Warm-ups in Math Education

Why do warm ups? Is it a waste of time? Is it really worth the bang for our buck?

Let me first start off by stating what I think the importance of using warm ups at the start of a class session. I will use a sports analogy here, for example, before the start of a game, a basketball player will commit some time beforehand to shoot some baskets, cover some drills, go over some plays and stretch! It'd be a foolish thing for the athlete to just jump right in to a game without properly warming up first. In a similar way in math, a student has to be forewarned about what to expect in the upcoming class whether it's a review of something in the past or just reviewing for the sake of reviewing.
Warm ups in math are crucial for students because it allows some time for the students to get settled down and ready to work. I've worked with teachers in the past that gave participation points for students to stay motivated in doing them. Providing warm ups are very simple to implement and does not cost the teacher much energy, money, or time. In my classroom, warm ups will be a form of informal assessment on a daily basis for me where I will strategically ask meaningful, well thought out problems that require critical thinking on my students' end and not just fluff problems that are just to pass the time. These warm ups will not just focus on computation, but the deeper rooted messages that problem solving requires.
Let me now show you an example of a poorly thought out warm up problem and one example of a more deeply thought out problem.

First, "What is the square root of 49?"

While this problem asks the student to regurgitate factual information, it lacks deeper critical thinking skills and does not apply to real life situations.

A better example would be:

A farmer wants to build a fence around part of his yard. He measures the sides which are all equal and there are 4 sides total, and 12 ft each. How much fencing will he need to buy if each foot costs him $5?