The Cloud phenomenon brings along the cost-saving benefit of dynamic scaling. As a result, the question of efficient resource scaling arises. Prediction is necessary as the virtual resources that Cloud computing uses have a setup time that is not negligible. We propose an approach to the problem of workload prediction based on identifying similar past occurrences of the current short-term workload history. We present in detail the Cloud client resource auto-scaling algorithm that uses the above approach to help when scaling decisions are made, as well as experimental results by using real-world traces from Cloud and Grid platforms. We also present an overall evaluation of this approach, its potential and usefulness for enabling efficient auto-scaling of Cloud user resources.