Making Measurement Meaningful

 I have recently begun the 4-week long measurement unit that is always painful and frustrating.  I find it this way, because students have been learning about measurement for years, and it should be a simple and quick topic, yet students often struggle with it.  I find they have no real concept of what a cup, a liter, a mile is.  They are able to quote facts about how many cups are in a gallon and how many inches are in a foot, but they struggle with answering questions like what would you use to measure how much water will fit into a pool or how many steps he took to walk to school that day.  Knowing this, and wishing to have a less frustrating unit, I decided to take my students down the path of experiments.  They are able to quote facts, but with these experiments, they must prove it to me.  The pictures you see here are three experiments that I did for our volume and capacity mini-unit.  

I began with having the students fill different amounts of water and pour them into both customary and metric containers.  This allowed the students to see which amount is bigger liters or gallons, cups or pints, milliliters or cups, liters or quarts.  The students were then asked to reflect and answer a couple standardized test questions to see if they could transfer their knowledge.  So far, they seem to have a better understanding but we will see if they retain it. My next lesson involved surface area and volume of rectangular prisms.  Using linker cubes, I wanted to show students that you have different shapes with the same amount of volume, but the surface area may not be the same.  This experiment also allowed them the chance to use the formula sheet that is provided on the standardized tests.  I have seen students never look at the formula sheet on the day of the test because they have no experience with it, and don't know what it means.  The last experiment was inspired by a pin I saw on pinterest. The students were given the task of making a box that would contain popcorn.  I gave them the challenge: The bigger the volume of your box the more amount of popcorn you will get.  In partners, they have to make a box out of 8 1/2 by 11 in. paper and calculate the volume and surface area of their container.  For my higher-level students, I then challenged them to create a container with a different shape.  They still had to find the volume and surface area using their formula sheet.  

If the students are able to retain this information, I will definitely do these experiments again.  In three 1-hour blocks, I have seen my students work collaboratively while using mathematical vocabulary, ask questions that furthered their understanding, and reflect on what their strengths and weaknesses are.  The students have been able to learn my objectives in a hands-on way that did not require me to lecture or create a PowerPoint presentation.  Instead, the only thing I had to do was get containers for the water, buy popcorn for the containers, and copy the handouts.  Not a bad deal, if it means my student is loving math, understanding the objectives, and retaining the information for longer than a week.