Based on your preference, the ideal solution would either be MagicSchool AI or a combination of MagicSchool AI and Prodigy Math. Here is a foolproof guide to integrate these tools into your teaching structure:

Getting started with MagicSchool AI for Lesson Planning and Student Collaboration

1. Register for a free account at the MagicSchool AI platform by providing your school email address.
2. Explore the extensive library of pre-planned lessons. This will assist you in saving time and incorporating best practices into your Geometry and Algebra lessons.
3. Use the content generation feature to create original, standards-aligned educational content for your students.
4. Generate custom assessments that align with the curriculum and learning objectives. This will assist in tracking student progress and identifying areas for additional instruction.
5. Use MagicSchool AI's advanced proofreading feature to provide constructive feedback on students' assignments.
6. Finally, to facilitate student collaboration, encourage students to peer review each other's work using the advanced proofreading tool. This will promote problem-solving and teamwork.

Engaging Students with Prodigy Math

1. If you want a more game-based approach to teaching Geometry and Algebra, sign up for Prodigy Math, which makes learning enjoyable and accessible.
2. Create a class on the Prodigy platform and add your students to it. You can then assign specific math topics to them aligned with your teaching curriculum.
3. Monitor your students' progress in the Prodigy platform, which gives detailed reports.
4. Encourage your students to help each other in solving game levels, thus promoting collaboration.

By integrating these tools you will not only have well-structured content and a lesson plan for your classes, but also the tools to mobilize your students into working collaboratively, all while ensuring an engaging classroom environment.