The phrase "intermediate grades" refers to the middle level of education, usually in elementary or primary school. It covers the grades between the early years and the higher years. Full definition
In intermediate grades, students will create their own pet budgets and figure out the lifelong cost of pet ownership. (torontohumanesociety.com)
This book would also be a good introduction for a library lesson for intermediate grades. (essentiallearningproducts.com)
Secondary and intermediate grade teachers rarely include such texts in their teaching because they believe them to be too immature for adolescents. (ascd.org)