost. The method was successfully tested with back-propagation (BP) neural network algorithm to identify the kernels targeted for energy optimisation. Based on the findings, we proposed several custom changes to the BP algorithms for lower energy alternatives to kernels, including options that trade off computational accuracy for higher energy saving.