After developing this lesson on home-made rulers during our last release day, Dale and I debated whether or not to actually do the lesson with our students. It seemed so labour intensive to prepare all the materials, and we were already struggling with limited time in which to complete too many many units before the onset of EQAO just a few short months away...
Wouldn't it just be easier to give students a short demo on how to use a ruler, and be done with it? Then we could get on to having them measure the length of various objects, give them a wee quiz, and get on to the next series of lessons, on area and perimeter.
I consulted Van de Walle, from whom we had originally gotten the idea for the lesson. He says this:
Wouldn't it just be easier to give students a short demo on how to use a ruler, and be done with it? Then we could get on to having them measure the length of various objects, give them a wee quiz, and get on to the next series of lessons, on area and perimeter.
I consulted Van de Walle, from whom we had originally gotten the idea for the lesson. He says this:
"By have students make and number their own rulers, you receive an enormous amount of assessment data about how well your students understand the measurement process. By contrast, if you carefully direct how to use the unmarked ruler and then how to number it, the students' attention is now focused on following directions." (Van de Walle, 2006, page 260)
Ugh.
So, off I went to cut strips of paper.
I began by showing students an example and a non-example of a "good" home-made ruler, asking them to decide which one was better, and why. In pairs, they discussed whether or not the first unit needed to begin right at the beginning of the ruler, and what the implications were of leaving spaces between some units but not others, or using units of different lengths on the same ruler. Then they set about making their own rulers.
And what do you know? Van de Walle was right!
As students began to estimate and then measure the length, width and height of various objects in the room, it was very easy to discern (and to record on my handy clipboard) which students understood the concepts of labling the end of each unit in order to count the number of units rather than the space between the units. We also had ample opportunity to discuss the concept of "half" or "less than/more than half", when an object's length fell somewhere between two numbers on the home-made ruler.
Knowing how to line up units (rather than rulers) end-to-end when measuring something longer, like, for example, the couch in the reading corner, was another skill that was easy for me to observe as students wandered about the room with their rulers.
Some students even began interjecting spontaneously when they noticed peers who were not measuring accurately or lining up their rulers precisely.
Suddenly, one student shouted, "Hey, who wants to measure the floor?!" And several of them got together to do it collaboratively (you can see them now taking care to line up their rulers NOT end-to-end, but rather so that one unit begins where another ends, to get a more accurate overall measurement).
During the debrief, we talked about how one might measure an item longer than 7 units (the length of their home-made rulers) if one only had one ruler. Then they went off to estimate, measure and record a few more items independently.
Homework? You guessed it: "Go home -- estimate, measure and record some more items"!!!
Homework? You guessed it: "Go home -- estimate, measure and record some more items"!!!