I found a great problem solving/critical thinking activity from www.mathpickle.com. As a class my students and I went through the rules of Termite Terrorists and discussed several samples that are solved on the website.
I created a few simple formats myself for my students to work on before they move on to the more complex problems on the website. They worked on these in pairs to create at least 3 solutions for a puzzle, along with explaining their thinking about why they thought they were the best solutions. Then each partner of the pair worked with a new partner to compare solutions and discuss further. Finally, each student worked with a 4th partner to create a product showing their work. Most students chose the My Story app, although 1 pair worked on paper and a couple used Drawing Pad.
Students then imported their work to iMovie to explain their thinking (not shown for privacy reasons).