Every month, we hold evening “Home & School Connection” meetings at my school. We encourage parents to attend and learn more about what their children do in school all day. (You may have read about our Reading CafÃÂ© in December.) Last week, Cindy Wall, the math coach at my school, facilitated a class on measurement with parents in every grade level. I asked her to share some of the thinking that went into putting this class together.
Cindy decided she needed to address measurement directly because the topic is overwhelming for teachers and often overlooked by parents. “When we think about teaching measurement,” she told me, “we sometimes feel like it’s all over the place and we don’t really know where to start. There are so many attributes involved: length, area, volume, capacity, weight, mass, time, etc. Then there are several different units you could use to measure — there are non-standard, standard, and metric units for each of the attributes, and all of the tools involved can get so confusing! There are so many decisions to be made, so it’s no wonder that it feels like it’s all over the place.”
On standardized tests, students in our school don’t typically perform well in the area of measurement, but we never hear parents express concern about this or ask how to help their children improve their measurement skills. Why is this? Perhaps they are as overwhelmed with all of the possibilities as the teachers are.
Cindy turned to Teaching Student-Centered Mathematics by John A. Van de Walle because she felt as though the chapter on measurement gave her structure and direction when tackling how to teach it. Van de Walle suggests choosing an attribute (length, weight, etc.), deciding which unit to use, then comparing the unit to the object. This is true no matter what students are asked to measure.
Cindy designed a class for parents and students that allowed them to experience various types of measurement in a hands-on way. They had opportunities to measure length, area, perimeter, and volume using both standard and non-standard units of measurement.
Activity One: Lots of Lines
This activity comes from Developing Number Concepts by Kathy Richardson and is used in several grade levels. Students and their parents measured two lines (one straight and one curved) with blocks then compared the measurements. Many students were surprised to find that the curved line, which looked shorter, was actually longer.
Activity Two: Area vs. Perimeter
Next, Cindy asked each participant to take 12 colored cubes and make a rectangle of any size. Some lined all 12 blocks up to make a long, skinny rectangle, and some made three rows of four for a shorter, wider rectangle. She then prompted them to measure the perimeter of their rectangle. Everyone shared their perimeter, and we found that everyone had a different number. Long skinny rectangles had a perimeter of 26 units, and three-by-four rectangles had a perimeter of 14 units, for example. Cindy then turned the conversation to area. Every student and parent measured the area of their rectangle by counting the cubes, and even though they knew they all started with 12 cubes, there was a widespread shock at finding that the area was the same for every rectangle!
Activity Three: Making Measurement Tools
One of the most common struggles in our school is using a ruler correctly. Students consistently measure incorrectly even when the ruler is in their hands, and they often miss test questions involving paper rulers. Cindy addressed this with students and parents by having them make their own rulers in order to understand them better. “We always have students make paper clocks to understand time — why aren’t they making rulers?”
Students and parents were given a blank 12-inch strip of paper, and they were asked to measure it with 1-inch cubes. Students then glued smaller strips of paper onto their ruler to help them see how this tool might be divided into smaller units. This helped develop the understanding that the numbers on a ruler refer to the space being covered, not just the marks.
If you have more tips for teaching measurement, I'd love to hear from you. Leave a comment below!