Here is a strategy I use to get students thinking. My year 11s have learned some trigonometry recently and everyone is working at their own pace. Some are still doing basic trig and others are doing complex multistep problems with bearings or in 3D. I used this slide (revealing one sentence at a time) to run a starter activity.
First I encouraged them to make a problem that would challenge their partner (who is the person sitting next to them). Then their partner was told to answer the question, but make a mistake on purpose. Then a third person checks over the work and tries to spot the error.
Each student is engaged in this starter and no one sits passively. (I created it after reading Kagan’s Cooperative Learning book, which states that as many students as possibly should be active during an activity.) The problems the students made up were more interesting and many were more challenging than textbook or worksheet questions. And each student was exposed to three problems: the one they created, the one they solved, and the one they checked. My year 11s enjoyed the social aspect, too.
“Swap and Spot the Error” is a task that you can use for many topics. Try it and let me know how it goes.