The importance of working memory (WM) in reading and mathematics performance has been widely studied, with recent research examining the components of WM (i.e., storage and processing) and their roles in these educational outcomes. However, the differing relationships between these abilities and the foundational skills involved in the development of reading and mathematics have received less attention. Additionally, the separation of verbal, visual and spatial storage and processing and subsequent links with foundational skills and downstream reading and mathematics has not been widely examined. The current study investigated the separate contributions of processing and storage from verbal, visual and spatial tasks to reading and mathematics, whilst considering influences on the underlying skills of verbal comprehension and counting, respectively. Ninety-two children aged 7- to 8-years were assessed. It was found that verbal comprehension (with some caveats) was predicted by verbal storage and reading was predicted by verbal and spatial storage. Counting was predicted by visual processing and storage, whilst mathematics was related to verbal and spatial storage. We argue that resources for tasks relying on external representations of stimuli related mainly to storage, and were largely verbal and spatial in nature. When a task required internal representation, there was a draw on visual processing and storage abilities. Findings suggest a possible meaningful separability of types of processing. Further investigation of this could lead to the development of an enhanced WM model, which might better inform interventions and reasonable adjustments for children who struggle with reading and mathematics due to WM deficits.