This first sample is something that I would use for providing time for investigation and practice. Our middle schools use Connected Math, which relies on investigation and discovery. However, before I jump into the lesson, you might notice that 15 minutes are for a math talk. I liked using this time to help students develop number sense which is a year-long goal for my students. My favorite resources are Which One Doesn't Belong, Estimation 180, and Clothesline Number Line. I suggest using 10 of those minutes for the actual discussion.
The next chunk is for an intro. If you are familiar with 3-Act tasks, I usually try to find a way to intro an investigation in the style of Act 1. So whether I'm using actual lessons from Dan Meyer, or finding a YouTube video myself, or even doing a little demo in front of the class using students, setting up interest with a "hook" is a must.
Next, students can work in partners on the investigation. They might be recording results on a table or playing a game. No matter what the activity, it should be leading them to look for patterns and coming to some mathematical conclusion.
I put in a brain break because at some point in the lesson, it's important to get the blood flowing to the brains. You might think that doing a brain break is too elementary or babyish for your middle school kids. Not true! Even 8th graders like being a little silly. But if you don't like using something like Go Noodle, think about some breathing exercises, simple yoga poses, or other mindfulness techniques.
After a short brain break, you might want to help the kids synthesize what they discovered during the investigation. Take a moment to write down important findings, formulas, or vocabulary that they can refer to later.
The next chunk might be having students continue in the investigation on their own or to do some individual practice. Using ClassKick or Formative might be good tech tools to use for this chuck so you can monitor student work and be pulling kids that need additional help from you.
Finally, I always leave 5 minutes at the end to make sure there is time to clean up the classroom and to do a quick summary or conclusion.