Algebra and Calendars

"Why do we need Algebra?"  A common refrain from students.  This problem might work for some of your junior students.  Cynthia Lanius from Rice University posted this over a decade ago about using Algebra and Calendars.    She starts by asking students to pick for days that form a square and adding the dates together.  The students tell her the sum and she tells them the 4 days.  She uses some basic algebra in her head to do this.  To see the site click here.  If you want to see the algebraic solution to the problem click here.