I was having a conversation with my brother just the other day about measurement. Warren is a finish carpenter and deals with measurements that have to be very exact. For instance in creating a wood inlay of almost any size, being off by even 1mm is noticeable — there is almost no margin of error. Our conversation went on to be about the idea of estimating linear measurements and what is “acceptable” when doing so. I went on to tell him one of the ways I give elementary students experience with estimating using string. It was Warren who suggested that I had my own “string theory”.
I give each student in the classroom a randomly cut piece of string, usually in lengths from about 8 cm long up to about 120 cm long. I then ask the students to take their individual pieces of string around the classroom and find some things that are about the same length as their string.
Once they have done this I give them a chance to share their various discoveries, and something interesting always happens: the students notice that the longer the string is, the greater the amount of leeway in the estimation. For instance, someone with a string nearly 120cm long may have as their item something about 110 cm long, a difference of 10 cm. But that difference is greater than the total length of string for the student who has only a piece of string 8 cm long. For a short string, the margin for saying “about as long” must be much smaller. Eventually the students notice that “about” is relative to the initial measurement.
Of course this principle of is true for measuring any attribute, whether mass, time, area, volume, etc., and it is important for students to have experiences with various units of measure to develop this understanding for themselves. It is easy to vary this activity by giving students either weights or particular items and asking them to try to find something in the room that has the same mass. It is interesting to watch them comparing with their hands as if using a balance scale. For sharing, make sure you have a scale available that will weigh both the original item (if it is a random item) and the “found” item.
I hope you will give “string theory” a try in your classroom!