The Dishes Problem

 A way to do this puzzle without algebra is by constructing a table using common factors, division and addition and gradually increasing the number of people (given that that number of people has factors of 2, 3, and 4 as those are the number of people using particular dishes for certain foods) to reach a point where the correct total number of dishes are achieved. An image is attached showing the table. 

Hence there are 60 guests. 

I do think it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures. I think it helps keep students engaged and provides more context to the material, as well allowing for personal connection to the material if it is from their culture. As well, for ELL students, including mathematics from diverse cultures is a great way for them to stay connected to their cultures. 

I absolutely think the word problem, puzzle story and imagery matter to both students' enjoyment in solving it and as well their self confidence in solving it. From personal experience and watching and helping others with math, word problems cause students to doubt their abilities as they believe the question will be more complicated given the way the question is presented. However including puzzles and imagery in material I think would create more enjoyment from the students perspective in solving it. Students may think of puzzles as a fun activity, although they are still demonstrating their math knowledge it may not seem as difficult as a word problem given the way it is presented to them. The same with imagery as creating an exciting visual representation to introduce a concept or ask a question may help students become more engaged in the material and feel a greater confidence in their ability to understand and solve the material given.