Warm-ups in Math Education

Warm-ups are an important aspect in a math classroom. Warm-ups serve many functions, including getting students in a “math” frame of mind, reviewing material from previous lessons, reviewing basic skills such as fractions, percents, etc, review skills that may not be a normal part of everyday lessons such as OAKS testing preparation or use of calculators, or even pre-viewing or priming what you will be doing that day.  Warm-ups can also provide the teacher an opportunity to check for students pre-existing knowledge and/or misconceptions on the lesson that is being taught that day, so the teacher can gauge how fast or slow he/she needs to go and which topics and students need special attention.

I believe that warm ups should take under 10 minutes, especially in a 40 minute or 50 minute period system. I also believe that warm-ups should not be graded, but instead should be checked by a group discussion or calling on individual students.    

Appropriate Use of Technology

Since I could not find an activity that matched my standards area of measurement, I chose to review the Area Tool at www.illuminations.nctm.org. The area tool is an exploratory tool that can be used to track how the area changes given different side lengths in triangles, parallelograms, and trapezoids. It could also be used in a lesson on proportions and similar triangles and shapes. Unfortunately, because the angles and lengths are on a slider scale and there is no way of getting exact measurements, it would be very difficult to use this tool in a lesson on the Pythagorean Theorem or trigonometry.

While it does have limitations, the area tool does accomplish its main objective of determining how the base length and height of a figure affects its area very efficiently. Using this tool is much more efficient than drawing the figures out on graph paper. Students can instantly make connections between the areas instead of painstakingly graphing the figures out and running the risk of losing the information through the tediousness of the activity.

This same lesson could be taught using graph paper, plastic shapes, or other manipulatives. While these other methods would work, they do not provide the same efficiency that the area tool can. If I were designing this tool, I would include the option to input exact measurements and angles, and output angle measurements.

Standards, standards, everywhere

I chose to evaluate how the NCTM standard of “understanding relationships among units and convert from one unit to another within the same system” compares with a similar standard in the Common Core and CMP standards. For the most part all three standards cover essentially the same thing. However, there are several differences between the three standards.  One is that the Connected Math Project standards include conversion between customary and metric systems whereas the Common Core and NCTM standards keep the conversions within the same system. Another difference is the NCTM and CMP consider converting measurements a sixth through eighth grade skill where the Common Core standards place it in the fifth grade classroom. Lastly, the common core standards are the only ones that explicitly state that the skill must be implemented in multi-step, real world problems, which is surprising to me since that seems to be one of the main objectives of the Connected Math Projects standards. While the standards do not match up identically one to one, creating multi-step, real world measurement problems that include converting between customary and metric systems would easily cover all three sets of standards.