This website provides you with numerous STEM based projects to engage your students, and get them thinking at a higher level. The projects are undeniably linked to real-world problems, which allows students to answer their own question, "when are we ever going to use this?". For example, one project asks students to discover how much water they use. They figure personal water usage, household water usage, and class water usage. They then go on to discuss how this impacts water shortages.
At Mathalicious, their motto is "The world is an interesting place. Math should be, too." This resource is filled with great lessons that get students thinking. Membership to this site is $185 per teacher per year, however if you are paying for this resource out of pocket without school reimbursement they have flexible pricing. They have a "pay what you can" philosophy which goes as low as $10/month. There are also several free lessons available for use without membership.
This website presents a wide variety of fun and creative math projects and activities. They are divided by grade level and aligned with common core standards. The lessons start with a challenge question or quick video to get students engaged. It goes on to provide questions for class discussion to get students thinking. Last year, we did a project that involved covering another teacher's classroom entirely in aluminum foil. The students practiced surface area and had a blast!
The Mathematics Assessment Project is an excellent resource with tons of lesson plans and project ideas, already fully formed. The lessons and projects vary in length from short activities to multi-day lessons. The "Task" activities come equipped with the task PDF, scoring rubric, student work-unscored, and student work- scored. The tasks are also divided into "Novice," "Apprentice," and "Expert" levels to better meet the needs of your students.
This article, by Linda Starr, opens up the general discussion about why math is applicable in real life. It gets you thinking about how you can show students the application of what they are learning, and it also provides links to a lot of other great resources to help you delve even deeper into the matter.
"Teaching Mathematics in the 21st Century" is an article that thoroughly discusses the challenges that face current math teachers. It encourages teachers to start by taking self-inventory to help get them in the proper 21st century mindset. The article continues on to discuss the shift in what students are learning and how they are learning it. Teachers now need to show math in a bigger world sense, while utilizing technology and a hands-on approach.