Potential Paths: Path 1: Using Pedagogical to convert lesson materials into different forms like quizzes or summaries, and using instructional diagrams for visual aid. However, its lack of testimonials and stillbeing in a beta state may mean incomplete and potentially buggy features. Though its free tier provides a good value proposition, there could still be risks involved. Path 2: Utilizing Prodigy as it offers adaptive learning which can cater to each student's learning pace. It provides real-time feedback and allows tracking of student's progress. The challenges here may be the game elements which can be a bit distracting, and its limitation to math subjects. Or MagicSchool AI, which offers a range of tools including content generation and lesson planning. It has an intuitive interface and is currently free for teachers.

Final Narrative: Considering the needs specified in your query, the optimal solution seems to be Prodigy which targets students from grades 1 to 8, offering a range of math topics and tailoring to each student's learning pace. This feature aligns with the need for differentiated instruction for your 7th grade mathematics class. The software also provides real-time feedback, helping your students quickly learn from and correct their mistakes. It aligns with the Common Core curriculum, making it ideal for classroom use. As a bonus, it works on various devices and can be used both at home and in the classroom, adding to its flexibility.

Simultaneously, MagicSchool AI can be an excellent supplementary tool to aid in lesson planning and content generation. The ability to generate standards-aligned educational content can assist in providing a broad range of resources for differentiated instruction. Furthermore, its text leveling feature can adapt reading materials to various proficiency levels for each student, further supporting differentiated instruction.

Thus, a combination of Prodigy for student engagement and tailored learning, along with MagicSchool AI for lesson planning and content generation seems to be a promising approach to meet your needs. Remember, Prodigydoes have a limitation that it is subject-specific to Mathematics. As for MagicSchool AI, it is currently free so cost won't be an issue for now but it's important to keep updated with their pricing model changes.