Recent progress in deep learning (DL) has revived the interest on DL-based computer aided detection or diagnosis (CAD) systems for breast cancer screening. Patch-based approaches are one of the main state-of-the-art techniques for 2D mammogram image classification, but they are intrinsically limited by the choice of patch size, as there is no unique patch size that is adapted to all lesion sizes. In addition, the impact of input image resolution on performance is not yet fully understood. In this work, we study the impact of patch size and image resolution on the classifier performance for 2D mammograms. To leverage the advantages of different patch sizes and resolutions, a multi patch-size classifier and a multi-resolution classifier are proposed. These new architectures perform multi-scale classification by combining different patch sizes and input image resolutions. The AUC is increased by 3% on the public CBIS-DDSM dataset and by 5% on an internal dataset. Compared with a baseline single patch size and single resolution classifier, our multi-scale classifier reaches an AUC of 0.809 and 0.722 in each dataset.